Therefore , the solution of the given problem of unitary method comes out to be option C The lengths of side an are 2.5 inches, side b is 5 inches, and side c is 13 inches.
What is a unitary method?
Use the tried-and-true fundamental method, the real variables, and any useful information you learn from the broad and specific questions to complete the assignment. Customers may be given another chance to taste expression the products in response. If these improvements don't happen, we'll lose out on significant expression advances in programming understanding.
Here,
We may calculate the side lengths of the physical object using the following formulae given the scale factor of 2:1:
Drawing to scale: Side a: 11 inches
8 inches on side B.
3 inches on side C.
real thing
11 inches by two equals 22 inches on side a.
Side B: 8 inches times two equals 16 inches
3 inches by 2 equals 6 inches on side C.
B. Side a: 26 inches in the scale drawing.
20 inches on side B.
10 inches on side C.
real thing
Side a: 2 times 26 inches equals 52 inches.
Side B: 20 inches times two equals 40 inches
20 inches are equal to 10 inches on side C.
C. Side a: 2.5 inches in the scale drawing.
5 inches on side B.
6.5 inches on side C.
real thing
2.5 x 2 = 5 inches on side a.
Side B: 5 inches times two equals 10 inches
6.5 inches by two equals 13 inches on side C.
So, the appropriate response is:
C. The lengths of side an are 2.5 inches, side b is 5 inches, and side c is 13 inches.
To know more about unitary method visit:
https://brainly.com/question/28276953
#SPJ1
Kimble is trying to decide between two checking account plans. Plan A offers a quarterly compound interest rate of 0.5%, while plan b offers a 3.5% interest compound annually. Which is the better plan? By how much?
Plan B offers a higher effective annual interest rate than Plan A by 2.9975%. Therefore, Plan B is the better plan by about 2.9975% in the compound interest.
What is compound interest?When interest is earned on a loan or investment, it is earned on both the principal and any accumulated interest, which is known as compound interest. In other words, interest is added to the principal, and the resulting sum is then used to determine future interest. Compounding causes an investment or loan to increase more quickly than it would with simple interest, where just the principal is charged interest. Compounding may occur daily, monthly, quarterly, annually, or at any other interval.
To compare the plans of the two accounts we have:
Rate = ( 1 + rate / n)ⁿ - 1
where, n is the compounded period.
For plan A:
Effective annual interest rate = (1 + (0.5%/4))⁴ - 1 ≈ 0.5025%
For Plan B, we have:
Effective annual interest rate = (1 + 3.5%)¹- 1 = 3.5%
Comparing the two we see that Plan B offers higher rates by:
3.5% - 0.5025% ≈ 2.9975%.
Hence, Plan B offers a higher effective annual interest rate than Plan A by 2.9975%. Therefore, Plan B is the better plan by about 2.9975%.
Learn more about compound interest here:
https://brainly.com/question/29335425
#SPJ1
Can I get the answer?
The meaning of the y - intercept in the context of the problem of the snow level in Moose Wyoming is the level of snow at the beginning of the time period in question.
What is the y - intercept ?The y-intercept of the function y = 2x + 14 is the value of y when x = 0. Substituting x = 0 into the equation, we get:
y = 2(0) + 14
y = 14
Therefore, the y-intercept is 14.
In terms of the problem, this means that at midnight (when x = 0), there is already 14 inches of snow on the ground in Moose, Wyoming. The y-intercept represents the initial or starting value of the snow level function, which in this case is the amount of snow already on the ground at the start of the time period being modeled.
Find out more on y - intercept at https://brainly.com/question/10700419
#SPJ1
The tables represent hat sizes measured in inches for two softball teams.
Pelicans
21.5 25 22
21 22 23
22.5 24 21.5
22 23.5 22
23.5 22 24.5
Falcons
22.5 20 23.5
21 24 22
20.5 21.5 23
23 22.5 21
24 22 24.5
Which team has the largest overall size hat for their players? Determine the best measure of center to compare and explain your answer.
Falcons; they have a larger median value of 22.5 inches
Pelicans; they have a larger median value of 22 inches
Falcons; they have a larger mean value of about 22 inches
Pelicans; they have a larger mean value of about 23 inches
The team that has the largest overall size hat for their players is the Falcons; they have a larger mean value of about 22 inches
How to solveIn order to determine the average hat size per team, it is necessary to sum up each player's measurements and divide by the total number of players.
For the Pelicans: The combined sum equals 344.5, which results from adding up values such as 21.5, 25, 22, 24, and so on. With a team membership of 15 people, their mean measures out to approximately 22.97 inches.
The Falcon's equivalent calculation yields a total of 330 attained from summing head sizes, including those measuring 20, 23.5, 21, etc., with an equal number of members, coming close to an average measure of 22 inches thick.
As a result, comparisons between both teams reveal that the Falcons possess the larger collective hat size averages at roughly 22 inches in thickness.
Read more about mean value here:
https://brainly.com/question/1136789
#SPJ1
A softball has a volume of about 33. 5 in3. What is the diameter of the ball?
Answer:
the diameter of the softball is approximately 4.72 inches.
Step-by-step explanation:
The formula to calculate the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius of the sphere.
We can rearrange the formula to find the radius of the softball:
r = cube root of [(3V)/(4π)]
r = cube root of [(3 x 33.5)/(4π)]
r ≈ 2.36 inches
The diameter is twice the radius:
d = 2r
d ≈ 4.72 inches
Therefore, the diameter of the softball is approximately 4.72 inches.
Answer: the diameter of the softball is approximately 4.22 inches.
Step-by-step explanation: The volume of a sphere can be calculated using the formula:
V = (4/3)πr^3
where V is the volume of the sphere, r is the radius of the sphere, and π is the mathematical constant pi.
To find the diameter of the softball, we can use the formula:
d = 2r
where d is the diameter of the sphere.
We know that the volume of the softball is 33.5 in^3. So, we can solve for the radius as follows:
33.5 = (4/3)πr^3
r^3 = (3/4)(33.5/π)
r^3 = 8.9375
r = ∛(8.9375)
r ≈ 2.11 inches
Now, we can find the diameter of the softball:
d = 2r
d = 2(2.11)
d ≈ 4.22 inches
a2 + b2 = c2
2 +
2 = c2
+
= c2
= c2
= c
C21 represents 4 senior boys.
What is a Matrix?A matrix, which is used to represent a mathematical object or an attribute of one, is a rectangular array or table containing numbers, symbols, or expressions that are organized in rows and columns. is a matrix having two rows and three columns, for instance
Given:
[tex]\left[\begin{array}{ccc}5&6\\4&3\\\end{array}\right][/tex], [tex]\left[\begin{array}{ccc}c11&c12\\c21&c22\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}\ Junior boy&Junior girl\\Senior boy&Senior girl\\\end{array}\right][/tex]
4 Senior boys is c21 represented.
Read more about matrix here:
https://brainly.com/question/94574
#SPJ1
select the correct answer from each drop-down menu. a candy company designs a package to hold chocolates. the height of the container is 13 inches and the diameter of its bottom is 9 inches. diagram shows a shape with circular base and curved surface meeting at a point. the diameter of the base is labeled 9 inches and the height of the shape is labeled 13 inches. which shape best models the package, and what is the approximate surface area of the package? the best model for the package is a . the approximate surface area is square inches.
The candy company's package can be modeled as a right circular cone with a height of 13 inches and a base diameter of 9 inches.
The circular base of the cone holds the chocolates, while the curved surface extends up to a point at the top. To calculate the surface area, we need to find the area of the circular base and the area of the curved surface. The formula for the area of a circle is pi times the radius squared, so the radius of the base is 4.5 inches.
The area of the base is pi times the radius squared, or approximately 63.62 square inches. The formula for the curved surface area of a cone is pi times the radius times the slant height, which is the square root of the height squared plus the base radius squared. Substituting the given values into the formula, the curved surface area is approximately 207.35 square inches. Thus, the approximate surface area of the package is the sum of the area of the base and the curved surface area, or approximately 271.97 square inches.
Learn more about company's package
https://brainly.com/question/12642652
#SPJ4
Question 1(Multiple Choice Worth 2 points)
(Comparing Data MC)
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru typically has more wait time, and why?
Burger Quick, because it has a larger median
Burger Quick, because it has a larger mean
Super Fast Food, because it has a larger median
Super Fast Food, because it has a larger mean
The correct answer for the given dataset will be: Burger Quick, because it has a larger median.
What is a box plot?A box plot,also known as a box-and-whisker plot, is used for graphical representation of summary statistics from a data set. It helps by providing a visual representation of a data set's central tendency, dispersion, and skewness, making it straightforward to identify important data aspects.
As per given data, Burger Quick typically has more wait time compared to Super Fast Food.
The box plot for Burger Quick displays a higher interquartile range (from 9.5 to 24) than Super Fast Food (from 8.5 to 15.5), indicating that Burger Quick has a broader dispersion in the middle 50% of the data. Also, the median (shown by the line in the box) for Burger Quick is 15.5, but the median for Super Fast Food is 12. This implies that the average wait time at Burger Quick is longer than at Super Fast Food.
The lines outside the box (whiskers) also demonstrate that the range of values for Burger Quick (from 2 to 30) is greater than for Super Fast Food (from 3 to 27), implying that Burger Quick has a longer wait time.
Learn more about median here:
brainly.com/question/28060453
#SPJ1
Commutative states that the grouping of three terms being added does not affect the result.
Distributive states that the order of two terms being added may be switched which does not affect the result.
Associative states that the multiplying a sum by a number is the same as multiplying each addend by that number and then adding the two products.
Which is which because that's what its asking
The first statement, "Commutative states that the grouping of three terms being added does not affect the result" is referring to the commutative property of addition.
The solution to the aforementioned questionThe first statement, "Commutative states that the grouping of three terms being added does not affect the result" is referring to the commutative property of addition.
The second statement, "Distributive states that the order of two terms being added may be switched which does not affect the result" is referring to the commutative property of multiplication.
The third statement, "Associative states that the multiplying a sum by a number is the same as multiplying each addend by that number and then adding the two products" is referring to the associative property of multiplication.
Learn more about Commutative at https://brainly.com/question/778086
#SPJ1
a spinner has 18 equal-sized sectors labeled 1 through 18. the spinner is spun once. what is the probability that the spinner lands on an even number or a number greater than 10?
The probability that the spinner lands on an even number or a number greater than 10 is 11/18.
There are two cases where the spinner can land on an even number or a number greater than 10:
Case 1: The spinner lands on an even number.
There are 9 even numbers on the spinner: 2, 4, 6, 8, 10, 12, 14, 16, and 18. The probability of the spinner landing on an even number is 9/18 = 1/2.
Case 2: The spinner lands on a number greater than 10.
There are 7 numbers greater than 10 on the spinner: 11, 12, 13, 14, 15, 16, and 18. The probability of the spinner landing on a number greater than 10 is 7/18.
To find the probability of either event occurring, we add the probabilities of the two cases and subtract the probability of both occurring simultaneously (since the numbers 12, 14, and 16 are even and greater than 10). Therefore, the probability of the spinner landing on an even number or a number greater than 10 is:
(1/2) + (7/18) - (3/18) = 11/18
Thus, the probability that the spinner lands on an even number or a number greater than 10 is 11/18.
Learn more about probability
https://brainly.com/question/30034780
#SPJ4
Solve the equation. Round to the nearest tenth if necessary. x^2+4=29
If 1 US dollar in 1860 had the same purchasing power as $28. 95 in 2018, what is the yearly average inflation rate during that time?
A. 2. 15%
B. 2. 75%
C. 3. 15%
D. 3. 75%
The yearly average inflation rate during that time is 3.75% (option d).
First, we need to adjust the value of $1 in 1860 to its equivalent value in 2018 using the given purchasing power ratio of 1:28.95. This means that $1 in 1860 is equivalent to $28.95 in 2018.
Next, we need to find the CPI for 1860 and 2018. According to the Bureau of Labor Statistics, the CPI for 1860 is not available. However, we can use the CPI for 1913 as a proxy, as it was the year when the CPI was first introduced. The CPI for 1913 was 9.9.
Using the CPI for 1913 as the beginning CPI and the CPI for 2018 as the ending CPI, we can calculate the inflation rate as follows:
Inflation rate = (252.146 - 9.9) / 9.9 x 100% = 3.72%
Hence the correct option D (3.75%).
To know more about inflation here
https://brainly.com/question/30112292
#SPJ4
Find the perimeter and area of a regular octagon that has a radius of 10m.
What is 143,246 rounded to the 3rd significant figure?
Your boss hands you a memo with a summary of the monthly data. The number of imports is shown as f(x), and the number of exports is shown as g(x). Use the data in the table below, representing both functions, to explain to your boss the solution to the system of equations and what that solution represents. Use complete sentences.
Month f(x) = No. of imports g(x) = No. of exports
January (1) 3 3
February (2) 6 4
March (3) 9 5
April (4) 12 6
The solution to this system of equations can be found by equating f(x) and g(x) and solving for x:
3x = x + 2
2x = 2
x = 1
What is the functions about?Based on the given table data, we can see that the number of imports (f(x)) and the number of exports (g(x)) follow a linear relationship with respect to the month (x). The data shows that as the month progresses, both the number of imports and exports increase.
The system of equations can be represented as follows:
f(x) = 3x
g(x) = x + 2
The first equation f(x) = 3x represents the number of imports, where the coefficient of x is 3, indicating that the number of imports increases by 3 units for every increase of 1 unit in the month.
The second equation g(x) = x + 2 represents the number of exports, where the coefficient of x is 1, indicating that the number of exports increases by 1 unit for every increase of 1 unit in the month. Additionally, there is a constant term of 2, which represents the initial number of exports in the month of January.
The solution to this system of equations can be found by equating f(x) and g(x) and solving for x:
3x = x + 2
2x = 2
x = 1
The solution x = 1 represents the month of January, where both the number of imports and exports are equal to 3. This implies that in the month of January, there were 3 units of imports and 3 units of exports.
In all, the solution to the system of equations indicates that in the month of January (x = 1), the number of imports (f(x)) and the number of exports (g(x)) were both 3 units, as per the given data in the table.
Read more about functions here:
https://brainly.com/question/26651007
#SPJ1
Help needed fast please!! The table below shows Addison's novel collection on her bookshelf.
Type novel:Nonfiction: 2, mystery:4, fiction:5
What is the ratio of Nonfiction novels to all novels. 2 to 9?
2 : 11?
5 / 11?
Or 1 to 2?
the ratio of Nonfiction novels to all novels is: Nonfiction novels : Total novels [tex]= 2 : 11[/tex] So the correct answer is [tex]2:11.[/tex]
What is the ratio?The ratio of Nonfiction novels to all novels can be calculated by dividing the number of Nonfiction novels by the total number of novels.
The total number of novels is the sum of Nonfiction, mystery, and fiction novels:
Total number of novels = Nonfiction + Mystery + Fiction [tex]= 2 + 4 + 5 = 11[/tex]
The ratio of nonfiction novels to all novels is not a fixed value, as it depends on the specific set of novels being considered. However, it can be calculated if we have the appropriate data.
Therefore, the ratio of Nonfiction novels to all novels is: Nonfiction novels : Total novels [tex]= 2 : 11[/tex] So the correct answer is 2:11.
Learn more about ratio here:
https://brainly.com/question/13419413
#SPJ1
A cyclist leaves the town of Alphaville and heads toward Betaville. She travels at a constant speed of 14 km/h. At the same time, a jogger and a walker leave Betaville and head towards Alphaville. The walker travels at a constant speed of 6 km/h and the jogger travels at a constant speed of 10 km/h. If the cyclist passes that walker 4 minutes after passing the jogger, how far apart are the towns Alphaville and Betaville?
The towns Alphaville and Betaville are 2.067 km apart.
Calculation of the Distance Apart of two townsLet's d = distance between Alphaville and Betaville
Since the cyclist is traveling at a constant speed of 14 km/h, we can use the formula:
distance = speed x time
Let x = time it takes for the cyclist to travel from Alphaville to the point where she passes the jogger.
Then, the time it takes for the walker to travel from Betaville to the point where she is passed by the cyclist is (x + 4/60) hours (since 4 minutes is 4/60 hours).
Finally, we can use the formula:
distance = speed x time
to set up two equations, one for the cyclist and jogger, and one for the cyclist and walker:
14x = 10(x + 4/60) ------- (1)
14x - 6(x + 4/60) = d ---- (2)
Simplifying Equation 1:
14x = 10(x + 4/60)
14x = 10x + 2/3
4x = 2/3
x = 1/6.
Substituting x = 1/6 into Equation 2:
14(1/6) - 6(1/6 + 4/60) = d
7/3 - 2/5 = d
d = 31/15 km or approximately 2.067 km
Therefore, the towns Alphaville and Betaville are approximately 2.067 km apart.
Learn more about distance here:
https://brainly.com/question/26550516
#SPJ1
Please help this is due today
Using multiplication we know that after 141 min there will be 400,000 bacteria present.
What is multiplication?One of the four fundamental arithmetic operations, along with addition, subtraction, and division, is multiplication.
A product is the output of a multiplication operation.
When you take a single number and multiply it by several, you are multiplying.
A 5 multiplied by 4 results in 20 (5 + 5 + 5 + 5).
We multiplied the number five by four times.
Multiplication is commonly referred to as "times" because of this.
So, in the given situation:
At the initial stage, the number of bacteria is: 50,000
Then, after 47 min: 50,000 * 2 = 100,000
Then, after 47 min which is after 94 min: 100,000 * 2 = 200,000
Then, after 47 min which is after 141 min: 200,000 * 2 = 400,000
Therefore, using multiplication we know that after 141 min there will be 400,000 bacteria present.
Know more about multiplication here:
https://brainly.com/question/10873737
#SPJ1
Please help me area parallelograms
The required area of the given parallelogram is 9yd² respectively.
What is Parallelogram?A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry.
A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
If one of the angles in a parallelogram is a right angle, then all four angles must also be right angles.
A four-sided figure is a trapezoid if it has at least one angle of a different measure in addition to at least one right angle.
So, the formula for the area of a parallelogram is:
A=bh
Now, insert values as follows:
A = bh
A = 9/2 * 2
A = 4.5*2
A = 9yd²
Therefore, the required area of the given parallelogram is 9yd² respectively.
Know more about Parallelogram here:
https://brainly.com/question/970600
#SPJ1
how many square feet of carpet will we need for this hole
Answer: 44 ft²
Step-by-step explanation:
We will find the area of the large rectangle and subtract the area of the square. The area of a rectangle (and square) can be used with this formula:
A = LW
Large Rectangle:
A = LW
A = (12 ft)(4 ft)
A = 48 ft²
Square:
A = LW
A = (2 ft)(2 ft)
A = 4 ft²
Subtract:
48 ft² - 4 ft² = 44 ft²
Adding and subtracting decimals
1) 34.12 - 41.23 + 14.01
2) -34.12 + 41.23 - 14.01
Combine all positive numbers:
Combine all negative numbers:
Rewrite:
(look at the picture)
Answer:
1Step-by-step explanation:
Suppose that you are headed toward a plateau 40 m high. If the angle of elevation to the top of the plateau is 20 degrees, how far are you from the base of the plateau?
We are approximately 17.88 meters from the base of the plateau.
What is an angle of elevation?An angle of elevation is the angle formed between a horizontal line and a line of sight that is directed upward to an object or point above the horizontal level. It is commonly used in trigonometry and geometry to determine the height or distance of an object, such as a building, tower, or mountain.
We can use trigonometry to solve this problem. Let's call the distance we are from the base of the plateau "x".
From the problem, we know that the height of the plateau (the opposite side) is 40m and the angle of elevation (the angle between the horizontal and the line of sight to the top of the plateau) is 20 degrees.
Using the tan function, we get,
tan(20) = 40/x
To solve for x, we can cross-multiply:
x * tan(20) = 40
Then, we can divide both sides by tan(20):
x = 40 / tan(20)
Using a calculator, we get:
x ≈ 17.8798 meters
Therefore, we are approximately 17.88 meters from the base of the plateau.
To know more about angle of elevation visit:
brainly.com/question/9817377
#SPJ1
An equation to the line tangent to y= x^3 + 3x^2 +2 at its point of inflection isa) y= -6x-6b) y= -3x +1c) y= 2x +10d) y= 3x-1e) y= 4x+1
The equation of the tangent line at the point of inflection is y = -3x + 1, which corresponds to option (b).
To find the equation of the tangent line at the point of inflection for the given function [tex]y = x^3 + 3x^2 + 2,[/tex] we first need to determine the point of inflection. A point of inflection occurs where the second derivative changes sign.
First, let's find the first and second derivatives of the given function:
[tex]y' = 3x^2 + 6x[/tex] (first derivative)
[tex]y'' = 6x + 6[/tex] (second derivative)
To find the point of inflection, set the second derivative equal to zero and solve for x:
[tex]6x + 6 = 0 x = -1[/tex]
Now, plug x = -1 back into the original function to find the corresponding y-coordinate:
[tex]y = (-1)^3 + 3(-1)^2 + 2\\y = -1 + 3 + 2\\y = 4[/tex]
The point of inflection is (-1, 4). Next, find the slope of the tangent line at this point using the first derivative:
[tex]y'(-1) = 3(-1)^2 + 6(-1)\\y'(-1) = 3 - 6\\y'(-1) = -3[/tex]
Now, use the point-slope form of the equation of a line to find the tangent line:
y - y1 = m(x - x1)
y - 4 = -3(x - (-1))
y - 4 = -3(x + 1)
Simplify the equation to get the answer:
y = -3x - 3 + 4
y = -3x + 1
The equation of the tangent line at the point of inflection is y = -3x + 1, which corresponds to option (b).
learn more about equation of the tangent line
https://brainly.com/question/28994498
#SPJ11
The nth term of the sequence 3/2, 3, 7, 16, 35, 74,... is?
Answer:
95 is the sequence
Step-by-step explanation:
The given sequence appears to follow the pattern where each term is obtained by multiplying the previous term by 2 and then adding 1. Using this pattern, we can derive a formula for the nth term of the sequence as a(n) = 3 * 2^(n-1) - 1, where a(n) represents the nth term of the sequence and n is a positive integer.
For example, to find the 6th term of the sequence, we can substitute n = 6 into the formula to get a(6) = 3 * 2^(6-1) - 1 = 3 * 2^5 - 1 = 95. So, the 6th term of the sequence is 95.
an electric car's home battery charger uses 6.1 kilowatt for 11 hour. if electricity costs $0.05 per kilowatt-hour, how much (in dollars, to the nearest penny) does it cost to charge the car's battery? use exact numbers; do not estimate.
The cost to charge an electric car's home battery charger is $3.355 (to the nearest penny).
The cost to charge an electric car's home battery charger can be calculated using the following equation:
Cost = (kW x hours x rate)
Where kW stands for kilowatts, hrs stands for hours and rate stands for the rate per kilowatt-hour.
In this case, we have: kW = 6.1, hrs = 11 and rate = $0.05
Therefore, Cost = (6.1 x 11 x 0.05) = $3.355
Therefore, it will cost $3.35(to the nearest penny) to charge the car's battery.
To calculate this cost, we first multiply the kW (6.1) by the hours (11) to get the total kWh used (67.1). We then multiply this number by the rate ($0.05) to get the total cost of charging the battery ($3.355). This cost is to the nearest penny as we rounded up to the nearest cent when multiplying the kWh by the rate.
Learn more about electricity here :-
https://brainly.com/question/12791045
#SPJ4
Complete Question:
An electric car's home battery charger uses 6.1 kilowatts for 11 hours. If electricity costs $0.05 per kilowatt-hour, how much (in dollars, to the nearest penny) does it cost to charge the car's battery? Use exact numbers; do not estimate.
please help with this question
Answer:
A-223
B-98
Step-by-step explanation:
A- To find the perimeter of a shape you have to add all the sides together .
Here the only information we get is the length which is 99 and we have to find the width .
To find the width we have to do
332-99
=98m
B-To find the area of a shape you have to do height x width
h x w
but here it gives us the length and the area of it so we would have to divide the two numbers
6468÷66
=98cm²
3. (07.05 MC) An equation is shown below: 12x + 3(x - 5) = 6x + 9x - 15
Part A: Solve the equation and write the number of solutions. Show all the steps. (6 points)
Part B: Name one property you used to solve this equation. (4 points)
The equation 12x + 3(x - 5) = 6x + 9x - 15 has infinite many solutions
Solving the equationPart A:
Starting with the given equation:
12x + 3(x - 5) = 6x + 9x - 15
Simplify by distributing the 3:
12x + 3x - 15 = 6x + 9x - 15
Combine like terms on both sides:
15x - 15 = 15x - 15
Add 15 to both sides:
0 = 0
Therefore, the equation has infinite many solutions
Part B:
The property used to solve this equation is the distributive property of multiplication over addition, which states that a(b + c) = ab + ac. In this case, we used the distributive property to simplify 3(x - 5) to 3x - 15.
Read more about equation at
https://brainly.com/question/148035
#SPJ1
Dr. Price uses a table to organize the types of sea life and the positions relative to sea level of each location. Complete each sentence. The difference between Location A and Location B is meters. The difference between Location B and Location C is meters. The difference between Location C and Location D is meters. After observing Location B, Dr. Price returns to Location A before descending to Location C. What is the total distance she travels? Dr. Price descends to Location D to observe shrimp. She then ascends and stops to observe sea life that is halfway between Location B and Location C. What is the total distance between Location D and where Dr. Price stopped to observe?
The total distance that Dr. Price travels during her observations is 2567.1 meters, and the distance between Location D and the point halfway between Locations B and C is 1,317.125 meters.
First, we can look at the distances between each location. The table tells us that the difference between Location A and Location B is 203.15 meters. The difference between Location B and Location C is 1686.55 meters, and the difference between Location C and Location D is 474.25 meters.
To calculate the total distance that Dr. Price travels, we need to add up the distances for each part of her journey. First, she travels from Location A to Location B, a distance of 203.15 meters. Then she returns to Location A, so she travels the same distance back, for a total of 406.3 meters. Next, she descends from Location A to Location C, a distance of 1686.55 meters. Finally, she descends further to Location D, a distance of 474.25 meters. Adding up these distances, we get a total distance of 2567.1 meters.
For the second part of the question, we need to find the distance between Location D and the point halfway between Locations B and C. To do this, we first need to find the depth at the midpoint between Locations B and C. We can do this by taking the average of the depths for Locations B and C, which gives us -1,941.875 meters.
Next, we can calculate the distance between Location D and the midpoint between B and C. This is simply the difference in depth between Location D (-3,259 meters) and the midpoint (-1,941.875 meters), which gives us a distance of 1,317.125 meters.
To know more about distance here
https://brainly.com/question/4199102
#SPJ4
Complete Question:
Dr. Price uses a table to organize the types of sea life and the positions relative to sea level of each location. Complete each sentence. The difference between Location A and Location B is meters. The difference between Location B and Location C is meters. The difference between Location C and Location D is meters. After observing Location B, Dr. Price returns to Location A before descending to Location C. What is the total distance she travels? Dr. Price descends to Location D to observe shrimp. She then ascends and stops to observe sea life that is halfway between Location B and Location C. What is the total distance between Location D and where Dr. Price stopped to observe?
Location Sea Life Depth Relative to Sea Level (m)
A Eels -895.9
B Eels -1,098 3/20
C Shrimp -2,784.75
D Shrimp -3,259
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If BD = 3 and DC = 9, what is the length of AC?
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If BD = 3 and DC = 9, the length of AC is: 4 units.
How to find the length?In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. Let's call the length of the hypotenuse AC as x, and the length of the segment containing point B as y. Then, the length of the other segment containing point C is x - y.
Using similar triangles, we can set up the following proportion:
BD/DC = y/(x - y)
Substituting the given values, we get:
3/9 = y/(x - y)
Simplifying this equation, we get:
x - y = 3y/9
x = 4y/3
We also know from the Pythagorean theorem that:
AC^2 = AB^2 + BC^2
Since triangle ABC is a right triangle, we have:
AB^2 + BC^2 = x^2
Substituting x = 4y/3, we get:
AB^2 + BC^2 = (4y/3)^2
But we also know that:
AB/BC = 3/4
So we can set up another proportion:
AB/BC = y/(x - y)
Substituting x = 4y/3, we get:
AB/BC = y/(4y/3 - y)
Simplifying this equation, we get:
AB/BC = y/((4/3)y - y)
AB/BC = y/((1/3)y)
AB/BC = 3
So we have:
AB = 3BC
Substituting this into AB^2 + BC^2 = (4y/3)^2, we get:
(3BC)^2 + BC^2 = (4y/3)^2
10BC^2 = 16y^2/9
But we also know that:
BC^2 + y^2 = x^2
Substituting x = 4y/3, we get:
BC^2 + y^2 = (4y/3)^2
5BC^2 = 7y^2/9
Combining this with 10BC^2 = 16y^2/9, we get:
15BC^2 = 21y^2/9
BC^2 = (7/3)y^2/3
Substituting this into BC^2 + y^2 = (4y/3)^2, we get:
(7/3)y^2/3 + y^2 = 16y^2/9
7y^2/9 + 9y^2/9 = 16y^2/9
16y^2/9 = 16y^2/9
So this equation is true for any value of y. Therefore, the length of AC is:
AC = x = 4y/3
Substituting y = BD = 3, we get:
AC = 4(3)/3 = 4
Therefore, the length of AC is 4 units.
Learn more about Length more about here:https://brainly.com/question/28108430
#SPJ1
A. Find the average rate of change over the interval (-1, 2] for each function. Show all steps and work for credit.
B. Which function has the greatest average rate of change over the interval [1, 2]
the average rate of change over the interval (-1, 2] in the given function is 1.17.all three functions have the same average rate of change over the interval [1, 2], which is 2
what is function and average rate?A function is a mathematical rule that takes an input and produces an output. The average rate of change of a function over an interval is the average amount the output changes per unit change in the input over that interval.
According to given informationFor the function f(x) = 2x + 3:
Let x1 = -1 and x2 = 2
f(x1) = 2(-1) + 3 = 1
f(x2) = 2(2) + 3 = 7
The average rate of change is:
[f(x2) - f(x1)] / [x2 - x1] = [7 - 1] / [2 - (-1)] = 6 / 3 = 2
Therefore, the average rate of change of f(x) over the interval (-1, 2] is 2.
For the function g(x) = x^2 - 1:
Let x1 = -1 and x2 = 2
g(x1) = (-1)^2 - 1 = 0
g(x2) = 2^2 - 1 = 3
The average rate of change is:
[g(x2) - g(x1)] / [x2 - x1] = [3 - 0] / [2 - (-1)] = 3 / 3 = 1
Therefore, the average rate of change of g(x) over the interval (-1, 2] is 1.
For the function h(x) = 2^x + 1:
Let x1 = -1 and x2 = 2
h(x1) = 2^(-1) + 1 = 1.5
h(x2) = 2^2 + 1 = 5
The average rate of change is:
[h(x2) - h(x1)] / [x2 - x1] = [5 - 1.5] / [2 - (-1)] = 3.5 / 3 = 1.17 (rounded to 2 decimal places)
Therefore, the average rate of change of h(x) over the interval (-1, 2] is approximately 1.17.
b)To determine which function has the greatest average rate of change over the interval [1, 2], we need to calculate the average rate of change for each function over that interval and compare the results.
Let's assume the functions are f(x), g(x), and h(x).
The average rate of change for f(x) over the interval [1, 2] is:
[f(2) - f(1)] / [2 - 1] = (2(2) + 3 - 2(1) - 3) / 1 = 2
The average rate of change for g(x) over the interval [1, 2] is:
[g(2) - g(1)] / [2 - 1] = (2^2 - 1 - 1^2 + 1) / 1 = 2
The average rate of change for h(x) over the interval [1, 2] is:
[h(2) - h(1)] / [2 - 1] = (2^2 + 1 - 2^1 - 1) / 1 = 2
Therefore, all three functions have the same average rate of change over the interval [1, 2], which is 2.
To know more about Function Visit:
https://brainly.com/question/14418346
#SPJ1
Select the correct number from each drop-down menu to complete the equation. 7 8 − ( − 2 + 3 4 ) = 8 7 −( − 2+ 4 3 )= ( + ) + 7 8 + 8 7
The value of the expression is 17/8.
Given is an expression, 7/8 - (-2+3/4) = ( ____+____) + 7/8, we need to solve it,
7/8-(-2+3/4)
= 7/8-(-8+3)/4
= 7/8 + 5/4
= 7+10 /8
= 17/8
Hence, the value of the expression is 17/8.
Learn more about expression, click;
https://brainly.com/question/14083225
#SPJ1