Answer:
Ok so we know it has to equal=180 right?
90+90=180
180/4
45
A boat leaves a pier and travels 15 miles due east, then turns and travels 15 miles in the direction N 20° E. Which diagram represents the boat’s current distance, x, from the pier?
(diagrams attached below)
Answer: 20.64 miles.
Step-by-step explanation: The assignment of nomenclature to the location of the boat's initiation as point A, the termination of the first course of the excursion as point B, and the termination of the second course of the journey as point C is proposed. The present study reveals that the spatial positioning of point A and point B is separated by a distance of precisely 15 miles in an eastward direction. Similarly, point B and point C are separated by a distance of 15 miles, but oriented along the vector of N 20° E.
The application of trigonometry provides a means to determine the spatial separation between point B and point C. Based on computations, the distance from point B to point C has been estimated to be approximately 7.83 miles along the northward direction and approximately 14.16 miles along the eastward direction.
Henceforth, the computation of the distance between point A and point C (i.e., the prevailing separation of the boat from the pier) can be determined by the ensuing method:
The mathematical expression denoting the distance between points A and C, designated as AC, is given by the square root of the sum of the squares of the distances between points A and B, designated as AB, and between points B and C, designated as BC. In formulaic notation, this can be expressed as AC = √((AB)² + (BC)²).
The magnitude of the distance denoted by AC, between two points A and C, can be calculated using the Euclidean distance formula, which involves the square root of the sum of the squares of the differences between the corresponding coordinates of the two points. In this particular case, the calculation results in the expression √(15² + 14.16²).
The distance between points A and C, denoted as AC, can be expressed mathematically as the square root of the sum of the squares of the horizontal and vertical distances between them. Thus, AC = √(225 + 200.89), where 225 and 200.89 represent the square of the horizontal and vertical distance, respectively. This equation can be simplified to yield the measurement of the physical distance between points A and C in the applicable units of length.
The distance between points A and C is determined to be the square root of 425.89 in units of length.
The measurement of the distance between point A and point C is approximately equivalent to 20.64 miles.
Answer: Graph A.
Step-by-step explanation:
Juan buys candy that costs $8 per pound. He will spend at least $48 on candy. What are the possible numbers of pounds he will buy?
Use p for the number of pounds Juan will buy.
Write your answer as an inequality solved for p.
In a case whereby Juan buys candy that costs $8 per pound and will spend at least $48 on candy the possible numbers of pounds he will buy written in inequality is is p>5 (at least 5 pounds).
How can these number be determined?Inequality in math refers to a statement that one quantity is either greater than, less than, or not equal to another quantity. Inequalities are often represented using symbols such as "<" (less than), ">" (greater than), or "≤" (less than or equal to) and "≥" (greater than or equal to). For example, the inequality "x > 3" states that the variable "x" is greater than the value of 3. The inequality "y ≤ 5" means that the variable "y" is less than or equal to 5.
From the question, p = number of pounds Juan will buy.
candy=costs $8 per pound
$20/$4 = 5 pounds
p>5
at least 5 pounds
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100 POINTS AND BRAINLIEST!!!! Uncle Fred gives his nephew, Jack, and niece, Jill, £60 between them every year
at Christmas. He splits it between them in the ratio of their ages.
(a) The first time he does this Jack is 1 and Jill is 3. How much does Jill
receive?
(b) How much does Jack receive the following Christmas?
(c) How old will Jack be when he receives £25 from Uncle Fred at Christmas?
Answer:
(a) The total ratio is 1 + 3 = 4, so Jill's share is (3/4) of £60:
Jill's share = (3/4) × £60 = £45.
(b) The ratio of their ages remains the same, so if Jack is one year older, Jill is also one year older. Therefore, Jill's age is 4 and Jack's age is 2, and Jack's share is (2/4) of £60:
Jack's share = (1/2) × £60 = £30.
(c) Let x be the age of Jack when he receives £25 from Uncle Fred. According to the problem, Jill is always two years older than Jack. Therefore, when Jack is x years old, Jill is x + 2 years old. The ratio of their ages is x : (x + 2), and this ratio is equal to 5/7 (25 pounds is 5/7 of 35 pounds, which is the total amount that they will receive). We can write an equation to solve for x:
x/(x+2) = 5/7
7x = 5(x + 2)
7x = 5x + 10
2x = 10
x = 5
Therefore, Jack will be 5 years old when he receives £25 from Uncle Fred at Christmas.
A) £45 because Jill will get 3/4 and Jack will get 1/4. To check our work, 60 divided by 4 is 15. 15 times 3 is 45 and 15 times one is 15.
B) £30 because it is a new year, both nephews will increase by one year. Now Jill is 4 and Jack is 2. So each kid will get half the share. 2 divided by 4 is 0.5 which is half of one. Half of 60 is 30.
C) 5 years Jill will always be 2 years older than Jack; this shows us that if some more years pass, Jill will be 7 and Jack will be 5 —> 1/4 x £60 = £25 Multiplying both sides by 4/60, we get:x = 5/4. This means Jack will be 5.
—————
Please remember to revise this and make it in your own words if you want! I am unsure about question C so comment!! I hope this helps you. -Doodle
—————
what is the cosine of angle b
For the given right angled triangle cosine of angle B is 5√89/89.(option A).
What is right angled triangle?
It is a particular type of triangle having one angle is 90° or right angle. The adjacent sides of the right angle are called base and the perpendicular and the opposite side of 90° is called hypotenuse.
The given triangle is the right angled triangle. The three sides of a right angled triangle are called base, perpendicular and hypotenuse.
In the given figure base= 5 inches and perpendicular = 8 inches
By Pythagoras theorem at first we will find out the hypotenuse. Let the hypotenuse= c inches
For any right angled triangle,
(perpendicular)² +(base)²= (hypotenuse)²
⇒ (8)² + (5)² = (c)²
⇒ 64+ 25 = c²
⇒ c² =89
⇒ c= ±√89
As hypotenuse cannot be negative
So hypotenuse = √89 inches.
Now to find cosine of angle B that is cos B we will use the trigonometric function.
cos B= Adjacent side/ hypotenuse
= 5/√89
= 5√89/89 [ Multiplying the numerator and the denominator by √89 ]
Hence, cosine of angle B is 5√89/89.
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Suppose that the function h is defined, for all real numbers, as follows.
h(x) =
-2 if x-2
-1 if x=-2
Find h(-5), h (-2), and h (5).
h(-5) =
h (-2) = 0
h (5) = 0
8
X
S
The given function h(x) is h(-5) = -2, h(-2) = -1 and h(5) = -2.
What is the defined function for all real numbers?The set of all possible inputs is the domain of a function. For instance, all real integers other than x=0 are in the domain of f(x)=x2 and g(x)=1/x, respectively. Additionally, custom functions with more restricted domains can be defined.
The definition of the function h(x) is as follows:
h(x) =
-2 if x < 2
-1 if x = -2
Using this definition, we can find the values of h(-5), h(-2), and h(5) as follows:
h(-5): Since -5 < 2, we use the first part of the definition and set h(-5) = -2.
h(-2): Since -2 = -2, we use the second part of the definition and set h(-2) = -1.
h(5): Since 5 > 2, we use the first part of the definition and set h(5) = -2.
Therefore, we have:
h(-5) = -2
h(-2) = -1
h(5) = -2
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Please see the attached.
Answer:
min: 56
lower quartile: 70
median: 74
upper quartile: 80
max: 86
Help !!!!!!!!!!!!!!!!!!!!!!!!!!!
The preimage of the quadrilateral is in the second quadrant. The quadrilateral is reflected across the x-axis, the image would lie in the fourth quadrant.
What is quadrilateral?A quadrilateral is a geometric shape that consists of four straight sides and four angles. It is a two-dimensional shape, also known as a 2D polygon, and can be defined as any closed shape that has four sides. There are many different types of quadrilaterals, each with its own unique set of characteristics.
According to given information:The second quadrant is characterized by negative x-coordinates and positive y-coordinates, while the fourth quadrant has positive x-coordinates and negative y-coordinates.
If the preimage of the quadrilateral is in the second quadrant, then its x-coordinates are negative and its y-coordinates are positive.
When the quadrilateral is reflected across the x-axis, its x-coordinates will remain the same but its y-coordinates will become negative. Therefore, if the preimage is in the second quadrant and the quadrilateral is reflected across the x-axis, the image would lie in the fourth quadrant.
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Suppose we are given the following....(picture below)
Line 1: slope = 1/4
Line 2: slope = -4
Line 3: slope = -1/12
Line 1 and Line 2: perpendicular
Line 1 and Line 3: neither
Line 2 and Line 3: neither
How to find the slope of the lines?Slope is the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.
Mathematically, the slope is the change in y divided by the change in x. That is:
Slope = (y₂-y₁) / (x₂-x₁)
Line 1:
(4, -1) and (8, 0)
Slope = (0--(-1)) / (8-4)
= 1/4
Line 2:
(2, -6) and (0, 2)
Slope = (2-(-6)) / (0-2)
= 8/(-2)
= -4
Line 3:
(3, -6) and (6, -7)
Slope = (-7-(-6)) / (6-(-6))
= -1/12
Remember:
1. When the two lines are parallel, they have the same (equal) slope.
2. When the two lines are perpendicular, the product of their slope is -1 i.e.
m₁ * m₂ = -1. Where m₁ and m₂ represent the slope of the lines.
Let's check:
Line 1 and Line 2:
They are not parallel but they are perpendicular (i.e. 1/4 * (-4) = -1).
Line 1 and Line 3:
Neither
Line 2 and Line 3:
Neither
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Find the length of each arc. Round your answers to the nearest tenth.
285⁰
A) 20.2 in
C) 5.8 in
OA
OB
OC
OD
16 in
B) 100.5 in
D) 79.6 in
The length of the arc with a central angle of 285 degrees and radius 16 inches is 79.6 inches
Finding the length of the arcFrom the question, we have the following parameters that can be used in our computation:
central angle = 285 degrees
Radius = 16 inches
Using the above as a guide, we have the following:
Length of arc = central angle/360 * 2 * 3.14 * Radius
Substitute the known values in the above equation, so, we have the following representation
Length of arc = 285/360 * 2 * 3.14 * 16
Evaluate
Length of arc = 79.6
Hence, the length of the arc is 79.6 inches
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18
If the mean for a data set was 8 and the standard deviation was 1.5, where would most of the data points be located?
A) Above 9.5
B) Between 6.5 and 9.5
Above 12
D) None of these answer choices are correct.
the correct answer is B, between 6.5 and 9.5.The solution of given standard deviations Problem isit is unlikely that most of the data points would be located there.
what is standard deviations?Standard deviation is a statistical measure of the amount of variation or dispersion in a set of data values. It represents the average distance of each data point from the mean of the data set.
According to given informationThe answer to this question can be found using the empirical rule, which states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations of the mean, and 99.7% falls within three standard deviations of the mean.
Given that the mean is 8 and the standard deviation is 1.5, one standard deviation above the mean would be 8 + 1.5 = 9.5, and one standard deviation below the mean would be 8 - 1.5 = 6.5. Therefore, approximately 68% of the data would be expected to fall between 6.5 and 9.5.
Based on this information, we can eliminate answer choices A and D. Answer choice C is more than two standard deviations above the mean, so it is unlikely that most of the data points would be located there. Therefore, the correct answer is B, between 6.5 and 9.5.
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Sophia has the following data:
131213141313h
If the range is 3, which number could h be?
A. 10
B. 11
Answer:
To determine the possible values of h, we need to first understand what is meant by the range.
The range is the difference between the highest value and the lowest value in a set of numbers. In this case, we don't know what the full set of numbers is, but we know that the range is 3.
The highest number in the set is 4 (since there are no higher numbers in the set than 4), and the lowest number in the set is either 1 or 2. This is because the range is 3, and there are only two possible sequences of three consecutive integers that include the number 4: 2, 3, 4 and 1, 2, 3.
So to find the possible values of h, we need to add 3 to each of the possible lowest numbers in the sequence.
If the lowest number is 1, then the possible highest numbers are 4 and 5 (4 + 3 = 7 but the sequence only goes up to 4 so the highest should be 5). Therefore, the possible values of h are either 10 or 11.
Therefore, the correct answer is B. 11.
NO LINKS!! URGENT HELP PLEASE!!
Select all that apply
b. Symmetric with respect to the x-axis
The ones that are symmetric with respect to the x-axis is:
y = -7x^2Checking the symmetric for all equationsA function is symmetric with respect to the x-axis if replacing y with -y in the equation does not change the equation. In other words, if the graph of the function is the same when reflected across the x-axis.
y = -7x^2 is symmetric with respect to the x-axis, since replacing y with -y gives -(-y) = y and the equation remains the same.y = 6x² - 9 is not symmetric with respect to the x-axis, since replacing y with -y gives -(-y) = y, but the equation changes to -y = 6x² - 9, which is not the same as the original equation.x=1/4y^2 is not a function, since it does not pass the vertical line test and has multiple values of x for some values of y.y=x^3-1 is not symmetric with respect to the x-axis, since replacing y with -y gives -(-y) = y, but the equation changes to -y = x^3 - 1, which is not the same as the original equation.x=-y^2+9 is not symmetric with respect to the x-axis, since replacing y with -y gives -(-y) = y, but the equation changes to x = -(-y)^2 + 9, which is not the same as the original equation.y=sqrt(x) is not symmetric with respect to the x-axis, since replacing y with -y gives -(-y) = y, but the equation changes to -y = sqrt(x), which is not the same as the original equation.y=sqrt(x)-6 is not symmetric with respect to the x-axis, since replacing y with -y gives -(-y) = y, but the equation changes to -y = sqrt(x) - 6, which is not the same as the original equation.Therefore, only the equation y = -7x^2 is symmetric with respect to the x-axis.
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HELP PLEASE!! A BRAINLIEST WOULD BE GIVEN FOR THE BEST ANSWER.
The requried [tex]\int_a^{oo} g(x) dx[/tex] must be convergent. Option C is correct.
Since f(x) is greater than or equal to g(x) for all x, we know that:
[tex]\int_a^{oo} f(x) dx\geq\int_a^{oo} g(x) dx[/tex]
If [tex]\int_a^{oo} f(x)[/tex]dx is convergent, then by comparison test, [tex]\int_a^{oo} g(x) dx[/tex] must also be convergent. Therefore, the correct answer is (C) g(x)dx is convergent.
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answer is a
i think question is about implicit differentiation
The x-coordinates of the points on the curve where the tangent line is horizontal will be option A.
How to explain the coordinate(x² + y²)² = 4(x² – y²)
x⁴ + 2x²y² + y⁴ = 4x² - 4y²
y⁴ + 2x^2y² + 4y² - 4x² = 0
Now we can use implicit differentiation to find the derivative of y with respect to x:
4y³(dy/dx) + 4xy² + 4y(dy/dx)x² + 8y(dy/dx) - 8x = 0
Simplifying this expression, we get:
4y³(dy/dx) + 4xy² + 4xy²(dy/dx) + 8y(dy/dx) - 8x = 0
(dy/dx)(4y³ + 4x²y²) + 8y(dy/dx) = 8x - 4xy²
(dy/dx)(4y³ + 4x^2y² + 8y) = 4x(2-y²)
(dy/dx) = 4x(2-y²)/(4y³ + 4x²y² + 8y)
Based on the information, x-coordinates of the points on the curve where the tangent line is horizontal will be option A.
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9. A counting number is totally odd if all its digits are odd and their sum is odd. How many totally odd counting numbers less than 1000 are there?
We need to first determine how many totally odd counting numbers there are between 1 and 9. The answer is 250.
What is odd counting number?It is an integer that is not divisible by two and therefore has a remainder of 1 when divided by two. It is also referred to as an odd number, an odd integer, or an uneven number.
For this, let us consider all the digits from 1 to 9, and their respective sums.
Digit: 1 Sum: 1 (odd)
Digit: 3 Sum: 3 (odd)
Digit: 5 Sum: 5 (odd)
Digit: 7 Sum: 7 (odd)
Digit: 9 Sum: 9 (odd)
Since all the digits between 1 and 9 and their respective sums are all odd, it means that any counting number less than 10 that is composed of only these digits would be totally odd. This means that there are 5 totally odd counting numbers less than 10, i.e., 1, 3, 5, 7 and 9.
Now, since any counting number less than 1000 can be composed of any combination of these 5 digits, the total number of totally odd counting numbers less than 1000 can be calculated by multiplying the number of digits (5) by the number of combinations of those digits (999). The result of this calculation is 250, which is the answer to the question.
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A teacher makes a garage showing the way students get to school he needs to have five more students two car how many fewer students get to school by skateboard then by car and bus combined into the answer in the Box
The number of fewer students to get to school by skateboard than by car and bus combined would be 60 fewer students.
How to find the number of students ?To find how many fewer students get to school by skateboard than by car and bus combined, we need to add the number of students who use car and bus and then subtract the number of students who use skateboard.
Car: 30 students
Bus: 40 students
Car + Bus = 30 + 40 = 70 students
Skateboard: 10 students
Difference = (Car + Bus) - Skateboard
Difference = 70 - 10 = 60 students
So, 60 fewer students get to school by skateboard than by car and bus combined.
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The factorization of x2 – 6x – 72 is:
Step-by-step explanation:
x^2 -6x - 72 = ( x-12)(x+6)
If you can't do this 'in your head' you can always use Quadratic Formula
with a = 1 b= - 6 and c= -72
to find roots x = 12 and -6 then write the equation as above
Describe a real-world problem that can be modeled by a circle.
A circle-based model is highly suitable for the design and construction of roundabouts, which present themselves as practical solutions to tackle traffic-related issues.
Describe a real-world problem that can be modeled by a circle.Roundabout intersections involve vehicles circulating around a central island in a counterclockwise direction. The circular form guarantees fluidity in traffic movements and significantly reduces the requirement for traffic lights and stops signs while enhancing security.
This model entails using a circle, ascertaining that the diameter corresponds with the width of the roadway, with its center accommodating the location of the island at equidistant distances from all contact points on the circle's periphery, thus ensuring optimal functionality.
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find the surface area of the figure
Answer:
The answer for Surface area is 332m²
Step-by-step explanation:
S.A=area of 2 triangle +Area of 2 rectangle +Area of rectangle
S.A=2×1/2×4×3 + 2(20×5) + 20×6
S.A=12+2(100)+120
S.A=12+200+120
S.A=212+120
S.A=332m²
Dean ran 2.3 fewer kilometers than Sam. If Dean ran 6.8 km, how far did Sam run? A 2-column table with 4 rows. Column 1 is labeled Situation with entries increasing, difference, finding part of a total, sharing or grouping. Column 2 is labeled Operation with entries +, minus, times, divided by. Select all that apply. You know the difference in the distances the boys ran, so this is a subtraction problem. You are finding the total distance the boys ran, so this is an addition problem. Dean ran part of the distance Sam ran, so this is a multiplication problem. The correct equation is s + 2.3 = 6.8. The correct equation is s – 2.3 = 6.8. The correct equation is 2.3s = 6.8.
The correct equation to use is "s - 2.3 = 6.8", where s represents the distance Sam ran.
What is distance?Distance is a measurement of how far apart two objects or points are from each other. It is usually measured in units such as meters, kilometers, miles, or feet. Distance can refer to physical space between two points, or it can be used to describe the extent of an abstract concept, such as a difference in opinion or a cultural divide.
According to question:The Situation column should have two entries: "finding part of a total" and "difference".
The Operation column should have only one entry: "minus".
The right formula is "s - 2.3 = 6.8", where s stands for the distance Sam ran.
To solve for s, we can add 2.3 to both sides of the equation:
s - 2.3 + 2.3 = 6.8 + 2.3
s = 9.1
Therefore, Sam ran 9.1 kilometers.
So, the Situation entries are: "difference" and "finding part of a total".
The Operation entry is: "minus".
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The polynomial function f has exactly one positive zero. Approximate the zero correct to two decimal places.
f(x) = 2x² - 1
-16x³-3x²-8x-2
The positive zero of f is approximately
(Round to two decimal places as needed.)
A college student takes the same number of credits each semester. She had 12 credits when she started, and after 3 semesters, she had 54 credits.
The rate at which the college student is earning credits, given the semesters taken, would be E. 14 credits per Semester.
How to find the credits ?The formula to find the number of credits the student takes per semester, would be :
( total credits after 3 semesters - total credits at the start ) / number of semesters = credits per semester
total credits after 3 semesters = 54 credits
total credits at the start = 12 credits
The credits per semester is therefore;
= ( 54 - 12 ) / 3
= 42 / 3
= 14 credits per semester
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The complete question is:
Which of these expresses the rate at which she is earning credits? Select the correct answer below:
3 credits per semester
42 credits per semester
14 semesters per credit
12 credits per semester
14 credits per Semester
7 semesters per credit
ANSWER NOW
t6
6 The spinner shown below is being used in a
game.
7
6
8
1
5 4
23
What is the probability of spinning the arrow once
with the result being an odd number greater than
3?
A.
B
Answer:
The answer for Probability is 1/2
Step-by-step explanation:
7,6,8,1,54,23
Probability of spinning an odd number greater than 3=1,7,23
P=3/6
P=1/2
find the surface area of the figure
The surface area of the square pyramid is 416.23 ft²
How to find the surface area of a square pyramid?
The surface area of a square pyramid is given by the formula:
A = a² + 2a√(a²/4 + h²)
Where a is the base length of the square pyramid and h is the height of the square pyramid.
From the figure, we have: a = 10 ft and h = 15 ft
A = a² + 2a√(a²/4 + h²)
A = 10² + 2*10√(10²/4 + 15²)
A = 100 + 20√(100/4 + 225)
A= 100 + 20√250
A = 416.23 ft²
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Find LM
A. 18
B. 24
C. 28
D. 36
Applying the Two-Tangent Theorem, the length of segment LM in the circle is: A. 18.
What is the Two-Tangent Theorem?
If two tangent segments are drawn to one circle from the same external point, the Two-Tangent Theorem states that both segments are congruent together.
Applying the theorem, we have:
4x - 2 = 3x + 3
Find the value of x:
4x - 3x = 2 + 3
x = 5
Find the length of LM:
LM = 3x + 3
Plug in the value of x:
LM = 3(5) + 3
LM = 18
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The quadrilateral
�
�
�
�
GRAY is shown below. Find the image of quadrilateral
�
�
�
�
GRAY if it has a translation of 4 units left and 2 units down and then is dilated by a scale factor of
1
2
2
1
The coordinates of the figure after translation & dilation are A''(1,3) ,R''(-1/2,1) , G''(-1,-3/2), Y''(5/2,5/2).
What is quadrilateral?A quadrilateral is a polygon with four sides and four vertices. Some examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and rhombuses.
What is meant by scale factor?Scale factor refers to the ratio of the length or size of an object in one dimension to the length or size of a corresponding object in another dimension. It is commonly used in mathematics and geometry to describe the relationship between two similar figures. For example, if one square has a side length of 4 cm and another square is similar to it with a side length of 8 cm, the scale factor between the two squares is 2:1.
A(2,8) R(3,4) G(2,-1) Y(9,7)
Translate it to 4 units left gives the result:
A'(-2,6) ,R'(-1,2) ,G'(-2,-3), Y'(5,5)
Now dilate it:
A''=(-1,3), R''(-1/2,1), G''(-1,-3/2), Y''(5/2,5/2)
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A rectangular patio has a length of (1 + 2x) yards and a width of (2 - 3x) yards. Which correctly describes the area and perimeter of the patio?
The correct statements describing the area and perimeter of the patio are:
The area of the patio is (1 + 2x)(2 - 3x) square yards.The perimeter of the patio is 2(3 - x) yards.The area and perimeter of the patio?The area of a rectangle is given by the product of its length and width. So, the area of the patio is:
Area = length x width
Area = (1 + 2x)(2 - 3x)
Therefore, the area of the patio is (1 + 2x)(2 - 3x) square yards.
The perimeter of a rectangle is given by the sum of the lengths of all four sides.
So, the perimeter of the patio is:
Perimeter = 2(length + width)
Perimeter = 2(1 + 2x + 2 - 3x)
Perimeter = 2(3 - x)
Therefore, the perimeter of the patio is 2(3 - x) yards.
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Find the positive solution to each equation.
If the solution is irrational, write the solution using square root or cube root notation.
Equation
Positive Solution
The solutions are explained in the solution below.
1) t³ = 216
t = ∛216
t = ∛6×6×6
t = 6
2) a² = 15
a = √15
a = 3.87
3) m³ = 8
m = ∛8
m = ∛2×2×2
m = 2
4) c³ = 343
c = ∛343
c = ∛7×7×7
c = 7
e) f³ = 181
f = ∛181
f = 5.65
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It took a crew 1 h 30 min to row 5 km upstream and back again. If the rate of flow of the stream was 8 km/h, what was the rowing speed of the crew in still water? km/h
The rowing speed of the crew in still water is:
x = 12 km/h.
What is meant by speed?
Speed is a measure of how fast an object is moving. It is usually expressed in units of distance per unit of time, such as miles per hour or meters per second. Speed can be calculated using the formula speed = distance/time.
According to the given information
We can use the formula:
distance = rate × time
to set up two equations based on the information given.
When the crew rows upstream for 5 km, the time it takes is:
time = distance/rate
time = 5 / (x - 8)
When the crew rows downstream for 5 km, the time it takes is:
time = distance/rate
time = 5 / (x + 8)
The total time for the round trip is 1 hour 30 minutes, or 1.5 hours:
total time = time upstream + time downstream
1.5 = 5/(x-8) + 5/(x+8)
To solve for x, we can start by multiplying both sides of the equation by (x - 8)(x + 8) to clear the denominators:
1.5(x - 8)(x + 8) = 5(x + 8) + 5(x - 8)
Expanding and simplifying, we get:
1.5x^2 - 72 = 10x
Bringing all the terms to one side of the equation, we get:
1.5x^2 - 10x - 72 = 0
We can factor this quadratic equation by first dividing both sides by 1.5:
x^2 - (10/1.5)x - 48 = 0
We can then factor this expression as:
(x - 12)(x + 4) = 0
This gives us two possible values of x: x = 12 and x = -4.
Since we are looking for a rowing speed (which is a positive quantity), we can discard the negative solution and conclude that the rowing speed of the crew in still water is:
x = 12 km/h.
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Solve for x:-
2^x=32
Answer:
x=5
Step-by-step explanation:
2^x= 32
2^x=2^5
(comparing, common denominator)
therefore x=5.