According to the conversion, 55 kg is equal to approximately 121.25 lbs.
In the world of mathematics, measurement plays a vital role in determining the quantity, weight, and size of any object. The standard units of measurement are different in various countries, and knowing how to convert from one unit to another is essential.
The question posed is, "What is 55 kg in lbs?" Here, 'kg' is a unit of mass, commonly used in the metric system, whereas 'lbs' stands for pounds, which is a unit of weight in the Imperial system. To convert from kg to lbs, we need to multiply the given value by a conversion factor.
1 kg is equal to 2.20462 pounds. Hence, we can use this conversion factor to convert 55 kg to lbs as follows:
55 kg x 2.20462 lbs/kg = 121.2542 lbs (rounded off to two decimal places)
In conclusion, understanding measurements and being able to convert from one unit to another is a fundamental aspect of mathematics. In this case, we used the conversion factor of 2.20462 lbs/kg to convert 55 kg to lbs.
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On a coordinate plane, a curved line with a minimum value of (negative 2.5, negative 12) and a maximum value of (0, negative 3) crosses the x-axis at (negative 4, 0) and crosses the y-axis at (0, negative 3).
Which statement is true about the graphed function?
F(x) < 0 over the interval (–∞, –4)
F(x) < 0 over the interval (–∞, –3)
F(x) > 0 over the interval (–∞, –3)
F(x) > 0 over the interval (–∞, –4)
The true statement about Graphed Function is:
f(x) > 0 over the interval (–∞, –4)
What is Interval in graph?A graph is referred to be an interval graph if each of its vertices can be connected to a real line interval in such a way that two vertices are only connected if and only if the connected intervals have a nonempty intersection.
Given:
Our curve has a minimum at (-2.5, -12)
Our curve has a maximum at (0, - 3)
We know that the curve crosses the x-axis at (-4, 0) and y-axis at (0, -3)
At the value x = -2.5 > (-4) the function is negative.
So, f(-2.5) = -12
f(-4) = 0
As a result, it is clear that the function is negative after f(x) crosses the x-axis at x = -4.
This implies that the function must be positive prior to that point.
Thus, the function > 0 for x values less than -4.
f(x) > 0 if x < -4
From this, we can conclude that in the range (-∞, –4), the function is above the x-axis.
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How much is $100 US in euro?
Because the exchange rate between the US dollar (USD) and the euro (EUR) changes over time, the exact conversion from $100 US to euros will be determined by the current exchange rate.
As of the 21 Feb 2023 cutoff date, the exchange rate was around 1 USD = 0.94 EUR.
Using this exchange rate, we can calculate the value of $100 US in euros:
$100 US x 0.94 EUR/USD = 94 EUR
Therefore, as of 21 Feb 2023, $100 US was equivalent to approximately 94 euros.
However, it's important to note that exchange rates are subject to change, and the exact conversion may differ depending on the current rate.
The price at which one currency can be exchanged for another is referred to as the currency exchange rate. Exchange rates fluctuate constantly and are determined by the global foreign exchange market's supply and demand for currencies.
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Your uncle has $1,375,000 and wants to retire. He expects to live for another 25 years and to earn 7.5% on his invested funds. How much could he withdraw at the end of each of the next 25 years and end up with zero in the account? a. 592,514.13 b.5127,052.74 OC $97,448.22 d. 5124,585.70 6.5123,352.17
He can withdraw $114746.17 (approx.) at the end of each of the next 25 years and end up with zero in the account. The solution has been obtained by using the concept of present value of annuity.
What is present value of annuity?
With a specific rate of return, or discount rate, an annuity's present value is the current worth of its expected future payments. The present value of the annuity decreases with increasing discount rates.
We are given that uncle has $1,375,000 and wants to retire. He expects to live for another 25 years and to earn 7.5% on his invested funds.
Using present value of annuity,
Present value of annuity due = P + P [(1 - (1 + r)⁻⁽ⁿ⁻¹⁾) / r]
1375000 = P + P [(1 - (1+0.075)⁻⁽²⁵⁻¹⁾)/0.075]
1375000 = P [1 + 10.98297]
P = 1375000/11.98297
P = $114746.17 (approx.)
Hence, uncle can withdraw $114746.17 (approx.) at the end of each of the next 25 years.
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a line has a slope of -1/5 and passes through point (-5,7). Write it's equation in slope-intercept form
Answer: The slope-intercept form of the equation of a line is y = mx + b, where m is the slope of the line and b is the y-intercept. We are given the slope m = -1/5, and a point (-5,7) through which the line passes.
To find the y-intercept b, we can substitute the point (-5,7) and the slope m = -1/5 into the slope-intercept form of the equation and solve for b:
y = mx + b
7 = (-1/5)(-5) + b
7 = 1 + b
b = 6
So the y-intercept is b = 6, and the equation of the line in slope-intercept form is:
y = (-1/5)x + 6
Therefore, the equation of the line is y = (-1/5)x + 6.
Step-by-step explanation:
The slope-intercept form of the equation of a line that has a slope of -1/5 and passes through point (-5,7) is:
y = -x/5 + 6
What is meant by the slope-intercept form of a line?
The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.
The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, denotes the y-coordinate of the location where the line's graph crosses the y-axis.
Given,
the slope of line m = -1/5
The point on the line = (-5,7)
Then the equation of a straight line is:
y -y1 = m (x-x1)
y1 = 7
x1 = -5
Then the equation becomes:
y - 7 = -1/5 ( x - (-5))
y-7 = -1/5 ( x+5)
y-7 = -x/5 -1
y = -x/5 + 6
Therefore the slope-intercept form of the equation of a line that has a slope of -1/5 and passes through point (-5,7) is:
y = -x/5 + 6
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Solve the inequality
[tex]x { \\ }^{2} < 16[/tex]
The solution of the inequality is x < -4 or x < 4
How to solve inequality?An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4
An inequality can be expressed using one of several symbols, including < (less than), > (greater than), <= (less than or equal to), >= (greater than or equal to), and != (not equal to).
x² < 16
Take the square root of both sides:
x < ±√16
x < ±4
x < -4 or x < 4
Therefore, the solution is x < -4 or x < 4
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The radius of a circle is 7 in. what is the nearest whole number.
Answer:
153.94 -> 154
Step-by-step explanation:
Have a good day
a car dealership pays $8,350 for a car. ther mask up the price by 17.4% to get the retail price. what is the retail price of the car at this dealership?
The retail price of the car at the dealership is $9,803.90. This means that the dealership is adding a markup of $1,453.90, or 17.4% of the cost, to sell the car to customers.
To find the retail price of the car at the dealership, we need to add 17.4% to the dealership's cost of $8,350. Here are the steps to do this calculation:
Multiply the cost of the car by the percentage markup as a decimal. To convert a percentage to a decimal, divide it by 100. So 17.4% as a decimal is 0.174.
Markup = $8,350 x 0.174 = $1,453.90
Add the markup to the cost of the car to get the retail price.
Retail Price = $8,350 + $1,453.90 = $9,803.90
It's important to note that the final selling price of the car may be negotiable, and that other fees and taxes may also be added to the retail price.
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What is the conversion of 1 hp to watts ?
To convert watts to horsepower, use the formula 1Hp = 735Watt.
Watt and horsepower are both power units.
Nevertheless, horsepower is a more potent unit of power. We measure the power of electrical instruments such as turbines, motors, and a variety of other devices using horsepower.
Hence, 1 Horsepower is 735 Watt using standard unit conversion rates.
1 Hp = 735 W
As a result, we have the conventional relationship 1Hp = 735 W. We can now simply convert any horsepower provided to the unit of Watt.
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How much would $10,000 due in 50 years be worth today if the discount rate were 7.5%? a $285.02 b. $266.20 c. S204.36 d. $217.80 e $268.89
The amount would $10,000 due in 50 years be worth today if the discount rate were 7.5% is,
P = $7,042
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
We know that;
The formula is,
⇒ Amount = P (1 + r)ⁿ
Hence, We get;
10,000 = P (1 + 0.75)⁵⁰
10,000 = P (1.75)⁵⁰
10,000 = P × 1.42
P = 10,000 / 1.42
P = $7,042
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The proportion of American adults who own a motorcycle is 2%. Samip believes the proportion of adults who own a motorcycle in his hometown is even lower. He randomly surveys 50 adults from his hometown and finds that 3 of them own a motorcycle. Identify why the sample in this situation does not meet all three conditions to perform a significance test using a z-statistic
The sample is not approximately normal because (50) (0.02) is not equal to or greater than 10.
The conditions for performing a significance test using a z-statistic require a sample size large enough to satisfy the Central Limit Theorem, which means that the sample should be approximately normal. In this case, the expected number of adults who own a motorcycle in the sample is only 1, which is less than the threshold of 10 needed for approximate normality. Therefore, the sample distribution is not normal, and a z-statistic cannot be used for hypothesis testing. The other conditions, such as random sampling and independence, are not relevant to this particular issue.
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Complete question:
The proportion of American adults who own a motorcycle is 2%. Samip believes the proportion of adults who own a motorcycle in his hometown is even lower. He randomly surveys 50 adults from his hometown and finds that 3 of them own a motorcycle. Identify why the sample in this situation does not meet all three conditions to perform a significance test using a z-statistic
The sample is not large enough because (50) (1-0.02) is not equal to or greater than 10.
The sample was not randomly selected.
The sample does not have independence.
The sample is not approximately normal because (50) (0.02) is not equal to or greater than 10.
Look at this set of 5 numbers:
24 58 24 24 53
How would the mode change if the number 24 were added to the set?
The mode would not change if the number 24 were added to the set, as it is still the number that appears most frequently in the set.
What is a mode in statistics?
In statistics, the mode is the value that appears most frequently in a set of data. In other words, it is the value that occurs with the highest frequency.
For the set of 5 numbers given: 24 58 24 24 53, the mode is 24 because it appears three times, which is more than any other number in the set.
If the number 24 were added to the set, then the set would become: 24 58 24 24 53 24. In this case, the mode would still be 24 because it still appears most frequently, now occurring four times in the set.
Hence, the mode would not change if the number 24 were added to the set, as it is still the number that appears most frequently in the set.
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lee makes $64 an hour. if he wants to make no less than $400 each day to save for a trip, at least how many hours must he work each day? brainly
Answer:
PAYMENT = 64
AMOUNT WANTED = 64
SO: 400 / 64 = 6.25
SO LEE NEEDS TO WORK FOR 6.25 HOURS IN EACH DAY.
For what types of associations are regression models useful?Choose the correct answer below.Non-linear Linear Both linear and non-linearFor all types of associations
Regression is a statistical procedure for determining the linear relationship between a number of variables. A simple regression model has one dependent variable and one independent variable [tex](y)[/tex]
It is used to forecast the amount of a dependent variable according to the results of one independent variable. [tex](x)[/tex]
The estimated least-squares line has the following shape :[tex]y=bo+b1x[/tex].
In this case, the dependent variable is, the independent variable is, the intercept is, and the slope coefficient is.
The slope of a linear regression describes how a unit change in x changes the y value.
When, the intercept represents the expected mean value of Y. When X never equals zero, the intercept has no intrinsic meaning.
Step (1) The process of estimating the linear relationship between two or more variables is known as regression. Only if there is a linear relationship between both variables can a regression equation be used to predict future.
Linear regression is the most fundamental a kind of regression and is the most widely used proposed model. A regression line can be used to predict dependent variables based on independent variables.
Step: (2) Outliers have a significant impact on the slope of the regression line. Influential points are also referred to as outliers in regression analysis.
Outliers can have a significant impact on the regression equation, so remove any outliers that are recognized errors. Consider the effects of any known inconsistencies that are outliers.
Step 3: Because outliers can have a large impact on the regression line, they are also referred to as important and powerful points.
An outlier is a data point that is located far away first from remaining pieces of data. These are additionally known as influencing points. Outliers have a significant influence on the slope of something like the regression line.
For linear associations, regression models can be utilized.
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Cindy left Hillview Town at 4.20 pm, travelling towards Beach Town which was 600 km away at an average speed of 108 km/h. Claudia left Hillview Town at 5 pm, travelling at an average speed of 124 km/h.
(a) How long did Claudia take to catch up with Cindy?
(b) How far away were they from Beach Town when Claudia caught up with Cindy?
Answer:
(a) To find out how long it takes for Claudia to catch up with Cindy, we can first calculate the head start that Cindy had before Claudia started. Cindy had a head start of:
d = rt = 108 km/h x 1 h 40 min = 180 km
where d is the distance that Cindy traveled during the 1 hour 40 minutes (1.67 hours) between her departure and Claudia's departure, r is Cindy's speed, and t is the time she traveled.
When Claudia started, both Cindy and Claudia were 180 km away from Beach Town. The distance between them decreases at a rate equal to the difference in their speeds, which is:
124 km/h - 108 km/h = 16 km/h
So Claudia catches up at a rate of 16 km/h. The time it takes for Claudia to catch up is then:
t = d / r = 180 km / 16 km/h = 11.25 hours
However, we need to subtract the 1 hour 40 minutes (1.67 hours) that Cindy traveled before Claudia started to find the actual time Claudia took to catch up with Cindy:
t = 11.25 hours - 1.67 hours = 9.58 hours
Therefore, Claudia took about 9 hours and 35 minutes (0.58 x 60 minutes) to catch up with Cindy.
(b) When Claudia catches up with Cindy, they are both the same distance away from Beach Town. Cindy has already traveled 180 km when Claudia catches up, so the distance they are from Beach Town is:
600 km - 180 km = 420 km
Therefore, they were 420 km away from Beach Town when Claudia caught up with Cindy.
A circle has a diameter of 28 m what is the circumference? Are used 3.14 for pie and do not round your answer. Be sure to include the correct unit in your answer
Help! 50 points, Sorry not the best picture…
The completed table in the question used to prove the proportional BD/AB = BC/(AB + AC), when AD is an angle bisector can be presented as follows;
Statement [tex]{}[/tex] Reason
1. EB ║ AD, AD bisects ∠ABC [tex]{}[/tex] 1. Given
2. ∠BEC = ∠DAC [tex]{}[/tex] 2. Corresponding angles theorem
3. ∠C = ∠C [tex]{}[/tex] 3. Reflexive property of congruence
4. ΔBEC = ΔDAC [tex]{}[/tex] 4. AAA similarity postulate
5. DC/AC = BC/EC [tex]{}[/tex] 5. Similar triangles have equivalent ratios
6. EC = EA + AC [tex]{}[/tex] 6. Segment addition postulate
7. DC/AC = BC/(EA + AC)[tex]{}[/tex] [tex]{}[/tex] 7. Similar triangles have equivalent ratios
8. AD/AB = DC/AC [tex]{}[/tex] 8. Triangle angle bisector theorem
9. BD/AB = DC/AC [tex]{}[/tex] 9. Substitution property
10. ∠EBA = ∠DAB [tex]{}[/tex] 10. Alt int. angles theorem
11. ∠DAB = ∠DAC [tex]{}[/tex] 11. Definition of a bisector
12. ∠EBA = ∠BEC [tex]{}[/tex] 12. Alt int. angles theorem
13. ΔEBA is isosceles [tex]{}[/tex] 13. Definition of isosceles triangles
14. CA = AB [tex]{}[/tex] 14. Side length of isosceles
15. BD/AB = BC/EC [tex]{}[/tex] 15. Similar triangles have equal ratios
16. BD/AB = BC/(EA + AC) [tex]{}[/tex] 16. Substitution property
17. EA = AB [tex]{}[/tex] 17. Definition of isosceles triangle ΔEBA
18. BD/AB = BC/(AB + AC) [tex]{}[/tex] 18. Substitution property
What is an angle bisector?An angle bisector is an line that divides an angle into two angles of the same measure.
The details of the some of the reasons useds to prove the specified proportion are presented as follows;
Corresponding angles theorem
The corresponding angles theorem states that the corresponding angles formed between parallel lines and a transversal are congruent
Reflexive property of congruence
The reflexive property of congruence states that a geometric figure, such as an angle is congruent to itself
AA similarity postulate
The AA similarity postulate states that triangles are similar two angles in one triangle are congruent to two angles in the other triangles.
Similar triangles have equivalent ratios
Segment addition postulate
The segment addition postulate states that the point B is located between the points A and C on a segment, only if AC = AB + BC.
Ratios of corresponding sides ar
Triangle angle bisector theorem
The triangle angle bisector theorem states that an angle bisector of a triangle divides the side facing the bisected angle in the ratio of the lengths of the other two sides.
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13 5/12 - 6 7/12 Please help me asap i really need this answer in fractions
When can a correlation coefficient based on an observational study be used to support a claim of cause and​ effect?
A. When the correlation coefficient is close to −1 or +1.
B. When the scatterplot of the data has little vertical variation.
C. When the correlation coefficient is equal to −1 or +1.
D. Never
A correlation coefficient based on an observational study can only measure the strength of the relationship between two variables, and it cannot be used to prove a cause-and-effect relationship.
Even if the correlation is close to -1 or +1, this does not necessarily mean there is a cause-and-effect relationship between the two variables—it could be due to chance. Similarly, if the scatterplot of the data has little vertical variation, this does not necessarily mean there is a cause-and-effect relationship. The only way to prove a cause-and-effect relationship is through a controlled experiment. Therefore, the correlation coefficient based on an observational study can never be used to support a claim of cause and effect.
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4/5=3/a what is a (solve for the variable using cross products)
Answer:
15/4 is a prime number so that's the answer to this question
Step-by-step explanation:
4/5 = 3/a
4•a = 5•3
4a = 15
4a/4 = 15/4
a = 15/4
How do you find the x and y coordinates of a location
See below for the steps to find the coordinates
How to determine the x and y coordinatesTo find the x and y coordinates of a point on a coordinate plane, follow these steps:
Identify the point: Look at the graph and locate the point for which you need to find the coordinates.Locate the x-axis and y-axis: Identify the x-coordinate: The x-coordinate of the point is the horizontal distance from the y-axis to the point. Identify the y-coordinate: The y-coordinate of the point is the vertical distance from the x-axis to the point.Lastly, write down the coordinates as an ordered pair (x, y)
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need help asap please answer all the questions.
2. The area of the cabin's window is 196 square inches.
3. The area of the doghouse is 32.5 square ft.
4. The farmer should purchase 2 begs of soil.
5. The artist needs 161.5 square in material to make the kite.
What is a trapezoid?
A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.
Trapezoids are defined differently by different people. A trapezoid can have one and only one pair of parallel sides, according to one school of mathematics, while another contends that a trapezoid can have multiple pairs of parallel sides. If we take into account the second definition, then a parallelogram is also a trapezoid by that definition. However, the first definition excludes parallelograms from the definition of a trapezoid since it is one of the quadrilateral types that we have already mentioned.
2. The formula for the area of a trapezoid is 1/2 × (sum of parallel side) × height.
The length of one parallel side is 10 inches. The length of the other parallel side is (10+4+4) inches = 18 inches.
The height of the trapezoid is 14 inches
The area of the trapezoid is 1/2 ×(10 + 18) × 14
= 196 square inches.
3.
The formula for the area of a trapezoid is 1/2 × (sum of parallel side) × height.
The length of one parallel side is 5 ft. The length of the other parallel side is (5+3) ft = 8 ft.
The height of the trapezoid is 5 ft.
The area of the trapezoid is 1/2 ×(5 + 8) × 5
= 32.5 square ft.
4.
The area of a parallelogram is the product of height and base.
The length of the base is (2.5 yards + 6.5 yard) = 9 yards
The height of the parallelogram is 6 yards.
The area of the parallelogram is 9 yards × 6 yards
= 54 square yards
Each beg can cover 40 square yards field.
The number of begs that the farmer need is 56/40 = 1.4 ≈2
5.
The area of the kite is half of the product of diagonals.
The length of diagonals are (8.5 in + 8.5 in) = 17 in and (6 in + 13 in) = 19 in
The area of the kite is (17×19)/2 = 161.5 square in.
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A number increased by five percent result is then increased by five percent what is the percent of increase
Answer:
Step-by-step explanation:
what is an acre in feet
An acre is a unit of measurement used to quantify land area, and it is commonly used in the United States to measure the size of plots of land, farms, and estates. One acre is equal to 43,560 square feet.
To visualize an acre, imagine a rectangle that is approximately 208 feet by 209 feet, or a square that is approximately 209 feet on each side.
To convert acres to square feet, you can use the following formula:
1 acre = 43,560 square feet
Therefore, to convert acres to feet, you can simply multiply the acre value by 43,560. For example, if you want to convert 5 acres to square feet, you can use the following formula:
5 acres x 43,560 square feet per acre = 217,800 square feet
So 5 acres is equal to 217,800 square feet.
It's worth noting that the acre is a unit of measurement used primarily in the United States, and other countries may use different units of measurement to quantify land area. For example, in the metric system, the hectare is commonly used to measure land area, with 1 hectare equal to 10,000 square meters (about 2.47 acres).
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y=40(1-0.4)^x growth or decay
The given function,[tex]Y=40(1-0.4)^x[/tex] is an exponential decay
What is an exponential function?
An exponential function is a mathematical function of the form [tex]f(x) = a^x[/tex], where "a" is a constant and "x" is the input variable. These functions are commonly used to model situations that involve continuous growth or decay.
In the given example you provided,[tex]Y=40(1-0.4)^x[/tex] represents an exponential decay function where the initial value is 40 and the common ratio is (1-0.4), which is 0.6. As x increases, the value of the function approaches zero, but never reaches it.
Hence, the given function,[tex]Y=40(1-0.4)^x[/tex] is an exponential decay.
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Help for number 4 please
The domain and ranges of the relations are;
3. Domain; {3, 5, -10, 9}
Range; {-4, 0, 6}
4. Domain; -2 ≤ x ≤ 4
Range; -2 ≤ y ≤ 4
What is the domain and range of a function?The domain is the set of the set of the possible input values of the relation and the range is the set of the possible output values of the relation
3. {(3, -4), (5, -4), (3, 0), (-10, 6), (9, 6)}
The above ordered pair are presented in the form (x, y), where, the input values are the x-values and the output values are the y-values
The domain which is the set of the input values is therefore;
Domain; {3, 5, -10, 9}The range is therefore;
Range: {-4, 0, 6}The x-value of 3 has two different y-values of -4 and 0. therefore, the relation is not a function
4. The relation is location of points on the circumference of a circle.
The input values are the x-values related to the graph, and the output values are the y-values related to the points on the circumference of the circle.
The diameter of the circle parallel to the x-axis extends from (-2, 1) to (4, 1)
The coordinates of locations on the diameter of the circle parallel to the y-axis are; (1, 4), and (1, -2)
The possible x-values, and therefore the domain are; -2 ≤ x ≤ 4
The possible y-values and therefore the range (vertical extension or reach of the circle) are; -2 ≤ y ≤ 4
The x-value of x = 1 has two y-values of -2 and 4, the relation between the x and y-values is therefore not a function.
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why did the congruent triangles get caught cheating
Which binomial is a factor of x4 − 4x2 − 4x 8?
Answer: The binomial factor is (x+2) . This was determined by factoring the given expression x4−4x2−4x+8 x 4 − 4 x 2 − 4 x + 8 by grouping then factoring one of the binomial terms
Step-by-step explanation:
please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A cone with height h and radius r has volume V = 1/3πr^2h. If a certain cone with a height of 9 inches has volume V = 3πx^2 + 42πx + 147π, what is the cone’s radius r in terms of x?
The cone’s radius r in terms of x is x + 7
How to determine tthe cone’s radius r in terms of x?From the question, we have the following parameters that can be used in our computation:
Volume, V = 3πx^2 + 42πx + 147π
Height, h = 9
The volume of a cone is
V = 1/3πr^2h
Substitute the known values in the above equation, so, we have the following representation
1/3πr^2 * 9 = 3πx^2 + 42πx + 147π
So, we have
3πr^2 = 3πx^2 + 42πx + 147π
Divide by 3π
r^2 = x^2 + 14x + 49
So, we have
r = √(x² + 14x + 49)
Take the square roots of both sides
r = x + 7
Hence, the value of r is x + 7
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30c^8d^3 - 3bc^6 d^2 + 6c^8 d divided by 12c^2 d (polynomials divided by monomials written in standard form)
To divide polynomials by a monomial written in standard form, you can divide each term of the polynomial by the monomial separately. Applying this to the given expression, we get:
(30c^8d^3 - 3bc^6d^2 + 6c^8d) / (12c^2d)
= 30c^8d^3/(12c^2d) - 3bc^6d^2/(12c^2d) + 6c^8d/(12c^2d)
= 2.5c^(8-2)d^(3-1) - 0.25bc^(6-2)d^(2-1) + 0.5c^(8-2)d^(1-1)
= 2.5c^6d^2 - 0.25bc^4d + 0.5c^6
= 5c^6d^2 - 0.5bc^4d + c^6/2
Therefore, the simplified expression is 5c^6d^2 - 0.5bc^4d + c^6/2.
Kayla is moving and must rent a truck. There is an initial charge for the rental plus a fee per mile driven. The total cost of renting the truck can be modeled by the equation C = 30 +2.50m, where m is the number of miles driven. What is the slope of the equation and what is its interpretation in the context of the problem? The slope of the function is which represents
The interpretation of the slope is that it represents the additional cost per mile driven, beyond the initial charge of $30.
What is the Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
The equation for the total cost of renting the truck is:
C = 30 + 2.50m
where C is the total cost
m is the number of miles driven.
The slope of the equation is the coefficient of "m", which is 2.50. The slope represents the rate of change of the total cost with respect to the number of miles driven.
In this case, the slope of 2.50 means that for each mile driven, the total cost of renting the truck increases by $2.50.
So, the interpretation of the slope is that it represents the additional cost per mile driven, beyond the initial charge of $30.
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