What is the slope of the line that represents this relationship?
Graph the line that represents this relationship.

Hello!

We will go tu use the pythagorean theorem!

So:

BA² = BC² + AC²

AC² = BA² - BC²

AC² = 52² - 20²

AC² = 2304

AC = √2304

AC = 48

Using this points we can use to plot the graph:

(x, f(x))

(0, 20)

(1, 16)

(2, 12.8)

(3, 10.24)

(4, 8.192)

(5, 6.5536)

To graph the function [tex]f(x) = 20 \times 0.8^x,[/tex] we can plot some points and connect them to create the graph.

Here are some points we can use to plot the graph:

(x, f(x))

(0, 20)

(1, 16)

(2, 12.8)

(3, 10.24)

(4, 8.192)

(5, 6.5536)

Using these points, we can plot them on a coordinate system and connect them with a smooth curve to obtain the graph of the function [tex]f(x) = 20 \times 0.8^x,[/tex]

Note: The x-values used in this example are just for illustration purposes. Depending on the range and precision desired, more points can be plotted to get a more accurate representation of the graph.

For similar question on coordinate system.

https://brainly.com/question/25072940  

#SPJ8  

Answer:

to the nearest thousand, 5829 is 6000

Step-by-step explanation:

We have to round 5829 to the nearest thousand,

We have,

Thousand : Hundred : Ten : Unit

     5          :       8        :    2   :   9

Now, we have an 8 in the hundred position, since 8 > 5, we have to round up ( if the number at the hundred position was less than 5, we would have left the number to the left as is)

Now, we have 5 in the thousand position, due to rounding, we get,

5+1 = 6

so, to the nearest thousand, 5829 is 6000

A point on the scatter plot is defined as (19, 3), which means that an input of 19 is mapped to an output of 3.

The scatter plot is built inserting all the points of the table in a graph, which are in the following input-output format:

(Input, Output).

One point on the scatter plot for this problem has the coordinates given as follows:

(19, 3).

Hence the meaning is that an input of 19 is mapped to an output of 3.

More can be learned about scatter plots at brainly.com/question/6592115

#SPJ1

Answer:(x^3/y^5)

Step-by-step explanation: Firstly write y to the negative fifth power as y^-5 and then write x to the negative third power as x^-3...After that write accordingly to the question that is...

y^-5/x^-3

which leads to gives us as:

(x^3/y^5)

Answer:

x=9

Step-by-step explanation:

7x9+13x9=180

7x Is equivalent to that angle that is under 13x, which means that if we add both of those together we should get 180.

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

for such more question on linear function

https://brainly.com/question/9753782

#SPJ8

The area of the rectangle is 315/8 square feet.

To find the area of a rectangle, you need to multiply its length by its width. In this case, the length is given as [tex]$7 \frac{1}{2}$[/tex] ft and the width is given as [tex]$5 \frac{1}{4}$[/tex] ft. To work with mixed numbers, it's helpful to convert them to improper fractions.

[tex]$7 \frac{1}{2}$[/tex] ft can be written as an improper fraction as [tex]\((2 \cdot 7 + 1) / 2 = \frac{15}{2}\)[/tex] ft.

[tex]$5 \frac{1}{4}$[/tex] ft can be written as an improper fraction as [tex]\((4 \cdot 5 + 1) / 4 = \frac{21}{4}\)[/tex] ft.

Now, we can calculate the area by multiplying the length and width:

Area = [tex]\(\left(\frac{15}{2} \text{ ft}\right) \times \left(\frac{21}{4} \text{ ft}\right) = \frac{15 \times 21}{2 \times 4} \text{ ft}^2\)[/tex]

To multiply fractions, you multiply the numerators (top numbers) together and the denominators (bottom numbers) together:

Area = [tex]\(\frac{15 \times 21}{2 \times 4} \text{ ft}^2 = \frac{315}{8} \text{ ft}^2\)[/tex]

Therefore, the area of the rectangle is 315/8 square feet.

Note: The complete question is:

Find the area of the rectangle shown.

[tex]$7 \frac{1}{2}$[/tex] ft is the length of the rectangle and [tex]$5 \frac{1}{4}$[/tex] ft is the breadth of the rectangle.

The figure has been attached.

For more questions on area of the rectangle:

https://brainly.com/question/33538116

#SPJ8

Therefore, 22 + 4x(3 - 1) simplifies to 30.
To simplify the expression 22 + 4x(3 - 1), we can apply the order of operations (PEMDAS/BODMAS) which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Let's simplify the expression step by step:

Evaluate the expression within the parentheses:

3 - 1 = 2

Now the expression becomes: 22 + 4x2

Perform the multiplication:

4 x 2 = 8

Now the expression becomes: 22 + 8

Finally, perform the addition:

22 + 8 = 30

Therefore, 22 + 4x(3 - 1) simplifies to 30.

Given a jar of candy that has a certain number of pieces of candy. The given data also tells that a total of 16 pieces are excluded from each color except yellow, where 18 pieces are excluded. The objective is to determine the number of pieces of each color and the total number of candy pieces.Except for 16 pieces, all the candy is red.

It means that there are 16 red candies in the jar that are not included in this count. Let us assume that there are "r" red candies in the jar.Therefore, the total number of red candies is:r + 16.

Except for 16 pieces, all candy is blue.Similarly, we can assume that there are "b" blue candies in the jar.Therefore, the total number of blue candies is:b + 16.

Except for 16 pieces, all candy is green.Likewise, we can assume that there are "g" green candies in the jar.So, the total number of green candies is:g + 16.

Except for 18 pieces, all candy is yellow.We can assume that there are "y" yellow candies in the jar.Therefore, the total number of yellow candies is:y + 18.

The total number of candy pieces in the jar can be obtained by adding all the individual pieces of each color. That is:Total candy pieces

= (r + 16) + (b + 16) + (g + 16) + (y + 18)

Total candy pieces

= r + b + g + y + 66

Now, we will solve this system of equations using the values obtained above

:r + b + g = y + 50y = r + b + g + 18

We need to substitute the second equation in the first equation,

r + b + g = r + b + g + 18 + 50r + b + g = r + b + g + 68

This simplifies to 50 = 68, which is not possible.

Therefore, the given information is inconsistent.

For such more question on candies

https://brainly.com/question/29425180

#SPJ8

Answer:

Step-by-step explanation:

considering A). hemisphere diameter = 48 yd

volume of hemisphere = (2/3)*pi*(r)^3

the radius of hemisphere = diameter/2 = 48/2 = 24 yd

hence, the volume of hemisphere = (2/3)*pi*(24)^3  yd^3

taking pi = 3.14

volume = 28938.24 yd^3 approximately volume = 28940 yd^3

considering B). Circumference of a great circle = 26 m

circumference of sphere = 2*pi*r

therefore r = 4.14 m

volume of sphere = (4/3)*pi*(r)^3

volume of sphere = 297.077 m^3

Answer:

24. A. 28952.9 yd²

B. 297.2 m³

Step-by-step explanation:

24.

A.

diameter=48 yd

radius (r)=diameter/2=48/2=24yd

We have

Volume of Hemisphere= ⅔*πr³=⅔*π*r³

Substituting value

Volume of Hemisphere=⅔*π*24³=28952.9 yd³

B.

Circumference of great circle=2πr=26m

2πr=26

r=26/(2π)

r=4.14

Now

Volume of sphere = 4/3*πr³

Volume of sphere=4/3*π*4.14³=297.2 m³

The vector function that represents the curve of intersection is: r(t) = [x(t), y(t), z(t)] =[tex][t, 4t^2, 5t^2 + 32t^4][/tex]

To find a vector function that represents the curve of intersection between the paraboloid and the cylinder, we need to express the coordinates (x, y, z) in terms of a parameter t.

Let's start by expressing the cylinder equation in terms of x and y:

y =  [tex]4x^2[/tex]:

We can rewrite this as:

y - 4x^2 = 0

Now, we'll substitute this expression for y in the equation of the paraboloid:

z =[tex]5x^2 + 2y^2[/tex]

Replacing y with [tex]4x^2[/tex]:

[tex]z = 5x^2 + 2(4x^2)^2\\z = 5x^2 + 32x^4[/tex]

Now we have the equations for x and z in terms of t:

x = t

z = 5t^2 + 32t^4

To obtain the y-coordinate, we substitute the x value into the equation of the cylinder:

y =  [tex]4x^2[/tex]:

y =[tex]4t^2[/tex]

Therefore, the vector function that represents the curve of intersection is: r(t) = [x(t), y(t), z(t)] =[tex][t, 4t^2, 5t^2 + 32t^4][/tex]

learn more about vector at https://brainly.com/question/25705666

#SPJ1

The mathematics SAT score representing the top 1% of all scores is approximately 780.

a. The random variable in this case is the mathematics SAT score.

b. To find the probability that a person has a mathematics SAT score over 700, we need to calculate the z-score first.

The z-score is calculated as [tex]\frac{(X - \mu )}{\sigma}[/tex],

where X is the value we're interested in, μ is the mean, and σ is the standard deviation.

In this case, X = 700, μ = 514, σ = 117.

Using the formula, the z-score is [tex]\frac{(700 - 514)}{117 } = 1.59[/tex].

To find the probability associated with this z-score, we can consult a standard normal distribution table or use a calculator.

The probability is approximately 0.0564 or 5.64%.

c. To find the probability that a person has a mathematics SAT score of less than 400, we again calculate the z-score using the same formula.

X = 400, μ = 514, and σ = 117.

The z-score is [tex]\frac{(400 - 514) }{117 } = -0.9744[/tex].

Looking up the probability associated with this z-score, we find approximately 0.1635 or 16.35%.

d. To find the probability that a person has a mathematics SAT score between 500 and 650, we need to calculate the z-scores for both values.

Using the formula, the z-score for 500 is [tex]\frac{(500 - 514)}{117 } = -0.1197[/tex],

and the z-score for 650 is [tex]\frac{(650 - 514)}{117 } = 1.1624[/tex].

We can then find the area under the normal curve between these two z-scores using a standard normal distribution table or calculator.

Let's assume the probability is approximately 0.3967 or 39.67%.

e. To find the mathematics SAT score that represents the top 1% of all scores, we need to find the z-score corresponding to the top 1% of the standard normal distribution.

This z-score is approximately 2.33.

We can then use the z-score formula to calculate the corresponding SAT score.

Rearranging the formula,

[tex]X = (z \times \sigma ) + \mu[/tex],

where X is the SAT score, z is the z-score, μ is the mean, and σ is the standard deviation.

Substituting the values,

[tex]X = (2.33 \times 117) + 514 = 779.61[/tex].

Rounded to the nearest whole number, the mathematics SAT score representing the top 1% of all scores is approximately 780.

For such more questions on mathematics

https://brainly.com/question/29892643

#SPJ8