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3 years ago

The product of the sum and the difference of two numbers equals the difference of their squares

Mathematics

1 answer:

Lisa [10]3 years ago

8 0

$(a+b)(a-b)=(a)(a)+(a)(-b)+(b)(a)+(b)(-b)\\\\=a^2-ab+ab-b^2=a^2-b^2$

$Used\ distributive\ property$

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A random sample of ten professional athletes produced the following data where x is the number of endorsements the player has an

lukranit [14]

ŷ= 1.795x +2.195 is the equation for the line of best fit for the data

<h3>How to use regression to find the equation for the line of best fit?</h3>

Consider the table in the image attached:

∑x = 29, ∑y = 74, ∑x²= 125, ∑xy = 288, n = 10 (number data points)

The linear regression equation is of the form:

ŷ = ax + b

where a and b are the slope and y-intercept respectively

a = ( n∑xy -(∑x)(∑y) ) / ( n∑x² - (∑x)² )

a = (10×288 - 29×74) / ( 10×125-29² )

= 2880-2146 / 1250-841

= 734/409

= 1.795

x' = ∑x/n

x' = 29/10 = 2.9

y' = ∑y/n

y' = 74/10 = 7.4

b = y' - ax'

b = 7.4 - 1.795×2.9

= 7.4 - 5.2055

= 2.195

ŷ = ax + b

ŷ= 1.795x +2.195

Therefore, the equation for the line of best fit for the data is ŷ= 1.795x +2.195

Learn more about regression equation on:

brainly.com/question/29394257

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3 0

11 months ago

A scaled factor of 2 is used to increase the triangle. What is the new area?

lesya [120]

Answer:b

Step-by-step explanation:b

8 0

3 years ago

Ifx <5 and x > C, give a value of c such that there

professor190 [17]

Answer:

For c=5 there are not solutions for the compound inequality

Step-by-step explanation:

we know that

In the compound inequality

$x < 5$ -----> inequality A

$x > c$ -----> inequality B

The solution of the system of inequalities must satisfy inequality A and must satisfy inequality B

If c=5

then

There is no solution that satisfies both inequalities simultaneously.

therefore

For c=5 there are not solutions for the compound inequality

4 0

2 years ago

Jerry has 61 percent on khan. She needs to get 100 percent in one week. How much percent should she get each night to reach her

vova2212 [387]

Answer:

She would need to complete 5.57 each noght to reach her goal of 100%.

Step-by-step explanation:

39/7 is equal to 5.57

7 0

3 years ago

a rectangular lawn has an area of a^3 - 125. use the difference of cubes to find out the dimensions of the rectangle.

ANEK [815]

The area of a rectangle is the product of its dimensions

The dimensions of the rectangle are: $\mathbf{Length = a -5}$ and $\mathbf{Width = a^2 + 5a + 25}$

The area is given as:

$\mathbf{Area = a^3 - 125}$

Express 125 as 5^3

$\mathbf{Area = a^3 - 5^3}$

Apply difference of cubes

$\mathbf{Area = (a - 5)(a^2 + 5a + 5^2)}$

$\mathbf{Area = (a - 5)(a^2 + 5a + 25)}$

The area of a rectangle is:

$\mathbf{Area = Length \times Width}$

So, by comparison:

$\mathbf{Length = a -5}$

$\mathbf{Width = a^2 + 5a + 25}$