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2 years ago

What must be true for lines a and b to be parallel lines? Select two options.

Mathematics

1 answer:

USPshnik [31]2 years ago

8 0

The answer is 58 degrees so e

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Find the average rate of change of f(x) = 4x² – 3 from 3 to 9.

Lina20 [59]

Answer:

Step-by-step explanation:

Given:

$f(x) = 4x^2 - 3$

Required:

Average range of change from 3 to 9

SOLUTION:

Step 1:

Find f(3) and f(9):

To find f(3), replace x with 3 in the given function

$f(3) = 4(3)^2 - 3$

$f(3) = 4(9) - 3$

$f(3) = 36 - 3$

$f(3) = 33$

To find f(9), replace x with 9 in the given function

$f(9) = 4(9)^2 - 3$

$f(9) = 4(81) - 3$

$f(9) = 324 - 3$

$f(9) = 321$

Average rate of change = $\frac{f(b) - f(a)}{b - a}$

Where,

$a = 3, f(a) = 33$

$b = 9, f(b) = 321$

Plug in the values into the formula for average rate of change.

$= \frac{321 - 33}{9 - 3}$

$= \frac{288}{6}$

$= 44$

Average rate of change = 44

3 0

3 years ago

What is the most logical first step in solving the equation x2 + 6x +9 = 10?

Shalnov [3]

Answer:

D

Step-by-step explanation:

The logical step is to factorize the left side of the equation, which becomes:

(x + 3)² = 10

Then, you can take the square root on both sides.

x + 3 = ±√10
x = ±√10 - 3

Not asked, but good to understand the procedure regardless.

8 0

2 years ago

If the numerator of a fraction is increased by 3, the fraction becomes 3/4. If the denominator is decreased by 7, the

Sauron [17]

7 over 1

Step-by-step explanation:

3 0

3 years ago

What is the quadratic regression equation for the data set? PLEASEE HELP ME

Soloha48 [4]

You're trying to find constants $a_0,a_1,a_2$ such that $\hat y=a_0+a_1\hat x+a_2{\hat x}^2$ . Equivalently, you're looking for the least-square solution to the following matrix equation.

$\underbrace{\begin{bmatrix}1&6&6^2\\1&3&3^2\\\vdots&\vdots&\vdots\\1&9&9^2\end{bmatrix}}_{\mathbf A}\underbrace{\begin{bmatrix}a_0\\a_1\\a_2\end{bmatrix}}_{\mathbf x}=\underbrace{\begin{bmatrix}100\\110\\\vdots\\70\end{bmatrix}}_{\mathbf b}$

To solve $\mathbf{Ax}=\mathbf b$ , multiply both sides by the transpose of $\mathbf A$ , which introduces an invertible square matrix on the LHS.

$\mathbf{Ax}=\mathbf b\implies\mathbf A^\top\mathbf{Ax}=\mathbf A^\top\mathbf b\implies\mathbf x=(\mathbf A^\top\mathbf A)^{-1}\mathbf A^\top\mathbf b$

Computing this, you'd find that

$\mathbf x=\begin{bmatrix}a_0\\a_1\\a_2\end{bmatrix}\approx\begin{bmatrix}121.119\\-3.786\\-0.175\end{bmatrix}$

which means the first choice is correct.

8 0

3 years ago

Explain why 7* x/7=x 7 times x over seven. why is it x?

Nikolay [14]

It is 1 because if you divided 7over 7 it 1 so x=1

5 0

3 years ago