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3 years ago

Use the Distributive Property to write each expression as an equivalent expression. Then evaluate it.

Mathematics

1 answer:

Alla [95]3 years ago

5 0

Distributive property means that you must multiply the number directly outside the parentheses to all the numbers inside the parentheses

Look at the image below for the work!

Hope this helped!

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Which of the following is the inverse of y=12^x

Elenna [48]

$y=12^x\ \ \ |log_{12}\\\\\log_{12}y=\log_{12}12^x\\\\\log_{12}y=x\log_{12}12\\\\x=\log_{12}y$

$y=12^x\to y^{-1}=\log_{12}x;\ x\in\mathbb{R^+}\to\ y^{-1}=\dfrac{\log x}{\log12};\ x\in\mathbb{R^+}\to y^{-1}=\dfrac{\ln x}{\ln 12}$

$Used:\\\\\log_aa=1\\\\\log_ab^n=n\log_ab\\\\\log_ab=\dfrac{\log_cb}{\log_ca}$

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3 years ago

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F(x) = 8x3 - 5x+12 Find the zeroes

Darina [25.2K]

Answer: x = 36/5
0=24-5x+12
0=36-5x
5x=36

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2 years ago

What is y=\dfrac{2}{3}x+4y=

lara [203]

Answer:

$12y+x-12=0$

Step-by-step explanation:

If I'm not mistaken by the question, we have

$x+4y=\dfrac{2}{3}x+4$

Multiply through by the LCM of all the denominators to clear the fractions. Since we have only one fraction, we multiply through by its LCM (3)

$3\timesx+3\times4y=3\times\dfrac{2}{3}x+3\times4$

$3x+12y=2x+12$

Putting all terms on the LHS (left hand side) and evaluating,

$12y+x-12=0$

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3 years ago

Find the second partial derivatives of the following functions

artcher [175]

(a) z = 3x ² - 4xy + 15y ²

has first-order partial derivatives

∂z/∂x = 6x - 4y

∂z/∂y = -4x + 30y

and thus second-order partial derivatives

∂²z/∂x ² = 6

∂²z/∂x∂y = -4

∂²z/∂y∂x = -4

∂²z/∂y ² = 30

where ∂²z/∂x∂y = ∂/∂x [∂z/∂y] and ∂²z/∂y∂x = ∂/∂y [∂z/∂x].

(b) z = 4x eʸ

∂z/∂x = 4eʸ

∂z/∂y = 4x eʸ

∂²z/∂x ² = 0

∂²z/∂x∂y = 4eʸ

∂²z/∂y∂x = 4eʸ

∂²z/∂y ² = 4x eʸ

∂z/∂x = 6 ln(y)

∂z/∂y = 6x/y

∂²z/∂x ² = 0

∂²z/∂x∂y = 6/y

∂²z/∂y∂x = 6/y

∂²z/∂y ² = -6x/y ²

6 0

3 years ago

On a unit circle, the terminal point of 0 is (sqrt3/2,1/2) What is 0?

san4es73 [151]

Answer:

The measure of $\theta$ is 30°.

Step-by-step explanation:

In the statement, the angle has been misrepresented. The corrected statement is described below:

"On a unit circle, the terminal point of $\theta$ is $\left(\frac{\sqrt{3}}{2}, \frac{1}{2} \right)$ . What is $\theta$ ?"

The measure of the angle ( $\theta$ ), in radians, is in standard form, that is, it is done with respect to the +x semiaxis. The measure of the angle whose terminal point is of the form $(x,y)$ is determined by the following inverse trigonometric function:

$\theta = \tan^{-1}\left(\frac{y}{x} \right)$ (1)

If we know that $x = \frac{\sqrt{3}}{2}$ and $y = \frac{1}{2}$ , then the measure of $\theta$ is:

$\theta = \tan^{-1} \frac{\sqrt{3}}{3}$

$\theta = 30^{\circ}$

The measure of $\theta$ is 30°.

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3 years ago

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