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3 years ago

Find the product. (2a^2+b) (3a-3b) Enter the correct answer.

Mathematics

1 answer:

Leona [35]3 years ago

3 0

<h3>Answer: 6a^3-6a^2b+3ab-3b^2</h3>

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Work Shown:

(2a^2+b)(3a-3b)

c(3a-3b) ..... let c = 2a^2+b

3ac-3bc .... distribute

3a(c)-3b(c)

3a(2a^2+b)-3b(2a^2+b) .... plug in c = 2a^2+b

3a(2a^2)+3a(b)-3b(2a^2)-3b(b) ... distribute

6a^3+3ab-6a^2b-3b^2

6a^3-6a^2b+3ab-3b^2

You could also use the FOIL rule to get the same result. The box method is a visual way to keep track of the terms.

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Find the following equation

adoni [48]

Answer:

$y=\frac{-1}{2}x+7$

Step-by-step explanation:

Slope intercept form: $y=mx+b$ when $m$ is the slope of the line and $b$ is the y-intercept (the y-coordinate of the point the line crosses the y-axis)

<u>1) Find the slope (</u> $m$ <u>)</u>

$m=\frac{y_2-y_1}{x_2-x_1}$ when the points are $(x_1,y_1)$ and $(x_2,y_2)$

We can use any two points that the table gives us to plug into this equation. For example, we can use the points (14,0) and (0,7):

$m=\frac{0-7}{14-0}\\m=\frac{-7}{14}$

Simplify the fraction

$m=\frac{-1}{2}$

So far, our equation looks like this:

$y=\frac{-1}{2}x+b$

<u>2) Find the y-intercept (</u> $b$ <u>)</u>

The y-intercept is the y-coordinate of the point the line crosses the y-axis, or in other words, it's the value of y when x is equal to 0.

Looking at the table, we can see that y is equal to 7 when x is equal to 0, so, therefore, $b=7$ .

Now, this is our final equation after plugging in $m$ and $b$ :

$y=\frac{-1}{2}x+7$

I hope this helps!

3 0

3 years ago

Select the correct answer.

ikadub [295]

Answer:

y= 1/3x + 7

Step-by-step explanation:

7 0

3 years ago

Solve for x. 4x + 5 = 20<br> a X = 5/4<br> b X = 15/4<br> c X = 3.5<br> d X = 15/3

Nonamiya [84]

Step-by-step explanation:

4x+5= 20
4x=20-5
4x= 15
x= 15/4

therefore the answer is option

b) X= 15/4

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4 0

3 years ago

A video store specializes in three types of movies: children's, American West, and horror. It's known that:

xenn [34]

X, y, z denote children's movies, western movies, and horror movies, respectively. The related system of equations is formed and solved.

$\left\{\begin{matrix} \qquad\qquad\ \dfrac{60}{100}x + \dfrac{50}{100}y =\dfrac{30}{100}(x+y+z)\\ \dfrac{20}{100}x+ \dfrac{60}{100}y+ \dfrac{60}{100}z= \dfrac{1}{2}(x+y+z) \\ \ \ \ x+100=y \end{matrix} \right.\$

Simplifying the system of equations, we have

$\left\{\begin{matrix} 3x + 2y -3z=0\\ -3x+ y+ z= 0 \\ \ \ \ x+100=y \end{matrix} \right.\ \ \Longrightarrow \ \left\{\begin{matrix} 5x-3z=-200\\ -2x+ z= -100 \end{matrix} \right.\$

$\ \ \ 5x-3z=-200\\\underline{-6x+3z=-300} \ \Rightarrow \ x=500\\\ \ -x+0= \ 500$

$y&=500+100=600\\ z&=3(500)-600=900$

The video store has 500 children's movies, 600 westerns and 900 horror movies.

6 0

2 years ago

Four years ago, you started a job with an annual salary of $40,000. At the end of each year on the job, you received a raise of

gogolik [260]

No it does not represent a linear function.

5 0

3 years ago

Read 2 more answers