A) 3y = 43 + x<br><br> b) 8y + 5x = 61

Mr. Brown chooses a fiction book at random from a list of books and then chooses a second fiction book from those remaining.

fgiga [73]

Independent would be when Mr. Brown chooses a fiction boom at random from a list of books.

Dependent would be when Mr.Brown then chooses a second fiction. book from those remaining.

5 0

3 years ago

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The graph of a function must pass the __________ line test. <br> A) vertical <br> B) horizontal

olga2289 [7]

Answer:

A) Vertical.

Step-by-step explanation:

It must pass the vertical line test. That is it must not have any vertical line passing through more than one point on the curve. If it does then it is not a function.

Thus , for example, a circle graph would not be a function.

5 0

3 years ago

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The line $y = 3$ intersects the graph of $y = 4x^2 + x - 1$ at the points $A$ and $B$. The distance between $A$ and $B$ can be w

raketka [301]

Answer:

61

Step-by-step explanation:

Let's find the points $A$ and $B$ .

We know that the $y$ -coordinates of both are $3$ .

So let's first solve:

$3=4x^2+x-1$

Subtract 3 on both sides:

$0=4x^2+x-1-3$

Simplify:

$0=4x^2+x-4$

I'm going to use the quadratic formula, $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ , to solve.

We must first compare to the quadratic equation, $ax^2+bx+c=0$ .

$a=4$

$b=1$

$c=-4$

$\frac{-1 \pm \sqrt{1^2-4(4)(-4)}}{2(4)}$

$\frac{-1 \pm \sqrt{1+64}}{8}$

$\frac{-1 \pm \sqrt{65}}{8}$

Since the distance between the points $A$ and $B$ is horizontal. We know this because they share the same $y-coordinate$ .This means we just need to find the positive difference between the $x$ -values we found for the points of $A$ and $B$ .

So that is, the distance between $A$ and $B$ is:

$\frac{-1+\sqrt{65}}{8}-\frac{-1-\sqrt{65}}{8}$

$\frac{-1+\sqrt{65}+1+\sqrt{65}}{8}$

$\frac{2\sqrt{65}}{8}$

$\frac{\sqrt{65}}{4}$

If we compare this to $\frac{\sqrt{m}}{n}$ , we should see that:

$m=65 \text{ and } n=4$ .

So $m-n=65-4=61$ .

5 0

3 years ago

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Given the functions, fx) = x - 8 and g(x) = x2 + x - 1, perform the indicated operation. When applicable, state the domain

adell [148]

Answer:

A

Step-by-step explanation:

(fg)(x) = f(x) × g(x)

= (x - 8)(x² + x - 1)

Each term in the second factor is multiplied by each term in the first factor, that is

x(x² + x - 1) - 8(x² + x - 1) ← distribute both parenthesis

= x³ + x² - x - 8x² - 8x + 8 ← collect like terms

= x³ - 7x² - 9x + 8 → A

There are no restrictions on the domain.

4 0

3 years ago

What is the benefit of dividing out greatest common factors (GCFs) before multiplying?

Nina [5.8K]

Lets get an example, for this example lets use 24/30 x 30/60
Without dividing out GCFs you would get 24x12 over 30 x 60 which is 288/1800
With dividing out GCFs you get 2/1 x 5/1 Which is 7 :)

7 0

3 years ago

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A) 3y = 43 + x b) 8y + 5x = 61