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3 years ago

Write the slope-intercept form of the equation of the line through the given point (5, -2) and (0, -5)

1 answer:

4 0

$\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{5}}}\implies \cfrac{-5+2}{-5}\implies \cfrac{-3}{-5}\implies \cfrac{3}{5}$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{\cfrac{3}{5}}(x-\stackrel{x_1}{5}) \\\\\\ y+2=\cfrac{3}{5}x-3\implies y=\cfrac{3}{5}x-5$

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Q(h)=-8h^2-5h , find q(-10)

Sergio [31]

Answer:

-750

Step-by-step explanation:

Q(h)=-8h^2-5h ,

Let x = -10

q(-10) = -8 (-10)^2 -5(-10)

=-8 *100 +50

=-800+50

= -750

3 0

2 years ago

A city council consists of seven Democrats and five Republicans. If a committee of four people is selected, find the probability

Hoochie [10]

Answer:

The probability of selecting two Democrats and two Republicans is 0.4242.

Step-by-step explanation:

The information provided is as follows:

A city council consists of seven Democrats and five Republicans.
A committee of four people is selected.

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

${n\choose k}=\frac{n!}{k!\times (n-k)!}$

Compute the number of ways to select four people as follows:

${12\choose 4}=\frac{12!}{4!\times (12-4)!}=495$

Compute the number of ways to selected two Democrats as follows:

${7\choose 2}=\frac{7!}{2!\times (7-2)!}=21$

Compute the number of ways to selected two Republicans as follows:

${5\choose 2}=\frac{5!}{2!\times (5-2)!}=10$

Then the probability of selecting two Democrats and two Republicans as follows:

$P(\text{2 Democrats and 2 Republicans})=\frac{21\times 10}{495}=0.4242$

Thus, the probability of selecting two Democrats and two Republicans is 0.4242.

6 0

2 years ago

A parabola has an x-intercept of -1, a y-intercept of -3, and a minimum of -4 at x = 1.

torisob [31]

Answer:

The graph in the attached figure

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

$y=a(x-h)^{2}+k$

where

a is a coefficient

(h,k) is the vertex

In this problem we have

(h,k)=(1,-4)

substitute

$y=a(x-1)^{2}-4$

we have

An x-intercept of (-1,0)

substitute and solve for a

$0=a(-1-1)^{2}-4$

$0=4a-4$

$4a=4$

$a=1$

The equation is

$y=(x-1)^{2}-4$

Verify the y-intercept

For x=0

$y=(0-1)^{2}-4$

$y=-3$

The y-intercept is the point (0,-3) -----> is correct

using a graphing tool

see the attached figure

4 0

3 years ago

I really need help with this problem?

s2008m [1.1K]

Here is the solution to it

7 0

3 years ago

PLEASE I RLLY NEED HELP WITH THIS I WILL MARK YOU AS BRAINLIEST IF YOU ANSWER CORRECTLY PLS AND TY

densk [106]

Answer:

The attached graph shows my answer.

Step-by-step explanation:

The graph has to start at the top because the number of carrots has to decrease and the graph slants down to the right because the time has to increase. Then the situation says that he eats one carrot at a time until half are eaten. The graph shows the line going down until approximately half. Then he doesn't eat any more, so the line is horizontal until the end of the graph to show no change.

4 0

3 years ago