All categories

2 years ago

PLEASE HELP ASAP ILL GIVE BRAINLIEST explain your steps too please

Mathematics

1 answer:

kirza4 [7]2 years ago

3 0

The answer is -12 (B)

You might be interested in

Find the area of a triangle bounded by the y-axis, the line f(x)=9−4/7x, and the line perpendicular to f(x) that passes through

Setler79 [48]

<u>ANSWER: </u>

The area of the triangle bounded by the y-axis is $\frac{7938}{4225} \sqrt{65} \text { unit }^{2}$

<u>SOLUTION:</u>

Given, $f(x)=9-\frac{-4}{7} x$

Consider f(x) = y. Hence we get

$f(x)=9-\frac{-4}{7} x$ --- eqn 1

$y=9-\frac{4}{7} x$

On rewriting the terms we get

4x + 7y – 63 = 0

As the triangle is bounded by two perpendicular lines, it is an right angle triangle with y-axis as hypotenuse.

Area of right angle triangle = $\frac{1}{ab}$ where a, b are lengths of sides other than hypotenuse.

So, we need find length of f(x) and its perpendicular line.

First let us find perpendicular line equation.

Slope of f(x) = $\frac{-x \text { coefficient }}{y \text { coefficient }}=\frac{-4}{7}$

So, slope of perpendicular line = $\frac{-1}{\text {slope of } f(x)}=\frac{7}{4}$

Perpendicular line is passing through origin(0,0).So by using point slope formula,

$y-y_{1}=m\left(x-x_{1}\right)$

Where m is the slope and $\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)$

$y-0=\frac{7}{4}(x-0)$

$y=\frac{7}{4} x$ --- eqn 2

4y = 7x

7x – 4y = 0

now, let us find the vertices of triangle, one of them is origin, second one is point of intersection of y-axis and f(x)

for points on y-axis x will be zero, to get y value, put x =0 int f(x)

0 + 7y – 63 = 0

7y = 63

y = 9

Hence, the point of intersection is (0, 9)

Third vertex is point of intersection of f(x) and its perpendicular line.

So, solve (1) and (2)

$\begin{array}{l}{9-\frac{4}{7} x=\frac{7}{4} x} \\\\ {9 \times 4-\frac{4 \times 4}{7} x=7 x} \\\\ {36 \times 7-16 x=7 \times 7 x} \\\\ {252-16 x=49 x} \\\\ {49 x+16 x=252} \\\\ {65 x=252} \\\\ {x=\frac{252}{65}}\end{array}$

Put x value in (2)

$\begin{array}{l}{y=\frac{7}{4} \times \frac{252}{65}} \\\\ {y=\frac{441}{65}}\end{array}$

So, the point of intersection is $\left(\frac{252}{65}, \frac{441}{65}\right)$

Length of f(x) is distance between $\left(\frac{252}{65}, \frac{441}{65}\right)$ and (0,9)

$\begin{aligned} \text { Length } &=\sqrt{\left(0-\frac{252}{65}\right)^{2}+\left(9-\frac{441}{65}\right)^{2}} \\ &=\sqrt{\left(\frac{252}{65}\right)^{2}+0} \\ &=\frac{252}{65} \end{aligned}$

Now, length of perpendicular of f(x) is distance between $\left(\frac{252}{65}, \frac{441}{65}\right) \text { and }(0,0)$

$\begin{aligned} \text { Length } &=\sqrt{\left(0-\frac{252}{65}\right)^{2}+\left(0-\frac{441}{65}\right)^{2}} \\ &=\sqrt{\left(\frac{252}{65}\right)^{2}+\left(\frac{441}{65}\right)^{2}} \\ &=\frac{\sqrt{(12 \times 21)^{2}+(21 \times 21)^{2}}}{65} \\ &=\frac{63}{65} \sqrt{65} \end{aligned}$

Now, area of right angle triangle = $\frac{1}{2} \times \frac{252}{65} \times \frac{63}{65} \sqrt{65}$

$=\frac{7938}{4225} \sqrt{65} \text { unit }^{2}$

Hence, the area of the triangle is $\frac{7938}{4225} \sqrt{65} \text { unit }^{2}$

8 0

3 years ago

An economist creates a scatter plot comparing years of experience to yearly salary (in dollars) at a particular company. The tre

marishachu [46]

Answer:

Step-by-step explanation:

c sdkwsofjodjedojeojewoj

8 0

2 years ago

Read 2 more answers

What is the 7th term of the geometric sequence where a1 = 625 and a2 = −125?

myrzilka [38]

Common ratio, r = (-125)/625 = -0.2
First term, a = 625

7 term
= ar^6
= 625(-0.2)^6
= -0.04

4 0

3 years ago

Read 2 more answers

If I make 11.50 an hour working full time (40 hours a week) how much money do i make a year after deducting 60 dollars of taxes

Kazeer [188]

Given:
hourly rate = 11.50
hours worked in a week = 40 hours
taxes per moth = 60

Every month may be 4 weeks or 5 weeks but we know that 1 year has 52.1429 weeks.

Let us compute for the whole year:

Earnings:
11.50 /1 hour * 40 hours/1week * 52.1429 weeks/1year
= 11.50 * 40 * 52.1429/year
= 23,985.734 per year

Taxes:
60 / per month * 12 months / 1 year
= 60 * 12/year
= 720 per year

Net earning per year
23,985.734 - 720 = 23,264.734

Net earning per month
23,264.734 ÷ 12 months = 1,938.81

You will earn 23,264.73 annually from a monthly earning of 1,938.81

7 0

3 years ago

Please help me solve this problem

stiks02 [169]

Step-by-step explanation:

it seems the answer is four (option a)

5 0

3 years ago