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2 years ago

Find x when y = 3 in the literal equation 3x + 6y= 24. A. 3 B. 18 C. 6 D. 2

Mathematics

2 answers:

svetlana [45]2 years ago

8 0

Answer:

D. 2

Step-by-step explanation:

Substitute y with 3

3x+18=24

Move 18 to the other side by subtracting by 18

3x=6

Divide 3 on both sides

x=2

Hope this helps!

alekssr [168]2 years ago

3 0

Answer: It is D

Step-by-step explanation:

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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

What is the value of r?

finlep [7]

Answer:

A.12

Step-by-step explanation:

2×r-13 = 11

r + 2 = 14

11 + 14 = 25

3 0

3 years ago

What is 60% of 125? Enter your answer in the box.

Law Incorporation [45]

Answer:

explanation: because i looked it up

7 0

2 years ago

The hypotenuse of a right triangle measures 6cm and one of its legs measures 3cm.Find the measure of the other leg. If necessary

belka [17]

Answer:

5.2

Step-by-step explanation:

a^2+b^2=c^2

Where c is the length of hypotenuse

and a, b are lengths of the legs.

Put in 6 for c,

Put in 3 for a and you get 9+b^2=36

Subtract 9 from both sides and get b^2= 27

Then find the square root of both sides to get b, so the answer is the square root of 27.

The cloest square root is 5, then apporixmate the tenths value and see if they work.

Answer: 5.2

8 0

1 year ago

Read 2 more answers

What is the area of the following figure:

xenn [34]

Answer:

180cm^2

Step-by-step explanation:

split it into 2 different triangles one is 24 x 4 and the other is 24 x 11 then add them together

24 x 4 is 96/2 is 48

24 x 11 is 264/2 is 132

add 48 + 132 to get an answer of 180 cm^2

if anything doesnt seem right just comment and i will try and figure out what has gone wrong

hope this helps :)

4 0

2 years ago