Evaluate the expression below for x = 4. 3x + 2 • X - 81

Will mark brainliest! Questions are in the picture!

alexdok [17]

Answer:

52.9 inches .

Step-by-step explanation:

Given that the triangular indentation has an area of 100 in.² and the base and height of this traingle are represented by expressions 3x and x+3 respectively . We need to find out the perimeter to the nearest tenth.

As we know that the area of triangle is ,

$\rm\longrightarrow Area_{\triangle}=\dfrac{1}{2}(base)(height)$

Substituting the respective values,

$\rm\longrightarrow 100\ =\dfrac{1}{2}(x+3)(3x)\\\\\rm\longrightarrow 2(100) = 3x(x+3)\\\\\rm\longrightarrow200 = 3x^2+9x\\\\\rm\longrightarrow 3x^2+9x-200=0$

On using the Quadratic formula , we have;

$\rm\longrightarrow x =\dfrac{-9\pm\sqrt{9^2-4(3)(-200)}}{2(3)} \\\\\rm\longrightarrow x =\dfrac{-9\pm \sqrt{81+1200}}{6}\\\\\rm\longrightarrow x =\dfrac{-9\pm \sqrt{1281}}{6}$

On simplifying above , we will get ,

$\rm\longrightarrow x = 6.802,-9.802$

Since sides can't be negative, therefore,

$\rm\longrightarrow\underline{\underline{ x =6.802}}$

Therefore ,

$\rm\longrightarrow Base = 3x =3(6.802)in = 20.406\ in\\$
$\rm\longrightarrow Height = x +3=6.802+3=9.802\ in$

Next let's find out the hypotenuse using Pythagoras theorem, as ;

$\rm\longrightarrow h=\sqrt{ b^2+p^2}\\$

$\rm\longrightarrow h =\sqrt{ (20.406)^2+(9.802)^2}\\$

$\rm\longrightarrow h =\sqrt{416.40+96.07}\\$

$\rm\longrightarrow h = 22.63\ in$

Now we may find perimeter as ,

$\rm\longrightarrow P = p + b + h \\$

$\rm\longrightarrow P = (22.63 + 9.802 + 20.406)in.$

$\\\rm\longrightarrow P = 52.89 \ in.\\$

$\rm\longrightarrow \underline{\underline{ Perimeter = 52.9\ in .}}$

8 0

2 years ago

Graph a direct variation function that goes through the point (-2, -6). what is the slope

Effectus [21]

Answer:

The slope is 3.

Step-by-step explanation:

A direct variation function will always go through the origin point (0, 0).

Therefore, we have the two points (0, 0) and (-2, -6).

We can use the slope formula to find the slope:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

Substitute and evaluate:

$\displaystyle m=\frac{0-(-6)}{0-(-2)}=\frac{6}{2}=3$

Therefore, the slope of the function is 3.

To graph, simply plot (0, 0) and (-2, -6) and draw a line connecting them. This is shown below.

6 0

2 years ago

Read 2 more answers

Am I correct ? If not the question is refer to the figure to complete this proportion r/h=h/? Answers A)r B)s C)h D)c

Harlamova29_29 [7]

Here we have two right triangles. And in such case we have to use altitude rule which is

ratio of part of hypotenue and altitude= ratio of altitude and remaining part of hypotenuse

So we get

r/h =h/s

So the correct option is s .

7 0

3 years ago

What number increased by 15% equal 161

kkurt [141]

Answer:

100%+15% = 115%

proportionally:

x - 100%

161 - 115%

x = (161 * 100%) / 115% = 140

4 0

3 years ago

Read 2 more answers

PLEASE HELP! 15 POINTS AND FIRST PERSON TO ANSWER GETS BRAINLIEST!!!

Natalija [7]

Answer:

This is a function because each x value has a different y value. If one of x values would of had two different y values then it would of not have been a function

Step-by-step explanation:

6 0

2 years ago

Evaluate the expression below for x = 4. 3x + 2 • X - 81 - 12