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3 years ago

An equilateral triangle has an altitude length of 27 feet. Determined the length of a side of the triangle

1 answer:

7 0

Ok equilateral triangle
altitude=27
height=27
if you drwa the height, you see that the equilateral triangle is split up into 2 right trnalges

base=1/2 of one side
hypotonuse=1 side
vertical side=27
represent measure of 1 side as x
base=x/2
hypotonuse=x
vertical side=27

we have a right triangle
use pythagoran theorem
a^2+b^2=c^2
a=x/2
b=27
c=x
so

(x/2)^2+27^2=x^2
(x^2)/4+729=x^2
multiply both sides by 4 to clear fraction
x^2+2916=4x^2
subtract x^2 fromboth sides
2916=3x^2
divide both sides by 3
972=x^2
squuare root both sides
18√3

one side is 18√3 feet or aprox 31.1769 feet

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3x + 1 = 5X-13 if anyone knows what to do can they please help

Elza [17]

Answer:

x = 7

Step-by-step explanation:

First, you look at the equation. Identify the locations of variable terms (both sides of the equal sign) and the constant terms (both sides of the equal sign).

If there are any parentheses, it is a good idea to use the distributive property to eliminate them. Here, there are none.

I like to start by subtracting the variable term with the smallest coefficient. Here, that is 3x, so we add -3x to both sides of the equation.

3x -3x +1 = 5x -3x -13

1 = 2x -13 . . . . . . . . . . . . combine like terms

Now, we have the only variable term on one side of the equal sign. We want it by itself, so we need to make the -13 go away. We do that by adding its opposite to both sides of the equation:

1 +13 = 2x -13 +13

14 = 2x . . . . . . . . . . . . combine like terms

Finally, we want the coefficient of 2 in the x-term to disappear. We make that happen by multiplying both sides of the equation by 1/2, the reciprocal of that coefficient.

(1/2)(14) = (1/2)(2x)

7 = x . . . . the solution

It is generally a good idea to check your work by seeing if your solution value satisfies the equation:

3(7) +1 = 5(7) -13 . . . . put 7 where x is in the original equation

21 +1 = 35 -13

22 = 22 . . . . . . x = 7 is the solution

_____

Additional comment

By subtracting 3x from 5x, the result is 2x with a positive coefficient. We could solve the equation just as easily by subtracting 5x from 3x. That result would be ...

-2x +1 = -13

Subtracting 1 would give

-2x = -14

and you would multiply by -1/2 to get x=7. I personally like to avoid having this many minus signs show up in the problem. That is why I choose to subtract the x-term with the smallest coefficient.

5 0

3 years ago

Write an equation in slope-intercept form for the line that passes through the point ( -1 , -2 ) and is perpendicular to the l

mamaluj [8]

The equation in slope-intercept form for the line that passes through the point ( -1 , -2 ) and is perpendicular to the line − 4 x − 3 y = − 5 is $y = \frac{3}{4}x - \frac{5}{4}$

Solution:

The slope intercept form is given as:

y = mx + c ----- eqn 1

Where "m" is the slope of line and "c" is the y - intercept

Given that the line that passes through the point ( -1 , -2 ) and is perpendicular to the line − 4 x − 3 y = − 5

Given line is perpendicular to − 4 x − 3 y = − 5

− 4 x − 3 y = − 5

-3y = 4x - 5

3y = -4x + 5

$y = \frac{-4x}{3} + \frac{5}{3}$

On comparing the above equation with eqn 1, we get,

$m = \frac{-4}{3}$

We know that product of slope of a line and slope of line perpendicular to it is -1

$\frac{-4}{3} \times \text{ slope of line perpendicular to it}= -1\\\\\text{ slope of line perpendicular to it} = \frac{3}{4}$

Given point is (-1, -2)

Now we have to find the equation of line passing through (-1, -2) with slope $m = \frac{3}{4}$

Substitute (x, y) = (-1, -2) and m = 3/4 in eqn 1

$-2 = \frac{3}{4}(-1) + c\\\\-2 = \frac{-3}{4} + c\\\\c = - 2 + \frac{3}{4}\\\\c = \frac{-5}{4}$

$\text{ substitute } c = \frac{-5}{4} \text{ and } m = \frac{3}{4} \text{ in eqn 1}$

$y = \frac{3}{4} \times x + \frac{-5}{4}\\\\y = \frac{3}{4}x - \frac{5}{4}$

Thus the required equation of line is found

8 0

2 years ago

Please help ASAP it’s due in 4 minutes

maxonik [38]

Answer:

a) well we know the hypotenuse and we know that all sides are 90 degrees, and that its an even square, so if we split it into a triangle , we know that the other 2 angles are 45 degrees total, with this we can calculate the other 2 sides, which round to 10 inches.

b) if we know the sides of the first side, knowing the fact that its a square we know that all sides are even, therefore, all sides are 10 inches, the formula the finding the perimeter is basic:

P=L(2) + W(2)

L being length, W being width and P being perimeter

so we add up all 4 sides, here is the equation:

10 + 10 + 10 + 10 = 10 x 4 = 40

With this, we know that the perimeter is 40 inches total

c) knowing how long the sides are, we can figure out the area through another basic formula:

A=L X W

With A meaning Area

since its a square, we know all the sides are even, so the width and length are both 10...

10 X 10 = 100

Step-by-step explanation:

I Hope I Helped!

3 0

3 years ago

David wants to purchase a new fish tank. His current tank is 36 in. long, 12 in. wide, and 18 in. high. His new tank

Serhud [2]

Answer:

It should be 14400 square inches. Sorry if i'm wrong

3 0

3 years ago

How far is 10% of a 2000 kilometer trip

aleksandrvk [35]

Answer:
10 2000
1x200=
200

5 0

3 years ago