How far apart is 27 and -54

The face of the triangular concrete panel shown has an area of 22 square meters, and its base is 3 meters longer than twice its

Elodia [21]

Answer:

The length of the base is 11 meters.

Step-by-step explanation:

The diagram of the triangle is not shown; However, the given details are enough to solve this question.

Given

<em>Shape: Triangle</em>

<em>Represent the height with h and the base with b</em>

$b = 3 + 2h$

$Area = 22$

Required

Find the length of the base

The area of a triangle is calculated as thus;

$Area = \frac{1}{2} * b * h$

Substitute 22 for Area and 3 + 2h for b

The formula becomes

$22 = \frac{1}{2} * (3 + 2h) * h$

Multiply both sides by 2

$2 * 22 = 2 * \frac{1}{2} * (3 + 2h) * h$

$44 = (3 + 2h) * h$

Open the bracket

$44 = 3 * h + 2h * h$

$44 = 3h + 2h^2$

Subtract 44 from both sides

$44 - 44 = 3h + 2h^2 - 44$

$0 = 3h + 2h^2 - 44$

Rearrange

$0 = 2h^2 +3h - 44$

$2h^2 +3h - 44 = 0$

At this point, we have a quadratic equation; which is solved as follows:

$2h^2 +3h - 44 = 0$

$2h^2 + 11h - 8h - 44 = 0$

$h(2h + 11) - 4(2h + 11) = 0$

$(h - 4)(2h + 11) = 0$

Split the above

$(h - 4) = 0\ or\ (2h + 11) = 0$

$h - 4 = 0\ or\ 2h + 11 = 0$

Solve the above linear equations separately

$h - 4 = 0$

Add 4 to both sides

$h - 4 + 4 = 0 + 4$

$h = 0 + 4$

$h = 4$ ---- <em>First value of h</em>

$2h + 11 = 0$

Subtract 11 from both sides

$2h + 11 - 11 = 0 - 11$

$2h = 0 - 11$

$2h = -11$

Divide both sides by 2

$\frac{2h}{2} = -\frac{11}{2}$

$h = -\frac{11}{2}$ <em> ------ Second value of h</em>

Since height can be negative, we'll discard $h = -\frac{11}{2}$

Hence, the usable value of height is $h = 4$

Recall that $b = 3 + 2h$

Substitute 4 for h

$b = 3 + 2(4)$

$b = 3 + 8$

$b = 11$

Hence, the length of the base is 11 meters

3 0

3 years ago

Find the indicated values

alexandr1967 [171]

☃︎☃︎☃︎☃︎ forget work look at these cute ash snowmen hub i boo boo okay for real the the answer is at his a fund and t that dis

6 0

3 years ago

What is the value of x in the figure?

finlep [7]

<h3>Answer: x = 29</h3>

======================================================

Work Shown:

x+61 = 90

x+61-61 = 90-61

x = 29

------------

Explanation:

The first step is valid because the two angles x and 61 are complementary angles. They form a right angle or 90 degree angle.
In the second step, I subtracted 61 from both sides to undo the "+61".

3 0

3 years ago

Read 2 more answers

WORTH 30 PTS

kifflom [539]

Answer:

Done

Step-by-step explanation:

8 0

3 years ago

Ryan planted flowers in a rectangular garden. The width of the garden is left parenthesis x minus 5 right parenthesis(x−5) feet

Nookie1986 [14]

｡☆✼★ ━━━━━━━━━━━━━━ ☾ ━━━━━━━━━━━━━━ ★✼☆｡

- The equation :

Area = length x width

- Substitute the values in :

Area = (x - 5)(x - 5 + 22)

(Note : the 'x' is for the algebraic expression x in the example above)

- Now you have to simplify the second parenthesis:

Area = (x - 5)(x + 17)

- Now expand :

Area = x^2 + 17x - 5x - 85

- Simplify by collecting like terms :

Area = x^2 + 12x - 85

(Note : x^2 means x squared)

Now you have your answer as:

x^2 + 12x - 85 feet^2

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- Ally ✧

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3 0

4 years ago