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2 years ago

What is the height of the trapezoid if the area was 26 units

Mathematics

1 answer:

miv72 [106K]2 years ago

8 0

Answer:

h = 4

Step-by-step explanation:

The area (A) of a trapezoid is calculated as

A = $\frac{1}{2}$ h( a + b) ← a and b are the parallel bases

here a = 5, b = 8 and A = 26, thus

$\frac{1}{2}$ h(5 + 8) = 26, that is

$\frac{1}{2}$ h × 13 = 26 ( divide both sides by 13 )

$\frac{1}{2}$ h = 2 ( multiply both sides by 2 to clear the fraction )

h = 4

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A 20 ft flag pole casts a shadow 32 ft long. What is the angle of elevation of the sun?

Nookie1986 [14]

Answer:

<em>The angle of elevation of the sun is 32°</em>

Step-by-step explanation:

<u>Right Triangles</u>

The flagpole and the ground form a right angle (90°). In triangles with right angles, the trigonometric ratios are satisfied.

Each acute angle has an adjacent leg and an opposite leg. The tangent ratio relates to both legs.

$\displaystyle \tan x=\frac{\text{opposite leg}}{\text{adjacent leg}}$

The opposite leg to angle x is 20 ft and the adjacent leg is 32 ft, thus:

$\displaystyle \tan x=\frac{20}{32}=0.625$

Calculate x by using the inverse tangent:

$x=\arctan 0.625$

$x=32^\circ$

The angle of elevation of the sun is 32°

7 0

3 years ago

Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Third-degree, with zeros of −3

RSB [31]

Answer:

$\Large \boxed{-\dfrac{5}{4}(x+3)(x+1)(x-2)}$

Step-by-step explanation:

Hello,

Based on the indication, we can write this polynomial as below, k being a real number that we will have to identify (degree = 3 and we have three zeroes -3, -1, and 2).

$\Large \boxed{k(x+3)(x+1)(x-2)}$

We know that the point (1,10) is on the graph of this function, so we can say.

$k(1+3)(1+1)(1-2)=10}\\\\4*2*(-1)*k=10\\\\-8k=10\\\\k=\dfrac{10}{-8}=-\dfrac{5}{4}$

Then the solution is:

$\large \boxed{-\dfrac{5}{4}(x+3)(x+1)(x-2)}$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

8 0

3 years ago

If ΔABC ≅ ΔEDF where the coordinates of A(0, 2), B(2, 4), and C(2, −1), what is the measure of DF?

allsm [11]

Answer:

C. 5

Step-by-step explanation:

Since Triangle ABC is congruent to EDF it mean that the sides are the same so the length of BC is congruent to the length of DF:

distance formula:

d = √(x2 - x1)^2 + (y2 - y1)^2

d = √(2 - 2)^2 + (-1 - 4)^2

d = √(0)^2 + (-5)^2

d = √0 + 25

d = √25

d = 5

4 0

3 years ago

Read 2 more answers

H Quarshie

Yuki888 [10]

Answer:

Step-by-step explanation:

f(6) = -3 * 6 + 10 = -18 + 10 = -8

g(f(6)) = g(-8)

g(-8) = $(-8)^{2} + 3 * (-8) - 12$ = 64 - 24 - 12 = 64 - 36 = 28

6 0

3 years ago

Divide.

krek1111 [17]

Answer:

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Step-by-step explaWnation:

7 0

2 years ago