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4 years ago

13

What is the height of the trapezoid if the Area = 77 ft²? The h we don't know but the base is 14 and the line on top is 8. pleas

e help im very lost

1 answer:

velikii [3]4 years ago

5 0

Answer:

h = 7.333....

Step-by-step explanation:

Formula is A = 1/2h(b1+b2)

Area 77 determine the height

77=1/2h(14+8)

77 = 1/2h(22)h

77/10.5 = 10.5h/1.5

solve for h = 7.333....

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If a and b are two angles in standard position in Quadrant I, find cos(a+b) for the given function values. sin a=15/17and cos b=

tensa zangetsu [6.8K]

The value of $cos(a+b)$ for the angles $a$ and $b$ in standard position in the first quadrant is $-\frac{36}{85}$

We need to find the value of $cos(a+b)$ . To proceed, we need to use the compound angle formula

<h3>Cosine of a sum of two angles</h3>

The cosine of the sum of two angles $a$ and $b$ is given below

$cos(a+b)=cos(a)cos(b)-sin(a)sin(b)$

We are given

$sin(a)=\dfrac{15}{17}\\\\cos(b)=\dfrac{3}{5}$

We need to find $sin(b)$ and $cos(a)$ , using the identity

$sin^2(\theta)+cos^2(\theta)=1$

<h3>Find sin(b)</h3>

To find $sin(b)$ , note that

$sin^2(b)+cos^2(b)=1\\\\\implies sin(b)=\sqrt{1-cos^2(b)}$

substituting $\frac{3}{5}$ for $cos(b)$ in the identity, we get

$sin(b)=\sqrt{1-cos^2(b)}\\\\=\sqrt{1-\left(\dfrac{3}{5}\right)^2}=\dfrac{4}{5}$

<h3>Find cos(a)</h3>

To find $cos(a)$ , note that

$sin^2(a)+cos^2(a)=1\\\\\implies cos(a)=\sqrt{1-sin^2(a)}$

substituting $\frac{15}{17}$ for $sin(a)$ in the identity, we get

$cos(a)=\sqrt{1-sin^2(a)}\\\\=\sqrt{1-\left(\dfrac{15}{17}\right)^2}=\dfrac{8}{17}$

<h3>Find the value of cos(a+b)</h3>

We can now make use of the formula

$cos(a+b)=cos(a)cos(b)-sin(a)sin(b)$

to find $cos(a+b)$ .

$cos(a+b)=cos(a)cos(b)-sin(a)sin(b)\\\\=\dfrac{8}{17}\cdot\dfrac{3}{5}-\dfrac{15}{17}\cdot\dfrac{4}{5}=-\dfrac{36}{85}$

Learn more about sine and cosine of compound angles here brainly.com/question/24305408

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2 years ago

Find each percent of $45.00 and complete the statements.

dexar [7]

10% - $4.50
20% - $9
5% - $2.25

4 0

3 years ago

Read 2 more answers

ankoles [38]

Answer:

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5 0

3 years ago

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A 450-gallon tank full of water is draining at a rate of 20 gallons per minute.

Stels [109]

Answer:

The answer is below

Step-by-step explanation:

A function show the relationship between an independent variable and a dependent variable. The independent variable (input) does not depend on other variables while the dependent variable (output) depend on other variables.

In this question, amount of water in tank is dependent variable and the time taken is the independent variable. Let y represent amount of water in tank and x represent the time it has been draining. Therefore:

a) This can be represented by the equation:

y = 450 - 20x

At 7 minutes (x = 7)

y = 450 - 20(7)

y = 310 gallons

b) For 200 gallons (y = 200), the time taken is:

200 = 450 - 20x

200 - 450 = -20x

-20x = -250

x = -250/-20

x = 12.5 minutes

c) y = 450 - 20x

d) The graph was plotted using geogebra onling graphing calculator.

e) When the tank is empty, y = 0, hence

0 = 450 - 20x

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3 years ago

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Rudik [331]

Answer:

t = 204

Step-by-step explanation:

Let t = initial number of trees

"remove 5 trees at the start of the season" means

(t - 5) remain

"each remaining tree made 210 oranges for a total of 41,790 oranges" means

( t - 5) * 210 = 41790

Now, you can solve for t:

(t-5)(210) = 41790 [just re-writing]

210t - 1050 = 41790 [distribute]

210t = 42840 [add 1050 to each side]

t = 204 [divide each side by 210]

There were initially 204 trees. After 5 were removed, the remaining 199 produced 210 oranges each for a total of 199*210 = 41790 oranges.

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3 years ago