What is the area of the trapezoid?

One supplementary angle is 15 degrees less than twice the other. Find the measure of the two supplementary angles.

o-na [289]

Hey there!

To find our answer, we need to set up a system of equations. Remember, supplementary angles equal 180 degrees when combined. We will call one of our angles A and the other one B. Let's set it up below! :)

A=2B-15 (one angle is 15 degrees less than twice the other)

A+B=180

We need to find one of our variables. To do this, we only put one variable in the equation. But how, there are two variables in both equations! Well, as you can see, we see the A is equal to 2B-15, so we can take 2B-15 and put it into the second equation in place of A because it is equal to A, and then we will only have Bs and we can solve for it. This method is known as solving systems of equations with substitution.

Let's solve with substitution!

2B-15+B=180

3B-15=180 We combine our Bs.

3B=195 We add 15 to both sides.

B= 65 We divide both sides by three.

Now, we need to find what A is, but this will be really easy to do! If you remember, our angles are supplementary, so when you combine them, we will get 180, as you can see in our second equation in our first system of equations. So, we simply subtract 65 from 180.

180-65=115

Our two angles are 65° and 115°.

We can also check this with the original problem.

If you double 65, we have 130. Then, if we subtract 15, we have 115. Systems of equations are a pretty awesome way to figure this out!

I hope this helps! Have a great day!

5 0

3 years ago

Drag each tile to the correct box.

Natasha_Volkova [10]

Answer:

1) Function h

interval [3, 5]

rate of change 6

2) Function f

interval [3, 6]

rate of change 8.33

3) Function g

interval [2, 3]

rate of change 9.6

Step-by-step explanation:

we know that

To find the average rate of change, we divide the change in the output value by the change in the input value

the average rate of change is equal to

$\frac{f(b)-f(a)}{b-a}$

step 1

Find the average rate of change of function h(x) over interval [3,5]

Looking at the third picture (table)

$f(a)=h(3)=4$

$f(b)=h(5)=16$

$a=3$

$b=5$

Substitute

$\frac{16-4}{5-3}=6$

step 2

Find the average rate of change of function f(x) over interval [3,6]

Looking at the graph

$f(a)=f(3)=10$

$f(b)=f(6)=35$

$a=3$

$b=6$

Substitute

$\frac{35-10}{6-3}=8.33$

step 3

Find the average rate of change of function g(x) over interval [2,3]

we have

$g(x)=\frac{1}{5}(4)^x$

$f(a)=g(2)=\frac{1}{5}(4)^2=\frac{16}{5}$

$f(b)=g(3)=\frac{1}{5}(4)^3=\frac{64}{5}$

$a=2$

$b=3$

Substitute

$\frac{\frac{64}{5}-\frac{16}{5}}{3-2}=9.6$

therefore

In order from least to greatest according to their average rates of change over those intervals

1) Function h

interval [3, 5]

rate of change 6

2) Function f

interval [3, 6]

rate of change 8.33

3) Function g

interval [2, 3]

rate of change 9.6

7 0

3 years ago

Abbey wants to use her savings of $1,325 to learn yoga. The total charges to learn yoga include a fixed registration fee of $35

Citrus2011 [14]

Is (-35)+50x one of the options

8 0

3 years ago

Classify the triangle with 9, 15, 19 as an acute right obtuse or not a triangle

Novosadov [1.4K]

Answer:

Hence the correct option is the last one . The triangle is an obtuse angled triangle.

Step-by-step explanation:

i) the sum of any two sides added together is greater than the third side hence this is a triangle.

ii) it is not a right angled triangle as $\sqrt{9^{2} + 15^{2} } \neq 19$ and $\sqrt{9^{2} + 15^{2} } < 19$

iii) the triangle is not acute from ii) above

iv) the triangle is an obtuse triangle from ii) above.

8 0

3 years ago

Andrew has a four-year college loan for $20,000. The lender charges a simple interest rate of 5 percent. How much interest will

Olegator [25]

Given that loan amount P=20000

Interest rate r=5% = 0.05

Time of loan t=4 years

Now to find the interest amount we just plug those values into formula

simple interest = P × r × t

simple interest = 20000* 0.05* 4

simple interest = 1000 * 4

simple interest = 4000

Hence final answer is choice b. $4000.

7 0

3 years ago

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