It looks like the first and the third are diagrams of similar triangles, and the third needs another right angle marker at E to be persuasive. So I'll go with
First diagram
We're given a congruent angle pair and we have another from vertical angles, so AA, similar triangles.
<h3>
Answer: Approximately 7.7 square inches</h3>
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Explanation:
See the diagram below. We're looking for the area of the shaded region in blue.
This is known as an inscribed circle since the circle is inside the square, touching each side at one point. This circle is as large as possible without spilling outside the square. Think of a balloon that has been inflated as much as possible to fill the room (it touches every wall at a tangent point).
The square has area s^2 = 6^2 = 6*6 = 36 square inches.
The circle has area pi*r^2 = pi*3^2 = 9pi square inches exactly. Note how I cut the diameter (6) in half to get the radius (3).
The blue shaded area is the difference of the square and circle areas, so we have 36 - 9pi as the exact area of the shaded region.
Using your calculator, you should find that 36-9pi = 7.72566611769187 approximately. I'm using my calculator's stored version of pi as opposed to something like pi = 3.14; but you may need to ask your teacher for clarification about what version of pi to use.
When rounding to the nearest tenth, we then get roughly 7.7 square inches as our final answer.
<h3>Answer: Malcom can run the furthest.</h3>
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Explanation:
Race 1
Let's convert Malcom's distance to inches so we can compare his distance to his sister's.
1 yard = 3 feet
10 yards = 30 feet (multiply both sides by 10)
1 foot = 12 inches
30 feet = 360 inches (multiply both sides by 30)
In Malcom's first race, he ran 360 inches. He has run the furthest compared to his sister who ran 300 inches.
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Race 2
Convert Malcom's distance from feet to inches.
1 foot = 12 inches
18 feet = 216 inches (multiply both sides by 18)
Malcom runs 216 inches compared to his sister's distance of 180 inches. Malcom is the winner again.
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Race 3
120 inches = 120/12 = 10 feet
Divide by 12 to convert from inches to feet, or you could have these steps
12 inches = 1 ft
120 inches = 10 feet
after multiplying both sides by 10.
Malcom runs 10 feet compared to 5 feet which his sister runs.
In each race, Malcom has ran the furthest.
<u>Given</u>:
Time,
t = 20 years
Rate,
r = 4.4%
Price
= $8,375
Now,
The yield will be:
=
= (%)
Time will be:
=
=
As we know the formula,
⇒
By substituting the values, we get
The face value will be:
($)
Learn more about face value here:
brainly.com/question/14862802
Is 20 and answer because I did this on a calculator and this is the only one to me that would make since