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Talja [164]
2 years ago
15

Howard is standing 87 yards from the bottom of a water reservoir. He estimates that the angle of elevation to the top of the wat

er reservoir is about 60°. How far is Howard from the top of the water reservoir?
Mathematics
1 answer:
nekit [7.7K]2 years ago
4 0
He is 174 yards from the top.

Since we have a 60° angle and a right angle, this is a 30-60-90 triangle.  In these triangles, we can label the sides as t, t√3 and 2t, with t being the side opposite the 30° angle (the smallest side); t√3 being the side opposite the 60° angle (the middle side); and 2t being the hypotenuse (the longest side).

Our 87 yard side is across from the 30° angle, so it is t.

The side we are looking for is the hypotenuse, which would be 2t; 2(87) = 174.
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Andre hit 46 balls at practice. He hit no fewer than 20 less than double the number of hits Jason had. Which inequality represen
Nostrana [21]

Answer:

  2j -20 ≤ 46

Step-by-step explanation:

"20 less than double the number Jason [hit]" can be represented by 2j-20.

We are told that 46 is no fewer than this value, so it is greater than or equal to this value:

  46 ≥ 2j -20

  2j -20 ≤ 46 . . . . . swapping sides to match answer choices

7 0
2 years ago
Read 2 more answers
Liz is buying a home for $426,000. She is making a 22% down payment and financing the rest with a 20-year loan at 5.25% interest
olga55 [171]

Answer:

  • <em><u>$869,776</u></em>

Explanation:

<u>1. Mortgage table</u>

Find attached a sample of a mortgage table per 1,000 dollars borrowed.

You have to use the number in the intersection of the row for 5.25% interest and the column for 20 years.

The number is $6.74.

That means that, for every $1,000 borrowed for 20 years at 5.25% interest you will pay $6.74 every month.

<u>2. Amount borrowed</u>

You will make a 22% down payment:

        22\%\times \$ 426,000=\$ 93,720

Thus the amount borrowed is $426,000 - $93,720 = $332,280

<u>3. Monthly payment</u>

Multiply the monthly payment per 1,000 by the amount borrowed divided by 1,000:

      \$ 6.74\times 322,280/1,000=\$ 2,239.57

<u />

<u>4. Total monthly payments:</u>

Multiply the number of payments by the monthly payment.

Number of payments = 20 years × 12 payments /year = 240 payments.

        \$ 2,239.57\times 240=\$ 537,496.13

<u>5. Total payment for the home.</u>

The total payment for the home will be the down payment plus the amount paid to the bank:

  • $322,280 + $537,496 = $869,776

6 0
2 years ago
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Simplify: −3x(4x − 5xy + 8y)
777dan777 [17]

Answer:

-12x - 9xy

Step-by-step explanation:

-3x(4x - 5xy + 8y)

distribute

-12x + <u>15xy - 24xy</u>

combine like terms

-12x - 9xy

3 0
2 years ago
Now let the figure show a scale drawing of a park. The scale is 1 unit : 25 meters. What is the horizontal distance across the p
insens350 [35]

The question is missing the figure. So, the figure is attached below.

Answer:

C. 350 m

Step-by-step explanation:

Given:

Scale  is given as:

1 unit  : 25 meters

This means that 1 unit on the grid is equivalent to 25 meters in actual.

Now, from the figure, the horizontal distance across the park is 14 units.

1 unit = 25 meter

Now, we can find the actual distance using unitary method and thus multiplying 25 and 14 to get the actual distance across the park horizontally.

∴ 14 units = 25\times 14=350 meters.

Therefore, the horizontal distance across the park is 350 m in actual.

So, the correct option is option C.

7 0
2 years ago
Victor baked 30 chocolate chip cookies,18 peanut butter cookies, and 24 sugar cookies. He wants to split them up into equal and
mylen [45]

Answer:

He can make 6 groups

Step-by-step explanation:

To solve this problem first you need to find the GCF or greatest common factor. Now you can put 5 chocolate chip cookies in each group, 3 peanut butter, and 4 sugar cookies. These are all relatively prime so that would be your final answer.

7 0
2 years ago
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