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erastova [34]
3 years ago
7

In baseball, the length of the path between each pair of consecutive bases is 90 feet. The paths form right angles. How far does

the ball need to travel if it is thrown from home plate directly to second base? A. 90 feet B. 127.3 feet C. 135.7 feet D. 180 feet
Mathematics
1 answer:
Tresset [83]3 years ago
6 0
This question boils down to this:
"What is the diagonal of a square with a side length of 90 ft?"

The key to this question is the properties of squares.
All of the angles in a square are right, (90°) but that diagonal is going to bisect two of those into 45° angles.
Now we have two triangles, each with angle measures of 45°, 45°. and 90°.
(an isoceles right triangle)

This 45-45-90 tirnalge is one of two special triangles (the other being the 30-60-90) and here is its special property: the sides opposite these angles can be put as x, x, and x√2 respectively. Why? Well, we know that our triangle is isoceles (the congruent base angles ⇔ congruent sides) and so we call those x...by the Pythagorean theorem...a² + b² = c²...2x² = c²...x√2 = c!

In our case here, that diagonal, being the hypotenuse of our triangle, is going to be 90√2 feet, or approximately 127.3 feet.
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Geometry ∠1 and ∠2 are vertical angles. If m∠1 = 17x + 1 and m∠2 = 20x – 14, find m∠2.
stiv31 [10]

Answer:

m∠2= 86

Step-by-step explanation:

since they are vertical angles, that means they are both equal to eachother.

so lets set them equal!

17x+1=20x-14

17x+15=20x

15=3x

x=5

now input x into m∠2

m∠2 = 20(5) – 14 = 86

7 0
3 years ago
Jill is buying new appliances. The cost of the dishwasher is $459 and the cost of the microwave is $289. What is the total price
romanna [79]

Answer:

$800.36

Step-by-step explanation:

429+289=748

7% of 748= 52.36

748 + 52.36=800.36

4 0
3 years ago
Select all the expressions that are equivalent to (2)^n+³
eimsori [14]

Answer:

The expressions which equivalent to  (2)^{n+3} are:

4(2)^{n+1}  ⇒ B

8(2)^{n} ⇒ C

Step-by-step explanation:

Let us revise some rules of exponent

  • a^{m} × a^{m}  = a^{m+n}
  • (a^{m})^{n} = a^{m*n}

Now let us find the equivalent expressions of  (2)^{n+3}

A.

∵ 4 = 2 × 2

∴ 4 =  2^{2}

∴  (4)^{n+2} =  (2^{2})^{n+2}

- By using the second rule above multiply 2 and (n + 2)

∵ 2(n + 2) = 2n + 4

∴  (4)^{n+2} =  (2)^{2n+4}  

B.

∵ 4 = 2 × 2

∴ 4 =  2²

∴  4(2)^{n+1} = 2² ×  (2)^{n+1}

- By using the first rule rule add the exponents of 2

∵ 2 + n + 1 = n + 3

∴   4(2)^{n+1} =  (2)^{n+3}

C.

∵ 8 = 2 × 2 × 2

∴ 8 =  2³

∴  8(2)^{n} = 2³ ×  (2)^{n}

- By using the first rule rule add the exponents of 2

∵ 3 + n = n + 3

∴  8(2)^{n} =  (2)^{n+3}

D.

∵ 16 = 2 × 2 × 2 × 2

∴ 16 = 2^{4}

∴  16(2)^{n} = 2^{4}  ×  (2)^{n}

- By using the first rule rule add the exponents of 2

∵ 4 + n = n + 4

∴  16(2)^{n} =  (2)^{n+4}

E.

(2)^{2n+3} is in its simplest form

The expressions which equivalent to  (2)^{n+3} are:

4(2)^{n+1}  ⇒ B

8(2)^{n} ⇒ C

3 0
3 years ago
Question Number 22 You work for a company that manufactures large tarps used for groundcover. An order was placed for a rectangu
Colt1911 [192]

Answer: the area of the finished tarp is 131872 square inches

Step-by-step explanation:

Search strip of tarp is rectangular. The formula for determining the area of a rectangle is expressed as

Area = length × width

An order was placed for a rectangular tarp that will be made up of 8 strips of fabric. Each strip is 26 inches wide and 634 feet long. The area of each strip of tarp is

Area = 26 × 634 = 16484 square inches

Therefore, the area of the finished tarp would be

8 × 16484 = 131872 square inches

4 0
3 years ago
18(−8c+16)−13(6+3c) =
slega [8]

your final answer should be.... -3 • (61c - 70)


8 0
3 years ago
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