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Serga [27]
3 years ago
11

A ladder leans against a building. The angle of elevation of the ladder is 70°. The top of the ladder is 25 ft from the ground.

Mathematics
1 answer:
exis [7]3 years ago
7 0
The distance from the base of the ladder to the way will be given by:
tan θ= opposite/adjacent
θ=70
adjacent=x
opposite=25 ft
thus
tan 70=25/x
thus
x=25/tan 70
hence:
x=9.1 ft

Answer: 9.1 ft


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F(x) = x^2 + 5x - 1 is shifted 3 units left the result is g(x). What is g(x)?
Sonja [21]

Answer:

A. g(x)=x^2+5x+2

Step-by-step explanation:

f(x) = x^2 + 5x - 1 Shift 3 units to the left. k=3

g(x)=x^2+5x-1+3=x^2+5x+2

g(x)=x^2+5x+2

Hope this helps!

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5 0
2 years ago
1. Use precise mathematical language to justify and explain each mathematical process.
iris [78.8K]

Mathematical processes are the steps used to determine the result of operations

  • The perimeter of the rectangle is 10x^2 - 14x + 28
  • The area of the rectangle is 5x^3 +17x^2  -31x + 45

The dimension of the rectangle is given as:

Length = 5x^2 - 8x + 9

Width = x + 5

<u>(1) The perimeter of the triangle</u>

This is the sum of the side lengths of the rectangle.

So, we have:

Perimeter = 2 \times (Length + Width)

This gives

Perimeter = 2 \times (5x^2 - 8x + 9 + x + 5)

Collect like terms

Perimeter = 2 \times (5x^2 - 7x + 14)

Open brackets

Perimeter = 10x^2 - 14x + 28

Hence, the perimeter of the rectangle is 10x^2 - 14x + 28

<u>(2) The area of the triangle</u>

This is the product of the dimensions of the rectangle.

So, we have:

Area = Length \times  Width

This gives

Area = (5x^2 - 8x + 9) \times  (x + 5)

Open brackets

Area = 5x^3 - 8x^2 + 9x +25x^2 - 40x + 45

Collect like terms

Area = 5x^3 - 8x^2 +25x^2+ 9x  - 40x + 45

Area = 5x^3 +17x^2  -31x + 45

Hence, the area of the rectangle is 5x^3 +17x^2  -31x + 45

Read more about areas and perimeters at:

brainly.com/question/15656646

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2 years ago
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5 0
3 years ago
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The sum of two numbers is 42, and one number is twice the other. Find the two numbers​
NikAS [45]

Answer:

28 and 14

Step-by-step explanation:

14 x 2 = 28

28 + 14 is 42.

3 0
3 years ago
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Sarah ran 2 miles and Jaime ran 15, 840 feet. How many miles did they run together? (The conversion factor is 5280 feet/mile.)
Korvikt [17]

Answer:

C. 5 miles

Step-by-step explanation:

Since we need to find how many miles they ran together, let us convert feet to miles. Sarah's length is already in miles so we'll leave it that way.

Jaime ran 15840 feet. We are given how many feet are there in one mile (5280), so we need to find how many miles are there in 15840 feet.

x = 15840 / 5280 = 3 miles.

So, Jaime ran 3 miles and Sarah ran 2 miles.

That means that together they ran 3 + 2 = 5 miles.

6 0
3 years ago
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