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olga55 [171]
3 years ago
15

Josue leans a 26-foot ladder against a wall so that it forms an

Mathematics
1 answer:
postnew [5]3 years ago
6 0

Answer:

25.61 feet

Step-by-step explanation:

First, we can draw a picture (see attached picture). With the wall representing the rightmost line, and the ground representing the bottom line, the ladder (the hypotenuse) forms a 80 degree angle with the ground and the wall and ground form a 90 degree angle.

Without solving for other angles, we know one angle and the hypotenuse, and want to find the opposite side of the angle.

One formula that encompasses this is sin(x) = opposite/hypotenuse, with x being 80 degrees and the hypotenuse being 26 feet. We thus have

sin(80°) = opposite / 26 feet

multiply both sides by 26 feet

sin(80°) * 26 feet = opposite

= 25.61 feet as the height of the wall the ladder reaches

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the fire hydrant sits 72 feet from the base of a 125-foot buiding. Find the ANGLE OF ELEVATION from the fire hydrant to the top
PSYCHO15rus [73]

Answer:

  60°

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationship between angles and sides in a right triangle. Here, we're given the side Adjacent and the side Opposite the angle of interest. This makes it appropriate to choose the relation ...

  Tan = Opposite/Adjacent

For our angle of elevation α, this means ...

  tan(α) = 125/72

  α = arctan(125/72) = 60.058°

  α ≈ 60°

The angle of elevation is about 60°.

5 0
3 years ago
I really need help<br> Solve for x
MakcuM [25]

\huge\underline{\overline{\mid{\bold{\red{ANSWER}}\mid}}}

1. Both are corresponding angles, hence they both are equal, so,

44x + 2 = 45x \\  =  > 2 = 45x - 44x \\  =  > 2 = x \\  =  > x = 2

Ans. C) 2

2. They both are in interior corressponding, hence their sum is equal to 180°, so,

10x + 6 + 104 = 180 \\  =  > 10x + 110 = 180 \\  =  > 10x = 180 - 110 \\  =  > 10x = 70 \\  =  > x =  \frac{70}{10}  \\  =  > x = 7

Ans. D) 7

3. They both are in interior corressponding, hence their sum is equal to 180°, so,

x + 75 + x + 125 = 180 \\  =  > 2x + 200 = 180 \\  =  > 2x = 180 - 200 \\  =  > 2 x =  - 20 \\  =  > x =  \frac{ - 20}{2}  \\  =  >  x =  - 10

Ans. A) -10

4. Both are corresponding angles, hence they both are equal, so,

12x + 3 = 11x + 9 \\  =  > 12x - 11x = 9 - 3 \\  =  > x = 6

Ans. A) 6

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6 0
3 years ago
Systems of Linear Equations What are the different ways to solve a system of linear equations? When do you get an answer to a sy
Mrac [35]

Answer:

Different ways to solve a system of linear equations:

  • isolate one variable in one equation and replace it in the other equation
  • multiply/divide one equation by a constant and then add/subtract it to the other one, so that only one variable remains
  • graph the equation and look at the intersection point

If you graph the system:

  • there is only one solution if the lines intersects at only one point
  • there is no solution if the lines don't intersect each other (they are parallel)
  • there are infinitely many solutions if the lines overlap each other (they are the same equation multiplied by some constant)

Step-by-step explanation:

1st system

y = -x – 7  

y = 4/3 x – 7  

solution: x= 0, y = 7

2nd system

y = -3x – 5  

y = x + 3  

solution: x = -2, y = 1

3rd system

y = -2x + 5  

y = 1/3 x – 2

solution:  x = 3, y = -1

4th system

3x + 2y = 2  

x + 2y = -2  

solution: x = 2, y = -2

5th system

x + 3y = -9  

2x – y = -4

solution:  x = -3, y = -2

6th system

x – 2y = 2

-x + 4y = -8

solution:  x = -4, y = -3

7th system

5x + y = -2  

x + y = 2

solution: x = -1, y = -3

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3 years ago
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Misha Larkins [42]
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3 years ago
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yan [13]

Answer:

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