MATHEMATICS MIDDLE SCHOOL

A telephone pole has a wire attached to its top that is anchored to the ground. The distance from the bottom of the pole to the anchor point is 63feet less than the height of the pole. If the wire is to be 9

feet longer than the height of the pole, what is the height of the pole?

Answers

Answer 1
Answer:

Answer:

Height of pole =108 feet

Step-by-step explanation:

Let height of the pole be= AB= x feet

Distance from bottom of the pole to anchor point =BC= x-63 feet

Length of wire =AC= x+9 feet

Applying Pythagorean theorem.

In the given \triangle ABC

AC^2=AB^+BC^2

Plugging in values of each.

(x+9)^2=x^2+(x-63)^2

Expanding the binomials using identities.

x^2+18x+81=x^2+x^2-126x-3969\n

Combining like terms.

x^2+18x+81=2x^2-126x+3969

Subtracting x^2 from both sides.

x^2-x^2+18x+81=2x^2-x^2-126x+3969

18x+81=x^2-126x+3969

Subtracting 18x+81 from both sides.

(18x+81)-18x-81=x^2-126x+3969-18x-81

0=x^2-144x+3888

We get the quadratic equation to solve.

x^2-144x+3888=0

Solving quadratic using formula:

x=(-b\pm√(b^2-4ac))/(2a)

Plugging in values.

x=(-(-144)\pm√((-144)^2-4(1)(3888)))/(2(1))

x=(144\pm√(20736-15552))/(2)

x=(144\pm√(5184))/(2)

x=(144\pm72)/(2)

x=(144\pm 72)/(2)

x=(144+72)/(2) and x=(144-72)/(2)

x=(216)/(2) and x=(72)/(2)

x=108 and x=36

Since distance from pole to anchor point is 63 feet less than the height of pole, thus the height of the pole has to be =108 feet

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What value or values of x satisfy 2x + 5.31 = 4.2?ESBE
x can only equal -3.2.
x can only equal 7.4.
O x can equal -3.2 or -7.4.
O x can equal -3.2 or 7.4.

Answers

Answer:  x can equal -3.2 or -7.4.

Step-by-step explanation:

The correct expression is:

2|x+5.3|=4.2

So, we have an absolute value equation, where it can be positive or negative:

  • Positive

2 (x+5.3)=4.2

2x+10.6 =4.2

2x=4.2-10.6

2x = -6.4

x= -6.4/2

x = -3.2

  • Negative

2[-(x+5.3)]=4.2

-2x-10.6 =4.2

-2x= 4.2+10.6

-2x= 14.8

x= 14.8/-2

x= -7.4

x can equal -3.2 or -7.4.

Feel free to ask for more if needed or if you did not understand something.  

Answer:

(C)

Step-by-step explanation:

x can equal –3.2 or –7.4.

It Was Correct On Edge

A real friend is one who walks in when the rest of the world walks out

HAVE A GREAT DAY :)

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Answers


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B. 5
C. 10
D. 20

Answers

The answer is C. 10 because you only need 2 unit cubes to make a rectangular prism

Is 45/5 a whole number or a mixed number?

Answers

45 ÷ 5 = 9. So 45/5 is a whole number.
45/5 is a whole number because it can be simplified down to 9/1 which will end up be just 9.

Kassie is building a bench that is 4 1/3 feet long, 2 1/2 feet high and 2 1/2 feet wide. what is the volume of the bench?

Answers

since volume = l×w×h
so =4 1/3×2 1/2×2 /2
then first change them into improper fraction = 13/3×5/2×5/2
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= 325÷12
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hope i helped
Volume = l*b*h

Volume = 4  1/3  *  2  1/2  *  2    1/2

               =  (13/3) * (5/2) * (5/2)

               = 325 / 12    or 27    1/12

Volume = 325/12 feet³    or    27    1/12 feet³

Evaluate 5x - 1 when x = 8.

Answers

Answer:

39

Step-by-step explanation:

5x - 1 when x = 8

plug the variable in

5(8) - 1

40 -1

39

Answer:

39

Step-by-step explanation:

5(8) is 40, minus one is 39.

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