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romanna [79]
3 years ago
9

A painter leans a 20-ft ladder against a building. The base of the ladder is 12 ft from the building. To the nearest foot, how h

igh on the building does the ladder reach?

Mathematics
2 answers:
Mazyrski [523]3 years ago
7 0
Use Pythagorean Theorem.
a^2 + b^2 = c^2
Substitute the numbers.
12^2 + b^2 = 20^2
144 + b^2 = 400
Subtract 144 from each side.
b^2 = 256
Take square root.
The answer is
b = 16
Mekhanik [1.2K]3 years ago
4 0
<h2>Answer:</h2>

The height of the building to which the ladder reaches is:

                            16 ft.

<h2>Step-by-step explanation:</h2>

We can model this problem with the help of a right angled triangle ΔABC such that the hypotenuse of the triangle is 20-ft and one of it's leg is: 12 ft.

Now we are asked to find the other leg of the triangle.

We will use the Pythagorean Theorem in order to find the other leg.

Pythagorean Theorem says that: If c is the hypotenuse of the right triangle and a and b are it's two legs then,

c^2=a^2+b^2

Hence, here we have:

c=20,\ and\ a=12

So,

20^2=12^2+b^2\\\\i.e.\\\\400=144+b^2\\\\i.e.\\\\b^2=400-144\\\\i.e.\\\\b^2=256\\\\i.e.\\\\b=\pm 16

Since, b can't be negative as it denotes a side of a triangle.

Hence, we get:

b=16

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Aleksandr-060686 [28]

Answer:

  \dfrac{k^2+5k}{4k^2}

Step-by-step explanation:

A suitable common denominator is 4k^2. (This eliminates the first and last choices.)

\dfrac{3k}{k^2}+\dfrac{k-7}{4k}=\dfrac{4(3k)}{4(k^2)}+\dfrac{k(k-7)}{k(4k)}\\\\=\dfrac{12k+k^2-7k}{4k^2}=\boxed{\dfrac{k^2+5k}{4k^2}}

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3 years ago
Bethany has 3.10$ in nickels and dimes. She has a total of 44 coins . What is the value of the nickels Bethany has
vlada-n [284]
Represent the unknows with n and d.

Then n+d = 44 (# of coins)

and 

$0.05n + $0.10d = $3.10   (value of coins)

Solving the first equation for n, we get n = 44-d.  Subst.  44-d for n in the 2nd equation:

0.05(44-d) + 0.10d = 3.10
Then 2.20 - 0.05d + 0.10d = 3.10, or
          2.20 + 0.05d             = 3.10, or    0.05d = 0.90.  Solving for d, 
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d = -------- = 18
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5 0
3 years ago
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Answer:

Step-by-step explanation:

4 0
2 years ago
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Aleks04 [339]
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7 0
3 years ago
The approximate height, h, in meters, traveled by golf balls hit with two different clubs over a horizontal distance of d meters
inna [77]

Answer:

a) 100 metres

b) 10 metres

Step-by-step explanation:

Given: the approximate height, h, in meters, travelled by golf balls hit with two different clubs over a horizontal distance of d meters is given by the functions: h=-0.002d^2+0.3d\,,\,h=-0.004d^2+0.5d

To find: distances when the ball is at the same height when either of the clubs  are used. Also, to find this height

Solution:

(a)

-0.002d^2+0.3d=-0.004d^2+0.5d\\d(-0.002d+0.3)=d(-0.004d+0.5)\\-0.002d+0.004d=0.5-0.3\\0.002d=0.2\\d=\frac{0.2}{0.002}=100\,\,metres

(b)

Put d = 100 in h=-0.002d^2+0.3d

h=-0.002(100)^2+0.3(100)\\=-20+30\\=10\,\,metres

4 0
3 years ago
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