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emmainna [20.7K]
2 years ago
14

A flagpole casts a shadow that is 12 ft long. A 6-ft tall man casts a shadow

Mathematics
1 answer:
Vikentia [17]2 years ago
4 0

Answer:

9ft

Step-by-step explanation:

Since the triangles are similar, the corresponding sides are proportional.

Let the height of the flag pole be x feet.

\frac{x}{6}  =  \frac{12}{8}

We multiply both sides by 6 to get:

x =  \frac{12}{8}  \times 6

We reduce the fraction to get:

x =  \frac{3}{2}  \times 6

We now simplify

x = 3 \times 3

x = 9ft

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If a rectangle has an area of x^2+x-20 and a width of x-4, what is the length?
Mrac [35]

Answer:

This (x - 5) represents the length of the rectangle.

Step-by-step explanation:

The formula for the area of a rectangle of length L and width W is A = L * W.

Here, the width is x - 4 and the area is x^2 + x - 20.  Dividing the width (x - 4) into the area results in an expression for the length:

x - 4  /   x^2 + x - 20

Let's use synthetic division here.  It's a little faster than long division.

If the divisor in long division is x - 4, we know immediately that the divisor in synthetic division is 4:

4   /   1    1    -20

              4     20

    --------------------

         1     5     0

This synthetic division results in a remainder of 0.  This tells us that 4 (or the corresponding (x - 4) is indeed a root of the polynomial x^2 + x - 20, and so *(x - 4) is a factor.  From the coefficients 1 and 5 we can construct the other factor:  (x - 5).  This (x - 5) represents the length of the rectangle.

4 0
2 years ago
(x + 7)(x + 10) = what is the answer
ch4aika [34]

We can use FOIL to solve.

(x + 7)(x + 10)

(x * x) + (x * 7) + (7 * x) + (7 * 10)

x² + 7x + 7x + 70

x² + 14x + 70

Best of Luck!

8 0
3 years ago
New math question!<br> (screenshot attached)
Lyrx [107]

Answer:

D

Step-by-step explanation:

hi again

because the cornets show that -4 and -2 are also by -4 and -6 so that would =x+1 and x-5

hope this helps have a good day

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3 0
3 years ago
Read 2 more answers
The length of a rectangular park is four timesfour times its width. The park is surrounded by a 33​-foot-wide path. Let x denote
tiny-mole [99]

Answer:

A(x) = 4x^2 + 330x + 4356

Step-by-step explanation:

width of park: x

length of park: 4x

width + path width = x + 66

length + path width = 4x + 66

area = (x + 66)(4x + 66)

area = 4x^2 + 66x + 264x + 4356

area = 4x^2 + 330x + 4356

A(x) = 4x^2 + 330x + 4356

7 0
2 years ago
There are 16 reams of paper in a case. How many total teams of paper are in 11 cases ?
pentagon [3]

Answer:

176 reams in 11 cases

Step-by-step explanation:

1 = 16

1 x 11 = 11

16 x 11 = 176

3 0
3 years ago
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