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Bad White [126]
3 years ago
11

Find the measure of HG¯¯¯¯¯¯¯¯. A. 12 B. 16 C. 14 D. 7

Mathematics
1 answer:
Paraphin [41]3 years ago
3 0

HG^2 = FG * (FG + EF)

Fill in the values:

(x+3)^2 = x * (7+x)

Simplify the right side:

(x+3)^2 = 7x +x^2

Rewrite the left side using the FOIL method

x^2 + 6x + 9 = 7x +x^2

Subtract x^2 from both sides:

6x +9 = 7x

Subtract 6x from both sides:

x = 9

Now you have x solve for HG

HG = x +3 = 9+3 = 12

The answer is A.

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Let p and q be different prime numbers. How many positive factors will (p^2 * q^4)^3 have?
Naily [24]

Answer:

  91

Step-by-step explanation:

p^6×q^12 will have (6+1)(12+1) = 7×13 = 91 positive integer divisors.

7 0
3 years ago
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Find the area of the figure. Use 3.14 as π.
Karolina [17]

Answer: D. 94.25 in²

Step-by-step explanation:

To find the total area, we will break the shape up into two different parts.

[] The rounded part is 39.25 in². Let us assume the rounded part is exactly half of a circle.

      Area of a circle:

A = πr²

      Use 3.14 for pi:

A = (3.14)r²

      Find the radius:

d / 2 = r, 10 / 2 = 5 in

      Subsittue:

A = (3.14)(5)²

A = 78.5 in²

      Divide by 2 since it is only half:

78.5 in² / 2 = 39.25 in²

[] The triangle is 55 in².

      Area of a triangle:

A = b*h/2

A = 11 * 10 / 2

A = 110 / 2

A = 55 in²

[] Total area. We will add the two parts together.

55 in² + 39.25 in² = 94.25 in²

7 0
2 years ago
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Natasha Pratt works as an administrative assistant for 40 hours a week, making $12 per hour. Her employer must pay FICA tax in t
viktelen [127]
$62.35  because 40*12=480 480 divided by 7.65=62.35     or just 62

I hope this helps:)
8 0
3 years ago
A cuboid with dimensions 45 cm by 16 cm by 12 cm is cut to form smaller cubes of
LenKa [72]

Answer:

<u>135 cubes</u>

Step-by-step explanation:

Volume of cuboid :

  • 45 x 16 x 12
  • 720 x 12
  • 8,640 cm³

Volume of a small cube :

  • (4)³
  • 64 cm³

Number of cubes :

  • n = 8,640/64
  • n = <u>135 cubes</u>
4 0
2 years ago
Find the sum or difference. a. -121 2 + 41 2 b. -0.35 - (-0.25)
s344n2d4d5 [400]

Answer:

2

Step-by-step explanation:

The reason an infinite sum like 1 + 1/2 + 1/4 + · · · can have a definite value is that one is really looking at the sequence of numbers

1

1 + 1/2 = 3/2

1 + 1/2 + 1/4 = 7/4

1 + 1/2 + 1/4 + 1/8 = 15/8

etc.,

and this sequence of numbers (1, 3/2, 7/4, 15/8, . . . ) is converging to a limit. It is this limit which we call the "value" of the infinite sum.

How do we find this value?

If we assume it exists and just want to find what it is, let's call it S. Now

S = 1 + 1/2 + 1/4 + 1/8 + · · ·

so, if we multiply it by 1/2, we get

(1/2) S = 1/2 + 1/4 + 1/8 + 1/16 + · · ·

Now, if we subtract the second equation from the first, the 1/2, 1/4, 1/8, etc. all cancel, and we get S - (1/2)S = 1 which means S/2 = 1 and so S = 2.

This same technique can be used to find the sum of any "geometric series", that it, a series where each term is some number r times the previous term. If the first term is a, then the series is

S = a + a r + a r^2 + a r^3 + · · ·

so, multiplying both sides by r,

r S = a r + a r^2 + a r^3 + a r^4 + · · ·

and, subtracting the second equation from the first, you get S - r S = a which you can solve to get S = a/(1-r). Your example was the case a = 1, r = 1/2.

In using this technique, we have assumed that the infinite sum exists, then found the value. But we can also use it to tell whether the sum exists or not: if you look at the finite sum

S = a + a r + a r^2 + a r^3 + · · · + a r^n

then multiply by r to get

rS = a r + a r^2 + a r^3 + a r^4 + · · · + a r^(n+1)

and subtract the second from the first, the terms a r, a r^2, . . . , a r^n all cancel and you are left with S - r S = a - a r^(n+1), so

(IMAGE)

As long as |r| < 1, the term r^(n+1) will go to zero as n goes to infinity, so the finite sum S will approach a / (1-r) as n goes to infinity. Thus the value of the infinite sum is a / (1-r), and this also proves that the infinite sum exists, as long as |r| < 1.

In your example, the finite sums were

1 = 2 - 1/1

3/2 = 2 - 1/2

7/4 = 2 - 1/4

15/8 = 2 - 1/8

and so on; the nth finite sum is 2 - 1/2^n. This converges to 2 as n goes to infinity, so 2 is the value of the infinite sum.

8 0
3 years ago
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