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Kamila [148]
3 years ago
12

Simplifying radicals! Please help me & Show WORK

Mathematics
1 answer:
andriy [413]3 years ago
3 0

Answer:

Solving the radical 4\sqrt{2}(-4\sqrt{15}+3\sqrt{18}) we get \mathbf{-16\sqrt{30}+72}

Step-by-step explanation:

We need to simplify the radical: 4\sqrt{2}(-4\sqrt{15}+3\sqrt{18})

Prime factors of 18 are: 2x3x3

Replacing \sqrt{18} with its factors

4\sqrt{2}(-4\sqrt{15}+3\sqrt{18})\\=4\sqrt{2}(-4\sqrt{15}+3\sqrt{2\times3\times3})\\=4\sqrt{2}(-4\sqrt{15}+3\sqrt{2\times3^2})

We know that \sqrt{3^2}=3

=4\sqrt{2}(-4\sqrt{15}+3\times3\sqrt{2})\\=4\sqrt{2}(-4\sqrt{15}+9\sqrt{2})

Multiplying 4\sqrt{2} with terms inside the bracket

=4\sqrt{2}(-4\sqrt{15})+4\sqrt{2}( 9\sqrt{2}))\\=-16\sqrt{2}\sqrt{15}+36\sqrt{2} \sqrt{2}

We know that \sqrt{2} \sqrt{2}=2

=-16\sqrt{2*15}+36(2)\\=-16\sqrt{30}+72

So, solving the radical 4\sqrt{2}(-4\sqrt{15}+3\sqrt{18}) we get \mathbf{-16\sqrt{30}+72}

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Keith has 7 yards of string. He needs ⅓ yard of string for each of his puppets. How many puppets can Keith make with his string?
Pani-rosa [81]

Answer:

the no of puppets that could be made with his string is 21

Step-by-step explanation:

Given that

There is 7 yards

And, it needs one -third of string for each of his puppets

= 7 × 3

= 21 puppets

We simply multiply the 7 yards with the 3 so that the no of puppets could come

hence, the no of puppets that could be made with his string is 21

8 0
3 years ago
The perimeter of a rectangle is 200 yards. What are the dimensions of the rectangle if the length is 60 yards more than the​ wid
puteri [66]

Answer:

L=80

W=20

Step-by-step explanation:

Perimeter = 2×L+2×w

L=w+60

Perimeter - 2×60 = 4×w

200-120 = 80

80/4= w = 20

L=w+60 = 80

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3 years ago
Please help me with this ​
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Step-by-step explanation:

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8 0
3 years ago
The sum of two numbers is 840. one of the numbers is 357. what is the other number?​
nlexa [21]

Answer:

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Step-by-step explanation:

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5 0
3 years ago
The measure of the supplement of an angle is seven times as large as the measure of its complement find the measure of the angle
8090 [49]

Answer: original angle = 75°

Its supplement 105°

Its complement = 15°

Step-by-step explanation:

We know that,

  • Sum of supplementary angles is 180 degrees.
  • Sum of complementary angles is 90 degrees.

Let x be the original angle , then its supplement = 180° - x

its complement = 90° - x

As per given,

180° - x = 7(90° - x)

⇒ 180° - x = 630° - 7x

⇒  7x- x = 630° -180°

⇒  6 x = 450°

⇒  x = 75°  [divide both sides by 6]

So, original angle = 75°

Its supplement =  180° - 75° = 105°

Its complement = 90° -75° = 15°

Hence,  original angle = 75°

Its supplement 105°

Its complement = 15°

4 0
3 years ago
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