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3 years ago

Take a factor out of the square root:

Mathematics

1 answer:

Andrews [41]3 years ago

3 0

Answer:

1. |y| sqrt(10)

2. |x| sqrt(x)

3. a^2 sqrt(a)

4. 4 |y|^3 sqrt(3)

5. 1/4 *|x| sqrt(3x)

Step-by-step explanation:

1. sqrt(10y^2)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt(y^2) sqrt(10)

|y| sqrt(10)

We take the absolute value of y because -y*-y = y^2 and the principle square root is y

2. sqrt(x^3)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt(x^2) sqrt(x)

|x| sqrt(x)

3. sqrt(a^5)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt(a^4) sqrt(a)

a^2 sqrt(a)

4. sqrt(16 y^7)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt(16) sqrt(y^6)sqrt(y)

4 |y|^3 sqrt(3)

5. sqrt(3/16x^3)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt(1/16) sqrt(x^2)sqrt(3x)

1/4 *|x| sqrt(3x)

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Greta is trying to determine the portion of green candies in various bags of green and yellow candies. Using the information bel

IrinaK [193]

Answer: a) $\dfrac{1}{3}$ b) $\dfrac{71}{100}$ c) $\dfrac{5}{9}$

Step-by-step explanation:

Since we have given that

There are green and yellow candies in each bag.

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Part of yellow candies in bag A = $\dfrac{2}{3}$

Part of green candies in bag A would be

$1-\dfrac{2}{3}\\\\=\dfrac{3-2}{3}\\\\=\dfrac{1}{3}$

Bag B: 29 % of the candies are yellow. What portion of the candies is green?

Percentage of candies are yellow = 29%

Portion of candies are green is given by

$1-\dfrac{29}{100}\\\\=1-0.29\\\\=0.71\\\\=\dfrac{71}{100}$

Bag C: 4 out of every 9 candies are yellow. What portion of the candies is green?

Portion of yellow candies = $\dfrac{4}{9}$

Portion of green candies would be

$1-\dfrac{4}{9}\\\\=\dfrac{9-4}{9}\\\\=\dfrac{5}{9}$

Hence, a) $\dfrac{1}{3}$ b) $\dfrac{71}{100}$ c) $\dfrac{5}{9}$

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3 years ago

A line has a slope of -3 and a y-intercept of 3.

vladimir1956 [14]

Answer:

y = -3x + 3

Step-by-step explanation:

If ... A line has a slope of -3 and a y-intercept of 3, then the equation of that line is y = mx + b => y = -3x + 3. You don't need the table of values.

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3 years ago

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Answer:

Step-by-step explanation:

The original price of the bicycle is x.

The discounted price of the bicycle is x - 30. It is a $30 discount.

The tax goes on the original price. 0.09x is the 9% tax applied to the original price x.

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3 years ago

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Our hearts beat approximately 70 times per minute. Express in scientific notation how many times the heart beats over a lifetime

earnstyle [38]

Answer:

2.69 x $10^{9}$

Step-by-step explanation:

We are given the heart's speed - 70 bpm

We count the number of minutes in 73 years :

1 year = 365 days
1 day = 24 hours
1 hour = 60 minutes
73 x 365 x 24 x 60 = 38,368,800 minutes

We multiply the heart's bpm with 73 years worth of minutes

38,368,800 x 70 = 2,685,816,000

Write the number in scientific notation = 2.68581 x $10^{9}$ ≈ 2.69 x $10^{9}$

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3 years ago