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3 years ago

Paula spent 3/8 of her allowance on clothes and 1/6 on entertainment what fraction of her allowance did she spend on other items

1 answer:

8 0

All you'd have to do is find a common denominator, which would be 24 (because both 8 and 6 go into it). So you'd multiply both 3 and 8 by 3 to get 9/24, and both 1 and 6 by 4 to get 4/24. Then you add 9/24 to 4/24 to get 13/24. Then you just get the left over fraction, which is 7/24. That's the allowance she spent on other items. I hope this helps!

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The answer for this question is 5,740

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3 years ago

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1-cot^2a+cot^4a=sin^2a(1+cot^6a) prove it.

aliina [53]

Step-by-step explanation:

We have

1-cot²a + cot⁴a = sin²a(1+cot⁶a)

First, we can take a look at the right side. It expands to sin²a + cot⁶(a)sin²(a) = sin²a + cos⁶a/sin⁴a (this is the expanded right side) as cot(a) = cos(a)/sin(a), so cos⁶a = cos⁶a/sin⁶a. Therefore, it might be helpful to put everything in terms of sine and cosine to solve this.

We know 1 = sin²a+cos²a and cot(a) = cos(a)/sin(a), so we have

1-cot²a + cot⁴a = sin²a+cos²a-cos²a/sin²a + cos⁴a/sin⁴a

Next, we know that in the expanded right side, we have sin²a + something. We can use that to isolate the sin²a. The rest of the expanded right side has a denominator of sin⁴a, so we can make everything else have that denominator.

sin²a+cos²a-cos²a/sin²a + cos⁴a/sin⁴a

= sin²a + (cos²(a)sin⁴(a) - cos²(a)sin²(a) + cos⁴a)/sin⁴a

We can then factor cos²a out of the numerator

sin²a + (cos²(a)sin⁴(a) - cos²(a)sin²(a) + cos⁴a)/sin⁴a

= sin²a + cos²a (sin⁴a-sin²a+cos²a)/sin⁴a

Then, in the expanded right side, we can notice that the fraction has a numerator with only cos in it. We can therefore write sin⁴a in terms of cos (we don't want to write the sin²a term in terms of cos because it can easily add with cos²a to become 1, so we can hold that off for later) , so

sin²a = (1-cos²a)

sin⁴a = (1-cos²a)² = cos⁴a - 2cos²a + 1

sin²a + cos²a (sin⁴a-sin²a+cos²a)/sin⁴a

= sin²a + cos²a (cos⁴a-2cos²a+1-sin²a+cos²a)/sin⁴a

= sin²a + cos²a (cos⁴a-cos²a+1-sin²a)/sin⁴a

factor our the -cos²a-sin²a as -1(cos²a+sin²a) = -1(1) = -1

sin²a + cos²a (cos⁴a-cos²a+1-sin²a)/sin⁴a

= sin²a + cos²a (cos⁴a-1 + 1)/sin⁴a

= sin²a + cos⁶a/sin⁴a

= sin²a(1+cos⁶a/sin⁶a)

= sin²a(1+cot⁶a)

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3 years ago

Find the slope and the y-intercept of the of the linear equation.<br><br> 0=2-3y+12x

andrew11 [14]

The slope is 4 and the y-intercept is $\frac{2}{3}$

Step-by-step explanation:

The general form of a linear equation is Ax + By + C = 0, where

A is the coefficient of x
B is the coefficient of y
C is the numerical term
A, B, and C are integers
The slope of the line = $\frac{-A}{B}$
The y-intercept = $\frac{-C}{B}$

∵ The linear equation is 0 = 2 - 3y + 12x

- Switch the two sides and arrange the terms as the general

form above

∴ 12x - 3y + 3 = 0

∴ A = 12

∴ B = -3

∴ C = 2

∵ The slope of the line = $\frac{-A}{B}$

- Substitute A by 12 and B by -3

∴ The slope of the line = $\frac{-12}{-3}$

∴ The slope of the line = 4

∵ The y-intercept = $\frac{-C}{B}$

- Substitute C by 2 and B by -3

∴ The y-intercept = $\frac{-2}{-3}$

∴ The y-intercept = $\frac{2}{3}$

The slope is 4 and the y-intercept is $\frac{2}{3}$

Learn more:

You can learn more about the linear equation in brainly.com/question/4819659

#LearnwithBrainly

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3 years ago

A school library has 160 DVDs in its collection. Given that 45% of the DVDs are about science and 40% are about history, how man

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Answer:

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Step-by-step explanation:

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40% of 160 = 64

72+64=136

160-136=24

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Answer:

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Step-by-step explanation:

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3 years ago

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