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neonofarm [45]
3 years ago
15

A yoga club had 54 members and the ratio of men to women is 4:5. This year, 18 new members joined the club and the ratio of men

to women became 3:5. Find the number of women who joined the club this year.
Mathematics
1 answer:
castortr0y [4]3 years ago
5 0

Answer:

23

Step-by-step explanation:

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What is the remainder R when the polynomial p(x) is divided by (x - 2)? Is (x - 2) a factor of p(x)? P(x) = -4x4 + 6x3 + 8x2 - 6
Trava [24]

Answer:

B

(x-2) is a factor since remainder is 0.

Step-by-step explanation:

We divide (x-2) into the polynomial -4x^4+6x^3+8x^2-6x-4 through long division or synthetic. We choose long division and look for what will multiply with (x-2) to make the polynomial -4x^4+6x^3+8x^2-6x-4 .

(x-2)(-4x^3)=-4x^4+8x^3

We subtract this from the original -4x^4-(-4x^4)+6x^3-(8x^3)+8x^2-6x-4.

This leaves -2x^3+8x^2-6x-4. We repeat the step above.

(x-2)(-2x^2)=-2x^3+4x^2.

We subtract this from -2x^3-(-2x^3)+8x^2-(4x^2)-6x-4=4x^2-6x-4. We repeat the step above.

(x-2)(4x)=4x^2-8x.

We subtract this from 4x^2-(4x^2)-6x-(-8x)-4=2x-4. We repeat the step above.

(x-2)(2)=2x-4.

We subtract this from 2x-(2x)-4-(4)=0. There is no remainder. This means (x-2) is a factor.


7 0
3 years ago
A recipe says to use 4 cups of sugar to make 96 cookies. What is the constant of proportionality that relates the number of cook
lutik1710 [3]

<u><em>Answer:</em></u>

The constant of proportionality is 24

<u><em>Explanation:</em></u>

The number of cups of sugar is directly proportional to the number of cookies made. This means that as the number of sugar cups increases, the number of cookies made will also increase.

<u>This is modeled by the equation:</u>

y = kx

where:

k is the constant of proportionality

y is the dependent variable (number of cookies)

x is the independent variable (number of cups of sugar)

<u>Now, we are give that</u> 4 cups of sugar are required to make 96 cookies. <u>Substitute with these values in the above equation and solve for k (the constant of proportionality) as follows:</u>

y = kx

96 = k*4

k = \frac{96}{4}=24

Hope this helps :)


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