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Margarita [4]
3 years ago
15

Mrs. Ruiz has 11/12 yard of string to hang 3 banners. She uses the same length of string to hang each banner. How much string do

es she use for each banner?
Mathematics
1 answer:
lesya [120]3 years ago
8 0

Answer:

\frac{11}{36} yard

Step-by-step explanation:

Length of string Mrs. Ruiz has = \frac{11}{12} yard

Mrs. Ruiz needs to hang 3 banners using the string.

Having known that each banner uses same length of string to be hung we can divide total length of sting into 3 equal parts.

So, we can divide \frac{11}{12} yard by 3 as

⇒ \frac{11}{12}\div 3

Changing the division sing to multiplication by taking reciprocal of divisor.

⇒ \frac{11}{12}\times \frac{1}{3}

We can now multiply numerators and denominators.

⇒ \frac{11}{36} yard

∴  Mrs. Ruiz must used  \frac{11}{36} yard of string for each banner.

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<u>Answer:</u>

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<u>Step-by-step explanation:</u>

According to the Remainder Theorem, when a polynomial f(x) is divided by a term (x - r), then the remainder must be f(r).

So first we will divide f(x) by (x - 2) using long division to get:

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= 3x^4 + 6x^3 + 5x^2 (-x^2 + 2) / (x - 2)

= 3x^4 + 6x^3 + 5x^2 -x -2 - (2) / (x -2)

= \frac{-2 + 3x^{5} - 7x^{3} - 11x^{2} + 2x}{x - 2} - 2

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Now check x = 2 for 3x^5 - 7x^3 -  11x^2 + 2:

3(2)^5 - 7(2)^3 -  11(2)^2 + 2 = -2

The Remainder Factor theorem also states that if (x - r) is a factor of f(x) then f(r) must be 0.

So we found that f(2) = -2, therfore (x - 2) is not a factor of f(x) .


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