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3 years ago

7

Nancy and her sister went to the store together. After the store, Nancy walked 2 blocks west to get a coffee and her sister walk

ed 7 blocks west back to work. How many blocks is the coffee shop that Nancy went to from her sister's work?

1 answer:

Dima020 [189]3 years ago

8 0

Answer:

5 blocks

Step-by-step explanation:

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In a certain function, y varies directly with x. If y = 6 when x = 8, find x when y = 9.

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If y = 6 when x = 8, then value of "x" when y = 9 is equal to 12

<u>Solution:</u>

Given that , In a certain function, y varies directly with x

And x = 8 when y = 6,

We have to find what will be the value of x when y = 9

Now, from the given information,

$\begin{array}{l}{y \alpha x} \\\\ {y=c x \rightarrow(1)}\end{array}$

where c is the proportionality constant

$\begin{array}{l}{\text { Now, substitute } x=8 \text { and } y=6 \text { in }(1)} \\\\ {\rightarrow 8=c(6) \rightarrow c=\frac{8}{6}} \\\\ {\rightarrow c=\frac{4}{3}} \\\\ {\text { Then, }(1) \rightarrow x=\frac{4}{3} y} \\\\ {\text { So, when } y=9} \\\\ {\rightarrow x=\frac{4}{3}(9)} \\\\ {\rightarrow x=4 \times 3} \\\\ {\rightarrow x=12}\end{array}$

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The polynomial of degree 5, P ( x ) has leading coefficient a=1, has roots of multiplicity 2 at x = 3 and x = 0 , and a root of

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Answer:

$p_{5} (t) = x^{5} - 5\cdot x^{4} + 3\cdot x^{3} +9\cdot x^{2}$ , for $r_{1} = 0$

Step-by-step explanation:

The general form of quintic-order polynomial is:

$p_{5}(t) = a\cdot x^{5} + b\cdot x^{4} + c\cdot x^{3} + d\cdot x^{2} + e \cdot x + f$

According to the statement of the problem, the polynomial has the following roots:

$p_{5} (t) = (x - r_{1})\cdot (x-3)^{2}\cdot x^{2} \cdot (x+1)$

Then, some algebraic handling is done to expand the polynomial:

$p_{5} (t) = (x - r_{1}) \cdot (x^{3}-6\cdot x^{2}+9\cdot x) \cdot (x+1)\\p_{5} (t) = (x - r_{1}) \cdot (x^{4}-5\cdot x^{3} + 3 \cdot x^{2} + 9 \cdot x)$

$p_{5} (t) = x^{5} - (5+r_{1})\cdot x^{4} + (3 + 5\cdot r_{1})\cdot x^{3} +(9-3\cdot r_{1})\cdot x^{2} - 9 \cdot r_{1}\cdot x$

If $r_{1} = 0$ , then:

$p_{5} (t) = x^{5} - 5\cdot x^{4} + 3\cdot x^{3} +9\cdot x^{2}$

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