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Mice21 [21]
3 years ago
11

How can you solve problems involving direct variation?

Mathematics
1 answer:
never [62]3 years ago
8 0

Answer:

Solving a Direct Variation Problem

Write the variation equation: y = kx or k = y/x.

Substitute in for the given values and find the value of k.

Rewrite the variation equation: y = kx with the known value of k.

Substitute the remaining values and find the unknown.

Step-by-step explanation:

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\bf \textit{now recall that }\qquad \cfrac{\frac{a}{b}}{\frac{c}{{{ d}}}}\implies \cfrac{a}{b}\cdot \cfrac{{{ d}}}{c}\\\\&#10;-----------------------------\\\\&#10;\cfrac{2}{3}\cdot \cfrac{1}{x}=\cfrac{1}{3}\cdot \cfrac{1}{1}\implies \cfrac{2}{3x}=\cfrac{1}{3}\implies 2\cdot 3=1\cdot 3x\implies 6=3x&#10;\\\\\\&#10;\cfrac{6}{3}=x

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3 years ago
Five times the sum of a number and 27 is greater than or equal to six times the sum of that
AleksAgata [21]

The complete version of question:

<em>Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26. What is the solution of this problem.</em>

Answer:

5\left(x+27\right)\ge \:6\left(x+26\right)\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-21\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-21]\end{bmatrix}

Step-by-step explanation:

As the description of the statement is:

'<em>Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26'.</em>

<em />

As

  • <em>Five times the sum of a number and 27  </em>is written as: 5(x + 27)
  • <em>greater than or equal </em>is written as:  \geq
  • <em>six times the sum of that number and 26'  </em>is written as: 6(x + 26)

so lets combine the whole statement:

<em />5\left(x\:+\:27\right)\ge \:6\left(x\:+\:26\right)<em />

solving

<em />5\left(x\:+\:27\right)\ge \:6\left(x\:+\:26\right)<em />

<em />5x+135\ge \:6x+156<em />

<em />5x+135-135\ge \:6x+156-135<em />

<em />5x\ge \:6x+21<em />

<em />5x-6x\ge \:6x+21-6x<em />

<em />-x\ge \:21<em />

<em />\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}<em />

<em />\left(-x\right)\left(-1\right)\le \:21\left(-1\right)<em />

<em />x\le \:-21<em />

Therefore,

5\left(x+27\right)\ge \:6\left(x+26\right)\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-21\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-21]\end{bmatrix}

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3 years ago
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The answer is

x =<span>‌ <span><span>−3/</span>17</span></span>

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3 years ago
Read 2 more answers
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