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3 years ago

2x+3 less than or equal to 5

2 answers:

6 0

$2x+3 \leq 5 \\ \\ (2x+3)-3 \leq (5)-3 \\ \\ 2x \leq 2 \\ \\ \frac{2x}{2} \leq \frac{2}{2} \\ \\ x \leq 1 \\ \\x=( -\infty} ,1]$

ycow [4]3 years ago

3 0

2x + 3 ≤ 5
 -3 -3
 2x ≤ 2
2x ≤ 2
 2 2
 x = 1

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3 years ago

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3 years ago

It is given that y varies inversely as x^2. If x is decreased by 50%, find the percentage change in y.

vova2212 [387]

Answer:

300%

Step-by-step explanation:

Given

$y\ \alpha\ \frac{1}{x^2}$

Required

Find the percentage change in y when x decreased by 50%

First, convert to equation

$y\ = \ \frac{k}{x^2}$

Where k is the constant of proportionality

When x decreased by 50%

$Y = \frac{k}{(x - 0.5x)^2}$

$Y = \frac{k}{(0.5x)^2}$

$Y = \frac{k}{0.25x^2}$

Expand

$Y = \frac{1}{0.25} * \frac{k}{x^2}$

Substitute $\frac{k}{x^2}$ for y

$Y = \frac{1}{0.25} * y$

$Y = 4 * y$

$Y = 4 y$

The percentage change is then calculated as:

$\%Change = \frac{Y - y}{y} * 100\%$

$\%Change = \frac{4y - y}{y} * 100\%$

$\%Change = \frac{3y}{y} * 100\%$

$\%Change = 3 * 100\%$

$\%Change = 300\%$

The percentage in y is 300%

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3 years ago