Find the ordered pairs for the x- y-intercepts of the equation 4x+2y=16

1 answer:

3 0

The x-intercept is what 'x' is when 'y' is equal to 0. So plug in 0 for 'y' and solve for 'x':

$\sf 4x+2y=16$

$\sf 4x+2(0)=16$

Simplify:

$\sf 4x=16$

Divide 4 to both sides:

$\sf x=4$

So the x-intercept is (4, 0).

The y-intercept is what 'y' is when 'x' is equal to 0. So plug in 0 for 'x' and solve for 'y':

$\sf 4x+2y=16$

$\sf 4(0)+2y=16$

Simplify:

$\sf 2y=16$

Divide 2 to both sides:

$\sf y=8$

So the y-intercept is (0, 8).

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Jake has a rectangular garden that measures 12 feet by 14 feet. He wants to increase the area by 50% and plans to increase each

emmasim [6.3K]

<em>In order to increase the area of a rectangular garden that measures 12 feet by 14 feet by 50% Jake must increase each dimension by equal lengths, x:</em>

$x\approx 2.9ft$

<h2>Explanation:</h2><h2 />

First of all, let's calculate the area of the original rectangular garden:

$A=b\times h \\ \\ b:base \\ \\ h:height \\ \\ \\ b=12ft \\ \\ h=14ft \\ \\ \\ A=12(14) \\ \\ A=168ft^2$

Jake wants to increase the area by 50%, so the new area would be:

$A'=168(1.5) \\ \\ A'=252ft^2$

He wants to increase the area by 50% and plans to increase each dimension by equal lengths, x, so this is represented by the figure below, therefore:

$(12+x)(14+x)=252 \\ \\ 168+12x+14x+x^2-252=0 \\ \\ x^2+26x-84=0 \\ \\ \\ Using \ quadratic \ formula: \\ \\ x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ a=1 \\ \\ b=26 \\ \\ c=-84 \\ \\ \\ x=\frac{-26 \pm \sqrt{26^2-4(1)(-84)}}{2(1)} \\ \\ x=\frac{-26 \pm \sqrt{1012}}{2} \\ \\ \\ Two \ solutions: \\ \\ x_{1}=-13+\sqrt{253} \approx 2.9\\ \\ x_{2}=-13-\sqrt{253} \approx -28.9 \\ \\ x_{2} \ is \ discarded \ because \ it \ can't \ be \ negatives$

Finally:

<em>In order to increase the area of a rectangular garden that measures 12 feet by 14 feet by 50% Jake must increase each dimension by equal lengths, x:</em>

$x\approx 2.9ft$

<h2>Learn more:</h2>

Dilation: brainly.com/question/10945890

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