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4 years ago

Dominique used the inequality below to find the maximum number of sweatshirts she could purchase with her savings.

1 answer:

6 0

We just have to find the closest number that can be multiplied by 32 and still be under 300. Do this by following this step:

Divide by 32 on both sides.

x < 9.375

We can't buy 9.375 sweatshirts though, and we can't add more decimals or it will go over 300, so you round down to 9.

Dominique can buy 9 sweatshirts without going over $300!

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Answer:

A.) k=0.5

Step-by-step explanation:

If we use the formula given: y=kx, we can plug in values.

0.5=k(1)

0.5=(0.5)(1)

0.5=0.5

We know that to get from 1 to 0.5, we need to divide by two, or multiple by 1/2. 1/2 in decimal form is 0.5

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3 years ago

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Kobotan [32]

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3 years ago

Question 9

Alenkasestr [34]

Answer:

$PX=4\\PY=4\sqrt{3}$

Step-by-step explanation:

Let $\angle PYZ=Q$

$\Rightarrow \angle XYP=90-\angle PYZ\\\angle XYP=90-\theta$

In the $\Delta PYZ$

$\tan\theta =\frac{opposite}{adjacent}=\frac{PZ}{PY}......(1)$

In the $\Delta YPX$

$\tan(90-\theta)=\frac{opposite}{adjacent}=\frac{PX}{PY}$

$\cot=\frac{PX}{PY}....(2)$

eqn(1) $\times$ eqn(2)

$\tan\times\cot\theta=\frac{PZ}{PY}\times\frac{PX}{PY}\\\\1=\frac{PZ\times PX}{PY^2}\ \ (as\ tan\theta\ =\frac{1}{\cot\theta})\\\\PY^2=PZ\times PX\\PY^2=12PX.......(3)$

Now in $\Delta XYP$

use Pythagorean theorem

$XY^2=PY^2+PX^2\\8^2=PY^2+PX^2\ \ (as\ XY\ =8)\\PX^2+PY^2=64\\\\PY^2=12PX\ \ (eqn(3)\\\\\Rightarrow PX^2+12PX=64\\\\PX^2+12PX-64=0\\\\PX^2+16-4PX-64=0\\\\(PX+16)(PX-4)=0\\\\PX=4,\ -16$

Length can not be negative

Hence $PX=4$

$PY^2=12PX=12\times4=48\\\\PY=\sqrt{48}=4\sqrt{3}$

Hence $PX=4,\ PY=4\sqrt{3}$

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3 years ago