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3 years ago

Solve each compound inequality and graph the solutions. -2 < x - 3 < 5

Mathematics

1 answer:

Greeley [361]3 years ago

8 0

Answer:

See attachment.

Step-by-step explanation:

The given inequality is -2 < x - 3 < 5.

We add 3 to each part of -2 +3< x - 3+3 < 5+3

We now simplify to get: 1 < x < 8.

To represent this on the number line, we have to draw open circles at 1 and 8 and connect them as shown in the attachment.

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What is the length of CD to the nearest 10th?

Snezhnost [94]

Answer:

$\huge \boxed{\mathrm{10.3 \ units}}$

Step-by-step explanation:

To solve for <em>CD</em>, we can create a right triangle.

Where <em>CD</em> becomes the hypotenuse.

The length of the base of the triangle is 9 units.

The length of the height of the triangle is 5 units.

Apply Pythagorean theorem to solve for the hypotenuse.

$\sf hypotenuse = \sqrt{(base )^2 +(height )^2 }$

$c=\sqrt{9^2 +5^2 }$

$c=\sqrt{106}$

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3 years ago

Need to know the population in 2015

Margarita [4]

$\bf P=1110.9e^{kt}\quad 
\begin{cases}
P=1200 &\textit{in thousands}\\
t=2 &\textit{in 2002}
\end{cases}\implies 1200=1110.9e^{k2}
\\\\\\
\cfrac{1200}{1110.9}=e^{2k}\implies ln\left( \frac{1200}{1110.9} \right)=ln(e^{2k})\implies ln\left( \frac{1200}{1110.9} \right)=2k
\\\\\\
\cfrac{ln\left( \frac{1200}{1110.9} \right)}{2}=k\implies 0.0385755\approx k\implies 0.0386\approx k\\\\
-------------------------------\\\\$

$\bf P=1110.9e^{0.0386t}\qquad 
\begin{cases}
t=14\\
\textit{year 2015}
\end{cases}\implies P=1110.9e^{0.0386\cdot 14}
\\\\\\
P\approx 1907.0747\implies about\ 1,907,075\textit{ once rounded up}$

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2 years ago

Pumpkins at a local farm sell for $.49 per pound. Jim Ring spent $73.50. How many pounds of pumpkins were purchased?

Leona [35]

Number of pounds purchased multiplied by price per pound equals the total $ spent.

x= # pumpkin pounds purchased
0.49x=$73.50
Divide both sides by 0.49
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Hope this helps! :)

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