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3 years ago

How do you do this for expanding and factoring expressions 8(4x-12)

Mathematics

1 answer:

Snezhnost [94]3 years ago

7 0

Answer:

32x - 96

Step-by-step explanation:

Apply the distributed property:

8 × 4x = 32x
8 × 12 = 96
Re-write the expression: 32x - 96

I hope this helps!

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Eric has 1 5/9 cups of yogurt to make smoothies.Each smoothie uses 1/3 of a cup of yogurt.What is the maximum number of smoothie

Vedmedyk [2.9K]

Maximum number of smoothies that Erica can make with the yogurt is 5

<h3><u>Solution:</u></h3>

Given that Eric has $1\frac{5}{9}$ cups of yogurt to make smoothie

Each smoothie uses $\frac{1}{3}$ of a cup of yogurt

To find: maximum number of smoothies that Erica can make with the yogurt

Let 'n' be the number of smoothies that Erica can make with the available yogurt

number of smoothies that Erica can make with the yogurt is calculated by divinding the total available cups of yogurt by cups of yogurt needed for one smoothie

<em><u>Therefore we get:</u></em>

$n=\frac{\text { total available cups of yogurt }}{\text { cups of yogurt needed for one smoothie }}$

total available cups of yogurt = $1\frac{5}{9} = \frac{9 \times 1 +5}{9} = \frac{14}{9}$

cups of yogurt needed for one smoothie = $\frac{1}{3}$

Substituting the values in above formula we get,

$\begin{aligned}&n=\frac{\frac{14}{9}}{\frac{1}{3}}\\\\&n=\frac{14}{9} \times \frac{3}{1}=\frac{14}{3}=4.66 \approx 5\end{aligned}$

Thus maximum number of smoothies that Erica can make with the yogurt is 5

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3 years ago

which functions have a range of all real numbers ? check all that apply. A. y=csc x B. y=sec x C. y=tan x D. y= cot x

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None of these. All of these functions are defined as ratio of trigonometric functions.

Trigonometric functions have infinite zeroes, so when you put them in the denominator, they lead to infinitely many points of ill-definition.

Specifically, we have:

$\csc(x) = \dfrac{1}{\sin(x)}$

which is undefined at

$\sin(x)=0\iff x=k\pi, k\in\mathbb{Z}$

$\sec(x) = \dfrac{1}{\cos(x)}$

which is undefined at

$\cos(x)=0\iff x=\dfrac{\pi}{2}+k\pi, k\in\mathbb{Z}$

$\tan(x) = \dfrac{\sin(x)}{\cos(x)}$

which is undefined at

$\cos(x)=0\iff x=\dfrac{\pi}{2}+k\pi, k\in\mathbb{Z}$

$\cot(x) = \dfrac{\cos(x)}{\sin(x)}$

which is undefined at

$\sin(x)=0\iff x=k\pi, k\in\mathbb{Z}$

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3 years ago

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