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2 years ago

Evaluate -9 - 13 + 2 + 13

Mathematics

2 answers:

Helga [31]2 years ago

8 0

Answer:

-7

Step-by-step explanation:

-9 - 13 + 2 + 13

-22 +2 +13

- 20 + 13

-7

Shkiper50 [21]2 years ago

5 0

Answer:

-7 :)))))

Step-by-step explanation:

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Jenna works in an ice cream shop. When she starts her shift the tub of chocolate ice cream is 23 full. When she finishes her shi

ipn [44]

Answer:

<em />

Step-by-step explanation:

Given

$Start = 23$

$End = 16$

$Hours = 6\frac{1}{2}h$

Required

Determine the hourly rate

First, we need to determine the ice cream sold

$Ice\ Cream = 23 - 16$

$Ice\ Cream = 7$

Next, we calculate the hourly rate:

$Rate = Ice\ Cream/Hours$

$Rate = 7/6\frac{1}{2}h$

$Rate = 7/\frac{13}{2}h$

$Rate = 7*\frac{2}{13h}$

$Rate = \frac{14}{13h}$

$Rate = 1.07692307692/hr$

<em /> $Rate = 1.1/hr$ <em> -- Approximated</em>

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2 years ago

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Whats 150-x-2x=120+2x

Stels [109]

Answer:

X=6

Step-by-step explanation:

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2 years ago

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If the graph of f(x)= 3^x is reflected over the x-axis, what is the equation of the new graph?

Lerok [7]

Answer:

g(x) = - 3^x

Step-by-step explanation:

<u>Reflection over x-axis results in:</u>

f(x) → - f(x) translation

<u>Therefore the new function is:</u>

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2 years ago

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What is the distance between the p&ints (8, 3) and (8, - 6) ?

baherus [9]

Answer:

Using distance formula:

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Answer: 9 units

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2 years ago

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4sin²<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D" id="TexFormula1" title="\frac{x}{2}" alt="\frac{x}{2}" align="absm

raketka [301]

Answer:

$\displaystyle x=\left \{\frac{2\pi}{3}+2\pi k,\frac{4\pi}{3}+2\pi k, \frac{8\pi}{3}+2\pi k, \frac{10\pi}{3}+2\pi k\right \}k\in \mathbb{Z}$

Step-by-step explanation:

Hi there!

We want to solve for $x$ in:

$4\sin^2(\frac{x}{2})=3$

Since $x$ is in the argument of $\sin^2$ , let's first isolate $\sin^2$ by dividing both sides by 4:

$\displaystyle \sin^2\left(\frac{x}{2}\right)=\frac{3}{4}$

Next, recall that $\sin^2x$ is just shorthand notation for $(\sin x)^2$ . Therefore, take the square root of both sides:

$\displaystyle \sqrt{\sin^2\left(\frac{x}{2}\right)}=\sqrt{\frac{3}{4}},\\\sin\left(\frac{x}{2}\right)=\pm \sqrt{\frac{3}{4}}$

Simplify using $\displaystyle \sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$ :

$\displaystyle \sin\left(\frac{x}{2}\right)=\pm \sqrt{\frac{3}{4}},\\\sin\left(\frac{x}{2}\right)=\pm \frac{\sqrt{3}}{\sqrt{4}}=\pm \frac{\sqrt{3}}{2}$

Let $\phi = \frac{x}{2}$ .

<h3><u>Case 1 (positive root):</u></h3>

$\displaystyle \sin(\phi)=\frac{\sqrt{3}}{2},\\\phi = \frac{\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\phi =\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z}$

Therefore, we have:

$\displaystyle \frac{x}{2}=\phi = \frac{\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\frac{x}{2}=\phi =\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z},\\\\\begin{cases}x=\boxed{\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z}},\\x=\boxed{\frac{4\pi}{3}+2\pi k , k \in \mathbb{Z}}\end{cases}$

<h3><u>Case 2 (negative root):</u></h3>

$\displaystyle \sin(\phi)=-\frac{\sqrt{3}}{2},\\\phi = \frac{4\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\phi =\frac{5\pi}{3}+2\pi k, k\in \mathbb{Z},\\\begin{cases}x=\boxed{\frac{8\pi}{3}+2\pi k, k\in \mathbb{Z}},\\x=\boxed{\frac{10\pi}{3}+2\pi k , k \in \mathbb{Z}}\end{cases}$

8 0

2 years ago