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3 years ago

Erin works as a computer support person after school. She earns $15 per day plus $0.50 for each computer she fixes.

Mathematics

2 answers:

Ostrovityanka [42]3 years ago

7 0

Answer:

Step-by-step explanation:

y=0.5x+15

We are told she earned $16.50 so

0.5x+15=16.5, subtract 15 from each side

0.5x=1.5, divide each side by 0.5

x=3

So she fixed three computers.

Keith_Richards [23]3 years ago

4 0

Answer:

She Fixed 1 computer but fixed it for two days

Step-by-step explanation:

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Help me with trigonometry

poizon [28]

Answer:

See below

Step-by-step explanation:

It has something to do with the Weierstrass substitution, where we have

$\int\, f(\sin(x), \cos(x))dx = \int\, \dfrac{2}{1+t^2}f\left(\dfrac{2t}{1+t^2}, \dfrac{1-t^2}{1+t^2} \right)dt$

First, consider the double angle formula for tangent:

$\tan(2x)= \dfrac{2\tan(x)}{1-\tan^2(x)}$

Therefore,

$\tan\left(2 \cdot\dfrac{x}{2}\right)= \dfrac{2\tan(x/2)}{1-\tan^2(x/2)} = \tan(x)=\dfrac{2t}{1-t^2}$

Once the double angle identity for sine is

$\sin(2x)= \dfrac{2\tan(x)}{1+\tan^2(x)}$

we know $\sin(x)=\dfrac{2t}{1+t^2}$ , but sure, we can derive this formula considering the double angle identity

$\sin(x)= 2\sin\left(\dfrac{x}{2}\right)\cos\left(\dfrac{x}{2}\right)$

Recall

$\sin \arctan t = \dfrac{t}{\sqrt{1 + t^2}} \text{ and } \cos \arctan t = \dfrac{1}{\sqrt{1 + t^2}}$

Thus,

$\sin(x)= 2 \left(\dfrac{t}{\sqrt{1 + t^2}}\right) \left(\dfrac{1}{\sqrt{1 + t^2}}\right) = \dfrac{2t}{1 + t^2}$

Similarly for cosine, consider the double angle identity

Thus,

$\cos(x)= \left(\dfrac{1}{\sqrt{1 + t^2}}\right)^2- \left(\dfrac{t}{\sqrt{1 + t^2}}\right)^2 = \dfrac{1}{t^2+1}-\dfrac{t^2}{t^2+1} =\dfrac{1-t^2}{1+t^2}$

Hence, we showed $\sin(x) \text { and } \cos(x)$

======================================================

$5\cos(x) =12\sin(x) +3, x \in [0, 2\pi ]$

Solving

$5\,\overbrace{\frac{1-t^2}{1+t^2}}^{\cos(x)} = 12\,\overbrace{\frac{2t}{1+t^2}}^{\sin(x)}+3$

$\implies \dfrac{5-5t^2}{1+t^2}= \dfrac{24t}{1+t^2}+3 \implies \dfrac{5-5t^2 -24t}{1+t^2}= 3$

$\implies 5-5t^2-24t=3\left(1+t^2\right) \implies -8t^2-24t+2=0$

$t = \dfrac{-(-24)\pm \sqrt{(-24)^2-4(-8)\cdot 2}}{2(-8)} = \dfrac{24\pm 8\sqrt{10}}{-16} = \dfrac{3\pm \sqrt{10}}{-2}$

$t=-\dfrac{3+\sqrt{10}}{2}\\t=\dfrac{\sqrt{10}-3}{2}$

Just note that

$\tan\left(\dfrac{x}{2}\right) = \dfrac{3\pm 8\sqrt{10}}{-2}$

and $\tan\left(\dfrac{x}{2}\right)$ is not defined for $x=k\pi , k\in\mathbb{Z}$

6 0

3 years ago

Describe two ways to write equivalent algebraic expressions

Zolol [24]

Answer:

See below.

Step-by-step explanation:

An example would be:

3x^2 + 6

and

3(x^2 + 2) .

The second way is found by dividing the first one by 3).

5 0

3 years ago

A total of 30 percent of the geese included in a certain migration study were male. If some of the geese migrated during the stu

Serggg [28]

<h2>Answer:</h2>

(B). $\frac{7}{12}$

<h2>Step-by-step explanation:</h2>

In the question,

Let the total number of geese be = 100x

Number of Male geese = 30% = 30x

Number of Female Geese = 70x

Let us say 'kx' geese migrated from these geese.

Number of migrated Male geese = 20% of kx = kx/5

Number of migrated Female geese = 4kx/5

So,

Migration rate of Male geese is given by,

$\frac{(\frac{kx}{5})}{30x}$

Migration rate of Female geese is given by,

$\frac{(\frac{4kx}{5})}{70x}$

So,

The ratio of Migration rate of Male geese to that of Female geese is given by,

$\frac{\left[\frac{(\frac{kx}{5})}{30x}\right]}{\left[\frac{(\frac{4kx}{5})}{70x}\right]}=\frac{350}{4\times 150}=\frac{7}{12}$

Therefore, the ratio of the rate of migration of Male geese to that of Female geese is,

$\frac{7}{12}$

Hence, the correct option is (B).

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4 years ago

Solve for x x−6/9=−5 x=

Vera_Pavlovna [14]

Answer:

4 4/9

Step-by-step explanation:

Move all terms not containing x

to the right side of the equation.

Exact Form:

x=−409

Decimal Form:x=−4.¯4

Mixed Number Form:

4 4/9

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3 years ago

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If you spend $3 on 6 apples what is the unit rate? Or in other words, what is the cost of each apple?

Andrew [12]

Each apple costs .50 cents :D

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3 years ago

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