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2 years ago

If you earn $634.38 for a 29-hour work week, how much would you earn for a 40-hour work week at the same hourly rate?

Mathematics

1 answer:

8090 [49]2 years ago

4 0

Answer:

you need another variable? because all you gave me was a total

Step-by-step explanation:

all you did was give 3 variables when 4 is needed

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Save me the headache

maxonik [38]

$(9\sin2x+9\cos2x)^2=81$

Taking the square root of both sides gives two possible cases,

$9\sin2x+9\cos2x=9\implies\sin2x+\cos2x=1$

$9\sin2x+9\cos2x=-9\implies\sin2x+\cos2x=-1$

Recall that

$\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta$

If $\alpha=2x$ and $\beta=\dfrac\pi4$ , we have

$\sin\left(2x+\dfrac\pi4\right)=\dfrac{\sin2x+\cos2x}{\sqrt2}$

so in the equations above, we can write

$\sin2x+\cos2x=\sqrt2\sin\left(2x+\dfrac\pi4\right)=\pm1$

Then in the first case,

$\sqrt2\sin\left(2x+\dfrac\pi4\right)=1\implies\sin\left(2x+\dfrac\pi4\right)=\dfrac1{\sqrt2}$

$\implies2x+\dfrac\pi4=\dfrac\pi4+2n\pi\text{ or }\dfrac{3\pi}4+2n\pi$

(where $n$ is any integer)

$\implies2x=2n\pi\text{ or }\dfrac\pi2+2n\pi$

$\implies x=n\pi\text{ or }\dfrac\pi4+n\pi$

and in the second,

$\sqrt2\sin\left(2x+\dfrac\pi4\right)=-1\implies\sin\left(2x+\dfrac\pi4\right)=-\dfrac1{\sqrt2}$

$\implies2x+\dfrac\pi4=-\dfrac\pi4+2n\pi\text{ or }-\dfrac{3\pi}4+2n\pi$

$\implies2x=-\dfrac\pi2+2n\pi\text{ or }-\pi+2n\pi$

$\implies x=-\dfrac\pi4+n\pi\text{ or }-\dfrac\pi2+n\pi$

Then the solutions that fall in the interval $[0,2\pi)$ are

$x=0,\dfrac\pi4,\dfrac\pi2,\dfrac{3\pi}4,\pi,\dfrac{5\pi}4,\dfrac{3\pi}2,\dfrac{7\pi}4$

5 0

3 years ago

Read 2 more answers

F(x) =2x-5 and g(x) =x+52 find f(g(x)

irga5000 [103]

If f(x) = 2x - 5 and g(x) = x + 52, then f(g(x)) can be deduced by placing g(x) in the spot of x in the f(x) equation as follows:

f(g(x)) = 2(g(x)) - 5

Since we know g(x) = x + 52, let's plug it in:

f(g(x)) = 2(x + 52) - 5
f(g(x)) = 2x + 104 - 5
f(g(x)) = 2x + 99

4 0

2 years ago

Read 2 more answers

Find the area of the triangle

Ray Of Light [21]

For this questions you need to memorize formula of triangle area. for question 5, just substitute the value into the formula. for Q6 you need to use pythagorean theorem formula to find the lenght of each triangle that i already seperated

4 0

3 years ago

2. After the relay race, Larry, Curly, and Moe went to the

jarptica [38.1K]

Using proportions, it is found that each of the 6 people got $0.5.

<h3>Proportions:</h3>

This question is solved by <em>proportions</em>, using a rule of three.

$3.00 is shared between 6 people, which are Larry, Curly, Moe, Alvin, Simon and Theodore. How much did each people(1 person) get?

The <em>rule of three</em> is:

$3.00 - 6 people

$x - 1 person

Applying cross multiplication:

$6x = 3$

$x = \frac{3}{6}$

$x = 0.5$

Each of the 6 people got $0.5.

To learn more about proportions, you can take a look at brainly.com/question/24372153

7 0

2 years ago

In a test (+5) marks are given for every correct answer and (-2) marks are given for every incorrect answer. Radhika answered al

kvv77 [185]

Answer:

10 incorrect answers

Step-by-step explanation:

From the information given, you can say that 5 marks for the number of correct answers minus two marks for the number of incorrect answers is equal to 30 that is the score that Radhika got:

(5*10)-2x= 30, where x is the number of incorrect answers.

Now, you can solve for x:

50-2x=30

50-30=2x

20=2x

x=20/2

x=10

According to this, the answer is that they attempted 10 incorrect answers.

4 0

3 years ago