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xenn [34]
3 years ago
9

Running at their respective constant rates, Machine X takes 2 days longer to produce w widgets than Machine Y. At these rates, i

f the two machines together produce 5 4 w widgets in 3 days, how many days would it take Machine X alone to produce 2w widgets.
A. 4B. 6C. 8D. 10E. 12
Mathematics
1 answer:
Doss [256]3 years ago
5 0
C. Hope this helps :)
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If <img src="https://tex.z-dn.net/?f=tan%20%28x%29%20%3D%20%5Cfrac%7B5%7D%7B12%7D" id="TexFormula1" title="tan (x) = \frac{5}{12
Alekssandra [29.7K]

Explanation:

First, we need to find the values of the sine and cosine of x knowing the value of tan x and x being in the 3rd quadrant. Since tan x = 5/12, using Pythagorean theorem, we know that

\sin x = -\frac{5}{13}\;\;\text{and}\;\;\cos x = -\frac{12}{13}

Note that both sine and cosine are negative because x is in the 3rd quadrant.

Recall the addition identities listed below:

\sin(\alpha + \beta) = \sin\alpha\sin\beta + \cos\alpha\cos\beta

\Rightarrow \sin(180+x) = \sin180\sin x + \cos180\cos x

\;\;\;\;\;\;= -\sin x = \dfrac{5}{13}

\cos(\alpha - \beta) = \cos\alpha \cos\beta + \sin\alpha \sin\beta

\Rightarrow \cos(180 - x) = \cos180\cos x + \sin180\sin x

\;\;\;\;\;\;=-\cos x = \dfrac{12}{13}

\tan(\alpha - \beta) = \dfrac{\tan\alpha - \tan\beta}{1 + \tan\alpha\tan\beta}

\Rightarrow \tan(360 - x) = \dfrac{\tan 360 - \tan x}{1 + \tan 360 \tan x}

\;\;\;\;\;\;= -\tan x = -\dfrac{5}{12}

Therefore, the expression reduces to

\sin(180+x) + \tan(360-x) + \frac{1}{\cos(180-x)}

\;\;\;\;\;= \left(\dfrac{5}{13}\right) + \left(\dfrac{5}{12}\right) + \dfrac{1}{\left(\frac{12}{13}\right)}

\;\;\;\;\;= \dfrac{49}{26}

5 0
2 years ago
Aline crosses the coordinates (-4,4) and (2.-5). What is the slope<br> of the line?
lisabon 2012 [21]

Answer:

Step-by-step explanation:

Use the slope formula:

m = \frac{y2 -y1}{x2 - x1}

where m = slope

Given the coordinates

(-4, 4) ---> this means x1 = -4 , y1 = 4

(2, -5) ---> this means x2 = 2 , y2 = -5

Substitute these values into the slope formula:

m = \frac{y2 -y1}{x2 - x1}

m = \frac{-5 -4}{2 - (-4)}  = \frac{-9}{2+4} = \frac{-9}{6} = \frac{-3}{2}

4 0
3 years ago
Please I need an answer
Vitek1552 [10]
The answer is 416 quarts please thank me and put brainliest
4 0
3 years ago
Read 2 more answers
The opposite of 1 is -1.<br><br><br><br>True False<br><br>Will mark as brainliest if correct
DedPeter [7]
Technically it is true
5 0
3 years ago
What 2+2.... I need help lololololol.olo
xxMikexx [17]

Answer:

4

Step-by-step explanation:

2+2 is 4

5 0
3 years ago
Read 2 more answers
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