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goldenfox [79]
3 years ago
12

At the gym, Tika spends twice as much time doing aerobics than weight training. She stretches for one fifth of the time she spen

ds on weight training. Let w be the amount of time Tika spends on weight training. Which expression represents her total workout?
Mathematics
1 answer:
Dafna1 [17]3 years ago
8 0

Answer:

Her total workout is 2w+w+\frac{w}{5}.

Step-by-step explanation:

Consider the provided information.

Let w be the amount of time Tika spends on weight training.

Tika spends twice as much time doing aerobics than weight training.

It means she spends 2w time doing aerobics.

She stretches for one-fifth of the time she spends on weight training.

It means she spends \frac{w}{5} time for stretches.

The total workout time is:

2w+w+\frac{w}{5}

Hence, her total workout is 2w+w+\frac{w}{5}.

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For positive acute angles A and B, it is known that cos A= 20/29 and tan B= 11/60. Find the value of cos(A + B) in simplest form
jek_recluse [69]

Answer:

\displaystyle \cos(A + B) =\frac{969}{1769}

Step-by-step explanation:

We are given that:

\displaystyle \cos A=\frac{20}{29}\text{ and } \tan B=\frac{11}{60}

Where A and B are positive acute angles.

And we want to find cos(A + B).

Recall that cosine is the ratio of the adjacent side to the hypotenuse. Using this information, find the opposite side with respect to Angle A:

o=\sqrt{29^2-20^2}=21

Tangent is the ratio of the opposite side to the adjacent side. Find the hypotenuse with respect to Angle B:

h=\sqrt{11^2+60^2}=61

In summary:

With respect to Angle A, the adjacent side is 20, opposite is 21, and the hypotenuse is 29.

With respect to Angle B, the adjacent side is 60, the opposite is 11, and the hypotenuse is 61.

We can rewrite our expression as:

\displaystyle \cos(A+B)=\cos A\cos B-\sin A\sin B

Using the above information, substitute in the appropriate values. Note that since A and B are positive acute angles, all trigonometric values will be positive. Hence:

\displaystyle \cos(A + B)=\left(\frac{20}{29}\right)\left(\frac{60}{61}\right)-\left(\frac{21}{29}\right)\left(\frac{11}{61}\right)

Simplify:

\displaystyle \cos(A + B) =\frac{1200-231}{1769}=\frac{969}{1769}

3 0
3 years ago
F. 15 times as much as 1 fifth of 12.
Vinvika [58]
(1/5×12)×15
12/5×15
12×15=180
180/5=36
the is 36
3 0
3 years ago
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marusya05 [52]

Answer:

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Step-by-step explanation:

Given the expression 5x(1+3x)

Generally, according to the distribution rule,

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A is distributed over B and C

Similarly,

5x(1+3x)

= 5x(1) + 5x(3x)

= 5x + 15x²

Hence the expression required is 5x + 15x²

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Answer: Gordon types 60 words per minute

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victus00 [196]

Answer:

D

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