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3 years ago

Twice a number increased by 11 is equal to 32 less than three times the number. What is the number?

Mathematics

1 answer:

MariettaO [177]3 years ago

6 0

Answer:

21/5 or 4.2

Step-by-step explanation:

2x+11=32-3x

5x+11=32

5x=21

x=21/5

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Cos^2x+cos^2(120°+x)+cos^2(120°-x)<br>i need this asap. pls help me

o-na [289]

Answer:

$\frac{3}{2}$

Step-by-step explanation:

Using the addition formulae for cosine

cos(x ± y) = cosxcosy ∓ sinxsiny

---------------------------------------------------------------

cos(120 + x) = cos120cosx - sin120sinx

= - cos60cosx - sin60sinx

= - $\frac{1}{2}$ cosx - $\frac{\sqrt{3} }{2}$ sinx

squaring to obtain cos² (120 + x)

= $\frac{1}{4}$ cos²x + $\frac{\sqrt{3} }{2}$ sinxcosx + $\frac{3}{4}$ sin²x

--------------------------------------------------------------------

cos(120 - x) = cos120cosx + sin120sinx

= -cos60cosx + sin60sinx

= - $\frac{1}{2}$ cosx + $\frac{\sqrt{3} }{2}$ sinx

squaring to obtain cos²(120 - x)

= $\frac{1}{4}$ cos²x - $\frac{\sqrt{3} }{2}$ sinxcosx + $\frac{3}{4}$ sin²x

--------------------------------------------------------------------------

Putting it all together

cos²x + $\frac{1}{4}$ cos²x + $\frac{\sqrt{3} }{2}$ sinxcosx + $\frac{3}{4}$ sin²x + $\frac{1}{4}$ cos²x - $\frac{\sqrt{3} }{2}$ sinxcosx + $\frac{3}{4}$ sin²x

= cos²x + $\frac{1}{2}$ cos²x + $\frac{3}{2}$ sin²x

= $\frac{3}{2}$ cos²x + $\frac{3}{2}$ sin²x

= $\frac{3}{2}$ (cos²x + sin²x) = $\frac{3}{2}$

5 0

2 years ago

There are 36 windows in the folsom’ house. the number of window is 3 times as many as the number of closets and 4 more than the

xz_007 [3.2K]

Answer:

Step-by-step explanation:

36x4=144

36x3=78

144-78=66

8 0

3 years ago

A test score of 48.4 on a test having a mean of 66 and a standard deviation of 11. Find the z-score corresponding to the given

Mariulka [41]

Answer:

A. -1.6; not significant

Step-by-step explanation:

The z-score of a data set that is normally distributed with a mean of $\bar x$ and a standard deviation of $\sigma$ , is given by:

$z=\frac{x-\bar x}{\sigma}$ .

From the question, the test score is: $x=48.4$ , the mean is $\bar x=66$ , and the standard deviation is $\sigma =11$ .

We just have to plug these values into the above formula to obtain:

$z=\frac{48.4-66}{11}$ .

This simplifies to: $z=\frac{-17.6}{11}$ .

$z=-1.6$ .

We can see that the z-score falls within two standard deviations of the mean.

Since $-2\le-1.6\le2$ the value is not significant.

The correct answer is A. -1.6; not significant

3 0

3 years ago

A. cos y<br> b. tan x<br> c. sin y<br> d. tan y

borishaifa [10]

Check the picture below, recall your SOH, CAH, TOA

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2 years ago

Evaluate the expression m=10 2m+10

Eddi Din [679]

The answer is 30
because (2)(10) + 10
20+10=30
the 10 came from the m!!

8 0

2 years ago