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2 years ago

What is the value of x

Mathematics

1 answer:

Natali [406]2 years ago

4 0

Answer:

x = 25

Step-by-step explanation:

The sum of the angles in a triangle are equal to 180 degrees. Since we know the value of one angle is 90 degrees, subtract 90 from 180 to get 90. Now we know the sum of the other two angles must equal 90 degrees. If we add the x and 2x + 15 together, we get 3x + 15 = 90. Subtract 15 from both sides to get 3x = 75. Divide both sides by 3 to get x = 25.

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What is cos (x)? 48/58 58/48 26/58 58/26

Evgen [1.6K]

We have to calculate the length of the missing side.
Use the Pythagorean theorem:

$a^2+32^2=58^2\\\\a^2+1024=3364\ \ \ |-1024\\\\a^2=2340\to a=\sqrt{2340}\\\\a=\sqrt{36\cdot65}\\\\a=6\sqrt{65}$

$\cos x=\dfrac{6\sqrt{65}}{58}=\dfrac{3\sqrt{65}}{29}$

I think. Your answers to choice are wrong.

8 0

3 years ago

If a rectangle is altered by increasing its length by 20 percent and its width by 10 percent, its area increases by a percent. W

aleksklad [387]

Answer:

Step-by-step explanation:

Remember that the formula for the area of a rectangle is:

$A=lw$

Where l is the our length and w is our width.

If we increase our length by 20%, this means that we add 20% or 0.2 of our old length to our old length. So, our new length will be:

$l_{new}=l+.2l$

Combine like terms:

$l_{new}=1.2l$

Similarly, if we increase our width by 10%, this means that we add 10% or 0.1 of our old width to our old width. So, our new width is:

$w_{new}=0.1w+w$

Combine like terms:

$w_{new}=1.1w$

Therefore, our new area will be:

$A_{new}=(l_{new})(w_{new})$

Substitute 1.2l and 1.1w. This yields:

$A_{new}=1.2l(1.1w)$

Multiply:

$A_{new}=1.32lw$

Our old area is:

$A_{old}=lw$

So, our area increased by a factor of 1.32.

This is the same as 32% of our old area.

So, our answer is D.

And we're done!

5 0

3 years ago

A magic carpet is made with three different colors of yarn. The ratio of each color is shown below. 10 parts gold yarn, 7 parts

serious [3.7K]

Answer: 22.5 yards

Step-by-step explanation:

There are a total of 20 parts yarn. This means that 3/20 of the carpet is silver. So in order to compare this to the 150 meters of total yarn, you would set up this equation:

3/20 = x/150

Next, you cross multiply:

3*150 = 20*x or simplified would be 450 = 20x

Next, you divide both sides by 20 to get x by itself.

450/20 = 22.5, so x is equal to 22.5

This means you have 22.5 yards of silver in the carpet.

7 0

3 years ago

The management of a relatively new social networking website named BooglePlus is conducting a pilot study comparing use of its o

zavuch27 [327]

Answer:

0.0623 ± ( 2.056 )( 0.0224 ) can be used to compute a 95% confidence interval for the slope of the population regression line of y on x

Step-by-step explanation:

Given the data in the question;

sample size n = 28

slope of the least squares regression line of y on x or sample estimate = 0.0623

standard error = 0.0224

95% confidence interval

level of significance ∝ = 1 - 95% = 1 - 0.95 = 0.05

degree of freedom df = n - 2 = 28 - 2 = 26

∴ the equation will be;

⇒ sample estimate ± ( t-test) ( standard error )

⇒ sample estimate ± ( $t_{\alpha /2, df$ ) ( standard error )

⇒ sample estimate ± ( $t_{0.05 /2, 26$ ) ( standard error )

⇒ sample estimate ± ( $t_{0.025, 26$ ) ( standard error )

{ from t table; ( $t_{0.025, 26$ ) = 2.055529 = 2.056

so we substitute

⇒ 0.0623 ± ( 2.056 )( 0.0224 )

Therefore, 0.0623 ± ( 2.056 )( 0.0224 ) can be used to compute a 95% confidence interval for the slope of the population regression line of y on x

5 0

3 years ago

The following shapes are similar. Set up equation and solve for the variables

koban [17]

Answer:

x=10

Step-by-step explanation:

For number 19.

The equation you get is:

X+2=6(2) this is because 5x2=10, so you have to do the same here.

so, X+2=12

-2 from both sides and you get

x=10

5 0

3 years ago