All categories

3 years ago

The angles shown below are supplementary: what is the value of x

Mathematics

2 answers:

Scorpion4ik [409]3 years ago

6 0

Answer:

x=12

Step-by-step explanation:

Supplementary angles add up to 180 degrees.

10x+60=180

Subtract 60 from both sides:

10x=120

Divide 10 to both sides:

x=12

Annette [7]3 years ago

5 0

Answer:

$x=12$

Step-by-step explanation:

By definition, supplementary angles add up to 180 degrees. Therefore, we can set up the follow equation to solve for $x$ :

$10x+60=180,\\10x=120,\\x=\boxed{12}$

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The circumference of a circle is 24 feet. What is the approximate length of the radius? Round to the nearest tenth

jarptica [38.1K]

<h3>given:</h3>

circumference= 24 feet

the radius of the circle.

<h3>solution:</h3>

$c = 2\pi \: r$

$r = \frac{c}{2\pi}$

$r = \frac{24}{2 \times \pi}$

$r = 3.81972$

$r = 3.8 \: ft$

therefore, the radius of the circle is 3.8 feet.

4 0

2 years ago

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A group of 14 and 15-year-olds were polled on their favorite season. The results are shown in the frequency table.

Yakvenalex [24]

Answer:

1. 4 categories are shown in the rows.

2. 2 categories are shown in the columns.

3. The number of 14 year olds that consider winter their favorite season is 12.

4. Total number of people polled is 82.

Step-by-step explanation:

The question is to test the ability of a student to group data using a frequency table accurately, and make appropriate deductions from it. Consider the attachment for the accurate table required to answer the given questions.

If the given information is grouped as required, thus the answers to the questions are:

i. 4 categories are shown in the rows.

ii. 2 categories are shown in the columns.

iii. The number of 14 year olds that considers winter their favorite season is 12.

iv. Total number of people polled is 82.

5 0

4 years ago

What is the volume of thiss figure ?

allochka39001 [22]

Answer:

18 ft³

Step-by-step explanation:

7 0

3 years ago

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What combination of transformations is shown below

Kay [80]

Answer:

rotation then translation

Step-by-step explanation:

I took it and I got it right

8 0

3 years ago

A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of t

Makovka662 [10]

Answer:

132.233 ft2

Step-by-step explanation:

Let's call the width of the rectangle 'w' and the length 'x'. So the area of the semicircle is:

$A_1 = \pi*radius^2/2$

$A_1 = \pi*(w/2)^2/2$

$A_1 = \pi/8*w^2$

And the area of the rectangle is:

$A_2 = w*x$

If the perimeter of the window is 41 feet, we have:

$Perimeter = length + 2*width + \pi*radius$

$41 = x + 2*w + \pi*w/2$

$x = 41 - w(2 + \pi/2)$

Now, the equation for the total area of the window is:

$A = A_1 + A_2 = \pi/8*w^2 + w*x$

$A = \pi/8*w^2 + w*(41 - w(2 + \pi/2))$

$A = (\pi/8-2 - \pi/2)*w^2 + 41w = -3.1781w^2 + 41w$

To find the maximum area, we can find the x-coordinate of the vertex of the quadratic equation:

$x\_vertex = -b / 2a = -41 / (-3.1781*2) = 6.45$

So the width that gives us the maximum area of the window is 6.45 feet, and the area will be:

$A = -3.1781w^2 + 41w = -3.1781*(6.45)^2 + 41*6.45 = 132.233\ ft^2$

3 0

3 years ago