In the diagram, the radius of the outer circle is 2x em and the radius of the inside circle is 6 cm. The area of the shaded region is 220 cm? What is the value of x2
Answers
Answer:
Answer: 8 (second choice)
Step-by-step explanation:
Area of a Circle
Given a circle of radius r, the area is calculated by the formula:
[tex]A=\pi\ r^2[/tex]
There are two circles in the diagram. The outer circle has a radius of r1=2x, thus its area is:
[tex]A_1=\pi\ (2x)^2[/tex]
The interior circle has a radius of r2=6 cm, thus its area is:
[tex]A_2=\pi\ 6^2=36\pi[/tex]
The shaded area is obtained by subtracting A1-A2:
[tex]A=\pi\ (2x)^2-36\pi[/tex]
The value of the shaded area is given as 220π cm2. Equating:
[tex]\pi\ (2x)^2-36\pi=220\pi[/tex]
Dividing by π:
[tex](2x)^2-36=220[/tex]
Adding 36:
[tex](2x)^2=220+36=256[/tex]
Taking square root:
[tex]2x=\sqrt{256}=16[/tex]
Dividing by 2:
x = 8 cm
Answer: 8 (second choice)
Related Questions
Larry is collecting one coin each year from 1952 to 2000. If Larry has collected 40% of the coins, how many does he have left to collect?
Answers
Answer:
29 coins
Step-by-step explanation:
Larry needs to collect [tex]60\%[/tex] of the coins still [tex]0.6[/tex]. [tex]2000-1952=48(+1)[/tex] because you're including 1952 [tex]=49[/tex]. [tex]49×0.6=29.4≈49[/tex].
what is the solution or -3y+1≥7
Answers
the answer is
[tex]y \leqslant - 2[/tex]
Which of the following statements could be translated to the equation n - 5 = -2?
A number less than five equals negative two.
The difference between a number and five is negative two.
If five is subtracted from a number, the result is two.
Five less a number is equal to two.
Answers
Answer:
its the first one i believe
Answer:
I believe it's, The difference between a number and five is negative two.
Step-by-step explanation:
What is the result when 4x^4+17x^3+10x^2-7x+184x
4
+17x
3
+10x
2
−7x+18 is divided by x+2x+2?
Answers
Answer:
-5x+18/x+2
Step-by-step explanation:
I'm pretty sure it's the answer
What is the distance between points (7,2) and (-4,2) on the coordinate plane?
help? please? maybe?
Answers
Choose the equation that shows the relationship of 80%, x, and 100.
Answers
Answer:
chipset buy showroom de en inglés
The number of fish in a lake decreased by 25% between last year and this year. Last year there were 60 fish in
the lake. What is the population this year? If you get stuck, consider drawing a diagram.
There are
fish in the pond.
HELLPPP
Answers
Answer:
theres
4
Step-by-step explanation:
HELP PLEASE PLEASE!!!
Answers
2.) area of US paper = 603.22cm
area of Europe paper = 623.7cm
therefore the standard sheet of Europe paper has a greater area
hope this helps :)
Mr. Setterloff drives 756 miles in 12 hours. How far does he drive in 1 hour?
Answers
Answer:
He drives 63 miles in 1 hour
Step-by-step explanation:
756/12= 63
WILL GIVE BRILLIANTIEST!
A small town voted to decide if a road should be expanded from two lanes to four lanes. The two-way table below shows the
results of the vote.
Favor
Oppose
Neutral
Total
33
12
46
91
45
15
36
96
Age
18-25
Age
26-40
Age
40+
Total
10
29
24
63
88
56
106
250
Which correlation does the two-way table suggest?
A Voters age 40 and over are least likely to favor road expansion.
B. The majority of the voters are most likely to favor road expansion
c. Voters between the ages of 26 and 40 are most likely to oppose road expansion
D.
Voters between the ages of 18 and 25 are least likely to favor road expansion
Answers
Answer:
the answer is D because it makes the most sense
Answer:
A.......,..............
Kendra plans to go to the gym on 15 different days this month.
• A one-day pass to the gym is $3.75.
• A monthly membership to the gym is $39.00.
How much money will Kendra save by buying a monthly pass?
$17.25
$16.75
$16.25
$15.75
Answers
Answer:4 answer
Step-by-step explanation:
z
Which of the following congruency statements is
correct?
2.4 cm
108
2.4 cm
O AYZX - ABCD
Y
36°
36
Ο ΔΥΖX2 ΔDCB
3.8 cm
Ο ΔZXΥ: ΔDCB
Х
O AYXZ – ACDB
B
3.8 cm
136
2.4 cm
36°
С
1089
2.4 cm
D
Orange
Answers
Answer:
the answer is c
Step-by-step explanation:
Consider the polynomial 9x2 – 16.
What is the value of ac?
What is the value of b?
What two numbers multiply to get ac and add to get b?
The factored form of 9x2 – 16 is
Answers
Step-by-step explanation:
The value of ac together is 16(9x^2) or 144x^2
The value of B is zero since there is no B
(b is x, ( note not x^2, but only 1x)
Answer:
What is the value of ac? -144
What is the value of b? 0
What two numbers multiply to get ac and add to get b? -12 and 12
The factored form of 9x² - 16 is (3x-4)(3x+4)
Step-by-step explanation:
Dude trust me
Please help!! I will be marking brainliest
Answers
Answer:
DVDs= $16.2
CDs = $11.9
Cassettes = $11.4
Step-by-step explanation:
The students in Jeanette's grade voted to select a guest speaker. 50% of the students voted for a famous athlete. If there are 22 students in Jeanette's grade, how many students voted for the athlete?
Answers
what is 2 +2 this 65 points.
Answers
Answer:
4
Step-by-step explanation:
2 + 2 = 4 lol
Arithmetic sequence of -10,8,26
Answers
Answer:
the sequence is going up by 18
Lines a b c and d are shown below. Which lines are parallel? Which line are perpendicular? Explain and jutsify your answer using slopes
Answers
Answer:
Lines A and C are parallel
Lines B and D are perpendicular
Step-by-step explanation:
Given
See attachment for lines A to D
Required
Determine the parallel and perpendicular lines
To start with, we calculate the slope of each line.
Line A
The points on line A are:
[tex](x_1,y_1) = (3,-4)[/tex]
[tex](x_2,y_2) = (-1,2)[/tex]
Calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{2 - (-4)}{-1 - 3}[/tex]
[tex]m = \frac{2 +4}{-4}[/tex]
[tex]m = \frac{6}{-4}[/tex]
[tex]m_1 = -\frac{3}{2}[/tex]
Line B
[tex](x_1,y_1) = (-1,8)[/tex]
[tex](x_2,y_2) = (2,6)[/tex]
Calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{6 - 8}{2 -(-1)}[/tex]
[tex]m = \frac{-2}{2 +1}[/tex]
[tex]m_2 = -\frac{2}{3}[/tex]
Line C
[tex]y - 9 = -\frac{3}{2}(x + 8)[/tex]
Open bracket
[tex]y - 9 = -\frac{3}{2}x -\frac{3}{2}* 8[/tex]
[tex]y - 9 = -\frac{3}{2}x -3* 4[/tex]
[tex]y - 9 = -\frac{3}{2}x -12[/tex]
Make y the subject
[tex]y = -\frac{3}{2}x -12+9[/tex]
[tex]y = -\frac{3}{2}x -3[/tex]
The slope intercept of an equation is: [tex]y = mx + b[/tex]
Where
[tex]m = slope[/tex]
By comparison:
[tex]m_3 = -\frac{3}{2}[/tex]
Line D
[tex]12x - 8y = 40[/tex]
Subtract 12x from both sides
[tex]12x-12x - 8y = -12x+40[/tex]
[tex]- 8y = -12x+40[/tex]
Divide through by -8
[tex]\frac{- 8y}{-8} = \frac{-12x}{-8}+\frac{40}{-8}[/tex]
[tex]y= \frac{12x}{8}-\frac{40}{8}[/tex]
[tex]y= \frac{3}{2}x-5[/tex]
The slope intercept of an equation is: [tex]y = mx + b[/tex]
Where
[tex]m = slope[/tex]
By comparison:
[tex]m_4 = \frac{3}{2}[/tex]
So, the slopes of the lines are:
[tex]m_1 = -\frac{3}{2}[/tex] [tex]m_2 = -\frac{2}{3}[/tex] [tex]m_3 = -\frac{3}{2}[/tex] [tex]m_4 = \frac{3}{2}[/tex]
Lines with the same slope are parallel.
So:
Lines A and C with slope of [tex]-\frac{3}{2}[/tex] are parallel
Lines with the following relationship are perpendicular:
[tex]m * M = -1[/tex]
Lines B and D are perpendicular because:
[tex]-\frac{2}{3} * \frac{3}{2} = -1[/tex]
[tex]-\frac{6}{6} = -1[/tex]
[tex]-1 = -1[/tex]
Geometry pls help thanks
Answers
Answer:
x=30
Step-by-step explanation:
it is an equilateral triangle, so all angles are the same. each angle is 60 degrees. 60/2 is 30, so 30 degrees is the answer.
Solve 3X-5 = 9.
Ox= -3
Ox= 2
Ox= 7
OX= 8
NEED HELP ASAP
Answers
Answer:
The value of x = 14/3
Step-by-step explanation:
Given the equation
[tex]3x-5 = 9[/tex]
Add 5 to both sides
[tex]3x-5+5=9+5[/tex]
Simplify
[tex]3x=14[/tex]
Divide both sides by 3
[tex]\frac{3x}{3}=\frac{14}{3}[/tex]
Simplify
[tex]x=\frac{14}{3}[/tex]
Therefore, the value of x = 14/3
Note: It seems you may have missed entering the correct answer choice as the value of x = 14/3 is not mentioned in your answer choices.
i don’t understand anything online school is hard.
Answers
use the pythagorean therom
WILL GIVE BRAINIEST!!!!!!
Answers
Answer:
The answer is y = x
Hope this helps!
[tex]9z + 6j = 98[/tex]
Answers
Answer:
Step-by-step explanation:
What variable are you solving for?
Help me plssss pls help plsss
Answers
Answer:
Step-by-step explanation:
5) Diameter of the circle = 2 * 11.5 = 23 in
6) Radius of the circle = 11.5 in
7) Circumference = πd = 3.142 * 23 = 72.26 in
8) Area = πr² = 3.142 * 11.5 *11.5 = 415.48 in²
If a 176-ounce fish consumes a 112-ounce fish in a single gulp, how much does the first fish weigh-in tons?
Answers
Explanation
176+112= 288 ounces
288/32000=0.009
32000 oz= 1 ton
A rock is thrown down from a cliff that is 180 m high. The function
h(t) = -5t^2 – 10t + 180 gives the approximate height of the rock
above the water, where h(t) is the height in metres and t is the time
in seconds. When will the rock reach a ledge that is 105 m above
the water?
Answers
Answer:
t = 3
Step-by-step explanation:
105 = -5t^2 -10t + 180
-75 = -5t^2 -10t
15 = t^2 +2t
t^2 +2t -15 = 0
(t+5)(t-3)
t = -5, 3
There's no such thing as negative time so you use the positive answer
Two fair dice are rolled at the same time. What is the probability that one die will show 3 and the other will show 4? A. 1/36
B. 1/18
C. 1/12
D. 1/6
Answers
Answer:
1/36
Step-by-step explanation:
There are 6 numbers on a die. You have a 1/6 chance of rolling a 3 and a 1/6 chance of rolling a 4. 1/6 times 1/6 = 1/36.
Simplify the expression: 9-2X + 8 + x + 5x
Answers
Answer:
4x + 17
Step-by-step explanation:
9 - 2x + 8+ x + 5x
Add/Subtract the values with variables together and the same case for the values without any variables.
5x + x - 2x = 4x
9 + 8 = 17
So you'll end up with the following,
4x + 17
what is the answer to this question
Answers
Answer:
the height is 4
Step-by-step explanation:
it is a right triangle and also a perfect 3-4-5 right triangle
[tex] {3}^{2} + {h}^{2} \: equals \: {5}^{2} [/tex]
[tex]9 + {h}^{2} \: eqauls \: 25[/tex]
subtract 9 from 25
[tex] {h}^{2} \: equals \: 16[/tex]
then you square root 16
[tex] \sqrt{16} [/tex]
and now you height is 4
The graph of a proportional relationship contains the point (8,4). What is the corresponding equation? Enter your answer as a fraction in simplest form by filling in the boxes.
y= — x
Answers
Given:
The graph of a proportional relationship contains the point (8,4).
To find:
The corresponding equation.
Solution:
If y in directly proportional to x, then
[tex]y\propto x[/tex]
[tex]y=kx[/tex] ...(i)
Where, k is the constant of proportionality.
The graph of a proportional relationship contains the point (8,4).
Putting x=8 and y=4 in (i), we get
[tex]4=k(8)[/tex]
[tex]\dfrac{4}{8}=k[/tex]
[tex]\dfrac{1}{2}=k[/tex]
Putting [tex]k=\dfrac{1}{2}[/tex] in (i), we get
[tex]y=\dfrac{1}{2}x[/tex]
Therefore, the required equation is [tex]y=\dfrac{1}{2}x[/tex].