Hi everyone, so I was doing some math homework and I got stuck. Please help me with these two questions (numbers 7 and 8). Thank you!
I'll also try my hardest to help you in return!
Answers
Answer:
7). x = 6, [tex]\frac{14}{3}[/tex]
8). x = 2
Step-by-step explanation:
7). Area of a circle = πr²
Here 'r' = radius of the circle
Area of the shaded region of the circle = Area of the large circle - Area of the small circle
= π(x)² - [tex]\pi (\frac{x}{2})^2[/tex]
= [tex]\pi x^{2} -\pi (\frac{x^2}{4})[/tex]
= [tex]\pi x^{2}(1-\frac{1}{4})[/tex]
= [tex]\frac{3\pi x^{2} }{4}[/tex] in²
If area of the shaded region is (8πx - 21π) in²
[tex]\frac{3\pi x^{2} }{4}=8\pi x - 21\pi[/tex]
[tex]\frac{3x^2}{4}=8x-21[/tex]
3x² = 32x - 84
3x²- 32x + 84 = 0
3x² - 14x - 18x + 84 = 0
x(3x - 14) - 6(3x - 14) = 0
(x - 6)(3x - 14) = 0
x = 6, [tex]\frac{14}{3}[/tex]
8). Area of the shaded region = Area of the largest circle - Area of the smaller semicircle - Area of the smallest semicircle
Area of the largest circle = π(2x + 2x)²
= 16πx²
Area of the smaller semicircle = [tex]\frac{1}{2}\pi (3x)^{2}[/tex]
= 4.5(πx²)
Area of the smallest semicircle = [tex]\frac{1}{2}\pi (2x)^{2}[/tex]
= 2πx²
Now area of he shaded region = 16πx² - [4.5(πx²) + 2πx²]
= 16πx² - 6.5πx²
= 9.5πx² mm²
If the area of the shaded region = 12πx + 14π
12πx + 14π = 9.5πx²
12x + 14 = 9.5x²
9.5x² - 12x - 14 = 0
19x² - 24x - 28 = 0
19x² - 38x + 14x - 28 = 0
19x(x - 2) + 14(x - 2) = 0
(19x + 14)(x - 2) = 0
x = [tex]-\frac{14}{19},2[/tex]
But the radius o a circle can't be negative.
Therefore, x = 2 will be the answer.
Related Questions
A company produces boxes of DVD's at a rate of 52 boxes per hour. They begin to produce boxes when they first open for the day and after three hours have 404 boxes in stock. How many boxes were in stock when they opened?
Answers
Answer: 248 boxes
Step-by-step explanation:
They produce boxes at a rate of 52 boxes an hour yet after only 3 hours they had 404 boxes.
The number they were supposed to have in 3 hours is:
= 52 * 3
= 156 boxes
They instead had 404 so the rest must have been there when they opened:
= 404 - 156
= 248 boxes
Look at this diagram.
If KM and NP are parallel lines and m<MLJ = 42°, what is m<MLO?
____°
Answers
9514 1404 393
Answer:
138°
Step-by-step explanation:
The angles of the linear pair are supplementary.
∠MLO = 180° -∠MLJ = 180° -42°
∠MLO = 138°
Answer:
angle MLO =180° - angle MLJ =(180°-42°)= 138°
138° is the right answer.18-12x=-2(6x-9)
fast please
Answers
Answer:
The answer is 18 -12x = -12x + 18
Arlene has raised $56 for her class field trip. This is $14
more than three times the amount Adam has raised.
Which equation could you use to find how much money
Adam has raised?
Answers
Assuming Adams amount is x, three times his amount will be 3x. $14 more than the times Adam's amount will be 14 +3x.
Therefore if Arlene's money is $56 which is $14 more than three times Adam's amount, then the equation will be ;
14+3x=56
I AM GIVING TEN POINTS I BEG YOU NOT TO SCAM PLEASE I NEED HELP JHERKWJFIOHWHOFEWHRHEFWH
Solve the system of equations using the substitution method. Make sure to check your solution.
y = 3x + 2
-4x + 4y = 16
In the blanks below, type just the number for the x-coordinate in blank 1 and just the number for the y-coordinate in blank 2.
x-coordinate:
y-coordinate:
Answers
Answer:
y = 5
x = 1
Step-by-step explanation:
y = 3x + 2
-4x + 4(3x+2)=16
y=3x+2
-4x+(4*3x+4*2)=16
x = 1
y = 5
Answer:
x-coordinate = 1
y-coordinate = 5
Step-by-step explanation:
By using the substitution method, we substitute either x-term or y-term in any equation.
the term must be only the subject in order to substitute in.
Our equation that has only the subject is the first equation.
Substitute y = 3x+2 in the second equation.
[tex] - 4x + 4(3x + 2) = 16[/tex]
Distribute 4 in 3x+2
[tex] - 4x + 12x + 8 = 16[/tex]
The constant cannot add up or subtract with the variable. Therefore, move 8 to subtract 16 on another side.
[tex]12x - 4x = 16 - 8 \\ 8x = 8[/tex]
Move 8 to divide 8 on the another side.
[tex]x = \frac{8}{8} \\ x = 1[/tex]
Our next goal is to find the y-value by substituting x = 1 in any given equation.
I will substitute x = 1 in the first equation. (You can substitute in the second equation if you want.)
[tex]y = 3(1) + 2 \\ y = 3 + 2 \\ y = 5[/tex]
Answer Check
Checking is to make sure that we have got the right answer. We can check the answer by substituting y-value and x-value in both equations.
[tex]x = 1 \\ y = 5[/tex]
First Equation Check
[tex]5 = 3(1) + 2 \\ 5 = 3 + 2 \\ 5 = 5[/tex]
The equation is true. Therefore, the answer is correct for first equation.
Second Equation Check
[tex] - 4(1) + 4(5) = 16 \\ - 4 + 20 = 16 \\ 16 = 16[/tex]
The equation is true. Both equations are true for x = 1 and y = 5.
Therefore, the answer is (1,5)
Santo made 4 less than twice as many cupcakes as Lynn write an equation to represent the number of cupcakes that santo made
Answers
number of cupcakes lynn made = x
number of cupcakes santo baked = 2x - 4
hope this helps and please mark me brainliesr. PLEASE!!!!
Stmatjatjatjatnatjatj
Wanna be brainlest thanked every day and 5 starred?
Just anwser this correctly
Answers
Answer:
1 Bag = 12.3 Ounces
5 Bags = 61.5 Ounces
123 Ounces = 10 Bags
Step-by-step explanation:
24.6 divided by 2 is 12.3.
12.3 times 5 is 61.5
61.5 times 2 is 123.
PLS HELLLLLPPPP ASAPPPP!
Interest = $45
Principal = ?
Interest rate = 3%
Time = 2 years
Answers
What interest is this. Simple or compound? Cause both have different formulas.
Simple interest
A(interest) = (Principal× Rate×time)
A= (P ×3×2years)/100%
$45 = 6/100P
4500= 6p
4500/6 = P
principal= $750.
what is the rate of change of the function represented by this graph?
Answers
Answer:
It's 0
Step-by-step explanation:
NOW FOR REAL ITS MISSING DUE YESTERDAY I NEED THIS DONE NOW
Distance (meters)
time (seconds)
Estimate when he had run 19.5 meters
Answers
Answer:
6.45
Step-by-step explanation:
6.9-6.0=0.9
0.9÷2=0.45+6=6.45
This is the middle between 18 and 21.
Hope this helps and give brainliest, thank me and rate it 5 please. :)
Answer:6.45
Step-by-step explanation:
ANSWER ASAP PLEASE
Timothy was trying to find the measure of
above. His answer was 7º. He is confused as he cannot
understand why m
Justify your answer.
Answers
Answer:
jim is correct, x does equal 7°. justify your answer by putting seven back into the equation. it gives you back that 180 equals 180, therefore it is correct
Step-by-step explanation:
so, all angles of a triangle have to add up to 180;
(15x) + (8x - 11) + (3x + 9) = 180
15x + 8x - 11 + 3x + 9 = 180
add your common numbers
26x - 2 = 180
add 2
26x = 182
divide 26
x = 7
put it back into the equation
15(7) + 8(7) - 11 + 3(7) + 9 = 180
180 = 180
Liam paints chairs at a constant rate. He paints 2 chairs in 20 minutes. Which equation represents the relationship between h, the number of hours Liam paints chairs, and n, the number of chairs he paints?
Answers
Answer:
6h
Step-by-step explanation:
1 per 10 minutes
that means 6 per hour
If 5 is added to twice a number, the result is 29. Find the number.
Answers
Answer:
12
Step-by-step explanation:
12 times 2 = 24 + 5= 29
Answer:
19
Step-by-step explanation:
29 minus five minus five
PLEASE HELP
...........
Answers
katie pays $725 a month for rent, $40 for cable and $3.60 an hour for local telephone service. if his monthly expenditures last month were $826.20 how much time did he spend on the phone.
Answers
Explanation: $826.20 - $725= $101.2 - $40= $61.12 / $3.60= 17hrs
Find the number that makes the ratio equivalent to 6:7
60:
Answers
Answer:
60:70
Step-by-step explanation:
[tex] \frac{60}{x} = \frac{6}{7} \\ \\ 60 \times \frac{7}{6} = x \\ \\ 70 = x[/tex]
Using the Triangle Sum Theorem, please solve for the value of x.
Please type out ALL OF YOUR WORK along with your answer for x. Work is worth 5 points, answer for x is 2 points.
3x
1
12x
55°
Answers
Answer:
x = 25
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the 3 angles and equate to 180
2x + 3x + 55 = 180, that is
5x + 55 = 180 ( subtract 55 from both sides )
5x = 125 ( divide both sides by 5 )
x = 25
You are a space alien. You visit planet Earth and abduct 97 chickens, 47 cows, and 77 humans. Then, you randomly select one Earth creature from your sample to experiment on. Each creature has an equal probability of getting selected. Create a probability model to show how likely you are to select each type of Earth creature. Input your answers as fractions or as decimals rounded to the nearest hundredth.
Answers
Answer:
there are 97 + 47 + 77 = 221 creatures from Earth in the alien spaceship.
the probability that a human being is chosen at random = 77 / 221 = 0.3484 = 34.84%
the probability that a chicken is chosen at random = 97 / 221 = 0.4389 = 43.89%
the probability of choosing a cow at random = 100% - 34.84% - 43.89% = 21.27%
Answer:
0.44
Response 2
0.21
Response 3
0.35
Step-by-step explanation:
A child ate 30 grams of cereal for breakfast and her brother ate 40% more than that. How many grams of cereal did the brother eat?
Answers
Answer:70%
Step-by-step explanation: 30 + 40 grams = 70
70 Grams
hiii please help i’ll give brainliest please please thank youuuuu
Answers
Answer:
5:3=8
120. 120÷8=15
5×15=75. 3×15=45
there are 45 children
I am so lonelyyyy and singllleee lol
Answers
Answer:
same :(
Step-by-step explanation:
Please help, Look at the picture
Answers
Answer:
the first one?
Step-by-step explanation:
I am like 67% sure.
A circular park is 1/3 mile long. Mr. M walks on this track, completing each lap in
1/12 of an hour. What is Mr. M's walking speed? Include the unit of measure.
Answers
Answer:
1.7 m/s
Step-by-step explanation:
1/3 mile = 536 m
1/12 hour = 5 minutes = 300 second
volecity = s/t = 536 / 300 = 1.7 m/s
9514 1404 393
Answer:
4 miles per hour
Step-by-step explanation:
Speed is the ratio of distance to time:
speed = miles/hours = (1/3)/(1/12) = (4/12)/(1/12) = 4/1 = 4
Mr. M's walking speed is 4 miles per hour.
Please answer this!!
Answers
Answer:
Step-by-step explanation:
Exercise 1
16/24
Exercise 2
3:6
Exercise 3
5:3
Exercise 4
3:20
Exercise 5
10:3
Karen has a gold bracelet that weighs 24 grams. She wants to sell the bracelet, but she needs a minimum of one ounce of gold to sell it. Can Karen sell her bracelet? Why or why not?
Answers
Answer:
It should be 28.35
Step-by-step explanation:
Hope this helped have an amazing day/month/year!
In order to select new board members, the Student Leadership club held an election. 14 members voted in the election and 6 did not vote. What percentage of the members voted?
Answers
Answer: 70%
Step-by-step explanation:
Based on the information, we told that 14 members voted in the election and 6 did not vote. There, the total number of members is 6 + 14 = 20.
The percentage of the members that voted will be:
= 14/20 × 100
= 70%
anyone know the answer to number 11? there’s only 2 options and you can see them in the picture.
Answers
Answer:
a)
Step-by-step explanation:
I am 100% sure it's the answer
Answer:
Step-by-step explanation:
using S[tex]\frac{o}{h}[/tex] C[tex]\frac{a}{h}[/tex] T[tex]\frac{o}{a}[/tex] (sin opposite/hypotenuse, cos adjacent/hypotenuse, tan opposite/adjacent)
Tan Y = 3/8
Tan Z = 8/3
hope this helps <3
how old am i if 2 times my age minus 10 is 60?
plz answer
Answers
The value of 6 nickels is _____% of the value of a dollar.
60
50
40
30
NEED HELP RIGHT AWAY!!!
Answers
Answer:
30%
Step-by-step explanation:
Becuase 6 nickels add up to 30
Hello please help I really don't understand this
Answers
Yes x and y is proportional because as it states, everytime y increases by 2, x increases by 1