Each square has a side length of 12 units. Compare the areas of the shaded regions in the 3 figures. Which figure has the largest shaded region? Explain or show your reasoning.
Answers
Answer:They are equal
Step-by-step explanation:
they will add up they are just token apart or in pieces
Three different figures are given. The area of the shaded region of all the figures is the same.
We need to determine the highest shaded area among all.
Now, the area of the square is common to all.
Thus,
[tex]\begin{aligned}\rm{Area\;of\;square}&=12^2\\&=144 \;\rm{units^2}\end{aligned}[/tex]
1). Calculate the shaded area for figure A.
The diameter of the circle is 12 units, hence its radius is 6 units.
Therefore,
[tex]\begin{aligned}\rm{Area\;of\;circle}&=\pi \times 6^2\\&=36 \pi \;\rm{units^2}\end{aligned}[/tex]
[tex]\begin{aligned} \rm{Shaded\; area} &= \rm{Area\; of\; the\; square - Area\; of\; the\; circle}\\&=144-36 \pi \end{aligned}[/tex]
Thus, the area of the shaded region for figure 1 is [tex]114-36 \pi[/tex].
2). Calculate the shaded area for the figure B.
The diameter of the circle is 6 units, hence its radius is 3 units.
Therefore,
[tex]\begin{aligned}\rm{Area\;of\;circle}&=\pi \times 3^2\\&=9 \pi \;\rm{units^2}\end{aligned}[/tex]
[tex]\begin{aligned} \rm{Shaded\; area} &= \rm{Area\; of\; the\; square - 4 \times Area\; of\; the\; circle}\\&=144-36 \pi \end{aligned}[/tex]
Thus, the area of the shaded region for figure 2 is [tex]114-36 \pi[/tex].
3). Calculate the shaded area for figure C.
The diameter of the circle is 4 units, hence its radius is 2 units.
Therefore,
[tex]\begin{aligned}\rm{Area\;of\;circle}&=\pi \times 2^2\\&=4 \pi \;\rm{units^2}\end{aligned}[/tex]
[tex]\begin{aligned} \rm{Shaded\; area} &= \rm{Area\; of\; the\; square - Area\; of\; the\; circle}\\&=144-36 \pi \end{aligned}[/tex]
Thus, the area of the shaded region for figure 3 is [tex]114-36 \pi[/tex].
Therefore, the area of the shaded region of all the figures is the same.
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Related Questions
Whats the answer to number 9?
Answers
Answer:
B and D
Step-by-step explanation:
Because only those two equations on the graphs are straight. and are increasing or decreasing in a constant pace.
The subject of the formula below is y
y=4x+3
Rearrange the formula to make x the subject
Answers
Answer:
x = (y - 3)/4.
Step-by-step explanation:
y = 4x + 3
y - 3 = 4x
x = (y - 3)/4.
Step-by-step explanation:
y=4x+3
all divide by 3
4x=y/3
cross multiple
12x=y
divide both sides by 12
therefore, x is equal to y/12
What is ⅓ divided by ¼? Use the model if needed. Answer should be in simplest form. Explain your answer
Answers
Answer:
The answer to the expression in simplest form is:
[tex]\frac{\frac{1}{3}}{\frac{1}{4}}=\frac{4}{3}[/tex]
Step-by-step explanation:
Given the function
[tex]\frac{\frac{1}{3}}{\frac{1}{4}}[/tex]
solving to get the simplest form
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}[/tex]
[tex]\frac{\frac{1}{3}}{\frac{1}{4}}=\frac{1\cdot \:4}{3\cdot \:1}[/tex]
[tex]\mathrm{Apply\:rule}\:a\cdot 1=a[/tex]
[tex]=\frac{4}{3}[/tex]
Thus, the answer to the expression in simplest form is:
[tex]\frac{\frac{1}{3}}{\frac{1}{4}}=\frac{4}{3}[/tex]
Whats the answer for number 3?
Answers
Answer:
B. There are no discounts or charges per month.
Step-by-step explanation:
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A banker earns a $75,000 annual salary, a 2,35% commission on any approved loans for the bank’s business customers, and a fee of $3.75 for each application processed. If the banker has a total of 2.8 million in approved business loans and processes 2,750 applications this year, what are the banker’s earnings rounded to the nearest dollar ??
Answers
Answer:
Amount earned = $151,113
Step-by-step explanation:
Here, we are interested in calculating the banker’s earnings rounded to the nearest dollar;
We proceed as follows; we have the following;
1. Annual salary of $75,000
2. 2.35% on approved loans.
Approved loans = 2.8 million
Commission = 2.35/100 * 2.8 million = $65,800
3. $3.75 for each processed loan application
Total = 2750
Amount = 3.75 * 2750 = $10,312.50
Total amount earned is thus;
$75,000 + $65,800 + $10,312.50 = 151,112.5 = 151,113 to the nearest dollar
Which is NOT true?
A. 16 + 3 = 11 + 8
B. 16 = 16
C. 16 - 4 = 7 + 6
D. 16 = 19 - 3
Answers
Answer:
c
Step-by-step explanation:
16-4=12
7+6=11
The false statement is;
C. 16 - 4 = 7 + 6
Given that;
The mathematical expression is;
A. 16 + 3 = 11 + 8
B. 16 = 16
C. 16 - 4 = 7 + 6
D. 16 = 19 - 3
We have to state the false statement.
What is an expression?
Expression in math is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The mathematical expression is;
A. 16 + 3 = 11 + 8
Left hand side,
16 + 3 = 19
Right hand side,
11 + 8 = 9
Left hand side = Right hand side
Hence, This is true.
B. 16 = 16
Left hand side = Right hand side
Hence, This is true.
C. 16 - 4 = 7 + 6
Left hand side;
16 - 4 = 12
Right hand side,
7 + 6 = 13
Hence, This is false.
D. 16 = 19 - 3
Left hand side;
16
Right hand side,
19 - 3 = 16
Left hand side = Right hand side
Hence, This is true.
Therefore, The false statement is;
C. 16 - 4 = 7 + 6
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Carly has some rope to mark off a rectangular area of grass for a field day game. The rectangle needs to be 6 feet wide. Which expression represents how much rope Carly needs if the rectangle is g feet long?
Answers
Answer:
B ) 2 g + 12
Step-by-step explanation:
Solve for y, Angle Q and Angle S
Answers
Answer:
hope
Step-by-step explanation:
Triangle ABC has vertices at A (1,-3), B (3,0)x and C (5,-3). What is the distance from vertex B to the midpoint of AC?
Answers
Answer:
The distance from vertex B to the midpoint of AC is 3 units
Step-by-step explanation:
we are given a triangle with vertices A (1,-3), B (3,0) and C (5,-3).
Mid point of of AC (x,y) = ( 1+5/2 , -3 -3/2)
= ( 6/2 , -6/2)
= (3 , -3)
Distance formula = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]
= [tex]\sqrt{(3-3)^2 + (0 + 3) ^2}[/tex]
= [tex]\sqrt{(3)^2}[/tex]
= 3 units
Michelle ran 3,168 meters at a constant speed over 11 minutes. What was Michelle's pace?
A.
288 meters per minute
B.
864 meters per minute
C.
290 meters per minute
D.
11 meters per minute
Answers
The correct answer is A
I need to know the minus 2 ounces
Answers
Answer:
Step-by-step explanation:
10 is your answer
what is the value of Z in degrees, in the figure shown?
Answers
Step by step solution - just subtract
Answer: 69.2
Step-by-step explanation:
A bag has 7 red marbles, 8 blue marbles and 5 purple marbles
Answers
7+8+5=20
Uhh lmk
Answer:
you didnt put anything like the full question but it equals 20
Step-by-step explanation:
so yea 2000
3x^2−18x+12=0 by completing the square
Answers
Answer:
mark me brailist if it helped
Find the slope that passes through (-1, -3) and (-2, 2).
A
-5
С
-2
B
-1/5
D
1/3
Answers
Answer:
A.-5
Step-by-step explanation:
I have used an online calculator to check my answer against so this answer is 100% correct. I used "Slope Calculator" by Omni.
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A teacher is buying bags of chips for a grade-level picnic. The teacher wants to spend at most $36 on chips.Each bag of costs 2.95.
Which inequality represents the number of bags of chips,x, the teacher can purchase?
Answers
An inequality that represents the number of bags of chips, x, the teacher can purchase is [tex]2.95x \leq 36[/tex].
Let the number of bags of chips be x.Given the following data:
Total amount spent = $36Cost of each bag of chips = $2.95To write an inequality that represents the number of bags of chips, x, the teacher can purchase:
In this exercise, you're required to write a mathematical expression to represent the total number of bags of chips (x) that a teacher can purchase without exceeding his or her budget of $36.
Translating the word problem into an algebraic expression, we have;
[tex]2.95x \leq 36[/tex]
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Which expressions are equivalent to the given complex number? 45 + 2i A. (2 + 8i) + 2(9 + 6i)(1 - i) B. (9 + 4i) + 2(4 + 7i)(1 - 2i) C. (13 + 4i) + 2(7 + 2i)(2 - i) D. (2 + 8i) + (30 - 6i) E. (9 + 4i) + (36 - 2i) F. (13 + 4i) + (32 - 6i)
Answers
The expressions which are equivalent to the complex number 45 + 2i is E. (9 + 4i) + (36 - 2i)
D. (2 + 8i) + (30 - 6i)
To determine which expressions are equivalent to the complex number 45 + 2i, we can simplify each expression and check if it matches the given number.
Let's evaluate each option:
A. (2 + 8i) + 2(9 + 6i)(1 - i) = 2 + 8i + 2(9 + 6i - 9i - 6i^2) = 2 + 8i + 2(9 + 6i - 9i + 6) = 2 + 8i + 2(15 - 3i) = 2 + 8i + 30 - 6i = 32 + 2i
B. (9 + 4i) + 2(4 + 7i)(1 - 2i) = 9 + 4i + 2(4 + 7i - 8i - 14i^2) = 9 + 4i + 2(4 + 7i - 8i + 14) = 9 + 4i + 2(23 - i) = 9 + 4i + 46 - 2i = 55 + 2i
C. (13 + 4i) + 2(7 + 2i)(2 - i) = 13 + 4i + 2(7 + 2i - 14i - 4i^2) = 13 + 4i + 2(7 + 2i - 14i + 4) = 13 + 4i + 2(24 - 12i) = 13 + 4i + 48 - 24i = 61 - 20i
D. (2 + 8i) + (30 - 6i) = 2 + 8i + 30 - 6i = 32 + 2i
E. (9 + 4i) + (36 - 2i) = 9 + 4i + 36 - 2i = 45 + 2i
F. (13 + 4i) + (32 - 6i) = 13 + 4i + 32 - 6i = 45 - 2i
From the evaluations above, we can see that options E and D are equivalent to the given complex number 45 + 2i.
The correct options are:
E. (9 + 4i) + (36 - 2i)
D. (2 + 8i) + (30 - 6i)
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The expressions that are equivalent to the given complex number 45 + 2i are: (9 + 4i) + (36 - 2i) and (2 + 8i) + (30 - 6i).
Thus, option (D) and (E) are correct.
Given complex number 45 + 2i.
A. (2 + 8i) + 2(9 + 6i)(1 - i)
Simplifying: (2 + 8i) + 2(9 + 6i - 9i - 6)
= (2 + 8i) + 2(3 + 3i)
= 2 + 8i + 6 + 6i
= 8 + 14i
B. (9 + 4i) + 2(4 + 7i)(1 - 2i)
Simplifying: (9 + 4i) + 2(4 + 7i - 8i - 14)
= (9 + 4i) + 2(-10 - i)
= 9 + 4i - 20 - 2i
= -11 + 2i
C. (13 + 4i) + 2(7 + 2i)(2 - i)
Simplifying: (13 + 4i) + 2(14 + 4i - 7i - 2)
= (13 + 4i) + 2(12 - 3i)
= 13 + 4i + 24 - 6i
= 37 - 2i
D. (2 + 8i) + (30 - 6i)
Simplifying: 2 + 8i + 30 - 6i
= 32 + 2i
E. (9 + 4i) + (36 - 2i)
Simplifying: 9 + 4i + 36 - 2i
= 45 + 2i
F. (13 + 4i) + (32 - 6i)
Simplifying: 13 + 4i + 32 - 6i
= 45 - 2i
Thus, option (D) and (E) are correct.
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Sasha is selling t-shirts. She uses the function f(x) = 2x + 8 to determine her sales, where
x represents the number of shirts and f(x) represents the sales in dollars. What would
her sales be if she sells 24 t-shirts?
Answers
Answer:
f(x)=56
Step-by-step explanation:
2(24)+8=56
eeeeeeeeeeeeeeeeeeeeeeeeeva fast answer
Answers
Answer:
51
Step-by-step explanation:
find the percent for each (34 and 33) subtract from their whole (220 and 170) then subtract from each other
A backpack is on sale for 30% off. If the sale price is $15.75, what is the original price to the nearest cent?
Answers
Answer:
$22.50
Step-by-step explanation:
As it is 30% off, $15.75 is 70% of the full price. You can then divide 15.75 by 70 [= 0.225] to get 1% of the full price. Multiply 0.225 by 100 to get the full price. 0.225 x 100 = 22.5
We can check that this answer is correct by multiplying 22.50 by 0.7. If you get 15.75 you know the answer is correct as 15.75 is 70% of the full price.
Find the equation of the line that is perpendicular to Y= -2/3x and contains the point (4,-8)
Answers
Answer:
Y=-3/5x
Step-by-step explanation:
Answer:
y = 3/2x -14
Step-by-step explanation:
y = -2/3 x
has a slope of -2/3
We want a line perpendicular
Take the negative reciprocal to find the slope
- (1 / -2/3)
3/2
The slope of a line perpendicular is 3/2
Using the slope intercept form of a line
y = mx+b where m is the slope and b is the y intercept
y = 3/2x +b
Substitute a point into the equation
-8 = 3/2(4) +b
-8= 6+b
Subtract 6 from each side
-8-6 = b
y = 3/2x -14
You are riding your scooter to a town that is 120 miles away and you can maintain a speed of 30 mph. How long will it take you?
Answers
Answer:
4 hours
Step-by-step explanation:
120 ÷ 30 = 4
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Your car has 10 gallons of gas. You use 1 gallon every 20 miles you travel. Fill in the table.
Answers
Answer:
(0, 0), (20, 1), (40, 2), (60, 3), (80, 4)
Step-by-step explanation:
1
2
3
4
These are the numbers you are looking for.
k=1/3 and k=3/2 which line would be steeper
Answers
Answer:
k = 3/2
Step-by-step explanation:
assuming k is your slope
rise/run = y/x
k = 1/3 therefore, (3,1) is your (x,y) points
k=3/2 therefore, (2,3) is your (x,y) points
as you can see, you move 2 more units up on the y-axis with k =3/2. Therefore, it is steeper.
Vanessa has 23 coins in nickels and dimes and has $1.50 in all. Which equation could
be used to find the number of
nickels, n?
A. 5n + 10 (23) = 1.50
B.5n + 10 (23 – n) = 1.50
C. 0.05%+0.10 (23 – 1) = 1.50
D. 0.05m+0.10 (m - 23) = 1.50
Answers
Answer:
a
Step-by-step explanation:
from the diagram, identify a pair of corresponding angles
i need helppp!
Answers
Answer:
2 and 6, 1 and 5
Step-by-step explanation:
Answer:
1&5
Step-by-step explanation:
what is the number if 50% of 25% of the number is 96
Answers
Let n = the number we need to find.
0.50(0.25)n = 96
0.125n = 96
Can you finish?
The number if 50% of 25% of the number is 96 is 768
Let the unknown number be x
50% of 25% of the number is expressed as 0.5(0.25)x
0.5(0.25)x = 0.125x
Equating the result to 96 will give;
0.125x = 96
Divide both sides by 0.125
0.125x/0.125 = 96/0.125
x = 96/0.125
x = 768
Hence the number if 50% of 25% of the number is 96 is 768
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6.
Solve the equation *x + 3 ={x +3
Answers
Answer:
x=4
Step-by-step explanation:
The fourth graders are going on a field trip to the Zoo. There are 83 students in the fourth grade. If tickets cost $26 each, how much will the field trip cost?
Answers
Answer:
Total trip cost = $2,158
Step-by-step explanation:
Given:
Cost of each ticket = $26
Number of student = 83
Find:
Total trip cost
Computation:
Total trip cost = Cost of each ticket x Number of student
Total trip cost = $26 x 83
Total trip cost = $2,158
A) What are the coordinates of the image of vertex G after a reflection across the line y = x?
B) What is the rule when reflecting across the line y = x
Answers
Answer:
b. (-5, 4)
Step-by-step explanation:
edge2020