For the figures below, assume they are made of semicircles, quarter circles and squares. For each shape, find the area and perimeter. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answers
Area of the quarter circle = 1/4 πr²
= 1/4π 12²
= 36π cm²
Area of the triangle = 1/2×base×height
= 1/2 × 12×12
= 72 cm²
Thus the area of the region
= (36π-72) cm²
2. Perimeter of the first figure
The length of the arc AC is 2πr/4
= 2π×12/4
= 6π cm
the length of line AC
√(12² +12²) = 16.97
Thus the perimeter of the figure
= (6π+16.97) cm
3. The are of figure 2
Area of the semi circle πr²/2
= 12²π/2 = 72π cm²
The area of the square
= 24 × 24 =576 cm²
Area of the semi circle = 72 π cm²
Thus the area of the part of the square
= (576-72π) cm²
total area
72π +576-72π
= 576 cm²
4. Perimeter of figure 2
The length of arc AD = (2πr)/2
= 2π×12/2 = 12π cm
but length of arc AD is equal to that of arc BC
Thus arc BC = 12πcm
Therefore, total perimeter
= 12π +12π +24 +24
= (24π +48) cm
Answer:
The perimeter of the first figure is [tex]6\pi +12\sqrt{2}[/tex]
Step-by-step explanation:
Besides that, they got everything right.
Related Questions
dolores is selling cucumbers from her backyard garden her garden is 48 square feet in total and she can grow 1 cucumber every 72 square inches if she can successfully grow cucumbers in every square foot of the garden and sell them for $2.50 each how much will she make?
Answers
Final answer:
Dolores will make $240 by growing and selling all the cucumbers possible in her 48 square feet garden, with each cucumber selling for $2.50.
Explanation:
To calculate the amount of money Dolores will make from selling cucumbers, we need to determine how many cucumbers she can grow in her 48 square feet garden, and then multiply that number by the selling price of $2.50 per cucumber. First, we'll convert the area of her garden into square inches since we know a cucumber takes up 72 square inches of space:
48 square feet × 144 square inches per square foot = 6,912 square inches.
Next, we divide this by the amount of space needed for one cucumber to find the total number of cucumbers she can grow:
6,912 square inches ÷ 72 square inches per cucumber = 96 cucumbers.
Finally, we'll multiply the number of cucumbers by the selling price:
96 cucumbers × $2.50 per cucumber = $240.
Therefore, Dolores will make $240 by selling all the cucumbers she can grow in her garden.
The area of the rectangle shown is given by the function A(x) = 2x2 - 5x. If the width of the rectangle is 13, what is the area
Answers
A(13)=2*(13)^2-5*(13)
A(13)=2*(169)-65
A(13)=338-65
A(13)=273
The area of the rectangle is 273 square units
The area of the rectangle is 273 square units.
The task is to find the area of a rectangle where the width of the rectangle is given as 13, and the area as a function of x is provided as A(x) = 2x² - 5x.
To find the area, we need the value of x that corresponds to the width. Since the width is 13, we set x as 13 and substitute it into the area function.
A(13) = 2(13)² - 5(13) = 2(169) - 65 = 338 - 65 = 273 square units.
Thus, the area of the rectangle is 273 square units.
Quadrilateral RJFT is similar to quadrilateral SYPA . JF=60 mm , AP=40 mm , and YP=25 mm . What is TF ?
Answers
So, for the given quadrilaterals, ratio of sides JF and TF of quadrilateral RJFT will be equal to the ratio of sides YP and AP of quadrilateral SYPA. Mathematically, we can write:
[tex]JF:TF = YP:AP \\ \\ \frac{JF}{TF} = \frac{YP}{AP} \\ \\ \frac{60}{TF} = \frac{25}{40} \\ \\ 60* \frac{40}{25}=TF \\ \\ TF=96mm [/tex]
So the measure of TF will be 96mm
Final answer:
To find the length of FT in the similar quadrilaterals RJFT and SYPA given specific side lengths, apply the scale factor method to determine FT = 37.5 mm.
Explanation:
Quadrilateral RJFT is similar to quadrilateral SYPA. Given that JF=60 mm, AP=40 mm, and YP=25 mm, we can solve for FT.
Calculate the scale factor between the two similar quadrilaterals using side lengths: JF/AP = FT/YP.
Substitute the given values to find the length of FT.
Calculate FT = (60 mm * 25 mm) / 40 mm = 37.5 mm.
Write the standard equation of a circle that passes through (1, −6) with center (7, −2).
Answers
(x ─ a) ^ 2 + (and ─ b) ^ 2 = r ^ 2
Where,
The ordered pair (a, b) represents the center of the circle.
The radius of the circumference is r.
In this case to find the radius of the circumference we must find the distance between the points (1, -6) and (7, -2).
We have then:
r = root ((x2-x1) ^ 2 + (y2-y1) ^ 2)
r = root ((7-1) ^ 2 + (-2 - (- 6)) ^ 2)
r = 2 * root (13)
The equation of the circumference will be:
(x ─ 7) ^ 2 + (y + 2) ^ 2 = (2 * root (13)) ^ 2
(x ─ 7) ^ 2 + (y + 2) ^ 2 = 52
Answer:
(x ─ 7) ^ 2 + (y + 2) ^ 2 = 52
Don't want any answers, just how to solve, step by step. please :)
Answers
is y=0.8(2.1)x exponential growth or exponential decay
Answers
______________________________________________________
Given: y = (0.8)(2.1)ˣ
______________________________________________________
Let us make a table and plug in some "x" values and see what the "y" values are:
______________________________________________________
x | y
_______________
1 | 1.68
_______________
2 | 3.528
_______________
3 | 7.4088
__________________________________________________________
The answer is: "exponential growth" .
__________________________________________________________
As "x" increases, "y" increases (by more than a linear relationship/proportion).
__________________________________________________________
A drawer contains 9 black socks, 8 gray socks, and 7 blue socks. Without looking, you draw out a sock and then draw out a second sock without returning the first sock. What is the probability that the two socks you draw are the same color?
Answers
First of all, there are total 9 + 8 + 7 = 24 socks.
Probability of a black socks in a row is 9/24
Probability of the second black socks without replacement, if first one was black, is 8/23
Therefore the probability of the 2 black socks in a row are 3/23 (I multiplied the two)
Using the same technique, the p of 2 gray socks are 7/69
The p of 2 blue socks are 7/92
Now you add them up, and you get 85/276 as your answer
Let me know if there are any other questions!
Help, what even is this?
Answers
If [tex]0 \ \textless \ t \le 30[/tex] then f(t) = 0. This means that for the first 30 minutes, the cost is $0, in other words the first half hour is free.
If [tex]30 \ \textless \ t \le 90[/tex] then f(t) = 5 indicating that the cost is $5 for the entire span from 30 minutes to 90 minutes (excluding t = 30 but including t = 90). Choice B is not the answer because the cost isn't $5 per minute. The cost for this entire timespan is simply $5
Finally, if t > 90, then f(t) = 10 telling us that any time value over 90 minutes will have the cost be $10. This is why the answer is choice D
This figure shows circle O with diameter QS . mRSQ=290∘ What is the measure of ∠ROQ ? Enter your answer in the box. °
Answers
we know that
mRSQ=290°
and
mRSQ+mORQ=360°
therefore
mORQ=360°-mRSQ---------------> mORQ=360°-290°=70°
the answer is 70°
Answer: 70 I just took the test!
Step-by-step explanation:
helpppppppppppppppppppppppppp
Answers
3x^2 (y^5)^1/4 which is the first choice
Explanation:
The fourth root means that the bracket under has the root has a power of 1/4.
So, the given expression is:
(81 * x^8 * y^5)^1/4
Now, we will distribute the power as follows:
(81 * x^8 * y^5)^1/4 = (81)^1/4 * (x^8)^1/4 * (y^5)^1/4
= 3 * x^2 * y^5/4
This expression is equivalent to:
3x^2 (y^5)^1/4 which is the first choice
Hope this helps :)
Quadrilateral ABCD is inscribed in this circle.
What is the measure of ∠A
Answers
106 degerees.
m<A + m<C = 180
m<A + 74 = 180
m<A = 106
What is the cricket’s hang time (amount of time the cricket is airborne)? Round to the nearest thousandth h(t) = –16t2 + 14t
Answers
h(t) = –16t² + 14t
using a graph tool
see the attached figure
the cricket’s hang time is the difference between point (0,0) and (0.875,0)
(0.875-0)=0.875 sec
the answer is 0.875 sec
The hang out time is 0.875 sec.
What is Quadratic equation?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. First, there must be a term other than zero in the coefficient of x²(a>0) for an equation to be a quadratic equation. The x² term is written first when constructing a quadratic equation in standard form, then the x term, and finally the constant term. The numerical values of a, b, and c are often expressed as integral values rather than fractions or decimals.
Given Equation:
h(t) = –16t² + 14t
For the Hangout time we can consider the function h(t)=0
0 = –16t² + 14t
16t² = 14t
16t= 14
t= 14/16
t= 0.875 sec
Hence, the hang out time is 0.875 sec.
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help help quickly!!!!!
Answers
The correct answers are A, B and C
hope it helps
Look at the isosceles trapezoid below.
Answers
Answer:
Not enough information to decideStep-by-step explanation:
If m were the midline, its length would be 32/2 = 16 cm. However, there is nothing in the figure to indicate that is the case. There is not enough information to decide.
given the conversion factor 3.28 ft/ 1m which cube above has the larger surface area
cube A is 7’ cube b is 2m
Answers
We have then:
Cube A:
7 * (1 / 3.28) = 2.13 m
Cube B:
2 m
The surface area of a cube is:
A = 6 * L ^ 2
Where,
L: side
Since cube A has a longer side (2.13m) then it will have the largest surface area.
Answer:
Cube A has the larger surface area
Final answer:
After converting Cube B's side length to feet, Cube A has a surface area of 294 ft² while Cube B has a surface area of 258.2016 ft², making Cube A the one with the larger surface area.
Explanation:
To determine which cube has the larger surface area, we must work with a common unit of measurement for both cubes. We'll convert Cube B from meters to feet using the conversion factor 3.28 ft/1m.
For Cube A with a side length of 7 feet, the surface area (SA) is calculated by the formula SA = 6 × s² (where 's' is the side length).
SA (Cube A) = 6 × (7 ft)² = 6 × 49 ft² = 294 ft².
For Cube B with a side length of 2 meters, we first convert meters to feet: 2 m × 3.28 ft/m = 6.56 ft. So, the surface area of Cube B becomes:
SA (Cube B) = 6 × (6.56 ft)² = 6 × 43.0336 ft² = 258.2016 ft².
Between Cube A and Cube B, Cube A has the larger surface area.
question 1.) simplify 6(2 + 0.3)5
A.) about 0.03
B.) about 12.01
C.) about 85.19
D.) about 386.18
question 2.) solve 32x = 7
A.) x = 0.22
B.) x = 4.57
C.) x = 25
D.) x = 39
Answers
Answer: Q1) 386.18
Step-by-step explanation:
Q1): You do the parenthesis first.
6(2+0.3)^5
2+0.3 = 2.3^5 = 64.36343
then do 6(64.36343) = 386.18
For Q2 I believe the answer is 0.22 if you do 7 divided by 32 you get 0.21875 and you round that to get 0.22
Zack deposited $1,200 in a savings account that paid 7.75% simple
interest. What was the balance in his account at the beginning of the
third year?
a. $180
b. $270
c. $1,393.21
d. $1,470
HELPPPPP ASAP AND GET BRAINEST
Answers
Explanation:
At the beginning of the Second year, the total balance would be:
$1200 + ($1200 * 7.75 / 100) = $1293
At the beginning of the Third year, the total balance would be:
$1293 + ($1293 * 7.75 / 100) = $1393.21 (Option C)
Answer:
$1386.
Step-by-step explanation:
We have been given that Zack deposited $1,200 in a savings account that paid 7.75% simple interest. We are asked to find the balance in his account at the beginning of the third year.
The balance in the account at the beginning of the third year will be equal to balance in the account at the end of 2nd year.
We will use simple interest formula to solve our given problem.
[tex]A=P(1+rt)[/tex], where,
A = Amount after t years,
P = Principal amount,
r = Annual interest rate in decimal form,
t = Time in years.
Upon converting our given interest rate in decimal form we will get,
[tex]7.75\%=\frac{7.75}{100}=0.0775[/tex]
Upon substituting our given values in simple interest formula we will get,
[tex]A=\$1200(1+0.0775\cdot 2)[/tex]
[tex]A=\$1200(1+0.155)[/tex]
[tex]A=\$1200(1.155)[/tex]
[tex]A=\$1386[/tex]
Therefore, an amount of $1386 will be in Jack's account at the beginning of third year.
Helen's Shop is 60 meters wide and 80 meters long. The parking lot in front of Helen's Shop is twice as long as it is wide and is 50 meters wide.What is the sum of the area of Helen's Shop and the parking lot?
Answers
Answer:
9,800
Step-by-step explanation:
Helen's Shop
60 m x 80 m = 4,800 m2
Parking Lot
Length = 2 × 50 m = 100 m
Area = 50 m × 100 m = 5,000 m2
Final Answer
4,800 m2 + 5,000 m2 = 9,800 m2
HELP ASAP!!
Given: ABCD is a parallelogram.
Prove: ∠A and ∠D are supplementary.
By the definition of a parallelogram, AB∥DC. AD is a transversal between these sides, so ∠A and ∠D are ? angles. Because AB and DC are ? , the same-side interior angles must be ? by the same-side interior angles theorem. Therefore, ∠A and ∠D are supplementary.
Answers
A parallelogram is a quadrilateral with four sides. The opposite sides of the parallelogram are equal and parallel.
In the given figure, AB||DC. AD is the transversal, such that:
∠A + ∠D = 180-degrees.
The parallelogram is a quadrilateral with equal and parallel sides, such that the interior angles present on the same side of the transversal are supplementary. The sum of supplementary angles is equal to 180-degrees. From the theorem of same-side interior angles, the supplementary angles present on the parallel lines must be intersected by a transversal. Since, in the parallelogram ABCD, AD is the transversal. From the property of transversal, the interior angles on the same side of the transversal are supplementary.Therefore, ∠A and ∠D are supplementary and their sum is equivalent to 180-degrees.
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Elio makes candles that are 14 cm tall. Each candle burns 8 hours before going out. He is wondering how many hours a 21 cm tall candle can burn for. He assumes that the relationship between the height of a candle and number of hours it burns (h) is proportional. How long can a 21 cm tall candle burn for?
Answers
Find the unit rate
14 ÷ 8 = 1.75 cm/h
Divide
21 ÷ 1.75 = 12
You can set this up as an algebraic equation to check the answer.
If the candle is 21 cm tall, it will burn for 12 hours.
Hope this helped you! :)
You and a friend tutor for a total of 12 hours. Use the tape diagram to find how many hours you tutor.
Answers
I teach 9 and 6 hours respectively
Left diagram:
In this diagram you show three quarters of the hours.
We have then:
(3/4) * (12) = 9
Answer:
You teach 9 hours.
Right diagram:
In this diagram you teach half of the hours.
We have then:
(2/4) * (12) = 6
Answer:
You teach 6 hours
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You tutored for 6 hours, your friend tutored for 6 hours as well.
Image:
You and a friend listen for a total of 2 hours.
You
Friend
You
The image shows a tape diagram with two sections labeled "You" and "Friend". The "You" section is longer than the "Friend" section, indicating that you tutored for more hours than your friend.
To find the number of hours that you tutored, we can divide the total number of hours tutored (12 hours) by the number of sections in the tape diagram (2).
Number of hours you tutored = 12 hours / 2 sections = 6 hours
Therefore, you tutored for 6 hours.
Explanation of tape diagrams:
A tape diagram is a visual representation of a mathematical equation. It is a horizontal bar that is divided into sections, with each section representing a different quantity. The length of each section represents the size of the quantity it represents.
Tape diagrams can be used to solve a variety of mathematical problems, including addition, subtraction, multiplication, and division problems. They are especially useful for solving problems that involve multiple quantities, as they can help to visualize the relationships between the different quantities.
In this case, the tape diagram is used to solve the following problem:
> You and a friend tutor for a total of 12 hours. Use the tape diagram to find how many hours you tutor.
The tape diagram is divided into two sections, one for you and one for your friend. The length of each section represents the number of hours that each person tutored. Since you tutored for more hours than your friend, the "You" section is longer than the "Friend" section.
To find the number of hours that you tutored, we can divide the total number of hours tutored (12 hours) by the number of sections in the tape diagram (2). This gives us the number of hours that you tutored, which is 6 hours.
Therefore, the answer to the question is "You tutored for 6 hours."
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If f(x)=3x^2-1 and g(x)=x+2, find (f+g)(x)
Answers
(f+g)(x) = 3x^2 + x + 1
Explanation:
We are given that:
f(x) = 3x^2 - 1
g(x) = x + 2
To find (f+g)(x), all we have to do is add the above to functions as follows:
(f+g)(x) = f(x) + g(x)
= 3x^2 - 1 + x + 2
= 3x^2 + x + 1
Hope this helps :)
Answer:
Step-by-step explanation:
X^2+3x-1 apex
Use the equation you have written above determine the cost for each bracelet. Show the algebraic steps that it takes to find the answer. Provide your conclusion.
Answers
Which rule describes the translation? T–3, –2(x, y) T–3, 2(x, y) T3, –2(x, y) T3, 2(x, y)
SOMEONE PLEASE ANSWER PLEASE
Answers
The rule which describes the translation of the figure is T–3, –2(x, y).
The translation T(x, y) → (x – h, y – k) moves a point (x, y) to a new point (x – h, y – k).
T–3, –2(x, y) moves the point 3 units to the right and 2 units down.
T–3, 2(x, y) moves the point 3 units to the right and 2 units up.
T3, –2(x, y) moves the point 3 units to the left and 2 units down.
T3, 2(x, y) moves the point 3 units to the left and 2 units up.
So the answer is T–3, –2(x, y).
Here is a table that shows the effect of each translation on the point (3, 4):
Original point | Translation | New point
(3, 4) | T–3, –2(x, y) | (0, 2)
(3, 4) | T–3, 2(x, y) | (6, 6)
(3, 4) | T3, –2(x, y) | (6, 2)
(3, 4) | T3, 2(x, y) | (0, 6)
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A doctor's office mails a survey to each of its patients. The results of the survey are based off of the total number of patients.
Which of the following could affect the outcome of their surveys?
A.The results could be flawed because the sample population was too large.
B.The results could be flawed due to a wide range of topics in the questions.
C.The survey is biased because they are only asking patients.
D.The results could be flawed due to non-response of patients.
Answers
Answer:
The results could be flawed due to non-response of patients.
Step-by-step explanation:
A doctor's office mails a survey to each of its patients. The results of the survey are based off of the total number of patients. The office is mailing the patients. It is very likely that patients do not read out the survey mail. So, they cannot respond to the survey or a very few patients will respond back. So, option 4th is the correct. The results could be flawed due to non-response of patients.
Consider this system of linear equations:
y = –3x + 5
y = mx + b
Which values of m and b will create a system of linear equations with no solution?
m = –3 and b = –3
m = 5 and b = –3
m = 3 and b = 5
m = 5 and b = –3
Engenuity answer is m= -3 and B= -3
Answers
Justification:
A system of linear equations will not have solutions if the two lines are parallel.
Two equations are parallel if their slopes (m) are equal and the y-intercep (b) are different.
Since the given equation is y = - 3x + 5, the value of m of the other equation, y = mx + b, in order to make a system with no solution, needs to be - 3, and the value of b need to be different to 5.
The only pair from the choices that meets that is the first option m = - 3 and b = -3.
m = –3 and b = –3 or A
Identify a possible first step using the elimination method to solve the system and then find the solution to the system.
12x – 3y = 6
2x – y = 2
A) multiply second equation by 6, solution (2,0)
B) multiply second equation by 6, solution (-2,0)
C) multiply second equation by -6, solution (0,2)
D) multiply second equation by -6, solution (0,-2)
Answers
Answer:
D) multiply second equation by -6, solution (0,-2)
Step-by-step explanation:
This pair of linear equations may be solved simultaneously by using the elimination method. This will involve ensuring that the coefficient of one of the unknown variables is the same in both equations.
As such, in the given set of equations
12x – 3y = 6
2x – y = 2
We may make the coefficients of x the same by multiplying the second by 6 or the coefficient of y by multiplying the second by 3. Using the first
12x – 3y = 6
12x – 6y = 12
equation 1 - equation 2
3y = -6
y = -2
2x + 2 = 2
x = 0
HELP FAST PLEASE!!
Martin simplified the composed function f(x)=sin(arctan x). His work is shown below.
Step 1: f(x)=sinA, where A=arctan x and x = tanA
Step 2: tanA= opp/adj=x/1
Step 3: hypotenuse= square root of 1^2-x^2= square root of 1-x^2
Step 4: sinA=opp/hyp=x/squareroot 1-x^2
In which step did Martin make is first error?
Answers
Step 1: f(x)=sinA, where A=arctan x and x = tanA-----> is correct
Step 2: tanA= opp/adj=x/1-----------> is correct
Step 3: hypotenuse= square root of 1²-x²= square root of 1-x²-----> is not correct
Because hypotenuse= square root of (1² + x²)=square root of (1+x²)
Step 4: sinA=opp/hyp=x/square root of (1+x²)
the answer is
In step 3 Martin make is first error
Answer:
1. B f(x)=4sinx/2-3
2. B, F, G (c=-1. a=2, b=2)
3. c. H(t)=-2.4cos(0.017t)+12
4. A, B, E, F (y=cos^-1x, y=cot^-1x, y=sin^-1x, y=tan^-1x)
5. C y=sin^-1x
6. C 48.7
7. C f(g(x))=sec(sinx) domain: all real #
8. C step 3
Step-by-step explanation:
Use the table provided to determine the total amount paid on a 30 year fixed loan, at 6.0%, of $75,000.
$162,000
c.
$143,820
b.
$153,750
d.
$133,250
Answers
The right answer is A.162,000
Answer:
162000
Step-by-step explanation:
For 75000 paying in 30 years at 6% we have
Mortgage Summary
Monthly Payment $449.66
Total Interest Paid $86,879
9
Total of 360 Payments $161,879
Pay-off Date Feb, 2049
We find out of 4 options given 162000 is nearer to this 161879
Hence option of 162000 is the right answer.
do you agree? explain why or why not
Answers
square root of 2(4)+1 = square root of 9 = 3
3+3 = 6
and 6 is not 0 so x cannot = 4
A student concluded that the solution of the equation [tex]\sqrt{2x+1}+3 = 0[/tex] is x = 4. The conclusion is true.
What is a perfect square?Perfect squares are those integers whose square root is an integer.
Let x-a be the closest perfect square less than x,
and let x+b be the closest perfect square more than x, then we get x-a < x < x+b (no perfect square in between x-a and x+b, except possibly x itself).
Then, we get:
[tex]\sqrt{x-a} < \sqrt{x} < \sqrt{x+b}[/tex]
[tex]\sqrt{2x+1}+3 = 0\\\\\sqrt{2x+1}= -3[/tex]
by taking square on both sides we get
[tex](\sqrt{2x+1})^2 = (- 3)^2 \\\\2x+ 1 = 9[/tex]
when x = 4
2(4) + 1
= 9
Thus, the solution of the equation is 4.
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