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
Figure 1)
a) The area is A = 36( π - 2) ст²
b) The perimeter is P = 6 (π + 2√2) [tex]cm^2[/tex]
Figure 2)
a) The area is A = 576 cm²
b) The perimeter is P = 24(π+2) [tex]cm^2[/tex]
Figure 1)
a) To find the area of the figure 1 we have to do the substraction
The area of figure 1 is equivalent to the area of a triangle less the area of a quarter circle.
The area of quarter circle is equal to
A = 2
we have
r = 12 cm
Put the value r as given
A = (12)2
A = 36 [tex]cm^2[/tex]
Area of a triangle formula is
A = (b)(h)
Given information,
b=12 cm
h = 12 cm
substitute
A = (12) (12)
A = 72 cm²
therefore
The area of the figure is
A = (36π - 72) [tex]cm^2[/tex]
Simplify
A = 36(π -2) [tex]cm^2[/tex]
b)
The perimeter of the figure 1 is equal to the circumference of a quarter circle plus the side AC of triangle
The perimeter of a quarter of circle is formula
C = 2πr
simplify
C = r
we have
r=12 cm
substitute
C = (12)
C = 67 cm
Find the length side AC
Applying the Pythagorean Theorem
[tex]AC^2 = 12^2 + 12^2[/tex]
[tex]AC^2 = 144+ 144\\AC^2 = 288\\AC = \sqrt{288}[/tex]
AC = 12√2 cm
P = (6π +12√2) cm
Taking 6 as a common multiplier we get
P = 6(π+2√2)
The perimeter of the figure 1 is
P = 6(π+2√2) cm
Part 2)
a) As we can see,
The area of a semicircle plus the area of a square less the area of a semicircle equals the area of figure 2.
The figure's area and the square's area are equal.
A = [tex]24^2[/tex]
A = 576 cm²
b) Find the perimeter of the figure 2
we know that
The perimeter of the figure 2 is equal to the length side AB plus the length side DC plus the circumference of two semicircles
The perimeter of the figure 2 is equal to two times the length side AB plus the circumference of one circle
P = 2(AB) + π D
P = 2(24) + π(24)
P = 48 + π(24)
Take out 24
P = 24 (2 + π ) cm
Related Questions
Please help quickly for 5 stars and brainliest!!
1. Omar set off a rocket in a field. The height h of the rocket in feet can be roughly estimated using the formula
h = -16t^2 + 128t, where t is the time in seconds. How long will it take the rocket to reach a height of 240 feet?
2. Josefina tosses a ball upward with an initial velocity of 76 feet per second.
She tosses it from an initial height of 2 feet. Find the approximate time that the ball hits the ground.
Use the function h(t) = -16t^2 + 76t + 2
Round to the nearest second.
3. Brandi, an amateur skier, begins on the "bunny hill," which has a vertical drop of 200 feet.
Her speed at the bottom of the hill is given by the equation v^2 = 64h, where the velocity v is in feet per second
and the height h of the hill is in feet. Assuming there is no friction, approximate Brandi's velocity at the bottom of the hill.
Answers
Height h = 240 feet
We insert it into formula.
[tex]240 = -16 t^{2} +128t[/tex]
Now we solve this for t:
[tex]16 t^{2} -128t +240 = 0 /16 \\ t^{2} - 8t +15 =0 \\ t_{1} = 5 t_{2} = 3[/tex]
We have two answers as the rocket will pass this height on it's way up and down.
2.
Height h = 0 feet
We insert it into formula.
[tex]0=-16 t^{2} +76t + 2[/tex]
Now we solve this for t:
[tex]16 t^{2} - 76t -2 = 0 /2 \\ 8t^{2} - 38t - 1 = 0 \\ t_{1} = 5 t_{2} = -1[/tex]
We do not consider solution -1 as the time can not be negative. Our solution is 5s.
3.
Height at bottom of hill h = 0 feet
We insert it into formula.
[tex] v^{2} = 64 * 0 = 0 ft/s[/tex]
A quadrilateral with two sets of parallel sides and four right angles is a
parallelogram
rhombus
rectangle
trapezoid
Answers
thats the answer
what are the lengths of the other two sides of the triangle?
Answers
A hybrid car averages 609 miles on a 12.5 gallon tank of gas. Manuel is planning a 1290- mile vacation in his hybrid car. Find how many gallons of gas he can expect to burn.
Answers
1 miles = 12.5 / 609
1 mile = 0.0205 gallon
1290 miles = 0.0205 gallons x 1290
= 26. 48 gallons
Using ratio and proportion, we deduced that Manuel's hybrid car travels 48.72 miles per gallon. Based on this, we estimated that Manuel would need around 26.5 gallons of gas for his 1290-mile vacation.
Explanation:The subject at hand requires the utilization of ratio and proportion in mathematics, specifically in the context of fuel economy of cars. The hybrid car Manuel owns averages 609 miles on a 12.5 gallon tank. This implies that for every one gallon of gas, the car can travel 609 / 12.5 = 48.72 miles.
Now Manuel is planning for a 1290-mile trip. To ascertain how many gallons of gas he might expect to consume, we divide the total distance of the vacation by the miles per gallon for his car: 1290 miles / 48.72 miles/gallon = 26.5 gallons.
Therefore, Manuel can expect to consume approximately 26.5 gallons of gas for his 1290-mile vacation.
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justin runs at a constant rate, traveling 17km in 2 hours whats the equation
Answers
17km/2 h=8.5 km/hour
Justin's constant rate of running can be represented by the equation
=17/2 =8.5, where r is his speed in kilometers per hour. This indicates that Justin runs at a steady pace of 8.5 kilometers per hour.
To find the equation that represents Justin's constant rate of running, we can use the formula for speed, which is distance divided by time. Given that Justin travels 17 km in 2 hours, we can use these values to determine his speed.
Step 1: Identify the variables:
Let's denote:
d as the distance traveled (in kilometers)
t as the time taken (in hours)
r as the rate or speed (in kilometers per hour)
Step 2: Write down the formula for speed:
Speed =Distance/Time
Step 3: Plug in the given values:
We know that Justin travels 17 km in 2 hours. So,
d=17 km and t=2 hours.
Step 4: Calculate the speed:
=17/2=8.5 km/hr
Step 5: Write down the equation:
Now that we know Justin's speed is 8.5 km/hr, we can express it as an equation:r=8.5
So, the equation representing Justin's constant rate of running is:
r=8.5
This equation states that Justin's speed is always 8.5 kilometers per hour, regardless of the distance he travels. It's a linear equation because his speed remains constant over time
complete question=
Justin runs at a constant rate, traveling 17 kilometers in 2 hours. What is the equation that represents Justin's rate of running?"
Cylinder A has a volume of 360 cm3. Cylinder B has a base and height identical to that of cylinder B, but leans to the right in such a way that its slant length is greater by 4 cm. What is the volume of cylinder B? V = 270 cm3 V = 360 cm3 V = 480 cm3 V = 600 cm3
Answers
This is because the volume of the cylinder is dependent on the base and the perpendicular height, therefore, the slanting of the cylinder wont change its volume
Step-by-step explanation:
ndkfkasdjfkjdasl;fkjalksdfjlasdjf
how do you do #8,9,10 ?? thank you !!
Answers
.. 3 represents a vertical expansion factor of 3
.. 2 represents a left shift of 2 units
9. g(x) = -2f(x)
.. 2 represents a vertical expansion factor of 2
.. the minus sign is a reflection across the x-axis
10. g(x) = f(x -1) +3
.. 3 represents a vertical shift upward by 3 units
.. -1 represent s right shift of 1 unit
Which equation of the least squares regression line most closely matches the data set?
Note: The variable x represents the years after 1970.
Y= -5.7x-67
Y= -0.98x+65
Y= -0.17x+76
Y= -5.7x +67
Answers
The 4th selection is appropriate.
Answer:
D. [tex]y = -5.7x + 67[/tex]
Step-by-step explanation:
Let us take the year 1970 as the 0th year.
So, the corresponding table of values is,
x y
0 65
2 58
4 45
6 32
8 21
Using the linear regression calculator, we see that,
The closest equation of the regression line is [tex]y = -5.7x + 67[/tex].
How do I find the slope of (2,3) and (5,9) by showing all of my work
Answers
(Hint: y is the rise and x is the run. To find slope, we need to know the change in “y” and the change in “x.” That is where the formula comes from)
2 will be x1
3 will be y1
5 will be x2
9 will be y2
You will get 3-9/2-5
Then: -6/-3
Then: 2
The slope is 2.
(Although this works with linear functions, for non-linear functions we use derivatives. I’m assuming you are using a linear function. Assuming the two points are on a linear function, the slope is 2)
Is this pattern a net for the three dimensional figure ?
Answers
The pattern net is not for the three-dimensional figure which is a hexagon prism the answer is No.
What is a regular polygon?A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.
We have a three-dimensional figure is shown in the picture.
As we know,
In the hexagonal prism, there are only two hexagons but in the net, there are three hexagons shown.
Thus, the pattern net is not for the three-dimensional figure which is a hexagon prism the answer is No.
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BRAINLIESTTTT!!!!
Write x^2 − 2x − 3 = 0 in the form (x − a)^2 = b, where a and b are integers.
(x − 4)2 = 3
(x − 3)2 = 2
(x − 2)2 = 1
(x − 1)2 = 4
Answers
x² − 2x − 3 = 0
Step 1
isolate the variable terms
x² - 2x = 3
Step 2
complete the square
x² - 2x + 1² = 3 + 1²
(x-1)² = 4
the answer is the option (x-1)² = 4
1
Which mathematical symbol would best fill in the blank to compare the two real numbers? 7.6 repeating____55 squared
<
>
=
≈
2
Convert 11.42424242 … to a rational expression in the form of a/b , where b ≠ 0.
42/999 with 11 whole number
42/9990 with 11 whole number
42/99 with 11 whole number
99/42 with 11 whole number
3
Order the set of numbers from least to greatest: -5/6, -5, -26 squared, -31/6
4
Identify the number that does not belong with the other three. Explain your reasoning
50.1 reapting , -50/2, , -50.1, 50 squared
Answers
1. 7.6 repeating ____ 55 squared
Find 55 squared.
7.6 < 3025
7.6 is less than 7.4.
2. We already know we have 11 as the whole number.
When you have a repeating decimal, you can keep it as a fraction but use 99 as the denominator.
42/99 with the 11 whole number is the answer.
3. -31/6, -5, -5/6, -26^2 <== least to greatest.
-31/6= -5.16667 -26^2= 676
4. I think the 50 is the square root. Everything else can be represented as a fraction or ratio. The square root of 50 is irrational, and cannot be represented by a fraction or ratio. 50 squared is the one that doesn't belong.
I hope this helps!
~kaikers
Solve 1-12 or any of them please.
Answers
2. y = -x + 4
3. y = 1/3x +1
4. y = ----
5. y = 1/7x + 2
6. y = -4x + 2.75
7. y = 3x + 5
8.
9.
10.
11.
12.
.. x/(x-intercept) +y/(y-intercept) = 1
2) x/4 +y/4 = 1 . . . . . an equation
.. x + y = 4 . . . . . . . . the equation in standard form
3) x/-3 +y/1 = 1 . . . . an equation
.. x -3y = -3 . . . . . . . the equation in standard form
10) x/4 +y/2 = 1
.. x +2y = 4 . . . . . . . in standard form
11) x/-3 +y/5 = 1
.. 5x -3y = -15 . . . . . in standard form
12) x/-10 +y/16 = 1
.. 8x -5y = -80 . . . . . in standard form
For the rest, the 2-point form of the equation of a line will work.
For points (x1, y1) and (x2, y2), the line through them can be written as
.. y = (y2 -y1)/(x2 -x1)*(x -x1) +y1
1) y = (1 -(-3))/(1 -0)*(x -0) +(-3)
.. y = 4x -3
guys please assist me
this is a system of equation word problem
Answers
.. 20t +100h = 10000 . . . . . . the total value of the payment was $10,000
.. t - h = 20 . . . . . . . . . . . . . . . she gave him 20 more twenties than hundreds
Using an augmented matrix, the solution can be found to be
.. t = 100
.. h = 80
She gave the crook only 100 20s, so did not meet the requirement for 105 twenty-dollar bills. Polly did not give him enough.
A toy manufacturer ships a toy in one of two different size boxes. The small box contains 6 of the toy and the large box contains 10 of the toy.
A client orders no fewer than 100 of the toy. Based on his storage and sales needs, the client requires that he receive no more than 8 of the large boxes and no fewer than 6 of the small boxes.
The cost to the client for a small box is $4 and the cost to the client for a large box is $6. The client does not wish to exceed $200 for his order of toys.
Let x represent the number of small boxes and y represent the number of large boxes.
What constraints are placed on the variables in this situation?
Answers
Answer:
Let x represent the number of small boxes.
Let y represent the number of large boxes.
The client receive no more than 8 of the large boxes and no fewer than 6 of the small boxes.
[tex]x \geq 6[/tex]
[tex]y \leq 8[/tex]
The cost of small box is $4 and the cost to the client for a large box is $6. The client does not wish to exceed $200.
[tex]4x+ 6y \leq 200[/tex]
The small box contains 6 of the toy and the large box contains 10 of the toy. A client orders no fewer than 100 of the toy.
[tex]6x+10y \geq 100[/tex]
Matias stacked his cubes to make this rectangular prism.
rectangular prism with grid lines
How many cubes did Matias use?
cubes
Answers
SEE ATTACHED IMAGE.
The problem can be modeled as a pair of matrices:
First matrix:
(4) * (4) = 16
Second matrix:
(16) * (5) = 80
Since the second matrix depends on the first, then the number of cubes is:
N = 80
Answer
80 cubes.
Answer:
The answer is 80
A group of kindergartners and first graders were asked whether or not they can ride a bike. This table shows the relative frequencies of the rows for the two-way table representing this situation. Select from the drop-down menus to complete the statement. The percent of kindergartners surveyed who can ride a bike is (choose-greater than ,less than, equal to) the percent of first graders surveyed who can ride a bike.
Can ride a bike Cannot ride a bike
Kindergartners. 0.32. 0.68
First graders. 0.56. 0.44
Answers
Answer: The percent of kindergartners surveyed who can ride a bike is less than the percent of first graders surveyed who can ride a bike.
Step-by-step explanation:
Given: The table shows the relative frequencies of the rows for the two-way table representing this situation.
The relative frequency for kindergartners surveyed who can ride a bike=0.32
Then, the percent of kindergartners surveyed who can ride a bike=[tex]0.32\times100=32\%[/tex]
The relative frequency for First graders surveyed who can ride a bike=0.56
Then, the percent of First graders surveyed who can ride a bike=[tex]0.56\times100=56\%[/tex]
Clearly, 32 is less than 56.
Therefore, the percent of kindergartners surveyed who can ride a bike is less than the percent of first graders surveyed who can ride a bike.
A) –2n + 9m – 17p
B) –2n – 9mn + 17np
C) –2n + 9mn – 17np
D) –18n + 81mn – 153np
Answers
All you do is simplify the equation by distributing and multiplying the 1/3n to each of the numbers.
Hope this helps!
_____________________________________________________
[tex] \frac{1}{3} [/tex] n (−6 + 27m − 51p) =
( [tex] \frac{1}{3} [/tex] n * −6 ) + ( [tex] \frac{1}{3} [/tex] n * 27m ) −
( [tex] \frac{1}{3} [/tex] n * 51p ) ;
= −2n + 9mn − 17np ; which is: Answer choice: [C]: " −2n + 9mn − 17np" .
__________________________________________________________
In the game of roulette, a player can place a $55 bet on the number 3434 and have a startfraction 1 over 38 endfraction 1 38 probability of winning. if the metal ball lands on 3434, the player gets to keep the $55 paid to play the game and the player is awarded an additional $175175. otherwise, the player is awarded nothing and the casino takes the player's $55. what is the expected value of the game to the player
Answers
In the game of roulette, a player can place a $5 bet on the number 34 and have a 1/38 probability of winning. if the metal ball lands on 34, the player gets to keep the $5 paid to play the game and the player is awarded an additional $175. otherwise, the player is awarded nothing and the casino takes the player's $5. what is the expected value of the game to the player
we know that
P(winning) = 1/38
P(losing) = 1-1/38 = 37/38
Expected value = 175*1/38 - 5*37/38
175/38 - 185/38 = - 10/38 =-$0.2632
The player's expected value is -$0.2632 ( is losing)
30 POINTS!!! HELP PLEASE!
Model each scenario with an equation and a sketch. Solve for the missing value and u. Use complete sentences to interpret the solution. In your final answer, include your equation, sketch, interpretation, and all calculations necessary for the solution.
1.) To get home from school, Bob walks four blocks north and three blocks east. What is the straight line distance between Bob’s house and his school?
2.)One of the requirements of your summer window-washing job is to provide yourself with all of the necessary supplies, including a fourteen foot ladder. When you arrive at your first job, you place your ladder on the ground six feet from the base of the house and lean it towards a second story window, only to realize that the ladder doesn’t reach the window. Given the length of the ladder and its current position, what is one possible height of the second story window? (Hint: There is more than one correct answer.)
3.) In a softball diamond, each of the bases, including home plate, are equidistant from each other. Although the name implies differently, a softball diamond is in the shape of a square. Given that the distance between the bases is unknown, determine an expression for the straight line distance between first and third bases.
4.) A sailboat drifts 600 meters west, makes a turn and sails 800 meters south. How far is the sailboat from its original position?
Answers
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]. Using our coordinates we have:
[tex]d=\sqrt{(4-1)^2+(5-1)^2} \\=\sqrt{3^2+4^2} \\=\sqrt{9+16} \\=\sqrt{25} \\=5[/tex] His house is 5 blocks from the school in a straight line.
#2) The ladder (14 ft) forms the hypotenuse of a right triangle, with the legs being the distance from the house (6 ft) and the height of the ladder (b ft). This gives us:
[tex]6^2+b^2=14^2 \\36+b^2=196[/tex]
Subtract 36 from both sides:
[tex]36+b^2-36=196-36 \\b^2=160[/tex]
Take the square root of both sides:
[tex]\sqrt{b^2}=\sqrt{160} \\b=12.6[/tex]
One possibility for the height of the second story window is 13 feet, since it is longer than 12.6.
#3) The distance from 1st base to 3rd base forms the hypotenuse of a right triangle, with each leg being equal to s, the side length of the square formed by the baseball diamond. Using the Pythagorean theorem we have:
[tex]s^2+s^2=d^2[/tex], where d is the distance from 1st to 3rd. Combining like terms gives us [tex]2s^2=d^2[/tex]. Taking the square root of both sides we have [tex]\sqrt{2s^2}=\sqrt{d^2} \\s\sqrt{2}=d[/tex] (this is due to the fact that square root cancels a squared variable, so s comes out of the radical sign).
#4) The straight distance from the boat's original position to its new position forms the hypotenuse of a right triangle, with the legs being the distance west (600) and the distance south (800) it traveled. Using the Pythagorean theorem we have:
[tex]600^2+800^2=d^2 \\360000+640000=d^2 \\1000000=d^2[/tex]
Taking the square root of both sides we have
[tex]\sqrt{1000000}=\sqrt{d^2} \\1000=d[/tex]
The straight distance between the two points would be 1000 meters.
Select the expression for the following word phrase.
12 less than v
Answers
For this case, the first thing we are going to assume is that we have the following terms:
Number = 12
Variable = v
We then have the following expression:
12 less than v
Writing the expression in algebraic form we have:
12 <v
Answer:
the expression for the word phrase is:
12 <v
4.2(3.9r – 5.9s) + 7.9s – 9.53r
A.
16.88r + 6.85s
B.
10.82r + 31.15s
C.
10.82r – 31.15s
D.
6.85r – 16.88s
Answers
Answer:
D. 6.85r – 16.88s
Step-by-step explanation:
Use the distributive property to eliminate parentheses, then collect terms.
4.2(3.9r -5.9s) +7.9s -9.53r
= 16.38r -24.78s +7.9s -9.53r
= (16.38 -9.53)r +(-24.78 +7.9)s
= 6.85r -16.88s
The function f(x) = −(x + 5)(x + 1) is shown.
What is the range of the function?
a.all real numbers less than or equal to 4
b.all real numbers less than or equal to −3
c.all real numbers greater than or equal to 4
d.all real numbers greater than or equal to −3
Answers
Since the shading would go from 4 all the way to negative infinity, the answer is all real numbers less than or equal to 4.
Best of luck!
Range of the given function is all real numbers less than or equals to 4.
What is the range of the function?The range of a function is the set of all its output values.
According to the given equation we have
f(x) = -(x+5)(x+1)
Let, y = -(x+5)(x+1)
To find the range of the given function, we will substitute different values of x.
At, x = -5
y = f(-5) = -(-5 +5)(-5+1) =0
At, x = -4
y = f(-4) = -(-4 + 5)(-4 + 1) = -(1)(-3) = 3
At, x = -2
y = f(-2) = -(-2+5)(-2+1) = -(3)(-1) =3
At, x = -3
y = f(-3) = -(-3 + 5)(-3 + 1) = -(2)(-2) =4
Similarly, we will find for the other values of x.
So, the coordinates are (-5, 0), (-4, 3), (-3, 4), (-2,3)
And the graph using this coordinates are already given. Here, the set of outputs are the values of y. So we can see that the range of the given function is all real numbers less than or equals to 4.
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Which of the following sets of points forms a linear function?
A. (0, 5) (1, 8) ( 2, 11) (3, 14)
B. (1, 2) (2, 4) (3, 8) (4, 16)
C. (-2, 5) (-1, 2) (0, 1) (1, 2)
D. (-4, 8) (-3, 3) (-2, 0) (1, 3)
Answers
x=1, y=a*1+5=8, a=8-5, a=3
x=2, y=2*3+5=11
x=3, y=3*3+5=14
A is the answer
find the number of liters in 90 gallons
Answers
PLEASSE HELLP! // 99 points // look at the picture below
Answers
Parallelogram is your answer
The opposite sides are parallel to each other, and are congruent.
hope this helps
What is the perimeter of this square?
A.
19 in.
B.
28.5 in.
C.
30.5 in.
D.
38 in.
Answers
An accountant pays 8% per year simple intrest, in year 1 the amount in the account is $850 how much is the account in year 6?
Answers
[tex]\bf ~~~~~~ \textit{Simple Interest Earned Amount}\\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to& \$850\\ r=rate\to 8\%\to \frac{8}{100}\to &0.08\\ t=years\to &5 \end{cases} \\\\\\ A=850[1+0.08(5)]\implies A=850(1.4)[/tex]
A = P(1 + rt) where A is the total amount of principle and interest: P is the initial investment; r is the rate of interest; and t is the time
Using P = 850, r = .08, and t = 5
A = 850(1+ .08(5))
A = 850(1.4)
A = 1190 the amount in the account in year 6
Solving quadratics by factoring 3x^2+33x+30=0
Answers
3(x^2+11x+10)=0
3(x+10)(x+1)=0
x=-10,-1
x = -1 and -10
Hope this helps!!
In order to circumscribe a circle on a triangle, which line must you construct?
a.median
b.altitude
c.diagonal
d.perpendicular bisector
Answers
Explanation:
By definition, a circumscribe circle passes through the three vertices of the triangle and to its constrution, you have to draw the triangle and then construct a perpendicular bisector to each side of it. The point where these perpendicular bisectors intersect each other, will be the center of the circle. Then, you should place the compass on the center point to draw the circle.
The answer is in fact perpendicular bisector