Answers
Answer:
The Area of the composite figure would be 76.26 in^2
Step-by-step explanation:
According to the Figure Given:
Total Horizontal Distance = 14 in
Length = 6 in
To Find :
The Area of the composite figure
Solution:
Firstly we need to find the area of Rectangular part.
So We know that,
[tex]\boxed{ \rm \: Area \: of \: Rectangle = Length×Breadth}[/tex]
Here, Length is 6 in but the breadth is unknown.
To Find out the breadth, we’ll use this formula:
[tex] \boxed{\rm \: Breadth = total \: distance - Radius}[/tex]
According to the Figure, we can see one side of a rectangle and radius of the circle are common, hence,
[tex] \longrightarrow\rm \: Length \: of \: the \: circle = Radius[/tex]
Since Length = 6 in ;[tex]\longrightarrow \rm \: 6 \: in = radius[/tex]
Hence Radius is 6 in.
So Substitute the value of Total distance and Radius:
Total Horizontal Distance= 14 Radius = 6[tex] \longrightarrow\rm \: Breadth = 14-6[/tex]
[tex] \longrightarrow\rm \: Breadth = 8 \: in[/tex]
Hence, the Breadth is 8 in.
Then, Substitute the values of Length and Breadth in the formula of Rectangle :
Length = 6Breadth = 8[tex] \longrightarrow\rm \: Area \: of \: Rectangle = 6 \times 8[/tex]
[tex]\longrightarrow \rm \: Area \: of \: Rectangle = 48 \: in {}^{2} [/tex]
Then, We need to find the area of Quarter circle :
We know that,
[tex]\boxed{\rm Area_{(Quarter \; Circle) } = \cfrac{\pi{r} {}^{2} }{4}} [/tex]
Now Substitute their values:
r = radius = 6 π = 3.14[tex]\longrightarrow\rm Area_{(Quarter \; Circle) } = \cfrac{3.14 \times 6 {}^{2} }{4} [/tex]
Solve it.
[tex]\longrightarrow\rm Area_{(Quarter \; Circle) } = \cfrac{3.14 \times 36}{4} [/tex]
[tex]\longrightarrow\rm Area_{(Quarter \; Circle) } = \cfrac{3.14 \times \cancel{{36} } \: ^{9} }{ \cancel4} [/tex]
[tex]\longrightarrow\rm Area_{(Quarter \; Circle)} =3.14 \times 9[/tex]
[tex]\longrightarrow\rm Area_{(Quarter \; Circle) } = 28.26 \: {in}^{2} [/tex]
Now we can Find out the total Area of composite figure:
We know that,
[tex]\boxed{ \rm \: Area_{(Composite Figure)} =Area_{(rectangle)}+ Area_{ (Quarter Circle)}}[/tex]
So Substitute their values:
[tex]\rm Area_{(rectangle)}[/tex] = 48 [tex]\rm Area_{(Quarter Circle)}[/tex] = 28.26[tex]\longrightarrow \rm \: Area_{(Composite Figure)} =48 + 28 .26[/tex]
Solve it.
[tex]\longrightarrow \rm \: Area_{(Composite Figure)} =\boxed{\tt 76.26 \:\rm in {}^{2}} [/tex]
Hence, the area of the composite figure would be 76.26 in² or 76.26 sq. in.
[tex] \rule{225pt}{2pt}[/tex]
I hope this helps!
Related Questions
14. There are 408 students at a school. There are 4 lunch periods. If there is the same number of students in each lunch period, how many students are in each period?
Answers
Answer:
There are 102 students in each period.
Find the surface area of the cylinder. Use 3.14 for pi. Do not round the answer
690.28
650.83
500.83
791.28
Answers
Answer:
C) 500.83
Step-by-step explanation:
Surface area for a cylinder formula:
SA = 2πrh + 2πr²
Given:
d = 11
r = d/2 = 11/2 = 5.5
h = 9
Work:
SA = 2πrh + 2πr²
SA = 2(3.14)(5.5)(9) + 2(3.14)(5.5)²
SA = 310.86 + 2(3.14)(30.25)
SA = 310.86 + 189.97
SA = 500.83
Graph the parabola.
y=3x²-4
Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function
button.
Answers
Answer:
Vertex: (0, -4)
Graph: I can't share a link so you can go to desmos and paste your equation
Step-by-step explanation:
the vertex is where the axis of symmetry meets with the parabola.
The axis of symmetry is (-b)/(2a) which equals 0 because there is no linear x value
therefore,
y=3(0)^2-4
=-4
so the vertex is (0, -4)
to find the other points, list two x values larger than 0 and substitute into the equation to find y
list two x values smaller than 0 and substitute to find the points on the left of the vertex.
Frank is on the swim team. Each week he swims a total of 6,000 meters. How many kilometers does he swim each week?
Be sure to include the correct unit in your answer
Answers
Answer:
6 km
Step-by-step explanation:
1 meter = 1/1000 km
(1 meter = 1/1000 km) x 1000
1000 meters = 1 km
6000 meters = ?
1 x 6000m = 1000 x ?
6000 = 1000 x 6
6000/1000 = 1000 x 6/1000
6 = 6
Both sides divided by 1000 are 6, so the answer is 6 km.
Solve the simultaneous equations
x+3y=11. X+2y=9
Answers
Answer:
y=2, x=5
Step-by-step explanation:
we can subtract the system of equations to eliminate x and to find the value of 1 y
x+3y=11
minus
x+2y+9
=y=2, now we can replace the value y (2) into either equation to find the value of x
x+3(2)=11
x+6=11
x=5
HELP i don’t know what the slope is or how to do this!!!
Answers
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
[tex]m = \frac{rise}{run} = \frac{y2 - y1}{x2 - x1} [/tex]
please like
Answer:
undefined
Step-by-step explanation:
Slope is a measure of the vertical change relative to the horizontal change. On an x-y graph, it will be the difference in y-coordinates divided by the corresponding difference in x-coordinates. It is often referred to using the letter m.
m = (y2 -y1)/(x2 -x1) . . . . . slope of line between points (x1, y1) and (x2, y2)
It does not matter which points you call point 1 and point 2.
__
For the points given on the graph we can compute the slope to be ...
m = (2 -(-3))/(-1 -(-1)) = 5/0
The zero in the denominator makes this value "undefined." So, we say the slope of any vertical line is "undefined."
PLEASE HELP ME QUICKKK, FIRST CORRECT PERSON GETS BRAINLIEST
Answers
Answer:
Tennessee
Step-by-step explanation:
Select the correct answer from each drop-down menu.
A researcher is examining the claims made by a water softener salt manufacturer. He performs an experiment using water from a variety of sources. For each water source, he has a sample with no treatment and a sample treated with the recommended amount of the water softener salt.
He then tests each sample to measure the softness and compares the results, determining that the claims made by the manufacturer are true.
The conclusion drawn from the study is
because the sample is
. In this instance, an
study was performed.
Answers
The conclusion is valid in this instance because the sample is homogenous and an experimental study was performed.
What is an experimental study?An experimental study is one in which there is a dependent variable and there is a dependent variable. Also a control is used to establish the validity of the results.
In this case the dependent variable is the level of softness after treatment while the independent variable is the type of water softener used.
The conclusion is valid in this instance because the sample is homogenous and an experimental study was performed.
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The supply and demand curves for a market are graft below with price in dollars and quantity in thousands. Which of the following would result from an increase in the supply curve? a. a market equilibrium price greater than $30 b. A market equilibrium price less than $30 c. A market equilibrium quantity less than $30 d. A market equilibrium quantity greater than $30
Answers
Answer:
B) A market equilibrium price less than $30
Step-by-step explanation:
When the supply curve increases, it shifts to the right, making the market equilibrium price lower because the oversupply of the quantity causes demand to drive down.
please help with step by step
Answers
Answer:
Alright breakdown
Step-by-step explanation:
#7. Constant of Proportionality.
divide the 276 by the 184: 276 / 184
which will give you an answer: 1.5
now, multiply 208 by 1.5: 312
Answer: YES
#8 same context, 300 / 425: 0.70
680 x 0.70 : 476
Answer NO
If A= (-4 -1 -9) (-9 6 9) (-1 -1 3) and B= (-10 -7 -5) (9 -7 -1) (9 -4 2), find 6A - 8B
Answers
Given the following data
Schools 2015-2016 2016-2017 2017-2018
AM 1,279 934 686
Dentistry 3,875 934 686
Dentistry 3,875 3459 2977
ELAMS 778 603 437
Med. Tech 2,244 1829 1259
Nursing 205 146 98
NHM 1,870 1321 846
Optometry 702 617 540
Pharmacy 2,336 1686 1075
Sci. Tech. 1,181 931 667
Grad. Sch. 493 601 599
TOTAL 14,963 12,127 9,184
Create visualizations using the appropriate charts to show the following:
1. the populations for the different schools for the year 2015-2016.
2. the proportion of the School of Nursing enrolment for the three school years.
Answers
To determine 1) the proportions of the populations for the different schools for the year 2015-2016, and 2) the proportion of the School of Nursing enrollment for the three school years, the following calculations must be made:
AM1,279/14,963 = 0.0854Dentistry 3,875/14,963 = 0.2589ELAMS 778/14,963 = 0.0519Med Tech 2,244/14,963 = 0.1499Nursing 205/14,963 = 0.0137NHM 1,870/14,963 = 0.1249Optometry 702/14,963 = 0.0469Pharmacy 2,336/14,963 = 0.1561Sci. Tech. 1,181/14,963 = 0.0789Grad.Sch. 493/14,963 = 0.0329146/12,127 = 0.012098/9,184 = 0.0106Therefore, 1) in 2015-2016, 8.54% of students enrolled in AM, 25.89% in dentistry, 5.19% in ELAMS, 14.99% in Med. Tech, 1.37% in nursing, 12.49% in NHM, 4.69% in optometry, 15.61% in pharmacy, 7.89% in Sci. Tech, and 3.29% in Grad. Sch.; and 2) the proportion of the School of Nursing enrollment for the three school years was 1.37%, 1.20% and 1.06% respectively.
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need help with rhis algebra 1 ques
Answers
Answer:
C. Quadrant I
Step-by-step explanation:
For a fact, that with radioactive substance it will decay and never stop halving itself. So the line of amount of radioactive substance always halves in a specific time. This type of graph are done in a positive unit grids, never on a negative because that would mean, the radioactive substance rather decaying, its absorbing. So the answer will be Quadrant I.
Visual likewise graph given below.
Answer:
C. Quadrant I onlyStep-by-step explanation:
Both the time and the amount of the substance are positive.
Since both input and output are positive, it is possible in the fist quadrant.
Correct choice is C
answer 7 and 10 only
Answers
7.
We are given:
abcissa(x-coordinate) of given point: -6
let's say the ordinate(y-coordinate) of the given point is y
distance of the given point from (1,3) = √74
we can rewrite the given information as:
the distance between the points (-6,y) and (1,3) is √74
finding y:
we know that in order to find the distance between any two points, we use the distance formula, which goes as follows:
distance = [tex]\sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}[/tex]
from the data we are given, let's say that:
(x₁, y₁) = (-6, y)
(x₂, y₂) = (1, 3)
(you can use them interchangably, there is no restriction on which point gets to be labelled as 1)
plugging this in the distance formula, we get:
distance = [tex]\sqrt{(-6-1)^2 + (y - 3)^2}[/tex]
we are also given that the distance is √74,
√74 = [tex]\sqrt{(-7)^2 + (y - 3)^2}[/tex]
squaring both sides to get rid of the square root
74 = (-7)² + (y - 3)²
74 = 49 + y² + (3)² -2(y)(3) (using the "square of sum" identity)
74 = 49 + y² + 9 - 6y
74 = 58 + y² - 6y
y² - 6y + 58 - 74 = 0 (subtracting 74 from both sides)
y² - 6y - 16 = 0
y² - 8y + 2y - 16 = 0 (splitting the middle term)
y(y - 8) + 2(y - 8) = 0
(y + 2)(y - 8) = 0
which means that:
y + 2 = 0 , y - 8 = 0
y = -2 , y = 8
These are the two possible values of y
8.
We are given:
points A and B
A: (3, y)
B: (6, 2)
distance between A and B = 5 units
finding possible values of y
here, we will use the distance formula again to find the value of y
distance formula: [tex]\sqrt{(x_a-x_b)^2 + (y_a - y_b)^2}[/tex]
plugging the given values, we get:
5 = [tex]\sqrt{(3-6)^2 + (y - 2)^2}[/tex]
25 = (3 - 6)² + (y - 2)² (squaring both sides)
25 = (-3)² + (y - 2)²
25 = 9 + y² + (2)² - 2(y)(2)
25 = 9 + y² + 4 - 4y
y² - 4y + 9 + 4 - 25 = 0 (subtracting 25 from both sides)
y² - 4y - 12 = 0
y² - 6y + 2y - 12 = 0 (splitting the middle term)
y(y - 6) + 2(y - 6) = 0
(y + 2)(y - 6) = 0
y + 2 = 0 , y - 6 = 0
y = - 2 , y = 6
These are the two possible values of y
Evaluate the expression for y=-29
-42(y+31)=
Please!!!!
Answers
Answer:
[tex] \huge{ \boxed{ \tt - 84}}[/tex]
Step-by-step explanation:
[tex] \sf \rightarrowtail - 42(y + 31)[/tex]
[tex] \\ \\ [/tex]
[tex] \sf \rightarrowtail - 42( - 29 + 31)[/tex]
[tex] \\ \\ [/tex]
[tex] \sf \rightarrowtail - 42(2)[/tex]
[tex] \\ \\ [/tex]
[tex] \sf \rightarrowtail - 42 \times 2[/tex]
[tex] \\ \\ [/tex]
[tex] \sf \rightarrowtail - 84[/tex]
PLS HELP
answer this quick questions please!!
1. c - (-3) = 15
2. (-7) + b = (-11)
3. d x (-4) = 32
Answers
-4
-8
Those should be the answers
Answer:
12, -4, -8
Step-by-step explanation:
1) c=12
c+3=15 subtract 3 from each side. c=12
2) b= -4
-7+b=-11 add 7 to each side. b = -4
3) d= -8
-4d=32 divide each side by negative 4. d = -8
Write a word problem that can be solved by dividing 6 by 5
Answers
Answer:
If john as 5 apples and has 6 friends That what an apple. How many apples will everybody get.
Step-by-step explanation:
a water tank has total capacity 1550 if 28% of the water got drained out how much water left the tank
Answers
Step-by-step explanation:
total capacity =1550l
water drained rate= 28%
amt of water drained =28% of 1550 =434l
now,
water left the tank =1550l-434l =1116l
What are the coordinates of the image of vertex D after
a reflection across the x axis?
Answers
Answer:
6. Which displays the properties of the selected object?
a) Timeline
b) Property Inspector Box
c) Tools Panel
d) Stage
7. What is the extension of the Animate CC file ?
a) .mp3
b) .fls
c) .xls
d) .fla
8. This is a list of clear instructions for solving a problem.
a) Algorithm
b) Abstraction
c) Decomposition
d) Analysis
9. This is a diagrammatic representation of steps to solve a problem.
a) Looping
b) Flowlines
c) Flowchart
d) Algorithm
10. The ____ tool is used to draw star shapes.
a) Rectangle
b) Oval
c) Square
d) Polygon
I dont understand this question can i please get help?
Answers
Answer:
3x2+(24)(x-(17)
############
What s the value of h expression (2) 8
Answers
Answer:
the value of h is 16
These 3 please!!! Properties of Kites and Trapzoids exercises 1-3
Answers
Answer:
area = 1/2(AC)(BD)yes; BE can be found using the Pythagorean theoremyesStep-by-step explanation:
1.Triangles ADB and CDB are congruent, so each is half the total area. The area of ADB is ...
A = 1/2bh
A = 1/2(DB)(1/2AC) = 1/4(DB)(AC)
The area of the kite is twice this value:
A = 1/2(DB)(AC)
__
2.In order to use the formula derived in part 1, we need to know the length of BE. That can be found using the Pythagorean theorem:
BE² +AE² = AB²
We know that AE = 1/2AC, so the desired dimension is ...
BE = √(AB² -(1/4)AC²)
Then the area of the kite is ...
area = 1/2(DB)(AC)
area = (1/2)(AC)(ED +√(AB² -(1/4)AC²)
__
3.Given three sides of a triangle, the area of it can be found using Heron's formula. If you have not yet seen that in your geometry class, you can always use the Pythagorean theorem and some algebra.
As before, we need to know the lengths of the diagonals. One is given. The other can be found considering the Pythagorean relations:
AD² = AE² +DE²
AB² = AE² +BE²
BE +DE = BD . . . . the sum of the horizontal diagonal lengths
Subtracting the second equation from the first gives ...
AD² -AB² = DE² -BE²
Using the third to write an expression for DE, we get an equation for BE:
AD² -AB² = (BD -BE)² -BE²
AD² -AB² = BD² -2BD·BE +BE² -BE²
(AB² +BD² -AD²)/(2BD) = BE
Substituting this into the original second equation, we can find AE, hence the area of the kite.
AE² = AB² -((AB² +BD² -AD²)/(2BD))²
Which means the kite area is ...
area = BD·AE = BD√(AB² -((AB² +BD² -AD²)/(2BD))²)
area = (1/2)√(4·AB²·BD² -(AB² +BD² -AD²)²
This area formula demonstrates it is possible to find the area of the kite given the three lengths AB, BD, DA.
_____
Additional comment
We have no doubt that the area formula of Part 3 can be rearranged to match Heron's formula. Here, we're interested in demonstrating area can be found.
1)Find the quadratic equation
3(3x [tex] {}^{2} [/tex]+ 1)=12x
2)Find the quadratic equation
[tex]9y {}^{2} - 12y - 14 = 0[/tex]
Answers
Step-by-step explanation:
"find" ?
the equations are already there.
do you mean solve in the sense of finding the zero points of the equations ?
if so,
the general solution of a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
3(3x² + 1) = 12x
9x² + 3 = 12 x
9x² - 12x + 3 = 0
a = 9
b = -12
c = 3
x = (12 ± sqrt(144 - 4×9×3))/18 = (12 ± sqrt(144-108))/18 =
= (12 ± sqrt(36))/18 = (12 ± 6)/18
x1 = (12 + 6) / 18 = 18/18 = 1
x2 = (12 - 6) / 18 = 6/18 = 1/3 = 0.3333333...
9y² - 12y - 14 = 0
same thing, we just use y instead of x.
a = 9
b = -12
c = -14
y = (12 ± sqrt(144 - 4×9×-14))/18 = (12 ± sqrt(144+504)/18 =
= (12 ± sqrt(648))/18 = (12 ± sqrt(324×2))/18 =
= (12 ± 18×sqrt(2))/18
y1 = (12 + 18×sqrt(2))/18 = 12/18 + sqrt(2) = 2/3 + sqrt(2) =
= 0.942809042...
y2 = (12 - 18×sqrt(2))/18 = 12/18 - sqrt(2) = 2/3 - sqrt(2) =
= -0.747546896...
what is the answer. help
Answers
Answer: 230
Step-by-step explanation:
Answer:
230.582
Step-by-step explanation:
math, sorry if its wrong im not good with math
a-3xb if a = 20 and b= 5
Answers
Answer:
5
Step-by-step explanation:
3x5 = 15
20-15 = 5
Answer:
5
Step-by-step explanation:
20-3x5=
3x5=15
20-15=5
hope this helps!!
The Gantry family has to pay the following bills for the month of June. Electricity $150, Gas $120, Groceries $530, Water $110, Phone and internet $70. What is the total amount the Gantry family needs to pay in bills for the month?
Answers
Analyze the diagram below and complete the instructions that follow.
Answers
Step-by-step explanation:
given hypotenuse (H), find opposite (O) :
using sin ( SOH),
sin 45° = opp. / hyp.
sin 45° = x / 4√2
x = 4√2 × sin 45°
x = 4
hope this helps you!
-s.
estimate 635/39 by first rounding each number so that each only has one 1 non-zero digit
Answers
Elsa currently has 375 g of sugar and then uses 7 ounces for baking a cake. How many grams (g) of sugar does she have left? 1 ounce = 28 g
Answers
Answer:
179g
Step-by-step explanation:
1ounce = 28g
7 ounces = 196g
375g - 196g
179g
Lin’s family is out for a bike ride when her dad stops to take a picture of the scenery. He tells the rest of the family to keep going and that he’ll catch up. Lin's dad spends 5 minutes taking the photo and then rides at 0.24 miles per minute until he meets up with the rest of the family further along the bike path. Lin and the rest were riding at 0.18 miles per minute.
Answers
It took Lin's dad about 3.6 miles for him to meet up with his family.
SpeedSpeed is the ratio of total distance travelled to total time taken. It is given by:
Speed = distance / time
Let d represent the distance travelled by Lin to meet up with his family. Hence:
Total time for Lin's Dad = d/0.24 + 5
Total time for Lin = d/0.18
Hence:
d/0.24 + 5 = d/0.18
100d/24 + 5 = 100d/18
1800d + 2160 = 2400d
d = 3.6 miles
Find out more on Speed at: https://brainly.com/question/4931057