This figure is made up of a triangle and a semicircle. What is the area of this figure? Use 3.14 for pi. Round only your final answer to the nearest tenth. Enter your answer, as a decimal, in the box. units²
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Answers
The area of the figure that is made up of a triangle and a semicircle is 23.137 units².
What is the area of a triangle?The area of a triangle is half the product of its base and its height.
[tex]Area \triangle = \dfrac{1}{2}\times base \times height[/tex]
In order to solve the problem, we will divide the given figure into two parts such that the first one will be a right-angled triangle while the second one is a semi-circle as shown below.
As we can see in the ΔABC, the height of the triangle is 3 units, while the length of the base of the triangle is 6 units. therefore, the area of the triangle can be written as,
[tex]\begin{aligned}\triangle ABC &= \dfrac{1}{2} \times height \times base\\\\&= \dfrac{1}{2} \times BC \times AB\\\\& = 0.5 \times 3 \times 6\\\\& = 9\rm\ unit^2 \end{aligned}[/tex]
Now, if we look at the semi-circle we will find that the diameter(BC) of the semi-circle is 3 units, therefore, the area of the semi-circle can be written as,
[tex]\begin{aligned}\text{Area of Semi-circle} &= \dfrac{\pi}{2}d^2\\\\ &= \dfrac{\pi}{2}(3)^2\\\\&= 14.137\rm\ units^2 \end{aligned}[/tex]
Further, in order to get the total area of the figure, simply add the two areas, therefore,
The area of the figure = Area of triangle + Area of the semi-circle
= 9 + 14.137
= 23.137 units²
Hence, the area of the figure that is made up of a triangle and a semicircle is 23.137 units².
Learn more about Area of Triangle:
https://brainly.com/question/15442893
Related Questions
A set of 5 numbers has a mode of 12 a median of 11 a mean of 10 what could the numbers be?
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The mode is 12. The value 12 shows up the most times. Let's say it shows up twice. So far the data set is {11, 12, 12}
Let's introduce two more numbers x and y
The new data set is {x, y, 11, 12, 12}
Add up the five values and then divide by 5. We want this result to be equal to 10
(x+y+11+12+12)/5 = 10
(x+y+35)/5 = 10
x+y+35 = 10*5
x+y+35 = 50
x+y = 50-35
x+y = 15
So we don't know what x or y is, but we know that they must add to 15. So all you have to do is list two numbers that add to 15. One such pair is x = 6 and y = 9. Another pair is x = 7 and y = 8. There are infinitely many possibilities if you can use any real number.
So one possible set is {6, 9, 11, 12, 12}
Another possible set is {7, 8, 11, 12, 12}
Can anyone help me I don’t know how to do this
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y = a(x -h)² +k . . . . . . . . for some stretch factor "a" and vertex (h, k)
1. Vertex = (h, k) = (0, 0). Stretch factor can be found from the given point (x, y).
8 = a(-2 -0)² +0
8 = 4a . . . . . . . . simplify
2 = a . . . . . . . . . divide by the coefficient of "a"
Your equation is y = 2x².
Note the above method for solving these problems. It repeats.
2. As above, substitute what's given and solve for what's not.
3 = a(1 -2)² +0
3 = a
Your equation is y = 3(x -2)²
3. Repeat
-4 = a(-5 +3)² +0
-4 = 4a
-1 = a
Your equation is y = -(x +3)²
4. Are you seeing the pattern yet?
0 = a(-1 -0)² +1
0 = a +1
-1 = a
Your equation is y = -x² +1
5 & 6. You know that if you want a zero (x-intercept) to be located at x=a, then a factor of the quadratic will be (x -a). Multiply the factors together to get your quadratic function.
5. y = (x -0)*(x -2) = x² -2x
6. y = (x +5)*(x -5) = x² -25 . . . . . . . . . . you should recognize this "special form", the factoring of the difference of squares
how is jimthompson so smart?
Also can you please help me with that question.
I got everything except for the Euler Diagram.
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Step 1) Draw a large circle and label it circle A
Step 2) Inside this large circle, draw a smaller circle and label it circle B
Circle A will represent the set of all obtuse angles (any angles that are between 90 and 180 degrees). Circle B represents only one item: the angle value of 150 degrees. All of circle B is inside circle A because 150 degrees is between 90 and 180; therefore, 150 is obtuse. This is simply the definition of what "obtuse" means.
So if you threw a dart and it landed in circle B, then you know for sure it landed in circle A as well. This is effectively saying "if you get a 150 degree angle, then you know its obtuse"
This is a visual way to back up the conditional statements you used earlier and help add more evidence that the statement "A 150 degree angle is an obtuse angle" is a valid statement.
Which of the following decimal numbers equals 4 thousand, 9 hundreds, 2 tens, and 6 ones?
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decimal numbers equals
4 thousand---------> 4000
9 hundreds--------> 900
2 tens-----------> 20
6 ones-------> 6
so
[4000+900+20+6]=4926
the answer is 4926
The Rotation R maps all 60° about O the center of the regular hexagon. State the image of B for the following rotation.
R^6 =
B
E
O
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Answer:
B will be at same place after all six rotations.
Step-by-step explanation:
If rotation maps to [tex]60^{\circ}[/tex]
Then [tex]R^6[tex] means six rotations .
The given B after one rotation will shift in place of A
After second rotation will shift in place of F
After third rotation will shift in place of E
After fourth rotation will shift in place of D
After fifth rotation will shift in place of C
After sixth rotation will shift in place of B itself.
Therefore, B will come back to same place after all the required rotations.
Translate three times the sum of a number and five
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number = n
the sum of a number and five: n + 5
3 times the sum of a number and five
3(n + 5) is your answer
hope this helps
What is the value of x? Please Answer
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This is a right angle and right angles are 90 degrees in total.
90-30= 60
We know that the missing part of the angle equals 60 degrees so we divide 60 by 4x.
60/4x=15.
I hope that was clear enough, sorry if it’s not. Have a great day and good luck!
Find the slope-intercept form of the line that passes through the given points. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
(1, -5) and (5, -1)
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A line has a slope of -1/2 and a y-intercept of –2. What is the x-intercept of the line? –4, –1, 1 ,4
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now, we have the slope and the y-intercept, well, let's plug those two in the slope-intercept form, reason why is called that anyway,
[tex]\bf y=\stackrel{slope}{-\cfrac{1}{2}}x\stackrel{y-intercept}{-2}\implies 0=-\cfrac{x}{2}-2\implies \cfrac{x}{2}=-2\implies x=-4[/tex]
Alex was thinking of a number. Alex subtracts 14 from it and gets an answer of 29.6. What was the original number?
Answers
43.6 - 14 = 29.6
Hope this helped!
Gina pumps 40 cubic inches of air per second into a balloon. The function below shows the total amount of air f(t) inside the balloon after t seconds. f(w) = 40t + 5 Which statement best describes the y-intercept of the graph of the function?
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Mathematically we have:
For t = 0:
f (0) = 40 (0) + 5
f (0) = 0 + 5
f (0) = 5
Answer:
The intersection with the y-axis represents the total amount of initial air before starting to pump air.
The initial air quantity is:
5 in ^ 3
F(x)=x+2/2 what is the value of f(-8)
A.-4
B.-3
C.-5
D.-6
Answers
------------------------------------------------------
Work Shown:
f(x) = (x+2)/2
f(-8) = (-8+2)/2 ... replace every x with -8; use PEMDAS
f(-8) = (-6)/2
f(-8) = -3
Please help, I’m kinda confused
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Can anyone answer this ???
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The payment is 190,000*(.0725/12)/(1 -(1 +.0725/12)^(-12*20)) ≈ 1501.71
The total of all payments is 240*1501.71 = 360,410.40, so the interest cost is this amount less the principal, or $170410.40.
Total loan cost = $2800 + 1%*190,000 +170,410.40 = 175,110.40
Mortgage B:
The payment is 190,000*(.0525/12)/(1 -(1 +.0525/12)^-240) ≈ 1280.30
The total of all payments is 240*1280.30 = 307,272.00, so the total interest cost is $117,272.00.
Total loan cost = $2800 +5%*190,000 +117,272.00 = 129,572.00
Mortgage A has a larger total cost than Mortgage B by $45,538.40
For each value of w, determine whether it is a solution to -56=7(w-3).
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Answer please anybody
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f(x) = 2x + 1
g(x) = x^2 - 7
(f - g)(x);
(2x + 1) - (x^2 - 7);
-x^2 + 2x + 8.
Your correct answer is C.)
I hope this helps!
Vertical line that passes through the point (3,-8)
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All vertical lines have an undetermined slope (since the formula which represents the slope has a denominator of 0). Therefore the general formula of a vertical line is the following x = c, with c representing the x-coordinate of the point that is passed by the line. Therefore, in your situation we get the line x = 3. When we plot this line, we can see it is a vertical line with x-coordinate 3 and that all values of y are passed, also y = - 8.
Can someone solve the equation |x+8| = x+8
Thank you!
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Hope This Helps Human <3
How do I solve for h
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.. AD = AC -DC = 20 -4
.. AD = 16
Then
.. (long leg)/(short leg) = AD/DB = BD/DC
.. 16/h = h/4
.. h^2 = 64
.. h = 8
Selection D is appropriate.
_____
You may see this again. The altitude (h) from the right angle in a right triangle is the geometric mean of segments AD and DC. That is,
.. h = √((AD)*(DC))
find the perimeter of the quadrilateral. if x = 2 the perimeter is
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then [tex]the perimeter=31+(4x^{2}+8x)+(7x+30)+(3x^{2}-5x+20)[/tex]
[tex] the perimeter= (4x^{2}+3x^{2})+(7x+8x-5x)+20+30+31=7x^{2}+10x+81[/tex]
for x=2
[tex] the perimeter= 7*(2)^{2}+10*2+81=7*4+20+81=28+101=129[/tex]
Note:
Please double check the substitution but the procedure is 100% right.
Answer:
Step-by-step explanation:
Since perimeter of any polygon is represented by sum of its all sides.
Therefore, perimeter of the given quadrilateral = (4x² + 8x) + (3x² - 5x + 20) + (7x + 30) + 31
4x
The graph of an exponential function is given. Which of the following is the correct equation of the function?
y = 0.65x
y = 2.4x
y = 3.5x
y = 0.32x
Answers
-----------------------------------------
Explanation:
We can rule out choice B and choice C which are y = 2.4^x and y = 3.5^x respectively. Why can we eliminate these? Because they are growth functions (the bases are larger than 1). The graph shown is a decay function. It goes downhill as you read it from left to right.
The answer is either choice A or choice D
If we plug in x = -2 into the equations for A and D, we get
y = 0.65^x = 0.65^(-2) = 2.36686
y = 0.32^x = 0.32^(-2) = 9.765625
The result for choice D is much closer to what the graph is showing. The graph appears to have the point (-2,11) on the curve. So that's why choice D is the best answer.
Note: the graph is a bit small and its not entirely clear which points are on this graph other than (0,1). So this is a bit of educated guesswork.
A hair salon charges a fixed rate of $25.00 for a haircut and an additional $15 for any other services. Write a function to model the cost of services at the salon and then evaluate the function to determine the cost for a haircut, shampoo, highlight, and blow dry.
Answers
Answer:
Function : Cost =25 + 15x
Cost for a haircut, shampoo, highlight, and blow dry = $70
Step-by-step explanation:
Hi, to answer this we have to write an equation:
The cost of the services will be equal to the fixed cost for the haircut (25.00) plus the product of the number of additional services (x) and the price of each additional service (15).
Mathematically speaking:
Cost =25 + 15x
To determine the cost for a haircut, shampoo, highlight, and blow dry, we have to substitute x = 3 (because shampoo, highlight, and blow dry are additional services ) in the equation and solve.
Cost = 25+ 15 (3)
Cost = 25+45
Cost = $70
Which represents the explicit formula for the arithmetic sequence
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7-3(n-1) = 7 - 3n + 3 = -3n +10 [tex]f(n) = -3n+10[/tex]
So the answer is D.
If 3x + 8 = 5x - 6, then what is the value of 10x?
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3x + 8 - 5x = 5x - 6 - 5x
-2x + 8 = -6
-2x + 8 - 8 = -6 - 8
-2x = -14
-2x/-2 = -14/-2
x = 7
10x
10 (7)
70
The value of 10x is 70. The value of x is 7.
3/5, give the equivalent numerator if the denominator is 80
3
16
48
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John says the transformation rule (x, y) --> (x + 4, y + 7) can be used to describe the slide of the pre-image (4, 5) to the image (0, –2). What was his error?
Answers
(x, y) -> (x + 4, y + 7)
The ordered pair to which the transformation is applied is:
(x, y) = (4, 5)
Therefore, applying the transformation we have:
(4, 5) -> (4 + 4, 5 + 7) -----> (8, 12)
The error for this case is that John made the following transformation:
(4, 5) -> (4 - 4, 5 - 7) -----> (0, -2)
That is, rest the numbers instead of adding.
Answer:
his error was subtract instead of adding.
The correct answer is:
(8, 12)
Answer:
The pre-image is the point you start with. To check the transformation rule, substitute the values of the coordinates (4, 5) into the rule. You get (4, 5) → (4+4, 5+7). Simplify to get (4, 5) → (8, 12). This is the image. Instead the rule was applied to the image. This is the source of the error.
What is the value of b^2 - 4ac for the following equation?
x^2 + 5x + 4 = 0
A: 9
B: 16
C: 25
Answers
a=1
b=5
c=4
b^2 -4ac =
25 -4 * 1 * 4 =
25 -16 =
9
answer is A
Can anyone help me with these two true/false questions? :)
9. Determine whether the statement is always, sometimes, or never true.
A cubic function has an inverse.
a. always true
b. sometimes true
c. never true
10. Determine whether the statement is always, sometimes, or never true.
A linear function has an inverse relation.
a. always true
b. sometimes true
c. never true
___
Thanks!,
Answers
Answer:
9. b. sometimes true
10. a. always true
Explanation:
9. Any function will have an inverse relation. This question is not specific as to whether that inverse relation must be a function. We will assume that that is the intent.
The attached graph shows a cubic function with an inverse function (green), and another without (red).
A cubic function will have an inverse function sometimes.
____
10. As stated above, any function will have an inverse relation.
A linear function will have an inverse relation always.
__
The graph shows a linear function with an inverse function (green), and one that has an inverse relation, but not an inverse function (red).
In a bag there are 4 blue marbles,8 red marbles, and 5 orange marbles. if two marbles are drawn without replacement find the probability that both marbles are the same color, the second marble being red. the first being blue the second being orange
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= 4/17 * 3/16 + 8/17 * 7/16 + 5/17 * 4/16 = 3/68 + 7/34 + 5/68 = 11/34 Answer
P( second marble being red) = P(first marble not being red) * P( second being red)
= 9/17 * 8/16 = 9/17 * 1/2 = 9/34 answer
P(first ble and second orange) = 4/17 * 5/16 = 5/68 answer
the statement 2n^2+5n-25=0 opens up because
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____
The statement 2n^2 +5n -25 = 0 defines two values of n.