Correct Answer will get BRAINLIEST!
Segment $AB$ has midpoint $C$, and segment $BC$ has midpoint $D$. Semi-circles are constructed with diameters $\overline{AB}$ and $\overline{BC}$ to form the entire region shown. Segment $CP$ splits the region into two sections of equal area. What is the degree measure of angle $ACP$? Express your answer as a decimal to the nearest tenth.
Answers
Answer:
The degree measure of ∠ACP is 112.5°
Step-by-step explanation:
The total area of the given diagram is the sum of two semicircles with arc AB and arc CB having radius R and r respectively
Where:
R = AC
r = DB
R = 2 × r
Therefore the area of the semicircles are given as follows;
For the semicircle with arc AB, we have;
Area, A₁ = π × R²/2 = π × (2×r)²/2 = 2×π×r²
For the semicircle with arc CB, we have;
Area, A₂ = π × r²/2 = 1/2×π×r²
The ratio of the two semicircles is presented in the following relation;
[tex]\dfrac{A_1}{A_2} = \dfrac{2 \cdot \pi \cdot r^2}{\dfrac{1}{2} \cdot \pi \cdot r^2} = \dfrac{2}{\dfrac{1}{2} } = 2 \times \dfrac{2}{1} = 4[/tex]
Therefore, the area of A₁ is four times that of A₂ or A₁ = 4 × A₂
The total area of the given diagram = A₁ + A₂ = 4 × A₂ + A₂ = 5·A₂
∴ Half of the area of the diagram, [tex]A_H[/tex] = 5·A₂/2 = 2.5·A₂ = 2.5 × 1/2×π×r² = 1.25×π×r²
The ratio of half of the diagram of the figure to the area of the semicircle with arc AB is found as follows;
[tex]A_H[/tex]/A₁ = (1.25×π×r²)/(2×π×r²) = 5/8
Therefore, the half of the diagram of the figure given by segment PAC is equivalent to 5/8 of the semicircle with arc AB
Given that the arc AB subtends an angle of 180° at the center (angle subtended by a semicircle), the arc AP will subtend 5/8×180 = 112.5°
To verify we have;
Area of a segment of a circle is presented in the following relation;
[tex]\dfrac{\theta}{360} \times \pi \times r^2[/tex]
As segment PAC is 5/8 of a semicircle, it is therefore 5/(8×2) or 5/16 of the whole circle
Hence;
[tex]\dfrac{5}{16} \times \pi \times r^2 = \dfrac{\theta}{360} \times \pi \times r^2[/tex]
[tex]\dfrac{5}{16} = \dfrac{\theta}{360}[/tex]
[tex]\theta \dfrac{}{} = \dfrac{360 \times 5}{16} = 112.5 ^ {\circ}[/tex]
Therefore the degree measure of ∠ACP is 112.5°.
Related Questions
Identify the parent function of f(x)=(x+3)3
Answers
Answer:
g(x) = x^3
Step-by-step explanation:
f(x)=(x+3)^3
The parent function is
g(x) = x^3
The function was shifted to the left 3 units from the parent function
f(x) = ( x- -3) ^3
f(x) = ( x+3) ^3
The Japanese Yen corresponds to the American Dollar. If the exchange rate is 150 Yen for 1 Dollar, then a Japanese car sold in America for $10,000 will bring in 1,500,000 Yen. If the exchange rate changes to 120 Yen for each Dollar, then what price in Dollars would the car have to be sold in America to bring the Japanese 1,500,000 Yen?
Answers
Answer:
125,000
Step-by-step explanation:
Take the Japanese yen and divide by 12
1,500,000 divided by 12 = 125,000
These triangles ARE similar! Which reason proves it?
Circle one:
AA~
SSS~
SAS~
SHOW CALCULATIONS to verify they are similar!
Answers
Answer:
I would say AA
Step-by-step explanation:
try to separate the picture to see the bigger picture and you can do it.
3. What is the value of x + y?
Answers
Answer:
y = 50 x = 10.
Step-by-step explanation:
Let's solve for y first.
We know the line angle 80 and angle 2y-5 is on a 180 degree line.
Now we can do our work:
180 - 85 = 95
2y - 5 = 95
95 + 5 = 100
100 ÷ 2 = 50
2(50) - 5 = 95?
The equation is correct, therefore y = 50.
No we do the same thing for the other angles, 90 and 3x + 55.
Again, 180 line.
180 - 95 = 85
3x + 55 = 85
85 - 55 = 30
30 ÷ 3 = 10
3(10) + 55 = 85?
The equation is correct therefore x = 10.
Thus, y = 50 and x = 10.
Find the difference
[tex]( - {3x}^{3} - {7x}^{2} + 5x - 4) - ( {6x}^{2} - 8)[/tex]
Answers
Answer:
Step-by-step explanation:
whats the answer???
Answers
Answer:
wtz i think is the answer. they are supplementary
Step-by-step explanation:
Answer:
WTZ
Step-by-step explanation:
Supplementary angles add to 180 degrees or form a straight line
WTV and WTZ make a straight line so they are supplementary angles
A line is drawn through the point (-1,-1), parallel to the line 2x-3y+9=0. Where will it cross the x-axis?
Answers
Answer:
2x-3y-1=0I hope I'm correct.Step-by-step explanation:
[tex]2x-3y+9=0\\Rearrange -in-form-of : y = mx+b\\-3y=0-9-2x\\-3y=-2x-9\\\frac{-3y=-2x-9}{-3} \\y =\frac{2}{3} \\\\For- parallelism- , m1=m2\\One -point- form (-1,-1)\\x1 = -1\\y1 = -1 \\m = \frac{2}{3}\\ y -y1=m(x-x1)\\y -(-1)=\frac{2}{3} (x-(-1))\\y+1=\frac{2}{3}(x+1)\\y+1=\frac{2}{3}x + \frac{2}{3}\\\\y = \frac{2}{3}x + \frac{2}{3}-1\\\\y = \frac{2}{3}x - \frac{1}{3}\\Multiply- through-: by 3 \\3[y = \frac{2}{3}x - \frac{1}{3}]\\\\3y = 2x -1\\Answer = 2x-3y-1=0[/tex]
If f(x) = 3x + 10x and g(x) = 4x – 2, find (f + g)(x).
A. 3x – 6x + 2
B. 3x + 6x + 2
C. 17x – 2
D. 3x + 14x – 2
Answers
Answer:
a is answer correct i think
Step-by-step explanation:
Find the value of the expression 8x↑3 if: x=3
Answers
Answer:
216
Step-by-step explanation:
8x³
Put x as 3 in the expression.
8(3)³
Solve the power.
8(27)
Multiply.
= 216
Assignment: The Discriminant
Part I: Practice Finding the Discriminant
Find the value of the discriminant for each quadratic equation below. Show all steps needed to
write the answer in simplest form, including substituting the values of a, b, and cin the
discriminant formula. Then use the value to determine how many real number solutions each
equation has.
1.
x + 6x-3.0
2. 3x + 2x+1=0
3. x + 4x + 4 = 0
4. 5x + x = 4
5. 2x -3x = -5
6.
X-X=12
Answers
Answer:
1. D = 48, two; 2. D = -8, none; 3. D = 0, one
4.D = 81, two; 5. D = -91, none; 6. D = 49, two
Step-by-step explanation:
The formula for a quadratic equation is
ax² + bx + c = 0
The quadratic formula gives the roots:
[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a} = \dfrac{-b\pm\sqrt{D}}{2a}[/tex]
D is the discriminant.
It tells us the number of roots to the equation — the number of times the graph crosses the x-axis.
[tex]D = \begin{cases}\text{positive} & \quad \text{2 real solutions}\\\text{zero} & \quad \text{1 real solution}\\\text{negative} & \quad \text{0 real solutions}\\\end{cases}[/tex]
It doesn't matter if the graph opens upwards or downwards.
If D > 0, the graph crosses the x-axis at two points.
If D = 0, the graph touches the x-axis at one point.
If D < 0, the graph never reaches the x-axis.
1. x² + 6x - 3 =0
a= 1; b = 6; c= -3
D = b² - 4ac = 6² - 4×1×(-3) = 36 - 4(-3) = 36 + 12 = 48
D > 0: two real solutions
2. 3x² + 2x + 1 = 0
a = 3; b = 2; c =1
D = b² - 4ac = 2² - 4×3×1 = 4 - 12 = -8
D < 0: no real solutions
3. x² + 4x + 4 = 0
a = 1; b = 4; c =1
D = 4² - 4×1×4 = 16 - 16 = 0
D = 0: one real solution
4. 5x² + x = 4
5x² + x - 4 = 0
a = 5; b = 4; c = -4
D = 1² - 4×5×(-4) = 1 - 20(-4) = 1 - (-80) = 1 + 80 = 81
D > 0: two real solutions
5. 5x² - 3x = -5
5x² - 3x + 5= 0
a = 5; b = -3; c = 5
D = (-3)² - 4×5×5 = 9 - 100 = -91
D < 0: no real solutions
6. x² - x = 12
x² - x - 12= 0
a = 1; b = 1; c = -12
D = 1² - 4×1×(-12) = 1 - 4(-12) = 1 + 48 = 49
D > 0: two real solutions
Please complete the attachment attached below
Answers
Answer:
The mode is 7 , median is 7 and the range of data is 2.8
Step-by-step explanation:
Stem leaf diagram :
5 | 7 7 9
6 | 5 6 8 8 9
7 | 0 0 0 2 5 5 7 8
8 | 4 4 5
Key : 5|7 means 5.7 cm
So, Data : 5.7,5.7,5.9,6.5,6.6,6.8,6.8,6.9,7.0,7.0,7.0,7.2,7.5,7.5,7.7,7.8,8.4,8.4,8.5
a)Mode : The most occurring number in the data is the mode
So, 7 is the mode of the data
b)
No. of observations = n = 19
[tex]Median = \frac{n+1}{2}\text{th term}\\Median = \frac{19+1}{2} \text{th term}\\Median = 10 \text{th term}\\Median = 7.0[/tex]
C)Range = Maximum - Minimum= 8.5 - 5.7 =2.8
Hence The mode is 7 , median is 7 and the range of data is 2.8
please answer need help
Answers
Answer:
Obviously, the negative numbers come first so the answer is -3.7, -1.9, -1/2, 1 1/3, 1.6, 2 1/3.
Answer:
-3.7, -1.9, -1/2, 1 and 1/3, 1.6, 2 and 1/3.
The sum of seven times a number—
PLEASE HELP!
Answers
Answer:
x = 6
y = 4
Step-by-step explanation:
Let the two numbers be x and y
Condition 1:
7x+3y = 54 -----------(1)
Condition 2:
x = 2+y -----------------(2)
Putting (2) in (1)
=> 7(y+2)+3y = 54
=> 7y+14+3y = 54
=> 10y = 54-14
=> 10y = 40
Dividing both sides by 10
=> y = 4
Now putting y = 4 in eq(2)
=> x = 2+4
=> x = 6
Answer:
[tex]4\\6[/tex]
Step-by-step explanation:
[tex]7x+3y=54\\x=y+2[/tex]
[tex]7(y+2)+3y=54\\7y+14+3y=54\\10y+14=54\\10y=40\\y=4[/tex]
[tex]x=y+2\\x=4+2\\x=6[/tex]
Natalia wants to attend Louisiana State University. One year at Louisiana State University costs approximately $24,000. She currently has $4,000 in savings. Natalia has received a one-time grant of $1,500 and an annual academic scholarship for $3,500. She plans to enroll in the work study program that will pay $12,000 annually for part-time work. How much will Natalia need to borrow in student loans in order to attend Louisiana State University for 4 years?
Answers
Answer:
He needs to borrow $28,500 to attend the University for 4 years.
Step-by-step explanation:
One year at the University costs $24,000. The total she has to pay are 4 * $24,000 = $96,000
minus the $4,000 she has in savings: $96,000 - $4,000 = $92,000
minus the $1,500 she received one time: $92,000 - $1,500 = $90,500
minus $3,500 per anual
4* $3,500 = $14,000
$90,500 - $14,000 = $76,500
minus $ 12,000 per anual
4 * $12,000 = $48,000
$76,500 - $48,00 = $28,500
Josephine bought a sweater for $9.99 and a skirt for $21.50. She gave the clerk $50. How much change did she receive
Answers
Answer: $18.51
Step-by-step explanation:
She paid $50
Her total purchases
$9.99 + $21.50 = 31.49
Change = (50 - 31.49) = 18.51
Step by step explanation:
$9.99 + $21.50 = $31.49
$50 - $31.49 = $18.51
Hope it helps
Alyssa walked 1/2 miles in 8 1/2 minutes. What is the unit rate in miles per minute?
Answers
Answer:
1/17 miles per minute
Step-by-step explanation:
Divide the miles by the minutes
.5 miles
---------------
8.5 minutes
5/85 miles per minute
1/17 miles per minute
Answer:
1/17
Step-by-step explanation:
You would divide the minutes and the miles.
8 1/2 divided by 1/2 which gives you1/17.
I hope this helped. I'm sorry if you get this wrong.
A group of tourists can be sorted into tour boats in groups of 4 or in groups of 6. In either case, there are no empty seats. Find the number of tourists if there are more than 25 and fewer than 45.
Answers
Answer: there are 36 tourists.
Step-by-step explanation:
Ok, we have two integer numbers:
T, the number of tourists and S, the number of seats.
Such that, if we divide the tourists into groups of 4 and in groups of 6, we end with no empty seats.
Knowing that the number S must be an integer, and when we divide T into groups of 4 and 6 we end with no empty seats, this means that T can be divided by 4 and by 6.
This means that T is a common multiple of 4 and 6
Now, we also know that 25 < T < 45.
Then let's see which ones are the multiples of 4 between 25 and 45.
4*7 = 28
4*8 = 32
4*9 = 36
4*10 = 40
4*11 = 44.
Now, the multiples of 6 in that range are:
6*5 = 30
6*6 = 36
6*7 = 42.
You can see that 36 is a common multiple, other way to see it is:
4*9 = (2*2)*(3*3) = 2*2*3*3 = (2*3)*(2*3) = 6*6
So the numer of tourist must be 36.
Which transformation will map an isosceles trapezoid onto itself?
Answers
Answer:
rotation by 180°
Step-by-step explanation:
about its center, reflection across a diagonal, reflection across a line joining the midpoints of the nonparallel sides,rotation by 360° about its center. hope this helps you :)
Write the converse, inverse, and contrapositive of the following conditional statement
“If I go to college, I will get a better job.”
Answers
Answer:
using implication
Step-by-step explanation:
let "if I go to college be (A)" and "I will get a better job be (B)"
therefore A implies B
(A ----------------> B)
If I go to college then I will get a better job.
Jessica has some round stickers. Each sticker has a radius of 2 cm. She is trying to cover as much of a sheet of paper that is 24 cm by 33 cm as possible without any overlap and modification of the stickers How much bare paper will be visible around the stickers?
Answers
Answer:
63 bare paper will be visible around the stickers
Step-by-step explanation:
We are given that Jessica has some round stickers. Each sticker has a radius of 2 cm.
Now she is trying to cover as much of a sheet of paper that is 24 cm by 33 cm
Area of rectangular sheet =[tex]Length \times Breadth[/tex]
Area of rectangular sheet = [tex]24 \times 33[/tex]
Area of rectangular sheet =792 cm^2
Area of 1 circular sticker =[tex]\pi r^2[/tex]
Area of 1 circular sticker [tex]=3.14 \times 2^2 =12.56 cm^2[/tex]
No. of circular stickers can be drawn from a sheet of paper that is 24 cm by 33 cm =[tex]\frac{792}{12.56}=63.057[/tex]
So, 63 bare paper will be visible around the stickers
I do not understand 2 column proof in Geometry. PLEASE HELP
Answers
Answer:
A two-column geometric proof consists of a list of statements, and the reasons that we know those statements are true. The statements are listed in a column on the left, and the reasons for which the statements can be made are listed in the right column.
hope this helped :)
Two-column proof:
Two-segment geometric evidence comprises of a rundown of explanations, and the reasons that we realize those announcements are valid. The announcements are recorded in a segment on the left, and the purposes behind which the announcements can be made are recorded in the correct section. A scientific evidence might be composed utilizing a passage, two-sections, or utilizing a stream diagram. The two-section verification is the strategy we use to introduce a sensible contention utilizing a table with two segments. Significant data is generally given to help start a proof and is normally the beginning stage everything being equal.
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Solve the equation. 1.25 =0.75+r
Answers
Answer:
0.50
Step-by-step explanation:
Do the opposite of addition
So 1.25 - 0.75
The solution to the equation 1.25 = 0.75 + r for r is r = 0.5
How to determine the solution to the equation for rFrom the question, we have the following parameters that can be used in our computation:
1.25 = 0.75 + r
Add -0.75 to both sides of the equation
so, we have the following representation
-0.75 + 1.25 = 0.75 + r + -0.75
Evaluate the like terms on the right hand side
This gives
-0.75 + 1.25 = r
Evaluate the like terms on the left hand side
This gives
0.5 = r
Rewrite as
r = 0.5
Hence. the solution is 0.5
Read more about equations at
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Two-step equations word problems. Please and thank you in advance!
Answers
Answer:
The equation is 3mx1/4t=9
Step-by-step explanation:
step 1) 3mx1/4t=9
step 2) 3m=36
step 3) there was 12 pieces of cake
Ken started a savings account for school. He plans on spending 10% of the money he earns for leisure activities. He needs to have $2,160 in the bank before he starts school. how much must he earn to have the amount needed for school?
Answers
Answer:
$2,400
Step-by-step explanation:
Ken intends to start a savings account
10% = leisure spending
This means 90% = Expenses for school
Let us represent the amount he must save as : x
Hence in other for him to have $2,160 in his savings account, the amount Ken must earn is calculated as:
90/100 × x = $2,160
Cross Multiply
90x = $2,160 × 100
x = ($2,160 × 100) ÷ 90
x =$2,400
Therefore, the amount Ken has to earn to have the amount needed for school is $2,400
What is one difference in midsegments for triangles versus midsegments for trapezoids?
Answers
Answer:
Step-by-step explanation:
Midsegments of a triangle and a trapezoid are alike, because their endpoints, are the midpoints of the sides they touch. ... whereas, the length of a midsegment of a triangle is base/2.
The one difference in midsegments for triangles versus midsegments for trapezoids Midsegments of triangles and trapezoids are different because we can draw 3 of them in triangles, but only one in trapezoids.
What are triangles and trapezoids?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
A trapezoid, commonly referred to as a trapezium, is a quadrilateral or a polygon with four sides. It has a set of parallel opposing sides and a set of non-parallel sides. The bases and legs of the trapezoid are known as the parallel and non-parallel sides, respectively.
If a line through the midpoint of a leg of a trapezoid is parallel to its bases, then the line passes through the midpoint of the other leg.
The midsegment of a trapezoid is half the length of the two parallel sides.
The midsegment theorem states that a line segment connecting the midpoints of any two sides of a triangle is parallel to the third side of a triangle and is half of it.
learn more about trapezoids here :
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PLEASE HELP ASAPPP!!! 15PT QUESTION!!! Suppose that a ball is rolling down a ramp. The distance traveled by the ball is given by the function s(t), where t is the time, in seconds, after the ball is released, and s(t) is measured in feet. For given function, find the ball’s average velocity from t1 to t2. s(t)=11t^2; t1=6, t2=6.5
Answers
Answer:
The average velocity of the ball is [tex]137.5 \:ft/sec[/tex]
Step-by-step explanation:
First find the velocities at given times and then form two points. Calculate the slope to find the average velocity. The two points are:
[tex]\left(6,\:396\right)\quad and \quad \:\left(6.5,\:464.75\right)[/tex]
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}=\frac{464.75-396}{6.5-6}[/tex]
[tex]m=137.5[/tex]
Best Regards!
Help plz will give brainliest
Answers
Answer:
150Step-by-step explanation:
[tex]30\% \times 500 \\ 0.3 \times 500 \\ = 150[/tex]
Answer: the answer is 150
Step-by-step explanation:
30% x 500
0.3 x 500
= 150
Use the diagram to find the angle measures.
Find m∠1, m∠3, and m∠4 if m∠2=117°.
Find the measures of all four angles if m∠2+m∠4=220°.
Answers
Answer:
1.) m∠1 = 63 degree
m∠3 = 63 degree
m∠4 = 117 degree
m∠2 = 117 degree
2.) m∠1 = 70 degree
m∠3 = 70 degree
m∠4 = 110 degree
m∠2 = 110 degree
Step-by-step explanation:
Given that
1.) m∠2 = 117°.
In the figure, m∠1 is vertically opposite to m∠3, and m∠4 is vertically opposite to m∠2
Therefore, m∠2 = m∠4 = 117° ( because vertically opposite angle are equal)
Also, the sum of angles at a point is equal to 360 degrees
m∠2 + m∠4 = 234°
Take 234 away from 360. That is,
360 - 234 = 126
126/2 = 63 degrees.
Therefore, m∠1 = m∠3 = 63°
2.) If m∠2 + m∠4 = 220°
Subtract 220 from 360 since the sum of angles at a point is equal to 360 degrees
360 - 220 = 140
Divide 140 by 2 and also 220 by 2 to get
140/2 = 70 and 220/2 = 110
Therefore,
m∠1 = 70 degree
m∠3 = 70 degree
m∠4 = 110 degree
m∠2 = 110 degree
Find the angle measure given the figure is a rhombus.
Answers
Answer:
Angle 1 = 156°
Step-by-step explanation:
The angle opposite 12 is also equal to 12 because the rhombus is split into two congruent triangles.
The other part about a rhombus is that the line angles in half meaning that where 12 is cut in half, the full angle is 24.
With this info, we now know that the other two angles that are in the triangle with angle 1 have a sum of 24°
Subtract: 180 - 24 = 156°
please look at image and tell me what the right answer is!!!
WILL REWARD BRAINIEST!!
Answers
Answer:
See below.
Step-by-step explanation:
Recall that the biggest angle will always be opposite from the biggest side.
IT is opposite from Angle S, which we can figure out to be 180-108-25=47.
SI is opposite from Angle T, which is 41.
ST is opposite from Angle I (the whole thing). Just from looking at it, we know that it is the biggest angle. If we want to figure it out, Angle I is 180-41-72+25=92.
The smallest side is SI, then IT, then ST.
The correct order is: SI, IT, and ST.