Is my work correct?
Given: ABCD is an inscribed polygon.
Prove: ∠A and ∠C are supplementary angles.
Answers
Solution:
Given: A B CD is an inscribed polygon.
To Prove: ∠A and ∠C are supplementary angles.
Proof: Join AC and B D.
Angle in the same segment of a circle are equal.
∠ACB=∠ADB→→AB is a segment.
Also, ∠A B D=∠A CD→→AD is a Segment.
In Δ ABD
∠A+∠ABD+∠ADB=180°→→Angle sum property of triangle.
∠A+∠A CD+ ∠ACB=180°
∠A+∠C=180°
Hence proved, that is, ∠A and ∠C are supplementary angles.
The method Adopted by you
∠1=2 ∠A----(1)
and, ∠2=2 ∠C-------(2)
The theorem which has been used to prove 1 and 2, Angle subtended by an arc at the center is twice the angle subtended by it any point on the circle.→(Inscribed angle theorem)
Also, angle in a complete circle measures 360°.→→Chord arc theorem
∠1+∠2=360°→→Addition Property of Equality
2∠A+2∠C=360°→→[Using 1 and 2, Called Substitution Property]
Dividing both sides by 2→→Division Property of Equality
2∠A+2∠C=360°→→[Using 1 and 2]
∠A+∠C=180°
→→Correct work.
A two-column proof to prove that angles A and C are supplementary angles should be completed as follows;
Statement Reason______________
ABCD is an inscribed polygon Given
mBCD = 2(m∠A) Inscribed Angle Theorem
mDAB = 2(m∠C) Inscribed Angle Theorem
mBCD + mDAB = 360° The sum of arcs that make a circle is 360°
2(m∠A) + 2(m∠C) = 360° Substitution Property
m∠A + m∠C = 180° Division Property of Equality
∠A and∠C are supplementary angles Defintion of supplementary angles.
In Mathematics and Euclidean Geometry, the inscribed angle theorem states that the measure of an inscribed angle is one-half the measure of the intercepted arc in a circle or the inscribed angle of a circle is equal to half of the central angle of a circle.
Generally speaking, a supplementary angle refers to two angles or arc whose sum is equal to 180 degrees.
Based on the defintion of supplementary angles, we can logically deduce that angle A and angle C are supplementary angles.
Related Questions
Find the sum of the summation of 2 i minus 12, from i equals 7 to 16.
22
110
220
440
Answers
S=[2(7)-12]+[2(8)-12]+[2(9)-12]+[2(10)-12]+[2(11)-12]+[2(12)-12]+[2(13)-12]+[2(14)-12]+[2(15)-12]+[2(16)-12]
S=2(7+8+9+10+11+12+13+14+15+16)-10(12)
S=2(115)-120
S=230-120
S=110
Answer: Second option 110
Answer: Second option is correct.
Step-by-step explanation:
Since we have given that
[tex]\sum_{7}^{16}(2i-12)\\\\=\sum_{7}^{16}2(i-6)\\\\=2\sum_{7}^{16}(i-6)\\\\=2[(16-6)+(15-6)+(14-6)+(13-6)+(12-6)+(11-6)+(10-6)+(9-6)+(8-6)+(7-6)]\\\\=2[10+9+8+7+6+5+4+3+2+1]\\\\\text{Sum of n natural numbers }\\\\=2(\frac{10\times (10+1)}{2})\\\\\=\frac{n(n+1)}{2}\\\\=2\times \frac{10\times 11}{2}\\\\=10\times 11\\\\=110[/tex]
Hence, the value of summation is 110.
Therefore, Second option is correct.
Line RS is tangent to circle Q at point R.
What is the measure of ∠SQR ?
Enter your answer in the box.
Answers
Now that we know 2 angles, we can find the 3rd:
180 - 90 - 32 = 58
Using the tangent and radius theorem, the measure of ∠SQR is 58°.
What is Circle Geometry??From the question, we are to determine the measure of ∠SQR
In the given diagram, QR is a radius
By the tangent and radius theorem,
If a tangent and a radius meet at the point of tangency, then they are perpendicular to one another
∴ ∠QRS = 90°
∠SQR + ∠RSQ + ∠QRS = 180° (Sum of angles in a triangle)
∠SQR + 32° + 90° = 180°
∠SQR + 122° = 180°
∠SQR = 180° - 122°
∠SQR = 58°
Hence, the measure of ∠SQR is 58°.
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If x varies directly as y, and x = 48 when y = 16, find x when y = 5.
A) 5/3
B) 153.6
C) 15
Answers
48 = k* 16
k = 3
x=3*5
x=15
Answer:
15
Step-by-step explanation:
x =ky
48 = k16
divide by 16
k = 3
plug k into x=ky
x=3*5
x=15
PLEASE ANSWER ASAP Becky purchased a home entertainment center for $2,254 using an 18-month deferred payment plan with an interest rate of 22.48%. She did not make any payments during the deferment period. What will Becky's monthly payment be if she must pay off the home entertainment center within three years after the deferment period?
$121.01
$87.45
$62.61
$113.72
Answers
Answer:
$62.61
Step-by-step explanation:
Data:
The price of home entertainment = $ 2 254
Time to pay = 18 months
interest rate = 22.48 %
monthly payment = $ 2254/ 18
= $ 125. 22
= - 22.48 (2254)/18
= $ 62.61
Sophia and Tyler are running around a 400-meter track. They start running from the same place, at the same time. Sophia runs at a speed of 5 m/s and Tyler runs at a speed of 4 m/s. How long will it take Sophia to lap Tyler?
Answers
S: Runner Sophia.
T: Runner Tyler.
At the beginning the distance between both runners is 400m
At t = 1s Sophia runs 5m and Tyler 4m
At t = 2s Sophia runs 10m and Tyler 8m
and so on.
So, for example at t = 1s, the distance between both runner is:
D = 400m - 5m(the advantage of Sophia) + 4m(what Tyler recovers)
So, we can find a general equation for this matter. Knowing that the distance, velocity and time are related by this equation:
[tex]d=vt[/tex]
Then, the distance between both runners, at any time, is given by:
[tex]D = 400-5t+4t[/tex]
So we need to find the how long it will take Sophia to lap Tyler. This happens when D = 0:
[tex]0 = 400 - 5t+4t[/tex]
∴ [tex]400-t = 0[/tex]
∴ [tex]t = 400s[/tex]
Answer: 400 seconds
Step-by-step explanation:
5x = 400 + y
4x = y
take 4x and add it to the top so it looks like this:
5x = 400 + 4x
cancel 4x if you don't know how to do it you do it like this you take +4x and instead you do -4x to cancel.
and you do it to 5x so you cancel 4x and 5x - 4x = x so x = 400
x = 400
Need this geometry answer quick!
Answers
90 + 6x + 4x = 180
Combine like terms:
90 + 10x = 180
Subtract 90 from both sides:
10x = 90
Divide both sides by 10:
x = 9
Answer: 9
Circle P is tangent to the x-axis and the y-axis. If the coordinates of the center are (r, r), find the length of the chord whose endpoints are the points of tangency.
2r
r²
r√2
Answers
.......................
triangle XYZ is obtuse which list could represent the angle measures of triangle XYZ?
A. 20 60 100
B. 30 60 90
C. 50 50 80
D. 60 60 60
Answers
Need help to write equations for 5, 6 & 7
Answers
The x-values go up by 1: -2, -1, 0, 1, 2
The y values are always 3 times the previous value.
This is an exponential function.
[tex] y = a(b)^x [/tex]
We need to find a and b.
Look at x = 0.
For x = 0, y = 4.
[tex] y = a(b)^x [/tex]
[tex] 4 = a(b)^0 [/tex]
Since b^0 = 1, this simplifies to
[tex] 4 = a [/tex]
Now we know a = 4. We have
[tex] y = 4(b)^x [/tex]
Look at x = 1. For x = 1, y = 12.
[tex] 12 = 4(b)^1 [/tex]
[tex] 12 = 4b [/tex]
[tex] b = 3 [/tex]
Now that we know a and b, we can write the function.
[tex] y = 4(3)^x [/tex]
Now that you have the function written out, notice the following.
In the exponential equation we found, the number raised to x
is the number you multiply each y value to get the next y value.
In this case, each y value is 3 times the previous one, so you have 3^x.
The way you find "a" in the exponential equation is to look at the y-coordinate
when x = 0. When x = 0, b^x is 1, so b^x drops out, and you get "a" equal to
the y-value. In this case, when x = 0, y = 4, so "a" is 4.
With b = 3, and a = 4, you can quickly write:
y = 4(3)^x.
A bin is constructed from sheet metal with a square base and 4 equal rectangular sides. if the bin is constructed from 48 square feet of sheet metal, then what is the largest volume of such a bin? what are its dimensions?
Answers
In the figure shown below we have the representation of this problem, so we know that the base of this bin is square. We also know that there are four square rectangles sides. This bin is a cube, therefore the volume is:
V = length x width x height
That is:
[tex]V = xxy = x^{2}y[/tex]
We also know that the bin is constructed from 48 square feet of sheet metal, so:
Surface area of the square base = [tex]x^{2}[/tex]
Surface area of the rectangular sides = [tex]4xy[/tex]
Therefore, the total area of the cube is:
[tex]A = 48 ft^{2} = x^{2} + 4xy[/tex]
Isolating the variable y in terms of x:
[tex]y = \frac{48- x^{2} }{4x}[/tex]
Substituting this value in V:
[tex]V = x^{2}( \frac{48- x^{2} }{x}) = 48x- x^{3} [/tex]
Getting the derivative and finding the maxima. This happens when the derivative is equal to zero:
[tex]\frac{dv}{dx} = 48-3x^{2} =0[/tex]
Solving for x:
[tex]x = \sqrt{\frac{48}{3}} = \sqrt{16} = 4[/tex]
Solving for y:
[tex]y = \frac{48- 4^{2} }{(4)(4)} = 2[/tex]
Then, the dimensions of the largest volume of such a bin is:
Length = 4 ft
Width = 4 ft
Height = 2 ft
And its volume is:
[tex]V = (4^{2} )(2) = 32 ft^{3}[/tex]
find the greatest common factor 6x^2a + 6xa^2
Answers
If you multiply 6xa with a and x ----> 6xa(x+a), you'll get 6x^2a + 6xa^2
Jason was hired to mow a lawn that covers an area of acres 2 3/4. It took him 4 1/8 hours to complete the job. What was his unit rate in hours per acre?
I understand the steps where I am stuck is how did you get 2/3/
Answers
Divide 2 3/4 acres by 4 1/8 hours:
Divide 2.75 acres by 4.125 hours:
2.75 acres
--------------- = 2.667 acres/hour, or 2 2/3 acres / hour.
4.125 hrs
If this is not entirely clear to you, please share the work you've done yourself and I will respond.
O is the center of the given circle. The measure of angle O is 128°. The diagram is not drawn to scale.
Assuming that lines that appear to be tangent are tangent, what is the value of x?
Answers
The measure of the external angle is the semi difference of the arcs that it covers.
so
see the picture attached to better understand the problem
m AB=128°--------> by central angle
m ACB=360°-128°-----> m ACB=232°
∠x=(1/2)*[m ACB-m AB]
∠x=(1/2)*[232-128]-----> ∠x=(1/2)*104°-----> ∠x=52°
the answer is
∠ x is 52°
Hope I helped :)
Identify a counterexample to disprove 6n>n^2/6,where n is a real number.
Answers
A counterexample to disprove the inequality [tex]6n > n^2/6[/tex] is n = 12, because when plugged into the inequality, it results in 72 > 24, which is false.
The question is asking for a counterexample to disprove the inequality [tex]6n > n^2/6[/tex], where n is a real number. To find a counterexample, let's test an arbitrary positive number, such as n = 7, to see if the inequality holds.
Substituting 7 for n, we get:
6 x 7 > 72/6
42 > 49/6
42 > 8.167
This is indeed true, so 7 is not a counterexample. However, we can think of a larger value of n. Let's try n = 12:
6 x 12 > 122/6
72 > 144/6
72 > 24
This is false. Hence, n = 12 serves as a counterexample to disprove the given inequality. So, the inequality does not hold for all real numbers.
The expression 8x + 2y
Answers
Hamilton received a 75 on his algebra exam. The professor is allowing students to take a 7-question bonus quiz to improve their algebra exam score. Each question answered correctly on the bonus quiz will add 3 points to the exam score. Hamilton needs to receive at least a 90 on his exam score in order to make an "A" for the semester. If x represents the number of questions answered correctly on the bonus quiz, which of the following inequalities symbolizes this situation?
A. 3x + 75 < 90
B. 7x + 75 > 90
C. 3x + 75 > 90
D. 7x + 75 < 90
Answers
Since each question answered right would add 3 points, the amount of questions answered correctly would be x. You then going to add that to his original score, 75. He needs at least a 90, so 90 is the lowest test grade he can afford. Therefore, 90 is should be the greatest number since there are no less than, equal to and such. Knowing that, the answer would be A
Hope this helps!
Final answer:
The correct inequality should be 3x + 75 ≥ 90 to indicate Hamilton needs at least 90 on his exam. The closest option given, which is not entirely accurate, is C. 3x + 75 > 90.
Explanation:
To determine the inequality that represents Hamilton’s situation, we need to calculate how many points he requires to reach a score of at least an “A”, which is 90. Each correct bonus question adds 3 points to his exam score of 75. We need to find the number of questions, x, Hamilton must answer correctly to achieve a total score of 90 or more. Therefore, the inequality that encompasses this scenario is 3x + 75 ≥ 90 because each correct answer contributes 3 points towards closing the 15-point gap between his current score and the desired score of 90.
However, the options given do not include the correct representation which would be 3x + 75 ≥ 90. Instead, the closest option is C. 3x + 75 > 90, which would imply that Hamilton must score more than 90, which is not a requirement for making an “A” (as “A” can include exactly 90).
Students washed cars to raise funds for their school. they collected $291 by charging $3.00 per car. how many cars did they wash?
Answers
=$291 total ÷ $3 a car
=97 cars
ANSWER: They washed 97 cars.
Hope this helps! :)
An investment of $450 increases at a rate of 6.5% per year. What is the growth factor, b?
Answers
What is the standard deviation of the following data set rounded to the nearest tenth? 52.1, 45.5, 51, 48.8, 43.6
Answers
[tex]\sigma = \sqrt{ \frac{1}{N} \sum (x_i - \mu)^2} [/tex]
where
N is the number of data (in this case, N=5)
[tex]x_i[/tex] are the data
[tex]\mu[/tex] is the average value
Let's calculate the average value:
[tex]\mu = \frac{52.1+45.5+51+48.8+43.6}{5}=48.2 [/tex]
And now we can apply the formula to calculate the standard deviation:
[tex]\sigma = \sqrt{ \frac{1}{5} \sum ( x_i - 48.2 )^2} =[/tex]
[tex]= \sqrt{ \frac{1}{5} ( (3.9)^2 + (-2.7)^2 + (2.8)^2 + (0.6)^2 + (-4.6)^2 ) } =[/tex]
[tex]= \sqrt{ \frac{1}{5} (51.86) } =3.2[/tex]
Answer:
Standard deviation is 3.2.
Step-by-step explanation:
Given data is,
52.1, 45.5, 51, 48.8, 43.6,
Let x represents the data points,
Now, mean of the data is,
[tex]\mu = \frac{52.1 + 45.5 + 51 + 48.8 + 43.6}{5}=48.2[/tex]
Population size, N = 5,
Hence, the standard deviation of the following data set is,
[tex]\sigma = \sqrt{\frac{1}{N}\sum_{i=1}^{N} (x_i-\mu )^2[/tex]
[tex]=\sqrt{\frac{1}{5}\sum_{i=1}^{5} (x_i-48.2 )^2[/tex]
[tex]=\sqrt{\frac{1}{5} (15.21+7.29+7.84+0.36+21.16)}[/tex]
[tex]=\sqrt{10.372}[/tex]
[tex]=3.2205589577[/tex]
[tex]\approx 3.2[/tex]
Simplify the trigonometric expression.
Answers
[tex](1+sin \alpha )(1-sin \alpha )=1-sin^2 \alpha [/tex]
Now we can rewrite our expression using the common denominator:
[tex]\frac{1-sin \alpha }{1-sin^2 \alpha } + \frac{1+sin \alpha }{1-sin^2 \alpha} = \frac{2}{1-sin^2 \alpha} [/tex]
Finally, we can use the trig identities: [tex]1-sin^2 \alpha =cos^2 \alpha [/tex] and [tex]sec \alpha = \frac{1}{cos \alpha } [/tex] to simplify our trig expression:
[tex]\frac{2}{cos^2\alpha}=2sec^2 \alpha [/tex]
We can conclude that the correct answer is the fourth one.
THe answer is letter D. 2 sec^2 theta
Hope it help! Goodluck!
Find the slope of the line on the graph
Answers
1st point ( -4,0)
2nd point (0,3)
slope = change in y over change in x
change in y = 3-0 = 3
change in x = 0 - -4 = 0+4 = 4
slope = 3/4
_________________ lines are lines that never intersect and are not coplanar. A) Parallel B) Perpendicular C) Skew D) Transversal
Answers
Skew lines are lines that never intersect and are not coplanar.
So the answer would be C. ^-^
Use substitution to determine which of the following points is a solution to the standard form equation below. 2y = 5
Answers
This is the complete question as I found in internet:
Use substitution to determine which of the following points is a solution to the standard form equation below 5x-2y = 10
these are the points:
-1,5
1,5
0,-5
0,5
Answer: (0, -5)
Explanation:
point x y 5x - 2y = 10 ?
-1,5 -1 5 5(-1) - 2(5) = - 5 - 10 = - 15 ≠ 10 ⇒ not a solution
1,5 1 5 5(1) - 2(5) = 5 - 10 = 5 ≠ 10 ⇒ not a solution
0,-5 0 -5 0 -2(-5) = 10 ⇒ a solution
0,5 0 5 0 - 2(5) = - 10 ≠ 10 ⇒ not a solution
Answer:
(10,5/2) answer is A
Step-by-step explanation:
just took test.
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
area of rectangle=length*width
let
x-----> the length side
y-----> the width side
y=13 units
A=2x²-5x
A=x*y------> 2x²-5x=x*13------> 2x²-18x=0-----> x²-9x=0
x*(x-9)=0
the solutions are
x=0
x=9
hence
the dimensions of the rectangle are
length is 9 units
width is 13 units
the area of rectangle is -----> 9*13-----> 117 units²
the answer is
117 units²
Solve the system of equations and choose the correct answer from the list of options. (4 points) x − y = 7 y = 3x + 12
Answers
y = -33/2
Start by plugging in the second equation for y in the first equation. Then solve for x. After you can use that value to solve for y.
What is cos 45? Please HELP !!!
Answers
Answer:
A) Cos ( 45) = [tex]\frac{1}{\sqrt{2}}[/tex].
Step-by-step explanation:
Given : Triangle 90 -45 -45 .
To find : What is cos 45.
Solution : We have given
Triangle 90 -45 -45
Hypotenuse = √2 ,
Adjacent side to 45 degree = 1 .
By the trigonometric ratio : cosine is the ratio of the adjacent side to angle to the hypotenuse .
Cos ( theta) = [tex]\frac{Adjacent}{hypotenuse}[/tex].
Plug the values Hypotenuse = √2 , Adjacent side to 45 degree = 1 .
Cos ( 45) = [tex]\frac{1}{\sqrt{2}}[/tex].
Therefore, A) Cos ( 45) = [tex]\frac{1}{\sqrt{2}}[/tex].
The cosine of 45° is √2 / 2.
In a triangle with angles of 90°, 45°, and 45°, we can use the trigonometric functions to find the ratios of the sides.
In this case, we want to find the cosine of 45°.
The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse.
In the given triangle, the adjacent side to the 45° angle is 1, and the hypotenuse is √2.
Using the formula for cosine, we have:
cos 45° = adjacent side / hypotenuse
Substituting the values, we get:
cos 45° = 1 / √2
To rationalize the denominator, we multiply both the numerator and denominator by √2:
cos 45° = (1 / √2) * (√2 / √2) = √2 / 2
Therefore, the cosine of 45° is √2 / 2.
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PLS HELP ME ASAP WITH 3, 4, AND 5! PLS! (Read directions carefully :)
(BRAINLIEST WILL BE GIVEN HOPEFULLY!)
(Random answers gets moderated!)
Answers
a. d(0) = 20
b. d(2) = 18
c. d(4) = 12
d. d(6) = 10
e. d(9) = 15
f. d(3) = 15, or d(9) = 15
4) The domain is the horizontal extent: 0 to 12.
The range is the vertical extent: 10 to 20.
5)
a. f(7) = -2*7 +5 = -9
b. f(-3) = -2(-3) +5 = 11
c. -2x +5 = 17; -2x = 12; x = -6, so f(-6) = 17
Quadrilateral ABCD has the following vertices: A(-4, -3), B(2, -3), C(4, -6), and D(-4, -6). Quadrilateral ABCD is a
A. trapezoid
B. parallelogram
C. square
D. rectangle
Answers
Quadlirateral ABCDwith vertices: A(-4, -3), B(2, -3), C(4, -6), and D(-4, -6) is s A. TRAPEZOID
the answer is TRAPEZOID
2=sqrt P solve for P
Answers
Square both sides;-
(sqrt P)^2 = 2^2
P = 4 Answer
2²=(√P)²
4=P
P=4
The square root of 136 is between which two whole numbers?
Answers
Hope this helps!