Find the values of x and y . Then find the measures of the interior angles of the polygon.
Answers
Step-by-step explanation:
It is a cyclic quadrilateral.
The sum of interior angles of this polygon is equal to 180 degrees.
ATQ,
2x+26y=180
x+13y=90 ....(1)
3x+21y=180
x+7y=60 ....(2)
Subtract equation (1) from (2).
x+7y-(x+13y) = 60-90
x+7y-x-13y=-30
-6y=-30
y = 5
Put the value of y in equation (1
x+13(5) = 90
x+65=90
x = 90-65
x = 25
So,
∠DAB = 26y = 26(5) = 130°
∠ABC = 3x = 3(25) = 75°
∠BCD = 2x = 2(25) = 50°
∠ADC = 21y = 21(5) = 105°
x = 25, y = 5
m∠DAB = 26(y) = 180°
m∠ABC = 3x = 75°
m∠BCD = 2x = 50°
m∠ADC = 21y = 105°
Property of a cyclic quadrilateral: Sum of the opposite angles of a cyclic quadrilateral is 180°.
From the picture attached,
ABCD is a cyclic quadrilateral. m∠A = 26y°, m∠B = 3x°, m∠C = 2x° and m∠D = 21y°By using the property of cyclic quadrilateral,
m∠A + m∠C = 180°
26y + 2x = 180
13y + x = 90 --------(1)
m∠B + m∠D = 180°
3x + 21y = 180
x + 7y = 60 --------(2)
Subtract equation (2) from (1),
(13y + x) - (x + 7y) = 90 - 60
6y = 30
y = 5
Substitute y = 5 in equation (1),
13(5) + x = 90
x = 90 - 65
x = 25
Substitute the values of 'x' and 'y' to get the measures of the angles,
m∠DAB = 26(y) = 180°
m∠ABC = 3x = 75°
m∠BCD = 2x = 50°
m∠ADC = 21y = 105°
Therefore, values of the variables will be,
x = 25, y = 5
m∠DAB = 26(y) = 180°
m∠ABC = 3x = 75°
m∠BCD = 2x = 50°
m∠ADC = 21y = 105°
Learn more about the cyclic quadrilateral here,
https://brainly.com/question/24142962?referrer=searchResults
Related Questions
What is the slope of the line that passes through the pair of points (3/2, -2) and (-3, 7/3)?
A. -27/26
B. -26/27
C. 26/27
D. 27/26
Can y'all explain, because I know the answer is B, but I can't figure out for the life of me how to get to that answer.
Answers
Explanation: The formula to find slope is as follows (y2-y1) / (x2-x1). You fill in the x and y coordinates to the corresponding spot. Meaning, you would place the 2nd y value, which is 7/3, at y2. Do this for the rest of the values. After filling in each value, you would then subtract accordingly, leaving you with the slope value. Hope this helps.
What is the value of x?
Answers
9514 1404 393
Answer:
x = 3
Step-by-step explanation:
The triangle is equilateral, so each side is equal to the others:
5x = 3x +6
2x = 6 . . . . . . . subtract 3x
x = 3 . . . . . . . . divide by 2
help plz I really need to finish
Answers
Answer:
[tex]26x^6y^4[/tex]
Step-by-step explanation:
the volume is like
[tex]V = length\cdot width\cdot depth[/tex]
so we have
[tex]V= 4yx^5\cdot 3xy\cdot 2y^2\\\\V=(4\cdot 3\cdot 2)(y\cdot y \cdot y^2)(x^5 \cdot x)\\\\V = 24(y^4)(x^6)\\\\V=24x^6y^4[/tex]
Peter has $12 in nickels and quarters. Altogether, he has 72 coins. Use the variables n and q to write and solve a system of equations to determine how many of each coin she has.
Answers
Step-by-step explanation:
n= nickels
q= quarters
Create a system of equations
n + q =72 number of coins
0.05n + 0.25q = 12 amount in money
solve by elimination ( anything would be fine)
n + q = 72
4( 0.05n + 0.25q = 12)
n+ q = 72
-
0.2n + q = 48
0.8n = 24
n= 30
now use substitution to find how many quarters she has
30 + q = 72
q = 42
He has 30 nickels and 42 quarters
Sorry for skipping some steps
I hope this helps!!!
The line graph below shows the number of chocolate bars and ice lollies sold at a small shop over a year.
Pick the month below in which more ice lollies were sold than chocolate bars.
January
July
April
May
Answers
Answer:
July
Step-by-step explanation:
Month in which more ice lollies were sold than chocolate bars are: Jun, Jul, Aug
This means that from the answer options only July is valid.
An apple juice factory produced 830.87 gallons of apple juice in 4 days. How much apple
juice, on average, did the factory produce each day?
Answers
Answer:
207.7175
Step-by-step explanation:
take the 830.87 and divide it by 4 to see how much is made in 1 day. thats the average.
find the values of y for which the distance between the point p2,-3 and q 10, y is 10 units
Answers
Answer:
y = - 9, y = 3
Step-by-step explanation:
Calculate distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (2, - 3) and (x₂, y₂ ) = (10, y)
d = [tex]\sqrt{(10-2)^2+(y+3)^2}[/tex]
= [tex]\sqrt{8^2+(y+3)^2}[/tex]
Given distance between points is 10, then
[tex]\sqrt{64 +(y+3)^2}[/tex] = 10 ( square both sides )
64 + (y + 3)² = 100 ( subtract 64 from both sides )
(y + 3)² = 36 ( take the square root of both sides )
y + 3 = ± [tex]\sqrt{36}[/tex] = ± 6 ( subtract 3 from both sides )
y = - 3 ± 6 , thus
y = - 3 - 6 = - 9
y = - 3 + 6 = 3
Lucy and JoJo need to make 140 cupcakes for the school dance. Lucy made 35 of the cupcakes JoJo made 42 cupcakes What fraction of the cupcakes do Lucy and JoJo still need to make? (Use / as a fraction bar.)
Answers
Answer:
16/35
Step-by-step explanation:
From the question we are given:
total number of cupcakes needed for the school dance = 140 cupcakes
Lucy made 35cupckes
JoJo made 42 cupcakes
Total cupcakes made by JoJo and Lucy = 35+42 = 76cupcakes
Remaining cupcakes still needed to be made = 140 - 76 = 64cupckes
Fraction of the cupcakes that Lucy and JoJo still need to make = 64/140
Fraction of the cupcakes that Lucy and JoJo still need to make = 16/35
Hence the fraction of the cupcakes that Lucy and JoJo still need to make is 16/35
Answer:
16/35
Step-by-step explanation:
convert y = -2x +5 to point slope form
Answers
Answer:
Converting y = -2x +5 to point-slope form will be:
[tex]y - 5 = -2(x-0)[/tex]Step-by-step explanation:
We know that the slope-intercept form of the line equation is
y = mx+b
where
m is the slopeb is the y-interceptGiven the equation
[tex]y = -2x +5[/tex]
comparing with the slope-intercept form
Slope of the line = m = -2
The y-intercept b = 5
We know that the value of y-intercept can be determined by setting x = 0, and determining the corresponding value of y.
Thus, the ordered pair or point representing the y-intercept will be:
(0, 5)Now, we have
The slope = m = -2The point = (0, 5)Now, using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where
m is the slope of the line(x₁, y₁) is the pointsubstituting the values m = -2 and the point (x₁, y₁) = (0, 5)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y - 5 = -2(x-0)[/tex]
Therefore, converting y = -2x +5 to point-slope form will be:
[tex]y - 5 = -2(x-0)[/tex]if 12% = £54
what does 100% =
Brainliest to first correct answer :)
Answers
Answer:
£450
Step-by-step explanation:
12%=£54
100%=?
we will criss cross it then 12%×?=100%×£54÷12
=£450
ASAP! Please do 1-5 and show work if possible!
Answers
Answer :
(1) The radius of a circle is 1.5 m.
(2) The diameter of a circle is 28 ft.
(3) The radius of a circle is 10 in.
(4) The circumference of circle is 47.14 m.
(5) The circumference of circle is 44 yd.
Step-by-step explanation :
Part 1:
Given: d = 3 m
Now we have to determine the radius of circle.
As we know that:
Radius of a circle = [tex]\frac{Diameter}{2}[/tex]
So,
Radius of a circle = [tex]\frac{3m}{2}=1.5m[/tex]
The radius of a circle is 1.5 m.
Part 2:
Given: r = 14 ft
Now we have to determine the diameter of circle.
As we know that:
Radius of a circle = [tex]\frac{Diameter}{2}[/tex]
So,
Diameter of a circle = [tex]Radius\times 2[/tex]
Diameter of a circle = [tex]14ft\times 2=28ft[/tex]
The diameter of a circle is 28 ft.
Part 3:
Given: d = 20 in
Now we have to determine the radius of circle.
As we know that:
Radius of a circle = [tex]\frac{Diameter}{2}[/tex]
So,
Radius of a circle = [tex]\frac{20in}{2}=10in[/tex]
The radius of a circle is 10 in.
Part 4:
Given: d = 15 m
Now we have to determine the circumference of circle.
Formula used:
[tex]C=\pi d[/tex]
where,
C = circumference
d = diameter
So,
[tex]C=\frac{22}{7}\times 15m[/tex]
[tex]C=47.14m[/tex]
The circumference of circle is 47.14 m.
Part 5:
Given: r = 7 yd
Now we have to determine the circumference of circle.
Formula used:
[tex]C=\pi d[/tex]
or we can write,
[tex]C=\pi (2\times r)[/tex]
where,
C = circumference
d = diameter
r = radius
So,
[tex]C=\frac{22}{7}\times (2\times 7yd)[/tex]
[tex]C=44yd[/tex]
The circumference of circle is 44 yd.
write a quadratic polynomial, sum of whose zeroes is 2 and product is -8
Answers
Answer:
x^2 +2x-8
Step-by-step explanation:
Here, we want to write the quadratic polynomial given the sum of the root and the product
mathematically, we can have the factors as -2 And +4
So we have the equation as;
(x-2)(x + 4)
= x^2+ 2x - 8
B
NEED HELP ASAP Angles A and B are
supplementary. If
MLB-IoTº, what is
the M
(The pic is of the question)
Answers
Answer:
79
Step-by-step explanation:
Supplementary are angles that will add up to 180. So to find the missing angle we do 180 - 101 and get 79.
hope this helps (:
Find the perimeter of a 35° slice of pizza that has a radius of 8 inches.
Answers
9514 1404 393
Answer:
20.9 inches
Step-by-step explanation:
The perimeter length is the sum of the lengths of the two straight edges and that of the curved edge.
P = r + r + rα . . . . . where α is the central angle in radians
35° is (35°/180°)π radians, about 0.6109 radians
Then the perimeter is ...
P = r(2 +α) = (8 in)(2 +0.6109) ≈ 20.9 in
The perimeter of the slice is about 20.9 inches.
Pls help me It would help alot
Answers
Answer: A=4πr2
I really hope this helped!!
SIMPLE INTEREST
Interest = ?
Principal = $1450
Interest rate = 9%
Time = 5 years
Answers
652.50
Step-by-step explanation:
1450 x .09 x 5 = 652.50
Han earns $33.00 for babysitting 4 hours. At this rate, how much will he earn if he
babysits for 7 hours. You may solve with any method but you must show your work.
Answers
Step-by-step explanation:
First, you want to find the unit rate, or how much Han earns per hour
You can do this by setting up an equation
x= amount earned per hour
4x= 33 Initial equation
4x/4 = 33/4 Isolating the variable
x = 33/4 = 8 1/4 = 8.25 The unit rate
Now you want to set up a new equation to find out how much he makes for 7 hours
x= amount earned per hour
y = total amount earned
y = 7x Initial equation
y = 7 ( 8.25) Substitution
y = 57.75 The answer
Han earns $57.75 for every 7 hours
Checking the answer....
y = 7x
57.75 = 7x Substitute y instead
57.75/7 = 7x/7
8.25 = x
Your answer should be correct
Hope this helps!!!
( 1/4) ꓥ -3 =
A= -64
B= -1/64
C= 1/64
D= 64
Answers
Answer:
C-1/64
Step-by-step explanation:
(1/4)(1/4)(1/4)=1/64
Mark the brainliest
The best player on a basketball team makes 95% of all free throws. The second-best player makes 90% of all free throws. The third-best player makes 80% of all free throws. Based on their experimental probabilities, estimate the number of free throws each player will make in his or her next 40 attempts. Explain.
Answers
Answer: See explanation
Step-by-step explanation:
The best player on a basketball team makes 95% of all free throws. The number of free throws the best player will make in his or her next 40 attempts will be:
= 95% × 40
= 95/100 × 40
= 0.95 × 40
= 38
The second-best player makes 90% of all free throws. The number of free throws the best player will make in his or her next 40 attempts will be:
= 90% × 40
= 90/100 × 40
= 0.90 × 40
= 36
The third-best player makes 80% of all free throws. The number of free throws the best player will make in his or her next 40 attempts will be:
= 80% × 40
= 80/100 × 40
= 0.80 × 40
= 32
Pls help!!!!! 20 points! and brainliest!!!
Answers
Answer:i tried
Step-by-step explanation:
On the swim team, for every 10 girls there are 7 boys. If there are 21 boys on the swim team, how many girls are there?
Answers
Answer:
30 girls
Step-by-step explanation:
Every 10 girls there are 7 boys.
So if there are 3 groups of 7 boys, there will be 30 girls.
Check:
10 girls: 7 boys
+10 girls: 7 boys
+10 girls: 7 boys
= 30 girls: 21 boys
QUESTION 23
Tamara has $50 to spend on craft supplies. She spends $30
plus a 5% tax at the store. How much change should she
receive?
Answers
Answer:
the answer is $18.5
Step-by-step explanation:
30 + tax is $31.50
Answer:
$18.50
Step-by-step explanation:
Before Tax Price: $30
Sales Tax Rate: 5%
After Tax Price: $18.50
How can you find how much the sales tax is? Let's say you're buying a $100 item with a sales tax of 5%. Your math would be simply:
[cost of the item] x [percentage as a decimal] = [sales tax]
Step 1 : $30 x .05 (5%) = $1.50 Step 2 : $30 + $1.50 = $31.50Step 3 : $50 - $31.50 = $18.50A rectangular swimming pool has a base of 200 square feet. The pool has a depth of 5 feet. What is the volume of the pool?
Answers
Answer:
200 X 5 = 1000 square feet
Step-by-step explanation:
V = L x W x H
Answer:
1,000
Step-by-step explanation:
Which number serves as a counterexample to the statement below. 2X < 3X
1- 2
2- 1/2
3- 1/4
4- -2
Plz help me :)
Answers
Answer:
-2
Step-by-step explanation:
Here, we want to select a value that makes the expression wrong
The correct answer will be a negative number
Thus, we have it that;
2(-2) > 3(-2)
-4 > -6
Which of the following equations is equivalent to 1/3x=2?
4x = 16
4x - 2 = 26
4x + 2 = 22
4x + 2 = 26
Will give brainest
Answers
Answer:
4x-2=26
Step-by-step explanation:
Triangle ABC is a right triangle. Triangle A B C is a right triangle. Angle A C B is 90 degrees, angle C B A is 31 degrees, and angle B A C is 59 degrees. What is the relationship between angles A and B?
Answers
Answer:
see explanation
Step-by-step explanation:
Complementary angles sum to 90°
∠ CBA = 31° and ∠ BAC = 59° , sum to 90° (31° + 59° = 90° )
Thus
∠ A and ∠ B are complementary angles
Answer: They are complementary
Step-by-step explanation: took the test on edge!
PLEASE HELP I NEED THE COORDINATES ASAP ILL GIVE BRAINLIEST
Answers
Answer:
Step-by-step explanation:
Slope of a line that passes through 19,3 and 4,3
Answers
Answer:
0
Step-by-step explanation:
y2-y1/x2-x1
3-3/4-19
0/-15
So its 0
Kayla thinks that the slope of a vertical line is undefined, while Joshua argues that the slope of a vertical line is zero. Who is correct? *
Answers
Answer:
Kayla is correct
Step-by-step explanation:
For a vertical line, the x-value is the same
This means there is no change in the x value
A slope is calculated by dividing by the change in x value
since in this case , we will be dividing by zero, it means that the value of our slope is going to be undefined
This means that Kayla is correct
Help plz I need to fin before today help
Answers
Answer:
BD = 12.1 (nearest tenth)
Step-by-step explanation:
∆ABC is an isosceles triangle, since it has two equal sides, AB and BC. Also, this means that <BAD and <BCD = 60° each.
BD divides ∆ABC into two equal parts.
Apply trigonometric ratio to find BD.
Reference angle = <BAD = 60°
Adjacent = AD = 7
Opposite = BD
Thus, we would have:
tan 60 = opp/adj
Tan 60 = BD/7
7*Tan 60 = BD
12.1 = BD
BD = 12.1 (nearest tenth)