3.3.4 Practice: Angle Relationships in Triangles
Practice
Math 8 Sem 2
Points Possible:5
Date:
Tips for Success
Read the assignment carefully and make sure you answer each part of the question or questions.
Check your work when you're done.
Your Assignment
Answer the questions to find the measures of ∠2 and ∠3.
1. What is the measure of ∠4? Explain how you know.
Write your answer in the space below.
2. What is the sum of the measures of the angles in a triangle?
Write your answer in the space below.
3. ∠1 is in a triangle with ∠4 and a 53° angle. What is the sum of the measures of those two angles?
Write your answer in the space below.
4. What is the measure of ∠1? Explain.
Write your answer in the space below.
5. Find the measure of ∠2. Explain how you found its measure.
Write your answer in the space below.
6. What is the measure of ∠3? Explain.
Write your answer in the space below.
For question 1 and 2, you should keep in mind that the sum of all angles in a triangle is 180°. 1. If the measure of one angle of a triangle is 90 degrees, you can assume that the sum of the other two triangles should be 90 degrees. Because
180 - 90 = 90
The sum of the three angles of any triangle is equal to 180 degrees.
Angle 2=127 because 180-53=127.
Angle 3=23 because 180-30-127=53
Angle 1=37 because 90-53=37
Angle 4=90
Angle 1+4=127
The measure of ∠1 is 125° .
Next x+64=110. The reason why you can do this is because ∠R is going to be an opposite interior angle. Subtract 64 from the left and right sides. x=46
Answer:
AP EX
Step-by-step explanation:
What is the surface area of the cylinder with height 8 ft and radius 5 ft? Round your answer to the nearest thousandth.
PLZ help me with this question
Answer:
I believe it's A and D.
If I helped you're welcome. If I didn't I'm sorry.
Answer:
A and D
Step-by-step explanation:
im not too good on fractions but hopefully its right
plases helpppppppppppppppppp
I need help with this
look at picture
Complementary angles
Answer:
x is equal to 11...........
90°-35°= 55°
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Order the steps for constructing a circle that is circumscribed about a triangle
Answer:
1. Construct the perpendicular bisector of one side of triangle.
2. Construct the perpendicular bisector of another side.
3. Where they cross is the center of the Circumscribed circle.
4. Place compass on the center point, adjust its length to reach any corner of the triangle, and draw your Circumscribed circle!
There are four steps for constructing a circle that is circumscribed about a triangle.
What exactly is the triangle?A triangle is a three-sided polygon with three angles. The total of the triangle's angles is 180 degrees.
The steps for constructing a circle that is circumscribed about a triangle are as follows;
1. Draw the perpendicular bisector of one of the triangle's sides.
2. Create another side's perpendicular bisector.
3. The intersection is the circumscribed circle's center.
4. Place the compass on the center point, change the length of the compass to reach any corner of the triangle, and draw your circumscribed circle.
Hence, the above steps help to construct a circle that is circumscribed about a triangle.
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Target buys video games for $25/game. They markup the price by 75%. How much do
they charge customers for a videogame? Do not enter a dollar symbol with your
answer.
9514 1404 393
Answer:
$43.75
Step-by-step explanation:
The amount of the markup is ...
$25 × 0.75 = $18.75
The final cost to the customer is ...
selling price = purchase price + markup
= $25.00 + 18.75 = $43.75
They charge customers $43.75 for a videogame.
Name 6 elements of PQR.
Answer:
josh
rabeesh
ronger
roger
roge
robert
Step-by-step explanation:
What's 16/12 + 11/6?
Answer:
It's 3 1/6 :) I hope it helps
please help me.......
A number divided by eight minus thirteen is greater than negative six.
Answer:
(x/8) - 13 > -6
Step-by-step explanation:
If you want to take it further, add 13 to both sides to make it x/8 > 7. Then divide both sides by 8 to get x by itself. you are left with x > 7/8
Random tip to remember: when dividing by negatives, remember to switch the inequality signs (this is just for future reference)
17 is between which two integers ?
Answer:
Step-by-step explanation:
two integers mean numbers that do not have decimals. Whole numbers
to figure out between what two integers get a calculator
which is 4.123 (to three decimal places)
thus it falls between 4 and 5. since it is above 4 and below 5 and there are no integers in between possible.
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A Ferris wheel has a 44-foot radius and the center of the Ferris wheel is 50 feet above the ground. The Ferris wheel rotates in the CCW direction at a constant angular speed of 3 radians per minute. Josh boards the Ferris wheel at the 3-o'clock position and rides the Ferris wheel for many rotations. Let tt represent the number of minutes since the ride started.
Write an expression (in terms of t) to represent the number of radians Josh has swept out from the 3-o'clock position since the ride started.
How long does it take for Josh to complete one full revolution (rotation)?
________ minutes
Write an expression (in terms of t) to represent Josh's height above the center of the Ferris wheel (in feet).
Write a function f that determine's Josh's height above the ground (in feet) in terms of t.
f(t)=
Answer:
Part A
The expression in terms of 't' representing the number of radians Josh has swept since the ride started is 3·t rad
Part B
The time to complete one revolution is (2·π/3) minutes
Part C.
The function 'f' that determines Josh's height above the ground (in feet) in terms of 't' is, f(t) = 44·sin(3·t + π/2) + 50
Step-by-step explanation:
The radius of the Ferris wheel = 44 foot
The height of the Ferris wheel above the ground = 50 feet
The direction of rotation of the Ferris wheel = CCW
The angular speed of the Ferris wheel, ω = 3 radians per minute
The position from which Josh boards the Ferris wheel = 3-O'Clock
The number of minutes since the ride started started = t
Part A
The expression in terms of 't' to represent the number of radians Josh has swept since the ride started = ω × t = 3 × t rad = 3·t rad
Part B
One complete revolution = 2·π radians
The time to complete one revolution = 2·π/ω = 2·π/(3 rad/minute) = (2·π/3) minutes = [tex]0.\overline{6}[/tex]·π minutes ≈ 2.0943951 minutes
Part C.
The height, 'h', of the Ferris wheel is given by the following sinusoidal relation
f(t) = A·sin(B·t + C) + D
Where;
A = The amplitude = The radius of the Ferris wheel = 44 ft.
The period, T = (2·π/3) minute
B = 2·π/T = 3
t = The time in minutes
D = The Ferris wheel's height above ground = 50 ft.
C = The horizontal shift = π/2 (Josh boards the Ferris wheel at t = 3-O'Clock which is the midline, a rotation of π/2 from the lowermost end of the Ferris wheel)
Therefore the function that determines Josh's height above the ground (in feet) in terms of 't' is presented as follows;
f(t) = 44·sin(3·t + π/2) + 50
The point (3 , k) is a distance of 5 units from (0 , 1). Find the two possible values of k.
7.5d=2.5d, lin divides each side by 2.5d, and elena subtracts 2.5d from each side
Answer:
2.5d is your answer right answer
How do you write your answer as a mixed number fraction?
Answer:
to convert an improper fraction to a mixed fraction, follow these steps:
-divide the numerator by the denominator.
-write down the whole number answer.
-then write down any remainder above the denominator.
Step-by-step explanation:
Answer:
Divide the numerator by the denominator. The quotient is the whole number, and the remainder is the other fraction.
Example: 46/17
46/17= 2 r 12
2 is the whole number, and 12/17 is the fraction next to it.
NEED IMMEDIATE HELP I DIDNT GET ANYTHING THE TEACHER TAUGHT ME TODAY! Can someone please answer all my questions? I would really appreciate it! I need to get my math grade up. :)
To see my questions download the PDF and you can answer all of them for me. :)))))
Answer:
Step-by-step explanation:
In similar triangles, the corresponding sides will be in same ratio
[tex]2) \frac{x}{8}=\frac{30}{15}\\\\x =\frac{30}{15}*8\\\\x=2*8\\\x = 16[/tex]
[tex]3) \frac{x}{20}=\frac{12.8}{16}\\\\x = \frac{12.8}{16}*20\\\\x= \frac{128}{8}\\\\x = 16[/tex]
[tex]\frac{y}{10}=\frac{12.8}{16}\\\\y=\frac{12.8}{16}*10\\\\\\y=8[/tex]
[tex]4) \frac{x}{15}=\frac{8}{6.4}\\\\x=\frac{8}{6.4}*15\\x=18.75[/tex]
[tex]5) \frac{x}{12}=\frac{22.5}{9}\\\\x=\frac{22.5*12}{9}\\\\x= 30[/tex]
[tex]6)\frac{14}{8}=\frac{7}{4}\\\\\frac{12}{6}=\frac{2}{1}\\\\\frac{10}{5}=\frac{2}{1}[/tex]
As the ratio of corresponding sides are not proportion, these are not similar triangles
About 16% of people who get their feet examined are found to have athlete's foot. What is the probability of a podiatrist examining five people until he finds the first patient who has athlete's foot? (0.16)^5 (0.84)^4(0.16)^1 (0.16)^4(0.84)^1 (0.84)5 1 − (0.16)^4
Answer:
Step-by-step explanation:
(84/100)^4(16/100)
(0.84)^4(0.16)^1
SOMEONE HELP PLZZZ ASAP
Answer:
Answer:
(2x−1)(2x−1)(2x−1)(2x−1)
Step-by-step explanation:
Factor 16x4−32x3+24x2−8x+1
16x4−32x3+24x2−8x+1
=(2x−1)(2x−1)(2x−1)(2x−1)
quater of 80? its for my maths, thanks xx
Simplify the ratio 16.8 to 11.2. is
Answer:
5.7
Step-by-step explanation:
Im not so sure if this is the correct answer but i hope if helps! <3
Help pls!!! Worth 16 points!!!:)))
Answer:
18: Safe volume: s <= 115. Unsafe: s > 115.
19: 2-a, 1-b, 3-c, 4-d
20a: Justin is incorrect. 12 is a solution. 12 >= 12 is a true statement.
20b: f > 12
Step-by-step explanation:
Please help me out here, I’ve been reposting the same questions and have not seen people not answer mine. :( just please i will give u brainiest
Answer:
There are infinite solutions because they are the same equation
2D + 1G = 12
and
4D + 2G = 24 (divide by 2) 2D + G = 12
2D + 1G = 12 is the same as 2D + 1G = 12
Joshua wants to buy sport shoe cost P435.30 if he saved from his allowance a total of P289.75 how much does he still need to buy the shoe
Answer:
P 145.55
Step-by-step explanation:
435.30 - 289.75 = 145 .55
For a dilation with a scale factor less than 1, how do the angles and side lengths of the preimage relate to the angles and side lengths of the image?
A. Angle are proportional;side lengths are larger
B. Angles are proportional;side lengths are smaller
C. Angles are congruent;side lengths are larger
D. Angles are congruent; side lengths are smaller
The dilation of an image with a scale factor less than 1 will have the angle proportional to the preimage, and the side lengths have been smaller. Thus, option B) is correct.
The dilation factor has been the scale factor that has been used for the enlargement or reduction of the image. The images with a dilation factor of more than 1 enlarge, while the images with a dilation factor less than 1 shrinks.
The angle of the image with a scale factor less than 1 has been proportional as with shrinking, the angles have been reduced proportionally with the scale factor.
The reduction in scale factor from 1 will shrink the image. The shrinked image will be consist of a smaller size. So there has been a reduction in the side length of the image.
So, with the image with dilation of scale factor less than 1, the angles are proportional while the side length is smaller. Thus option B) is correct.
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What are the solutions to the equation (m + 1)2 +1 = 5? (1 point)
m = 3 or m = -5
m = 1
m = l or m = -3
m = -3
Answer:
yes c is correct ... go on keep going
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Which of the following circles has the greatest circumference? Use 3.14 for the pi.
A circle with radius 4 meters
A circle with diameter 7 meters
A circle with circumference 24 meters
A circle with circumference 5 pi
Answer:
24 m
Step-by-step explanation:
it is 24metre ok......
The greatest circumference is 25.12 meters.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
The area of a circle is πr².
We have,
A circle with a radius of 4 meters.
Circumference.
= 2πr
= 2 x 3.14 x 4
= 25.12 meters
A circle with a diameter of 7 meters
Radius = 7/2 meters
Circumference.
= 2πr
= 2 x 3.14 x 7/2
= 21.98 meters.
A circle with a circumference of 24 meters
Circumference = 24 meters
A circle with a circumference of 5 pi
Circumference = 5π
= 5 x 3.14
= 15.7 meters
Thus,
The greatest circumference is 25.12 meters.
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Use the drop-down menu to identify what each label shows.
Answer:
please put a picture so i can awnser
Step-by-step explanation:
Answer:
where is the picture ?
Step-by-step explanation:
Given the polynomials p(x) and g(x), which of these are guaranteed to be polynomials, too?
Select all that apply.
p(x) + g(x)
p(x) = g(x)
p(x) 9(%)
p(x) - g(x)
Michelle deposited $1,600 into an account that is compounded continuously with an annual interest rate of 8%. After t years, there was $3,200 in the account. Based on the given information, if the formula for continuously compounded interest is A = P e r t , where P represents the initial amount of money, r represents the annual interest rate (as a decimal), t represents the number of years, and A represents the amount of money after t years, how many years had the money been in the account? Express your answer as a logarithm.
Answer:
As a logarithm, the money had been in the account for [tex]t = \frac{\ln{2}}{0.08}[/tex] years.
Step-by-step explanation:
The amount of money in the account after t years is given by:
[tex]A(t) = Pe^{rt}[/tex]
In which P is the initial amount deposited and r is the interest rate, as a decimal.
Michelle deposited $1,600 into an account that is compounded continuously with an annual interest rate of 8%.
This means that [tex]P = 1600, r = 0.08[/tex]
After t years, there was $3,200 in the account. How many years had the money been in the account?
This is t for which [tex]P(t) = 3200[/tex]. So
[tex]A(t) = Pe^{rt}[/tex]
[tex]3200 = 1600e^{0.08t}[/tex]
[tex]e^{0.08t} = \frac{3200}{1600}[/tex]
[tex]e^{0.08t} = 2[/tex]
[tex]\ln{e^{0.08t}} = \ln{2}[/tex]
[tex]0.08t = \ln{2}[/tex]
[tex]t = \frac{\ln{2}}{0.08}[/tex]
[tex]t = 8.67[/tex]
As a logarithm, the money had been in the account for [tex]t = \frac{\ln{2}}{0.08}[/tex] years.
The value of time t is [tex]\frac{ln(2)}{0.08}[/tex].
Given: P=1600
r=8%=0.08
t = ?
A=3200
Using the given compound interest formula we get:
[tex]A=Pe^{rt}\\3200=1600e^{0.08t}\\2=e^{0.08t}\\[/tex]
Take ln on both sides,
[tex]ln(2)=ln(e^{0.08t})\\ln(2)=0.08t\\t=\frac{ln(2)}{0.08}[/tex]
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