The measures of the obtuse angles in the isosceles trapezoid are five more than four times the measures of the acute angles. Write and solve a system of equations to find the measures of all the angles.

Answers

Answer 1

Answer:

a. i. x + y = 180 (1) and x - 4y = 5 (2)

ii. The two acute angles are 35° each and the two obtuse angles are 145° each.

Step-by-step explanation:

a. The measures of the obtuse angles in the isosceles trapezoid are five more than four times the measures of the acute angles. Write and solve a system of equations to find the measures of all the angles.

i. Write a system of equations to find the measures of all the angles.

Let x be the obtuse angles and y be the acute angles.

Since we have two obtuse angles at the top of the isosceles trapezoid and two acute angles at the bottom of the isosceles trapezoid, and also, since the sum of angles in a quadrilateral is 360, we have

2x + 2y = 360

x + y = 180 (1)

Its is also given that the measures of the obtuse angles in the isosceles trapezoid are five more than four times the measures of the acute angles.

So, x = 4y + 5 (2)

x - 4y = 5 (2)

So, our system of equations are

x + y = 180 (1) and x - 4y = 5 (2)

ii. Solve a system of equations to find the measures of all the angles.

Since

x + y = 180 (1) and x - 4y = 5 (2)

Subtracting (2) from (1), we have

x + y = 180 (1)

x - 4y = 5 (2)

5y = 175

dividing both sides by 5, we have

y = 175/5

y = 35°

From (1), x = 180° - y = 180° - 35° = 145°

So, the two acute angles are 35° each and the two obtuse angles are 145° each.

Related Questions

What is the slope? What is the y-intercept? What is the equation of line (write is slope intercept form)?

Answers

Answer:

[tex]2x+1[/tex]

Step-by-step explanation:

Use the rise over run method.

[tex]\frac{rise}{run}[/tex] = [tex]\frac{2}{1}[/tex]

To find the y-intercept, look where the line crosses on the y-axis. In this case, the line crosses on 1.

Now plug in the numbers:

[tex]y=mx+b[/tex]

m = slope

b = y-intercept

[tex]y=2x+1[/tex]

[tex]2x+1[/tex]

Hence the equation of the line is, [tex]2x+1[/tex].

Draven's computer downloads files at a rate of 220 kilobytes per second. The computer has already downloaded the first 550 kilobytes of a 2310-kilobyte file. Solve the equation 550 + 220s = 2310 to find the number of seconds it will take to download the rest of the file.

Answers

Answer:

no se

Step-by-step explanation:

grfdskhcifewdsoheuwifhgtvihgfdsfdsseyuwryewgrgewtfrggsdgfyusdgfgsdgfuysdgfuygsuygfysgfugsdyfgsdgfhsdgfhgshfgsdhgfhjsd

The radius of a sphere is 6 units.

Which expression represents the volume of the sphere, in cubic units?

Three-fourthsπ(6)2
Four-thirdsπ(6)3
Three-fourthsπ(12)2
Four-thirdsπ(12)3

Answers

Answer:

The answer is Three-Fourthst(12)2

Answer:

C. or 3

Step-by-step explanation:

For each 48 mm of coloured fabric Fiona uses to make her curtains, she also uses 1.2 cm of white fabric. Express the amount of white fabric to coloured fabric as a ratio in its simplest form

Answers

Answer:

1:40

Step-by-step explanation:

white - 1.2 coloured - 48

= 1.2 : 48 to put this in its simplest form you...

*make them both whole numbers... Divide both by 10

=12 : 480 now find highest common factor, which is 12

12 divide by 12 = 1

48 divide by 12 = 10

= 1 : 40

Median of 4 3 8 6 21 3

Answers

Answer:

Step-by-step explanation:

order from least to greatest: 3, 3, 4, 6, 8, 21

4 and 6 are in the middle

6+4=10

10/2=5

hope this helps

Please help!!!!!I’ll mark you as brainliest!!!!!!

Answers

Answer:

Step-by-step explanation:

Amy spins a spinner with equal sections numbered 1 through 5 and flips a fair coin. Which statement represents the probability of spinning a 4 and landing on
heads?

Answers

Answer:

There is a 1 out of 10 chance of spinning a 4 and landing on heads, so the probability is 110.

The probability of spinning a 4 and landing on heads is 1/10.

What is Probability?

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

We have two experiments here.

Spinning a spinner with sections 1 to 5 and flipping a coin.

Spinning the spinner will have five outcomes.

Flipping a coin will have two chances, either head or tail.

Total number of outcomes = 5C₂ = 10

There is only a chance of getting a 4 on the spinner and landing on heads.

Probability = 1/10.

Hence the required probability is 1/10.

To learn more about Probability, click :

https://brainly.com/question/29095225

#SPJ2

Pls help with this circles problem for math.

Answers

9514 1404 393

Answer:

see attached

Step-by-step explanation:

Point A is arbitrarily located. We have drawn the circle on a grid, so have made points A and E on orthogonal axes through point O.

1. Point B can be anywhere on the circle except on line AO.

2. Making circle A have the same radius as circle O puts points C and D 120° apart.

3. In this diagram, OF bisects right angle EOA, so central angle EOF is 45°.

please solve for M<PRQ

Answers

Answer:

[tex] m\angle PRQ =49\degree [/tex]

Step-by-step explanation:

[tex] m\angle PSQ = 360\degree - (128\degree + 134\degree )[/tex]

[tex] m\angle PSQ = 360\degree - 262\degree [/tex]

[tex] m\angle PSQ = 98\degree [/tex]

Now, by inscribed angle theorem:

[tex] m\angle PRQ = \frac{1}{2} \times m\angle PSQ [/tex]

[tex] m\angle PRQ = \frac{1}{2} \times 98\degree [/tex]

[tex] m\angle PRQ =49\degree [/tex]

khan academy! please helppp

Answers

Answer: Figure A to Figure B is a scale factor of 0.5

Step-by-step explanation:

It's not too hard to figure out scale factor, since the two shapes are the same aside from their scale. Notice how Figure A is 4 units tall, and that Figure Bis 2 units tall. From one figure to another, use the equation Figure B/Figure A to find the scale factor. Although you won't really need to memorize all this, you can count the amount of units on your fingers and figure it out from there.

Find the area of the parallelogram

Answers

Answer:

45 m

Step-by-step explanation:

Here,

Base (b) = 9m

Height (h) = 5m

Area of parallelogram = b * h. = 9*5. = 45m

Can somebody help with my 2 way table assignments..? i know some of you will take this as a fre.e points question and i don't really care LOL.. just want some help.

Answers

Answer:

what is the question

Step-by-step explanation:

I WILL GIVE BRAINLIEST!!!

Answers

Answer:

it even

Step-by-step explanation:

Answer:

even

Step-by-step explanation:

it was correct in the test

Students in Mrs. Kirby's English class recorded the number of hours they studied for final exams. The results are shown in the bar graph.
Mrs. Karty's English Com
Hours of Study
.
Days of the Week
Based on the information in the graph, what percent of the time spend studying was done from Monday to Wednesday?
A A) 45%
8 B) 18%
C C) 35%
D D) 50%

Answers

Where’s the bar graph?

If a penceil has 25 grams and a apple has 75 grams more then the penceil how many grams is the apple

Answers

Answer:

The answer is 100

Step-by-step explanation:

It's 100 because it's saying that the apples is 75 more grams than the pencil. So we do 25 grams plus 75 grams which gets us 100. If your wondering where I got the 25 from it's from the amount of the pencil.

100 because when you add 25 to 75 you get 100. You add these two together because the apple is 75 grams more than the pencil so you add to find the product of the apple.

Please help me with these two :/

Answers

The first answer is 80, and the second answer is still 65.5. Hope this helps!

Write the equation of a vertical line that passes through the point (-7,3).

Answers

ANSWER= x+7=0

If line is vertical then the slope/m=1/0= undefined

But we know that it’s x value will always remain constant

(-7,3) tells us that the x value is -7

x=-7

So

x+7=0

What is being done to the variable in the equation = -40?

It's being multiplied by -40.
It's being multiplied by -5.
It's being divided by -40.
It's being divided by 5.

Answers

Answer:

3rd one

Step-by-step explanation:

because of the cheese

Answer:

3rd

Step-by-step explanation:

mmm cheese

Find the outlier of the data set {20, 100, 75, 85, 90, 80, 75).

Answers

Answer:

20.00

Step-by-step explanation:

In the set of data, the number furthest from the average is the number provided. Therefore, this must be the correct answer.

Can someone help ill choose brainliest if best

Answers

Answer:

Statistical Questions: 1 and 3

NOT Statistical Questions: 2 and 4

Step-by-step explanation:

A statistical question is one that can be answered by collecting data and where there will be variability in that data. This is different from a question that anticipates a deterministic answer.

For example, "How many minutes do 6th grade students typically spend on homework each week?" is a statistical question.

how do i solve
-4(2x+5)+8x+20

Answers

Answer:

Step-by-step explanation:

-4(2x+5)+8x+20

-8x-20+8x+20

0+0=0

Which expression is NOT equivalent to 100 + 20

Answers

Answer:

the answer is 2(50+9)

Step-by-step explanation:

2(50+9)=100+18=118 not 120

PLease answer this quickly, my friend doesn't get the question.

Answers

Step-by-step explanation:

2 pepperoni and 1 cheese

Answer:Its exactly 2 whole pizzas but dont tell your friend this and tell him the answer is 3 pizzas so you get the right answer and can laugh at him

Step-by-step explanation:

also who WANTS 2/6 of a pizza LIKE imagine someone saying that in real life

For an employee training, the employee to instructor ratio is 24 to 2. If there are 39 instructors for the training, how many employees participated in the training?

Answers

Answer:

468

Step-by-step explanation:

Employee : instructor = 24 : 2

If there are 39 instructors

Employee = x

Employee : instructor = x : 39

Equate both ratios

24 : 2 = x : 39

24/2 = x/39

Cross product

24 * 39 = 2 * x

936 = 2x

x = 936/2

x = 468

Employees = x = 468

NO LINKS!!! PLEASEE HELPP MEE QUICK I NEED TO GRADUATE PLS :( Find the midpoint of the segment below and enter its coordinates as an
ordered pair. If necessary, express coordinates as fractions, using the slash
mark (/) for the fraction bar
(18,5)
(-6,-9)

Answers

Answer:

(5,-2)

Step-by-step explanation:

I hope this helps :)

HELP THIS IS SO HARD ASP PLS

Answers

Answer:

Step-by-step explanation:

plss help i’ll give brainliest thank you!

Answers

Answer:

Step-by-step explanation:

The formula of LCM is LCM(a,b) = ( a × b) / GCF (a,b)

The Greatest Common Factor of (9,12) = 3

Therefore

LCM of 9 and 12 = (9 × 12) / 3

= 108/3 = 36

LCM of 9 and 12 = 36

Irrespective of the method, the solution to our question LCM of 9 and 12 is the same.

Therefore, LCM of 9 and 12 is 36

plz help asap!!!!!!!!!!!!!!!

Answers

the answer is C

i chose two points from the graph like (6,20)
and (12,40)

and find the slope will give you 3.333
which is the closest to 45/14 or 3.2

Let f() = 3x - 1 and g(x) = 2x + 3 and find f(g(3))

Select the correct

response

f(g(3)) = 21

f(g(3)) = 19

f(g(3)) = 26

f(g(3)) = 17

Answers

Answer:

f(g(3)) = 26

Step-by-step explanation:

f(g(3))

g(3) = 2x + 3

= 2(3) + 3

= 6 + 3

= 9

f(9) = 3x - 1

= 3(9) - 1

= 27 - 1

= 26

plug in 3 for g(x) which is 9 then plug in 9 for f(x) which is 26

find the value of x.

Answers

Answer:

x = 4

Step-by-step explanation:

Given a line parallel to a side of the triangle and intersecting the other 2 sides then it divides those sides proportionally, that is

[tex]\frac{10-x}{x}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )

3x = 2(10 - x)

3x = 20 - 2x ( add 2x to both sides )

5x = 20 ( divide both sides by 5 )

x = 4

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