In an equilateral hexagon, four of the exterior angles each have a measure of x degrees. The other two exterior angles each have a measure of twice the sum of x and 48. Find the measure of each exterior angle. (Show work!!)

Answers

Answer 1

Final answer:

The measure of each of the four exterior angles of the hexagon is 21 degrees, and the measure of the remaining two exterior angles is 138 degrees each. This was determined by setting up an equation based on the sum of exterior angles of a polygon, which is always 360 degrees, and solving for x.

Explanation:

To solve this problem, we start by understanding that the sum of the exterior angles of any polygon is always 360 degrees. For a hexagon, this sum is divided among six exterior angles. According to the problem, four of these angles are each x degrees, and the remaining two are each twice the sum of x and 48.

Let's set up the equation reflecting this information:
4x + 2(2x + 96) = 360.

Simplifying this equation, we get:
4x + 4x + 192 = 360,
which combines to:
8x + 192 = 360.

Now, we'll solve for x:
8x = 360 - 192,
8x = 168,
x = 21.

Therefore, each of the four exterior angles is 21 degrees, and each of the remaining two exterior angles is twice the sum of 21 and 48, which is:
2(21 + 48) = 2(69) = 138 degrees.

Related Questions

5% sales tax on a $81.08 bookcase

Answers

81.08 * .05 = 4.054
$4.05

Pe ling needs 2 yard of fabric for a craft project. She has 3 feet already. How many inches of fabric does she still need ?

Answers

First, you want them to be the same units.
We'll convert yards to feet.

Since there are 3 feet in a yard

2 yards * 3 = 6 feet

So she needs 6 yards and has 3 feet.

6-3=3 3 feet is needed

So to make things easier convert 3 feet to inches
12 in. in a foot

12*3 feet= 36 inches
She needs 36 inches of fabric

She needs 2 yards.

2 yards = 6 feet

3 feet = 36 inches

So, she has half of it done already.
If 2 yard = 6ft, then 1 yard = 3ft.
In 1 foot, there is 12in.

Therefore, she still needs 36 inches of fabric.

These data show the age in years of 9 members of the youth orchestra.

12 14 16 17.5 10 18 15 15.5 19

What is the IQR (interquartile range) for these data?

4.75

9.00

15.50

17.75

Answers

Hey there!

the answer is 4.75.

4.75 is the IQR for the data

Hopes this helps u :)

Answer:

[tex]IQR=4.75[/tex]

Step-by-step explanation:

The given data is:

12,14,16,17.5,10,18,15,15.5,19

In order to find the interquartile range, we have to arrange the given data set in ascending order, thus

10, 12, 14, 15, 15.5, 16, 17.5, 18, 19

Now, the lower quartile is: 10, 12, 14, 15

Median is given as:

[tex]M=\frac{14+16}{2}=\frac{26}{2}=13[/tex]

And the upper quartile is given as:

16, 17.5, 18, 19

Median is given as:

[tex]M=\frac{17.5+18}{2}=17.75[/tex]

thus, the Interquartile range is given as:

[tex]IQR=Upper quartile-Lower quartile[/tex]

[tex]IQR=17.75-13[/tex]

[tex]IQR=4.75[/tex]

When are two triangles said to be in perspective?
a.
If the corresponding vertices of two triangles form three lines that intersect in a single point
c.
If the corresponding vertices of four triangles form three lines that intersect in a single point
b.
If the corresponding vertices of three triangles form three lines that intersect in a single point
d.
If the corresponding vertices of two triangles form three lines that intersect in two points.

Answers

Answer - A

Two triangles are said to be in perspective from a point, O if the corresponding vertices of the two triangles form three lines that intersect in that single point, O. The two triangles can also be described as homologic from point, O.

A student claims that the equation y = 7 is not a linear equation because it does not have the form y = mx + b. Do you agree or disagree? Why? Complete the explanation.

The equation...... be written in the form y = mx + b, and the graph of the solution is a...... . So, I ...........

Answers

The equation does not have to be written in the form y = mx + b, and the graph of the solution is a horizontal line with the y intercept of 7. So, the student is incorrect.

Hope this helps!

A geometric sequence has a growth factor of 0.85 and an initial starting value greater than 0 which of the following values will be the greatest ? The 10th term , the 5th term, the 2nd term, not enough info

Answers

maybe the website math-way without the dash might help

8 to the thrid power

Answers

its 512

p.s. spread le cheese ⌂

Hey there!

8 to the 3rd power means you multiply the number 8 three times:

8 x 8 = 64

64 x 8 = 512

512 is your final answer <------------

Hope this helps you.
Have a great day!

I am a solid figure with two congruent polygons that are based connected with lateral faces that are rectangles

Answers

I believe that a rectangular prism since (hence the name) it's made up of rectangles, only with 2 squares helping to close it up.

Carter has 60 balloons. 4/12 of the balloons are black, and 3/12 of the balloons are white. The rest of the balloons are red. Which series of calculations shows how many red balloons Carter has?

Answers

Let

B------------> black balloons
W-----------> white balloons
R-----------> red balloons

Step 1
calculate the amount of black balloons and white balloons
the total of balloons is 60
B=(4/12)*60=20 balloons
W=(3/12)*60=15 balloons

Step 2
calculate the amount of red balloons
R=60-[B+W]---------> R=60-[20+15]
R=60-(35)=25 balloons

the answer is 25 red balloons

Final answer:

To find the number of red balloons Carter has, subtract the number of black and white balloons from the total number, using fractions to represent the proportion of black and white balloons. Multiply the total number of balloons by the fraction representing red balloons to find the number of red balloons.

Explanation:

To find the number of red balloons Carter has, we need to subtract the number of black and white balloons from the total number of balloons. Since 4/12 are black and 3/12 are white, we can add these fractions together to find the total fraction of balloons that are either black or white: 4/12 + 3/12 = 7/12.

To find the fraction of balloons that are red, we can subtract the fraction of black and white balloons from 1 (since the sum of all fractions should equal 1): 1 - 7/12 = 5/12.

To find the actual number of red balloons, we can multiply the total number of balloons (60) by the fraction of red balloons: 60 x 5/12 = 25 red balloons.

how do you convert minutes to seconds

Answers

Multiply the amount of minutes by 60 to find seconds, M * 60 = S

Multiply 60 by the number of mins to get the number of seconds

Find the magnitude and direction of the vector. Round the length to the nearest tenth and the degree to the nearest unit. Diagram is not drawn to scale.

Answers

Refer to the diagram shown below.

The vector has a magnitude of a and a direction of θ degrees south of west.

Use the Pythagorean Theorem to calculate a.
a² = (-530)² + (-200)² = 320900
a = √(320900) = 566.48 mi ≈ 566.5 mi

By definition,
tan θ = (-200)/(-530) = 0.3774
θ = tan⁻¹ 0.3774 = 20.68° ≈ 21°

Answer: about 566.5 mi; 21° south of west.

Quadrilateral MNPQ has vertices at (−3, 5), (−4, 6), (−5, 7), and (−6, 8). If the Quadrilateral MNPQ is reflected over the x−axis, what will the new coordinates be?

(3, 5), (4, 6), (5, 7), (6, 8)
(5, −3), (6, −4), (7, −5), (8, −6)
(−3, −5), (−4, −6), (−5, −7), (−6, −8)
(3, −5), (4, −6), (5, −7), (6, −8)

Answers

The best choice is answer choice D

Hello there!

The answer is D.

Find x and y, given that line KL and line MN are parallel. Please show how you got your answer.

Answers

Answers:
x = 19/2 = 9.5
y = 44/3 = 14.667
The decimal value of y is approximate

-----------------------------------------------------

The triangles are similar. So the corresponding sides form a proportion

KM/KJ = LN/LJ
(x-2)/5 = 12/8
8(x-2) = 5*12
8x-16 = 60
8x = 60+16
8x = 76
x = 76/8
x = 19/2
x = 9.5

Similarly,
MN/KL = LN/LJ
22/y = 12/8
22*8 = 12y
12y = 176
y = 176/12
y = 44/3
y = 14.667 (value is approximate)

jackie says that if a solid figure cannot roll,then it has faces.is jackie correct?

Answers

Yes Jackie is correct

Answer:

Yes, Jackie's answer would be correct

A coffeepot contains 1 1⁄2 quarts of coffee. After Tonya pours an equal amount of coffee into two cups, 3 1⁄2 cups of coffee remain in the pot. How much coffee did Tonya pour into each cup?

Answers

The correct answer is:

1 1⁄2 qt = 6 cups

6 cups - 3 1⁄2 cups = 2 1⁄2 cups = 20 oz

20 oz ÷ 2 = 10 oz = 1 cup + 2 oz

A cone - shaped building has a height of 6 meters and a base with a diameter of 10 meters. The building will be filled with road salt that costs $25 per cubic meter. How much will it cost to fill the building with road salt? Use 3.14 for π Round to the nearest hundredth HELP ME ASAP!!!!

Answers

The formula for the volume of a cone is
.. V = (1/3)*π*r^2*h
The radius (r) is half the diameter, so is 5 m. Fill in the numbers and do the arithmetic.
.. V = (1/3)*3.14*(5 m)^2*(6 m) = 157 m^3

The cost will be $25 for each of those cubic meters, so is
$25*157 = $3925.00.

Formula
V= (1/3) pi r^2 h
r = d/2 = 10/2 = 5
h = 6
pi = 3.14
V = (1/3) * 3.14 * 5^2 * 6
V = (1/3) * 471
V = 157 cubic meters.

1 cubic foot cost $25
157 cubic feet cost x Cross multiply.

x = 25 * 157
x = 3925 dollars.

Kevin is making a picture frame. He has. Piece of trim that is 4 feet long. How many 14-inch-long pieces can Kevin cut from the trim? How much of a foot will he have left over ————
Pls explain how u got the answer

Answers

hello

First, convert 4 feet into inches - 48 inches. Then, divide 48 by 14 to get 3.43, so he can have 3 14-inch long pieces. To get the left over out of a foot, take 14 x 3 to get 42, then subtract 42 from your original 48 inches to get 6 inches left, which is half of a foot.
have a nice day

4 times 12 (12 inches in foot)
48 divided by 14
3.42...... so 3 sections of 14
42% of 12 is 5.16 so there will be 5 inches left over

The width of a rectangle is half its length. What if the perimeter of a rectangle with width 26 feet?

A. 39 feet

B. 52. feet

C. 78 feet

D. 156 feet

Answers

B is the answer?????????????

Answer:

The answer is B. 52. feet

Step-by-step explanation:

26 times (X) 2 = 52. feet because;

26 + 26 = 52

Final Answer:

B. 52. feet

Extra:

Please give brainlest!

What is the d in 3.5d=70

Answers

d=20 because if you divide 70 by 3.5 you get d. hope this helps!

your answer is 20 (I think) you would divide each term by 3.5 and simplify

Need help with pythgoream theorem

Answers

Upper Left for certain.
Lower right. You can check it out using
a^2 + b^2 = c^2
14^2 + 48^2 = 50^2
196 + 2304 =? 2500
2500 = 2500 This checks out to being true. I don't think there are any others.

The bus travels 3 hours going 35 miles per hour. How far does the bus travel in that amount of time? *

Answers

The answer is: " 105 mi. " .
____________________________________________

Explanation:
____________________________________________
Note that: "that amount of time" is "3 hours".

→ [tex] \frac{35 mi}{h} * \frac{3h}{1} [/tex] = ? ;

→ The units of "h" (for "hour/s") cancel out to "1" ; since ("h/h = 1") ;

→ and we are left with (35 * 3) mi. = 105 mi.
____________________________________________
The answer is: " 105 mi. " .
____________________________________________

(50 POINTS)
A table of values for Function A and the graph of Function B are shown. State the slope of Function B

Answers

The formula of a function is the rise over run.

The slope would be 2/5.

Hope this helps!

Answer:

bruh it's only 5 points

A pedigree chart is used to?

Answers

I'm pretty sure a pedigree chart is used to do that

The answer you picked is right. (Hint Hint if you feel positive that your answer is right like you are absolutely sure then don't second guess your self a lot of times you are right)

Leta is making strawberry-almond salad for a party. For every head of lettuce that she uses, she adds 5 ounces of almonds and 10 strawberries. If she uses 75 ounces of almonds, how many heads of lettuce, how many strawberries does Leta use?

Answers

Strawberries= 75x10=750
Heads of lettuce=15

60 out of 300 is what percent?

Answers

100%/x%=300/60(100/x)*x=(300/60)*x - we multiply both sides of the equation by x100=5*x - we divide both sides of the equation by (5) to get x100/5=x 20=x x=20
now we have: 60 is 20% of 300

Hope I helped!
~ Zoe

60 is 20% of 300.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

Let x% be a number such that

x% of 300 is 60

This forms an equation in one variable which can be solved by transposition.

[tex]x/100\times 300=60[/tex]

Simplifying it to calculate value of x.

On multiplying 100 both sides,

[tex]300x=6000[/tex]

On dividing 300 both sides,

x=20%

Thus, 20% of 300 is 60.

Learn more about percentage, here:

brainly.com/question/16797504

#SPJ6

WILL GIVE BRAINLIEST AND RATE!

Michael is making cookies. Each batch uses 2 cups of flour. He plans to use less than 30 cups of flour for cookies so that he has enough left to make muffins. He has already used 4 cups of flour for cookies.

Which statement describes how many more batches of cookies Michael can make?

A. Michael can make fewer than 13 batches of cookies.

B. Michael can make fewer than 14 batches of cookies.

C. Michael can make fewer than 15 batches of cookies.

D. Michael can make fewer than 26 batches of cookies.

Answers

The answer for this question is letter A

Answer:

Step-by-step explanation:

What is the area of this trapezoid, I WILL GIVE BRAINLIEST TO THE CORRECT ANSWER! URGENT WORTH 90PTS

Answers

192 in.

Hope this helped! ♡

First, you have to do the formula:

A= 1/2(b1+ b2)×h

-----------------------------------------------------

Now plug in the numbers:

A=1/2(18+14)×12

----------------------------------------------------

Now solve:

A=1/2(18+14)×12

A=1/2(32)×12

A=16×12

A= 192in²

-------------------------------------------------------------

Finally, the answer is 192in²

which numbers are rational? select all that apply. A. pi B. √50 C. 2.3 D. √144

Answers

C. 2.3
D.√144

Rational roots or decimals are numbers that have an end point.

pi 'technically' never ends, while √50 = 7.07106781…, which never ends either

hope this helps

Answer:

C and D

Step-by-step explanation:

2.3 (repeating) repeats itself over and over again into infinity.

pi goes on into infinity.

The graph of the equation y = x2 - 3 is shown. Which equation will shift the graph up 6 units?
A) y = x2 + 3
B) y = x2 - 6
C) y = x2 + 6
D) y = (x + 6)2

Answers

A should be the right answer.
The picture show the graph that shift down 3 units
The equation that I chose shift up 3 units from 0, in which it compares to the picture from -3 up to 3 will be 6 units

In this exercise we have to use the knowledge of quadratic equations and graphs to identify the correct alternative, so we have;

Letter A

Remembering what a quadratic function looks like and its form:

[tex]y=x^2[/tex]

where X is the quadratic form, we know that we see that in the graph we have to go down 3 units, we can write it as follows:

[tex]y=x^2+3[/tex]

See more about quadratic functions at brainly.com/question/4119784

The line plot above shows the distance in miles Luna runs each day. What is the difference in distance between the fewest miles she ran and the most miles she ran in a day?

A) 2 1/2

B) 3

C) 4

D) 1/2

Answers

c

hope this helps have a good day!! :)
please mark brainliest

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