Answer:
a) The smallest possible number of sides of the polygon is a regular polygon with 5 sides
b) The largest possible number of sides of the polygon is a regular polygon with 9 sides
Step-by-step explanation:
a) The smallest exterior angle of the polygon = 40°
The largest exterior angle of the polygon = 80°
Therefore, we have the interior angles are;
The smallest interior angle of the polygon = 180° - 40° = 140°
The largest interior angle of the polygon = 180° - 80° = 100°
Therefore, we have
The interior angles of a regular polygon are given by the following formula;
[tex]Interior \ angle =\dfrac{(n-2) \times 180 ^{\circ}}{n}[/tex]
For an interior angle of 100°, we have;
[tex]100^{\circ} =\dfrac{(n-2) \times 180 ^{\circ}}{n}[/tex]
100/180 × n = n - 2
2 = n - 100/180 × n = 4/9·n
2 = 4/9·n
n = 18/4 = 4.5
Therefore, given that a square has an interior angle of 90° we have the smallest possible number of sides polygon = 5 sides
b) For 140°, we have;
[tex]140^{\circ} =\dfrac{(n-2) \times 180 ^{\circ}}{n}[/tex]
140/180 × n = n - 2
2 = n - 140/180 × n = 2/9·n
2 = 2/9·n
n = 18/2 = 9
n = 9 sides
Therefore, the largest possible number of sides = 9 Sides.
Terrence took a total of 16 pages of notes during 8 hours of class. In all, how many hours will
Terrence have to spend in class before he will have a total of 18 pages of notes in his
notebook? Assume the relationship is directly proportional.
Find the modulus of the complex number 6-2i
Answer:
The modulus of the complex number 6-2i is:
[tex]|z|\:=2\sqrt{10}[/tex]
Step-by-step explanation:
Given the number
[tex]6-2i[/tex]
We know that
[tex]z = x + iy[/tex]
where x and y are real and [tex]\sqrt{-1}=i[/tex]
The modulus or absolute value of z is:
[tex]|z|\:=\sqrt{x^2+y^2}[/tex]
Therefore, the modulus of [tex]6-2i[/tex] will be:
[tex]z=6-2i[/tex]
[tex]z=6+(-2)i[/tex]
[tex]|z|\:=\sqrt{x^2+y^2}[/tex]
[tex]|z|\:=\sqrt{6^2+\left(-2\right)^2}[/tex]
[tex]=\sqrt{6^2+2^2}[/tex]
[tex]=\sqrt{36+4}[/tex]
[tex]=\sqrt{40}[/tex]
[tex]=\sqrt{2^2}\sqrt{2\cdot \:5}[/tex]
[tex]=2\sqrt{2\cdot \:5}[/tex]
[tex]=2\sqrt{10}[/tex]
Therefore, the modulus of the complex number 6-2i is:
[tex]|z|\:=2\sqrt{10}[/tex]
True or false: a translation produces congruent figures?
A.) true
B.) false
can a system of linear equation have exactly 2 solutions ? why or why not?
Answer:
Under normal circumstances a system of two linear equations can have 0, 1 or infinitely many solutions.
Step-by-step explanation:
A blueprint for a house has a scale of 1:30. A wall in the blueprint is 3 in. What is the length of the actual wall?
30
60
90
120
Answer:
C.90
Step-by-step explanation:
1 inch = 30
30 * 3 = 90
Rachel got 18 out of 30 correct on her science test. What percent did she get on her test?
Answer:
60% or D
Step-by-step explanation:
Divide 100 by 30
3.333333. . .
Multiply 18 by 3.333333. . .
The answer is 60%
Hope this helped :)
Donny joined a club that costs $40 per month. Is the cost over time a proportional or non-proportional relationship?
Answer:
The cost over time is a proportional relationship
Step-by-step explanation:
Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality"
Will mark Brainliest
what is the range of the function
Suppose there are two blocks of solid iron. One block is a cube, three inches on a side. The other block is a cube three miles on a side. Obviously, the large cube is many, many times greater volume than the small cube, and many, many times heavier. Is the large cube more dense than the small cube, or less dense?
Answer:
The density is the same because both cubes are composed of the same element Iron(Fe).
Answer:
I believe the large cube would be denser.
Step-by-step explanation:
Solve for a
C = ab/
a + b
A = cb / c + b PLESAE GIB BARNILEST
ratio// please help!!
Answer:
The loose sweets
Step-by-step explanation:
100 divided by 0.89 = 112
120 divided by 1.49 = 80
Answer:
Step-by-step explanation:
1.49 ÷ 120 = 0.0124 GBP per gram
0.89 ÷ 100 = 0.0089 GBP per gram < 0.01 (The price of loose sweets is better value)
A kitchen sink faucet streams 0.5 gallon of water in 10 seconds. A bathroom sink faucet streams 0.75 gallon of water in 18 seconds. Which faucet will fill a
3-gallon container faster?
Answer:
the kitchen sink faucet will fill the container faster than the bathroom faucet.
Step-by-step explanation:
I found the unit rate for both faucets in order to be able to compare them.
Kitchen faucet:
.5 gallons in 10 seconds = 1 gallon in 20 seconds (0.5 x 2= 1 gal, 10 sec x 2=20 seconds)
.75 gallons in 18 seconds = 1 gallon in 24 seconds (0.75 = 3/4 3/4 x 4/3=1 gallon, 18 x 4/3 = 24 seconds)
please help... please need help!!!
Answer:
2 gallons maybe?
Step-by-step explanation:
Mr. Moretti is making welcome bags to give to the 18 students in his homeroom on the first day of school he puts m mechanical pencils in each bag he puts twice as many regular pencils in each bag
Answer:
The total number of pencils is 6
Step-by-step explanation:
According to the given scenario, the computation of the total number of pencils is as follows:
There are 18 students
And let us assume there is m mechanical pencils that put in each bag
also he put twice of the regular pencil
So if he put the 3 mechanical pencil
So, the total number of pencils is
= 3 × 2
= 6
As it twice of the regular pencil
hence, the total number of pencils is 6
How many solutions does the nonlinear system of equations graphed below
have?
Solve for C p=b+c/5 I need help
Answer:
Step-by-step explanation:
p = b + c/5 Subtract b from both sides
p - b = c/5 Put brackets around the left side
(p - b) = c/5 Multiply by 5
5(p - b) = c
Help ASAP plz
Jacob bought 5 boxes of pencils for his drawing class. Each box contains 12 pencils. Which point on the graph shows the number of pencils he bought?
Answer:
it would be (5,60)
Step-by-step explanation:
he bought 5 boxes
each box has 12 pencils
5*12=60
can u peoples help me
plzzzzzz helpppppp plzzz
Answer:
D. 6
Step-by-step explanation:
Answer:
B, 6
I think! hope it helped
Mary is writing invitations for her birthday party. She plans to invite 16 friends. So far, Mary has written 12 invitations. Which of the following show the amount of invitations Mary has written? Select two that apply.
25/100
25%
75/100
75%
WILL RECIEVE A LOT IF YOU HELP ME
Answer:
The answer is 75% and 75/100
Henry took a total of 9 quizzes over the course of 3 weeks. How many weeks of school will Henry have to attend this quarter before he will have taken a total of 15 quizzes? Assume the
relationship is directly proportional
Answer:
5 weeks if it stays the rate of 3 quizzes a week
brainliest if correct please
Step-by-step explanation:
An ostrich is being chased by a cheetah,
The ostrich is running at 44 feet per
second and the cheetah at 110 feet per
second. If the two started at the same
place and the ostrich got a 60-second
head start, how many seconds will it be
before the cheetah catches it?
Answer:
40 seconds
Step-by-step explanation:
(ostrich speed * seconds) + head start = (cheetah speed * seconds)
44x + (44 * 60) = 110x
44x + 2640 = 110x
2640 = 66x
x = 40
No. of seconds before cheetah catches ostrich = 40 seconds
What is speed?Speed tells us how slow or fast an object moves. It describes the distance travelled divided by the time taken to cover the distance.
Speed is directly Proportional to Distance and Inversely proportional to Time.
Speed = Distance/Time
Given,
Speed of ostrich = 44 feet per second
Speed of cheetah = 110 feet per second
Starting point is same
Ostrich got 60 second head start
Distance travelled by ostrich in 60 second = 44 × 60 = 2640 feet
let S be the number of seconds that it will take the cheetah to catch the ostrich
Distance covered by cheetah = 110S
Distance that the ostrich will cover before being caught is 2640 + 44S
According to the question
110S = 2640 + 44S
110S - 44S =2650
66S = 2640
S = 2640/66
S = 40 seconds.
Hence, It will be 40 seconds before cheetah catches the ostrich.
Learn more about speed here:
https://brainly.com/question/7359669
#SPJ2
Help please I really need it thanks
Answer:
the last triangle
Step-by-step explanation:
the pythagorean theroem only works for right triangles. a right triangle is a triangle that has a 90 degree angle it the last one is the only one. so its d
pls mark branilest
five less than three times a number is 1. What is the number?
Answer: 3 times a number can be written as 3x.
Five less than 3x means you must subtract 5 from 3x.
the word "is" means equals,
so 3x-5=10
Step-by-step explanation:
since it is given that 3 times a number less than five is 1
since it is given that 3 times a number less than five is 1 getting equation:- 3x-5=1
since it is given that 3 times a number less than five is 1 getting equation:- 3x-5=1 x=6/3
since it is given that 3 times a number less than five is 1 getting equation:- 3x-5=1 x=6/3 x=2
Solve the system by elimination
Answer:
x= -2 y= -5
Step-by-step explanation:
Eliminate y by subtract = 3x-6x-2y+2y=6 ; x=-2
plug-in x = -2
-6-2y = 4 y = -5
Answer:
(- 2, - 5)
Step-by-step explanation:
[tex]\left \{ {{3x-2y=4} \atop {6x-2y=-2}} \right.[/tex]
(2) - (1)
(6x - 3x) + [- 2y - (- 2y)]= - 2 - 4
3x = - 6 ⇒ x = - 2
3( - 2) - 2y = 4 ⇔ - 6 - 2y = 4 ⇒ y = - 5
(- 2, - 5)
(50 points) Use the spinner below. Show your work, making sure to simplify your answers. (Note: The smallest section of the circle is 1/16 of the circle.)
16. What is P(red, yellow, blue)?
17. What is P(orange, yellow)?
18. P(green, blue, purple)?
19. P(pink)?
20. P(red, orange, yellow, green, blue, purple)?
Thank you!!
Answer:
I have the same questions and I got them right
Step-by-step explanation:
16. What is P(red, yellow, blue)?
P(red, yellow, blue)= 6/16= 3/8.
4/16+ 1/16+ 1/16= 6/16= 3/8
17. What is P(orange, yellow)?
P(orange, yellow)= 1/8
1/16+1/16= 2/16= 1/8
18. P(green, blue, purple)?
P(green, blue, purple)= 5/8
7/16+1/16+2/16= 10/16= 5/8.
19. P(pink)?
P(pink)=0
There is no pink color.
20. P(red, orange, yellow, green, blue, purple)?
P(red, orange, yellow, green, blue, purple)= 16/16= 1.
4/16+ 1/16+ 1/16+ 7/16+1/16+2/16 =16/16= 1.
Hope it helps!!!
Need help will mark brainliest
Answer:
I am grade 5 and I don't know about what it is at all. but please make me as the brainliest
1
If x = 4 and y = -2, the value of
2
1 xy² is
Answer:
16
Step-by-step explanation:
PEMDAS
HEEEEEELP MEEEEEEEEEE PLZZZZZZZZZZZZZZZ WITH NUMBER 4
Answer:
4 2/3 cups of water
Step-by-step explanation:
The original recipe has 3 1/2 cups of potatoes and 3 1/4 cups of water.
4.
If you put 5 cups of potatoes, you can find the amount of water you need using a proportion.
3 1/2 cups of potatoes is to 3 1/4 cups of water as 5 cups of of potatoes is to x cups of water.
(3 1/2) / (3 1/4) = 5/x
(7/2) / (13/4) = 5/x
7/2 * x = 13/4 * 5
2/7 * 7/2 * x = 2/7 * 13/4 * 5
x = 130/28
x = 65/14
x = 4 9/14
4 9/14 as a decimal is 4.64 which is close to 4.6666...
Answer: 4 2/3 cups of water
Marcus buys a pair that cost $35.99 plus 5.5% tax. Tai buys a pair of shoes that cost $ 39.99 plus 9% tax. Tai uses a coupon off her purchase. What is the difference in the total cost to the nearest cent that Marcus and Tai pay for their shoes?
Answer:
The difference is $5.62
Step-by-step explanation:
The total cost Marcus will pay is
35.99 + 5.5% of 35.99
= 35.99 + 0.055(35.99) = 35.99 + 1.97945 = 37.96945
The total cost Tai will pay is;
39.99 + 9% of 39.99
= 39.99 + 0.09(39.99) = 43.5891
The difference between the total costs will be;
43.5891 - 37.96945 = 5.61965
To the nearest cent, this is 5.62