The sun of interior angles of a regular polygon is 1260°.Calculate the number of sides of the polygon and the size of each exterior angle.
Answer:
a)The number of sides of the polygon = 9 sides
b) The size of each exterior angle = 40°
Step-by-step explanation:
The sun of interior angles of a regular polygon is 1260°.Calculate the number of sides of the polygon and the size of each exterior angle.
a) The number of sides of the polygon
We solve using the formula
S = ( n - 2 ) × 180 °
Where S = Sum of the Interior angles = 1260°
1260° = (n - 2) × 180°
Divide both sides by 180°
1260°/180° = n - 2
7 = n - 2
n = 7 + 2
n = 9 sides
b) The size of each exterior angle
The sum of each exterior angle of a polygon = 360°
Hence, size of each exterior angle = 360°/number of sides of the polygon
= 360°/9
= 40°
For a summer job, Lucy is in charge of chickens and sheep. There are 16 animals total. The number of chickens, y, is 4 less than the number of sheep, x. Which ordered pair (x, y) represents the number of chickens and sheep?
Answer:
(10,6)
There are 10 sheep and 6 chickens.
Step-by-step explanation:
Let y represent the number of chickens.
Let x represent the number of sheep.
1) Form a system of equations
"There are 16 animals in total"
⇒ [tex]x+y=16[/tex]
"The number of chickens is 4 less than the number of sheep"
⇒ [tex]y=x-4[/tex]
2) Substitute equation 2 into equation 1
[tex]x+(x-4)=16[/tex]
Solve for x
[tex]x+x-4=16\\2x-4=16\\2x=16+4\\2x=20\\x=10[/tex]
Therefore, there are 10 sheep.
3) Solve for y
[tex]x+y=16\\10+y=16\\y=16-10\\y=6[/tex]
Therefore, there are 6 chickens.
The ordered pair (10,6) represents the number of chickens and sheep.
I hope this helps!
find two numbers if their sum is 115 and their difference is 7
Answer:
54+61
Step-by-step explanation:
54 + 61 = 115
61 - 54 = 7
. Please HELP me WITH this EQUATION ; A triangle has two base angles of 35º and another angle of 110º. Select any words which accurately describe the triangle. AObtuse-angled BScalene CEquilateral DRight-angled EIsosceles FAcute-angled
Answer:
Isosceles
Step-by-step explanation:
pls heeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeelp
HELP!! <3 Right now, the gym covers an area of x square feet. Ms.Lauren wants to increase the size of the gym by 20%. Which expression below could not be used to find the new size of the gym?
a) 1.20x c) .20x
b) x + .20x. d) x(1 + .20
Answer:
C
Step-by-step explanation:
0.20x only tells you 20% of the original gym size, not the increased size of the gym.
Answer:
Answer C can not be used to find the new size of the gym.
Step-by-step explanation:
Let's use process of elimination!
A is stating 1.20x, or 120% of x. This is correct, because we have x and then were increasing by 20%, which is just 120%. A is however not the answer because we are asking which expression below could not be used, and A could be used. B is also incorrect because of what I just stated, x + 0.20x is the same thing as 1.20x. C is 20% of x, but that won't get us the answer. C is the correct answer since it cannot be used to find the new size of the gym, but if you really want to you can check answer D as well. In answer D you can distribute the x to the 1 and the 0.20, and you get x + 0.20x, which is the same as answer B. Therefore C is the correct answer.
100 POINT PLEASE HELP QUICK!!!!
Answer:
[tex]adjacent = \sqrt{ {50}^{2} - {14}^{2} } = 48 \\ \\ \sin(Q) = \frac{14}{50} = \frac{7}{25} \\ \cos(Q) = \frac{48}{50} = \frac{24}{25} \\ \tan(Q) = \frac{14}{48} = \frac{7}{24} [/tex]
[tex] \sin(R) = \frac{48}{50} = \frac{24}{25} \\ \cos(R) = \frac{14}{50} = \frac{7}{25} \\ \tan(R) = \frac{48}{14} = \frac{24}{7} [/tex]
Base
√50²-14²√2500-196√48²48Now
sinQ=P/H=14/50cosQ=B/H=48/50tanQ=P/B=14/48cotQ=B/P=48/14secQ=H/B=50/48cosecQ=H/P=50/14Which statement describes the solutions of this equation?
A. The equation has no valid solutions and two extraneous solutions
B. The equation has one valid solution and no extraneous solutions
C. The equation has one valid solution and one extraneous solution
D. The equation has two valid solutions and no extraneous solutions
Answer:
D
Step-by-step explanation:
If the product of two numbers and is 180 and their HCF is 3, then find the LCM of and .
Answer:
60
Step-by-step explanation:
Product of the two numbers = HCF* LCM
[tex] \therefore \: 180 = 3 \times lcm \\ \\ \therefore \: lcm = \frac{180}{3} \\ \\ \therefore \: lcm = 60[/tex]
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 18 centimeters cubed.
A sphere with height h and radius r. A cylinder with height h and radius r.
What is the volume of the sphere?
12 centimeters cubed
24 centimeters cubed
36 centimeters cubed
54 centimeters cubed
Answer:
12 cm^3
Step-by-step explanation:
Before we do anything, we should set up the proportion.
[tex]\frac{\pi * r^2*h}{\frac{4\pi r^3}{3}} = \frac{18}{x}[/tex]
Now do the Cancelations of \pi r^2 on the left.
h// (4/3) r = 18/x
but h = 2*r
2r // (4/3) * r = 18/x Cancel the rs on the left
2// (4/3) = 18/x Make 2 = 2/1 so you can handle the fraction
2/1 // (4/3) = 18/x Invert and multiply the denominator
2/1 * 3/4 = 18/x
6/4 = 18x You can reduce the left side
3/2 = 18x Cross multiply
3x = 2*18 Combine the right
3x = 36 Divide by 3
x = 12
So what you have found is the volume of the sphere. 12 cm^3
This is a very interesting question. Keep in mind that physics does this all the time for any of the force formulas (but not all).
I'm a little long winded here, but the first time you see this, you should be given very small steps.
Round 47.44 to 1 decimal place
Answer:
47.4 is the correct answer.
Step-by-step explanation:
Helpful?❤️
Answer:
47.4
Step-by-step explanation:
47.44
47.40
47.4
What is the radius and diameter of each circle ?
Please help
PLEASE HELPPPPP
I WILL GIVE THE BRAINIEST THINGY
Answer:
The answer is the last one....
Step-by-step explanation:
Sorry for possible a vague answer, but you can divide out all the answers and you will see that only the last one proves the point...
if you do these problems in a class you are taught for sum/diff of cubes
the pattern ( a b) (a^ ab b^2) ...notice that there are no signs between the variables... the next teaching point is that the signs use this pattern...
"SAME" , "OPPOSIT", "ALWAYS A PLUS"... that is not me look that up in an algebra book.. same opposite, always a plus... I think some people call is "SOAP" same, opposite Always plus (that works) ....
bottom line here is that you answer needs cubes under the division, and the
end part has to have a "+" , given that after multiplying by "-b" you have to end up with a "-B^3" only a "+b^2" will do , that is consistent with the fourth answer
John, Jack, Jim, and Joe all decided to take up horseback riding. Jim went twice as many times as Jack, and John went four more times than Joe but three less times than Jim. Joe went 15 times altogether. How many times did Jack go?
Answer:
11 times
Step-by-step explanation:
Given
[tex]Jim = 2 * Jack[/tex]
[tex]John = 4 + Joe[/tex]
[tex]John = Jim - 3[/tex]
[tex]Joe = 15[/tex]
Required
Find [tex]Jack[/tex]
Substitute [tex]Joe = 15[/tex] in [tex]John = 4 + Joe[/tex]
[tex]John = 4 + 15[/tex]
[tex]John = 19[/tex]
Substitute [tex]John = 19[/tex] in [tex]John = Jim - 3[/tex]
[tex]19 = Jim - 3[/tex]
Collect like terms
[tex]Jim = 19 +3[/tex]
[tex]Jim = 22[/tex]
Substitute [tex]Jim = 22[/tex] in [tex]Jim = 2 * Jack[/tex]
[tex]22 = 2 * Jack[/tex]
Divide both sides by 2
[tex]Jack = \frac{22}{2}[/tex]
[tex]Jack = 11[/tex]
Which statement is true about Angle C P B?
Answer:
Step-by-step explanation: the second answer im not vary sure but ist kinda resonable
probability, please help i will give brainliest
The total perimeter of a square shaped
garden is of a meter. Find the dimensions of the
garden.
Please helppp I need it fasttttttt
Answer:
this makes no sence
Step-by-step explanation:
you did no include any of the details needed
Mr sharma can do 1/15part of piece of work in 1 day he worked for 3 days and left if Vishnu finished the remaining work how much work is done by bishnu?
Answer:
12/15
Step-by-step explanation:
if in one day mr sharma did 1/5 part of piece of work and he worked three days he did 3/15, if vishnu finished the remaining work then he did 12/15 parts, they did 15/15
help plzzzzzzzzzzzzzzzzz asap i don't have time i will give brainlist
Step-by-step explanation:
i. Looking at the table, he got 3 odd numbers out of 9 scored so the probability is 33% or 3/9 or 1/3
ii. He got 4 square numbers so the probability is 4/9( remeber 0 is a square number).
iii. Only two number are multiples of 5 so the probability is 2/9.
iv. No number is greater than 15 so the answer is 0%
v. 5 numbers are less than zero so the answer is 5/9
[tex]\text{Solve for x:}\\4x + 54 = 55\\\\\text{Thank you.}[/tex]
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]x = \frac{1}{4}[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Solving the equation for x...}}\\\\4x + 54 = 55\\----------\\\rightarrow 4x + 54 - 54 = 55 - 54\\\\\rightarrow 4x = 1\\\\\rightarrow \frac{4x=1}{4}\\\\\rightarrow \boxed{x=\frac{1}{4}}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
[tex]\sf{4x+54=55 }[/tex] [tex]\sf{ 4x=55-54 }[/tex] [tex]\sf{4x=1 }[/tex] [tex]\sf{x=\dfrac{1}{4} }[/tex] [tex]\sf{ }[/tex]put the following equation of a line into slope intercept form simplifying all fractions 10x-2y=6
Answer:
Slope-Intercept form: y = m x + b
y = value of y corresponding to value of x
2 y = 10 x - 6
y = 5 x - 3 equation of line where m is the slope and -3 value of y when x
equals zero
What is the conjugate? x - square root 2
Answer:
conjugate of (x-[tex]\sqrt{2}[/tex]) is (x+[tex]\sqrt{2}[/tex])
Step-by-step explanation:
when Maria was born, her mother was 24 years old. At present, Maria's age is 20% of her mother's age. How old is Maria now?
Answer:
the mother is older than maria by 24 years.
if Maria's age = x
mother's age = x+24
x=0.2(x+24)
x=0.2x+4.8
x-0.2x= 4.8
0.8x=4.8
x=4.8/0.8
x=6
Maria's age is 6 years
An animal starts from rest and accelerates to its top speed in 7 seconds. It continues at this speed for 9 seconds and then slows to a stop in a further 4 seconds. Calculate the total distance that the animal travelled
Answer:
hggffffxdfffdsddfdohgfffdedss
Please give real answers with an explaination. 50 points + 5-star rated. No Docs/No Files/No Links only answer with explaination.
Answer:
Te diagonal of a kite will form a parallelogram.
explanation:
Kite properties include (1) two pairs of consecutive, congruent sides, (2) congruent non-vertex angles and (3) perpendicular diagonals. Other important polygon properties to be familiar with include trapezoid properties, parallelogram properties, rhombus properties, and rectangle and square properties.
hope it helps
Mark me as brainlist
Solve for M and show work
[tex]\left[\begin{array}{ccc}3&4\\8&-5\end{array}\right] \left[\begin{array}{ccc}4&6\\3&0\end{array}\right][/tex] evaluate
Answer:
Step-by-step explanation:
Hope this helps u!!!
Mrs. Hanger is painting the following picture of an H to hang in the entryway of her home. She has made the following scale drawing as her model. The scale used on the drawing is 1:6.
As you can see, the "H" is going to be painted brick red in the center of a rectangular beige background. This means the distance from the "H" to the top of the picture will be the same as the distance from the "H" to the bottom of the picture. Similarly, the distance from the "H" to the left side of the picture will be the same as the distance from the "H" to the right side of the picture. Finally, each segment of the "H" will have the same width.
What is the actual width of the painting?
What is the actual height of the painting?
On the scale drawing, the top edge of the "H" is inches from the top edge of the drawing. What is the actual height of the "H"?
What is the actual width of the "H" (through the center)?
What is the actual distance from the left edge of the painting to the left edge of the "H"?
actual width of the painting: inches
actual height of the painting: inches
actual height of the "H"?: inches
actual width of the "H" (through the center): inches
actual distance from the left edge of the painting to the left edge of the "H": inches
text mentions a scale model... wich we can't see here unless you post it
Evaluate the expression. 202 + 6(9 + 3) =
Answer:
274
Step-by-step explanation:
202 + 6(9 + 3) =
PEMDAS says parentheses first
202 + 6(12) =
Then multiply
202 +72
Then add
274
Answer:
274
Step-by-step explanation:
202 + 6(9 + 3)
202 + 6(12)
202 + 72
274
What does b stand for in this equation?
3b=12
A 1
B 2
C 3
D 4
Answer:
4
Step-by-step explanation:
3b=12
Divide each side by 3
3b/3 =12/3
b =4
Answer:
D. 4Step-by-step explanation:
Given,
3b = 12
=> b = 12 ÷ 3
=> b = 4 (Ans)