Learning Task 2
Solve the following problems. (Show your complete solutions.)
1.) What is the sum of the interior angles of a polygon having 8 sides?
2.) Find the measure of the exterior angle of a regular decagon.
3.) Find the number of diagonals of a nonagon.
4.) What is the measure of each angle of a regular nonagon?
5.) if the sum of the measures of the angles of a regular polygon is 900, then
what is the number of sides?
1. 1080°
2. 36°
3. 27 diagonals
4. 140°
5. 7 sides
Step-by-step explanation:1. The sum S of the interior angles of a polygon is given by;
S = (n-2) x 180°
Where;
n = number of sides of the polygon.
Therefore, to get the sum of the interior angles of a polygon having 8 sides, we substitute n = 8 into equation (i) as follows;
S = (8 - 2) x 180°
S = 6 x 180°
S = 1080°
Therefore, the sum of the interior angles of a polygon having 8 sides is 1080°
2. The sum of interior angles of a polygon is given by;
S = (n - 2) x 180°
For a polygon which is a regular decagon where the number of sides n = 10, the sum is;
S = (10 - 2) x 180°
S = 8 x 180°
S = 1440°
Since the decagon is regular, then each of its interior angles is given by;
1440° / 10
=> 144°
Now, since we know that the sum of the interior angle and exterior angle will give 180°, then;
The exterior angle of a regular decagon is;
180° - 144° = 36°
Therefore, the exterior angle of a regular decagon is 36°
3. The number of diagonals N of a polygon with n sides is given by;
N = [tex]\frac{1}{2} n(n-3)[/tex]
So, for a nonagon which has 9 sides (i.e n = 9), the number of diagonals is;
N = [tex]\frac{1}{2}*9(9-3)[/tex]
N = [tex]\frac{1}{2}*9(6)[/tex]
N = 9(3)
N = 27
Therefore, a nonagon has 27 diagonals.
4. The sum of interior angles of a polygon is given by;
S = (n - 2) x 180°
For a polygon which is a nonagon where the number of sides n = 9, the sum is;
S = (9 - 2) x 180°
S = 7 x 180°
S = 1260°
Since the nonagon is regular, then each of its interior angles is given by;
1260° / 9
=> 140°
Therefore, the measure of each angle (interior angle) of a regular nonagon is 140°
5. The sum of the interior angles of a polygon is given by;
S = (n - 2) x 180°
So if the sum is 900, then to get the number of sides of the polygon, we substitute S = 900 into the equation;
900° = (n - 2) x 180°
Divide through by 180°
5 = (n - 2)
Solve for n;
n = 5 + 2
n = 7
Therefore, the regular polygon has 7 sides.
if there are twelve apples and someone takes -24 how many apples will there be left
Equation = 12 - -24 = ?
After keep, change, flip: 12 + 24 = ?
Answer = 36
Wait someone takes negative 24 or just 24?
If negative then it would be 36
If positive then it would be -12
Hope this helps! :)
an estate valued at $75 000 is divided among three daughters Natasha, Natalie and Nadia in the ratio 5:8:2 respectively. Calculate the amount each receives
Answer:
Natasha: $25000
Natalie: $40000
Nadia: $10000
Step-by-step explanation:
5 : 8 : 2
5 + 8 + 2 = 15
$75000 ÷ 15
$5000
$5000 × 5 = $25000
$5000 × 8 = $40000
$5000 × 2 = $10000
The choices are
A. 2/13
B. 3/13
C. 5/13
D. 8/13
Step-by-step explanation:
The answer is A
Sam, a researcher, and his team conduct a study to examine the effect of WakeMe, an energy drink, on intelligence levels of people in a small town. The people from this town are randomly divided into two equal, representative groups. Members of one group, Group MW, are made to drink WakeMe and then take an intelligence test. Members of the other group, Group NoMW, are made to drink plain water packaged in WakeMe bottles and then take an intelligence test. In this scenario, ______ is the control group and the ______ is the experimental group.
Answer:
Hence, In this scenario, __Group NoMW____ is the control group and the ___Group MW___ is the experimental group.
Step-by-step explanation:
The control group is the one which is not subjected to any testing situation or condition.
While the experimental group is the one which is subjected to testing condition.
Hence, In this scenario, __Group NoMW____ is the control group and the ___Group MW___ is the experimental group.
A retail store served 923 customers in October, and there were 45 complaints during that mo
What is the experimental probability that a customer complains?
Let's try that again
Answer:
Experimental probability [Customer complains] = 45 / 923
Step-by-step explanation:
Given:
Total number of customer in store = 923 customers
Total number of complaints in October = 45 Find:
Find;
Experimental probability [Customer complains]
Computation:
Probability of an event = Number of favorable outcomes / Total number of outcomes
Experimental probability [Customer complains] = Total number of complaints in October / Total number of customer in store
Experimental probability [Customer complains] = 45 / 923
Solve: 36(x + 4)= 36
Answer:
x = -3
Step-by-step explanation:
36(x + 4) = 36
Divide both sides by 36
x + 4 = 1
Subtraact 4 from both sides
x = -3
Answer:
-3
Step-by-step explanation:
A=755y/t^2
Solve for y.
Answer:
y = At²/755
Step-by-step explanation:
A = 755y/t²
multiply both sides by t²
At² = 755y
Divide both sides by 755
At²/755 = y
Flip
y = At²/755
Please Help me. I get so confused doing these questions.
Answer:
It should be -24
Step-by-step explanation:
I found it online, since I wasn't entirely sure, but remember that studying can be fun, and everyone have an amazing day :)
Chỗ hình chóp S.ABCD có đáy ABCD là hình vuông .SA=AB=2 SA vuông góc với đáy.Gọi T là điểm thoả mãn vector ST=1/2 vectơ AB tính thể tích khối đa diện ABCDST
Answer:
Step-by-step explanation:
how do u find volume of a rectangle
Answer:
the length of the rectangle times the wedth of the rectangele by 2
Kaylee and her children went into a movie theater and will buy drinks and candies.
She must buy no less than 15 drinks and candies altogether. Write an inequality that
would represent the possible values for the number of drinks purchased, d, and the
number of candies purchased, c.
Answer:
c+d>15
Step-by-step explanation:
Usually there's more to the question.. the inequality doesn't look too right, but it could be.
Answer:
c+d>15
Step-by-step explanation:
please help confused tyy
Gerald wants to buy a sweater that is $41.60 because it is on sale for 20% off
Answer: $33.28
Step-by-step explanation: 41.60x .20 = 8.32
41.60 - 8.32 = 33.28
10. A trapezold has a base of x and a helght of 3 units. If there is also a square with sides measuring x,
what formula would be used to calculate the total area of both figures (the ^sign represents the
exponent or power of the number): *
09x
Ox2
4x + x3
1x 2 + 3
Answer:
I Think 0x2 Or 4x + x3 I'm not 100% Sure
Step-by-step explanation:
I Tried..
Make x the subject xa = xb + c
Step-by-step explanation:
xa - xb = c
x (a - b) = c
× = c / (a -b)
Find the value of x and y. NEED HELP ASAP
Answer:
11) 2√3
12) 4√3
Step-by-step explanation:
11)
tg60 = 6/x
x= 6/tg60
x= 6/ √3
x= 2√3
12)
a2= (b)2 + (c)2
a2= (6)2 + (√3)2
a2= 36 + 12 = 48
a= √48
a= 4√3
I hope this helps you :)
A 2m tall man observes the angle of elevation of a tower 45m to be 30 degree.find the distance between man and the tower
Answer:
CARRY ON LEARNING BEGGINER PALANG PO KASI AKO EH
Step-by-step explanation:
sorry po
If John had 9 apples and doubles them 5000 times how many apples would he have
He would have 45000 apples, right?
Write the equation of a line that has a slope of 1/2 and passing through the point (-8, 5).
Answer:
[tex]y=\frac{1}{2}x+9[/tex]
Step-by-step explanation:
Slope-Intercept Form:
[tex]y=mx+b[/tex]
Plug in the slope:
[tex]y=\frac{1}{2}x+b[/tex]
Solve for b, the y-intercept, given the point (-8,5):
[tex]5=\frac{1}{2}(-8)+b[/tex]
[tex]5=-4+b[/tex]
[tex]9=b[/tex]
Therefore, the equation [tex]y=\frac{1}{2}x+9[/tex] produces a line with a slope of [tex]m=\frac{1}{2}[/tex] and passes through the point [tex](-8,5)[/tex]
Answer:
hbbvhghvbvvgvb
_ gfjjg
Step-by-step explanation:
yfjjgnkgckitfv
For the image below, state the line of reflection:
Answer choices:
y = -2
x-axis
y-axis
x = -1
Answer:20
Billions
Step-by-step explanation:
Answer:
Kjxiycdafgousdgkuafveligfasa
Simplify the following by collecting like terms.
c + c +c+c
Answer:
4c
Step-by-step explanation:
c + c +c+c
Factor out c
c(1+1+1+1)
c(4)
4c
Danielle purchased a picture frame with an area of 120 cm^2. She measured the length to be 10 cm. What is the width? Danielle has another picture frame with an area of 288 cm^2 and the same width. What is the length of the second frame?
Answer:
Step-by-step explanation:
the width of the first frame is 12cm because 120/10 = 12
the length of the second frame is 24cm because 288/12 = 24
answer?? please answer
Answer:
The y-value of Function A when x = 2 is GREATER than the y-value of Function B when x = 2
Step-by-step explanation:
✔️Find the equation of Function A:
To do this, find the y-intercept (b) and slope (m):
Slope (m) = change in y/change in x
Using (4, 13) and (5, 17),
Slope (m) = (17 - 13)/(5 - 4) = 4/1
m = 4
To find b, substitute (x, y) = (4, 13) and m = 4 into y = mx + b
13 = 4(4) + b
13 = 16 + b
13 - 16 = b
b = -3
To write the equation for Function A, substitute m = 4 and b = -3 into y = mx + b
Thus:
y = 4x - 3
Next, find the y-value of Function A when x = 2 by substituting x = 2 into y = 4x - 3
Thus:
y = 4(2) - 3
y = 8 - 3
y = 5
✅The y-value of Function A when x = 2 is 5
✔️Equation for Function B is given as,
y = ½x + 1
Find the y-value of Function B when x = 2 by substituting x = 2 into y = ½x + 1
Thus:
y = ½(2) + 1
y = 1 + 1
y = 2
✅The y-value of Function B when x = 2 is 2
Therefore, the correct statement is:
The y-value of Function A when x = 2 is greater than the y-value of Function B when x = 2
Lisa, Taryn, and Catherine go to a store to buy party supplies. The store has a sale on the supplies they want for 3_4 the original price. The girls agree to each pay 1_3 of the cost.
Answer:
1/4 of the cost
Step-by-step explanation:
Lisa, Taryn, and Catherine go to a store to buy party supplies. The store has a sale on the supplies they want for 3/4 the original price. The girls agree to each pay 1/3 of the cost. What fraction of the original price did each girl pay?
Discounted price = 3/4 the original price
Each girl agreed = 1/3 of the cost
Amount each girl paid = 3/4 * 1/3
= (3 * 1) / (4 * 3)
= 3 / 12
= 1/4 of the cost
Amount each girl paid = 1/4 of the cost
Will rank the correct answer brainliest!
Answer:
Step-by-step explanation:
diameter=2*radius
=2*9
=18 in
given central angle=72 degree
arc length=central angle /360° *πd
=72/360 *3.14*18
=1/5 *56.52
=56.52/5
=11.304
Answer:
arc length=2πr×0.2
=2×3.14×9×0.2
=11.304 inch²
Total cost for cookie and lemonade is 1.80. If lemonade costs 1.00 more than the cookie, how much was the lemonade?
Answer:
The lemonade costs 1.4.
Step-by-step explanation:
This question is solved using a system of equations.
I am going to say that:
x is the cost of a cookie.
y is the cost of a lemonade.
Total cost for cookie and lemonade is 1.80.
This means that [tex]x + y = 1.8[/tex].
As we want y, we have that [tex]x = 1.8 - y[/tex]
Lemonade costs 1.00 more than the cookie?
This means that:
[tex]y = x + 1[/tex]
So
[tex]y = 1.8 - y + 1[/tex]
[tex]2y = 2.8[/tex]
[tex]y = \frac{2.8}{2}[/tex]
[tex]y = 1.4[/tex]
The lemonade costs 1.4.
Mr. Norris buys a boat for $125,000. He has to pay a 5% tax on his purchase of the boat. How much money is the tax?
6250 is 5% of 125000
(6 - i)(6 + i) multiplying complex numbers
Answer:
[tex](6 - i)(6 + i) \\ = (36 + 6i - 6i - {i}^{2} ) \\ = 36 - {i}^{2} \\ = 36 - ( - 1) \\ = 36 + 1 \\ = 37[/tex]
Each day, Deanne starts working at 10:00 a.m. and Stephanie starts working at noon. At which time each day are the earnings for Deanne equal to the earnings for Stephanie?
Answer:
Time when both earnings are equal = 5:00 Pm
Step-by-step explanation:
Given:
Total earning of Deanne = 6.50x
Total earning of Stephanie = 9.10(x -2)
Work started at 10:00 am
Find:
Time when both earnings are equal
Computation:
Total earning of Deanne = Total earning of Stephanie
6.50x = 9.10(x - 2)
6.5x = 9.1(x-2)
6.5x = 9.1x - 18.2
9.1x - 6.5x = 18.2
2.6x = 18.2
x = 18.2 / 2.6
x = 7 hour
So,
Time when both earnings are equal = Work started at 10:00 am + 7 hour
Time when both earnings are equal = 5:00 Pm