How can I find the area of an 18gon with a radius length 1ft
Answer:
Step-by-step explanation:
If we draw radii from the center of this 18-gon to each vertex, we end up with 18 triangles that are all congruent to each other. If we divide 360 by 18 we get the measure of the vertex angle of each of these 18 triangles. 360/18 = 20. So we take one of these triangles and pull it out and use it as a representative triangle from which we use trig to find its height and its base length.
The formula for the area for a regular polygon is
[tex]A=\frac{1}{2}ap[/tex] where a is the apothem (the height of our triangle) and p is the perimeter (found from the base of our triangle).
If we split this triangle we extracted right down the center vertically, we get 2 right triangles. Pull one of those out and this is the triangle we work with. The vertex angle is split in half and it now measures 10. The one base angle is the right angle and, by the Triangle Angle-Sum Theorem, the other base angle is 80. To find the height (or the apothem) of this right triangle that has a hypotenuse of 1 (the radius of the polygon is the hypotenuse of the right triangle), we use the sin or cos ratio. I used cos:
[tex]cos10=\frac{a}{1}[/tex] so
a = .9848
To find the base of this right triangle, I used the sin ratio:
[tex]sin10=\frac{p}{1}[/tex] so
p = .1736. But this is only half the length of one of the sides of the polygon, so multiply it by 2 to get the length of the whole side.
.1736 * 2 = .3473
Now, in order to find the perimeter, we multiply that one side by 18 to get
p = 6.2514
Now we're ready to find the area:
[tex]A=\frac{1}{2}(.9848)(6.2514)[/tex] so
A = 3.078 square feet
Need help what is the slope line that passes though the points
Slope = change in y / change in x
Slope = (4 - -8) / (-14 - -6)
Slope = 12/-8
Simplify:
Slope = -6/4
Answer:
-3/2
Step-by-step explanation:
To find the slope, use the slope formula
m = (y2-y1)/(x2-x1)
m = (4 - -8)/(-14 - -6)
= ( 4+8)/(-14+6)
= 12/-8
-3/2
In the number pattern above each term is 2 less than the previous term which of the following is also true about the pattern
A. All the numbers are odd
B.all the numbers are even
C.all the numbers are multiplies of 3
D. All of the numbers are prime
please help me with this equation
It was very cold in Canada on Monday. On Tuesday, the temperature dropped one degree and was -2. What is x, the temperature on Monday?
Answer:
-3
Step-by-step explanation:
-2= x+1
-2-1=x
-3=x
I need to pass so can somebody answer this plz
B. x = y
Hope this helps! :)
Answer:
x = y
Step-by-step explanation:
∠x and ∠y are corresponding angles
corresponding angles are congruent ( equal to each other )
Hence x = y
A cylinder has a radius of 6 and a height of 10 find the volume
Answer:
30cm
Step-by-step explanation:
Vn = Vc
1/3 X Pie x 6^2 x hn = Pie x 6^ x 10
hn = 30cm
Given: Radius=7cm,
Height=10cm
Volume of the cylinder=πr2h
=722×7×6×10=1540cm3
I don’t understand what to do on these question, some help would be nice (trigonometry)
Step-by-step explanation:
> find the angle of center circle:
cos~¹ 5/(5+12) = cos~¹ 5/17 = 72°
so the sector area of the shaded
region =
(360-72)/360 × 3.14 × 5²
= 288/360 × 78.5
= 62.8
> the height of triangle (red Line) =
4×tan 72° = 4× 3.078 = 12.31
the height of pyramid (green
Line) = √12.31²-8.5² =√74.16
= 8.61
so the volume of pyramid =
⅓×(17×8)×8.61 = 390.32
pls help me i need to hand in this project today
Answer:
it is too fine i cant really see the work
Order the integers from least to greatest. 4, –4, –2, 2, –8
A rental car company charges $80 per day to rent a car and $0.10 for every mile driven. Alyssa wants to rent a car, knowing that: She plans to drive 150 miles. She has at most $300 to spend. Which inequality can be used to determine xx, the maximum number of days Alyssa can afford to rent for while staying within her budget?Geq30080x+15≥300 15x+80\leq30015x+80≤300 80x+15\leq30080x+15≤300 15x+80\geq30015x+80≥300
Multiply the number of days (x) by the amount per day (80) to get 80x.
She is driving 150 miles at 0.10 per mile so multiply to get the mileage cost: 150 x 0.10 = 15
Add this to the daily amount:
80x+15
She can spend up to 300, so less than or equal to 300:
80x +15 <=300
Four friends share the profit of a lawn care service equally. The friends charge $45 per lawn and spend $30 of their
total earings on gasoline for the lawnmowers each week. Which inequality can be used to find m, the number of
lawns they need to mow next week so that each person earns at least $275? (14 Points)
A. 45m - 30 over 4 ≥ 275
B. 45m over 4 - 30 ≥ 275
C. 45m - 30 over 4 ≤ 275
D. 45m over 4 - 30 ≤ 275
Answer:
I think the answer is A. 45m - 30 over 4 ≥ 275
For question 12, use the graph to guess one zero for the polynomial whose graph is shown. Then, factor completely.
12) f(x) = x³ - 6x² + 6x + 8
Answer:
x³ - 6·x² + 6·x + 8 = (x - 4) × (x - (1 + √3)) × (x + 1 + √3)
Step-by-step explanation:
From the given graph of the polynomial, x³ - 6·x² + 6·x + 8, we have that one of the zeros of the polynomial, which is one point the graph cuts the x-axis is given as follows;
At a zero, we have, x = 4
∴ x - 4 = 0 is a factor of the polynomial
Dividing the given polynomial by (x - 4), gives;
x² - 2·x - 2
(x³ - 6·x² + 6·x + 8)÷(x - 4)
x³ -4·x²
-2·x² + 6·x + 8
-2·x² + 8·x
-2·x + 8
-2·x + 8
0
∴ (x³ - 6·x² + 6·x + 8)÷(x - 4) = x² - 2·x - 2
∴ (x - 4) × (x² - 2·x - 2) = x³ - 6·x² + 6·x + 8
Factorizing x² - 2·x - 2, gives;
x = (2 ± √((-2)² - 4×1×(-2)))/(2 × 1) = (2 ± 2·√(3)/(2) = (1 ± √(3)
Therefore, x = 1 + √3, (x - (1 + √3)) = 0 or x = 1 - √3, (x - (1 - √3)) = 0 which gives the factors, after factorizing completely as follows;
x³ - 6·x² + 6·x + 8 = (x - 4) × (x - (1 + √3)) × (x + 1 + √3)
54) Ashley and Nicole each improved their yards by planting daylilies and ornamental grass. They
bought their supplies from the same store. Ashley spent $43 on 2 daylilies and 3 bunches of
ornamental grass. Nicole spent $87 on 6 daylilies and 3 bunches of ornamental grass. Find the
cost of one daylily and the cost of one bunch of ornamental grass.
dalilar.
Answer:
Daylilies- $11, Ornamental grass- $7
Step-by-step explanation:
For this one, you want to convert this into simultaneous equations.
If we let d be cost of one daylily and o be cost of one bunch of ornamental grass, we can write the equations as 2d+3o=43 and 6d+3o=87.
From there, we can see they share a like term (3o), so we subtract one equation from the other (since they both are preceded by a +). This gives 4d=44.
Dividing both sides by 4 isolates d, leaving d=$11.
We can substitute this value into either equation to work out o (I'm using the first one as it is easier). This makes it 2×11+3o=43, or 22+3o=43.
From there, we subtract 22 from both sides, giving 3o=21, and dividing by 3 gives a final result of o=$7.
**This content involves writing and solving simultaneous equations, which you may wish to revise. I'm always happy to help!
All working out:
d- cost of one daylily o- cost of one bunch of ornamental grass
2d+3o=43 6d+3o=87
6d+3o=87
- - -
2d+3o=43
= = =
4d =44
÷4 ÷4
d =11
2d+3o=43
2×11+3o=43
22+3o=43
3o=21
o=7
I need help pls it’s a final
Answer:
A.Both of the students did the problem correctly.
Step-by-step explanation:
B. Nikki multiplied the fraction(8/3) to the items in the parentheses. Then multiplied each side with 3. Jon did the opposite. He first removed the fraction by multiplying each side by 3. Then he multiplied 2 to the items in the paranthesis.
C. I prefer Jon's method. Fractions can be tricky. I prefer to remove them as soon as possible. This time the items in the paranthesis had whole numbers. But had any of them been a fraction too, the problem would have gotten a lot more tricky and it would very easy to make a mistake or miscalculate something.
9) Solve for w:
W +12
2w
Answer:
w = 26
Step-by-step explanation:
set up an equation; since this is a right angle, it equals 90 degrees
90 = w + 12 + 2w
90 - 12 = w + 2w
78 = 3w
78/3
w = 26
Answer:
w = 26
Step-by-step explanation:
2w +w + 12 =90
3w +12 = 90
-12 -12
3w = 78 then 3w/3 = 78/3
w=26
Evaluate the expression when x = 4 and y=5.
Answer:
49
Step-by-step explanation:
Answer:
49
Step-by-step explanation:
3x² + 4y⁰ - x⁻¹
3(4)² + 4(5)⁰ * (4)⁻¹
3(16) + 4(1) * 1/4
48 + 4 * 1/4
48 + 4/4
48 + 1
49
What is the total weight of all the fruit she bought?
Image included
Answer:
1/3 kilograms
Step-by-step explanation:
Tell whether the triangle with the given side lengths is a right triangle.
28, 45,54
The answer is yes or no
Answer:
No
Step-by-step explanation:
CAN SOMEONE PLEASE HELP ME FAST?
Answer:
whats the question
Step-by-step explanation:
Questlon 2 of 10
Is SAM- FIG? If so, identify the similarity postulate or theorem that
applies.
MOA
16
110 24
12
G
A. Similar - SAS
B. Similar - SSS
C. Similar - AA
D. Cannot be determined
no links please!!!!!!!!!ty!!!
Answer:
<2 = 75
Step-by-step explanation:
<1 and <2 form a straight line which means that they add to 180
<1+<2 =180
105+<2 =180
Subtract 105 from each side
<2 =180-105
<2 = 75
At a local university, there are 4340 students enrolled in History. The ratio of males to
females in therprogram is 3:7. How many males and females are enrolled?
Answer:
1302 males & 3038 females
Step-by-step explanation:
3x + 7x = 4340
10x = 4340
x = 434
3(434) = 1302 males
7(434) = 3038 females
The area of a circular plate is approximately 50.24 in2. What is the radius of the plate?
Answer:
area of the circular plate =πr²
50.24 =3.14×r²
r² =50.24/3.14
r² =16
radius =4 inch
Answer:
4 in
Step-by-step explanation:
The slope of the line that represents the data Nicholas collected is -63, and the y-intercept is 825. Explain what these represent in the context of the situation. Remember that x is the number of days, and y is the number of canned goods.
Find the slope and y-intercept of the line.
m =
b =
Answer:
Step-by-step explanation:
They tell you the slope of the line is -63 :/ m= -63
and then they tell you the y-intercept is 825 b= 825
Why did you even need to ask about this ?
Which expression is equivalent to the expression shown (5^3) ^9 divided 5^12
Answer:5 exponent of 15
Step-by-step explanation:trust
Which one is it?
a) <
b) =
c) >
Answer:
A: less that
Step-by-step explanation:
4( 14)+3
36+3= 39
39 (2+9)6-7
(11)6-7
66-7
59
39<59
What is the solution to 3+ 4e^X+1=11?
O x = In 2-1
O X=In2+1
O X- x-
e
e+2
OX-
e
Answer:
x = 1 ,or x = -7
Obviously, the true answer is not in the options given.
Step-by-step explanation:
x² + 6x - 6 = 10
The above equation can not be factorized, hence the use of Almighty Formula.
x = [-b +- √b² - 4ac] / 2a
Where a = 1, b = 6, c = -6
x = [-6 +- √6² - (4*1*-6)] / 2*1
x = [-6 +- √36 - (-24)] / 2
x = [-6 +- √36 + 24] / 2
x = [-6 +- √60] / 2
x = [-6 +- 7.75] / 2
x = [-6 + 7.75] / 2 ,or x = [-6 - 7.75] / 2
x = 1.75/2 ,or x = -13.75/2
x = 0.875 ,or x = -6.875
Approximately
x = 1 ,or x = -7
Answer:
x=In2+1
Step-by-step explanation:
3+4ex+1-3=11-3
0+4ex+1=8
4ex+1=8
Find the value of x
Answer:
x=56
Step-by-step explanation:
Since the angles are all the same,
D=78
F=46
All you have to do is subtract these numbers from 180, which gives you 56
Answer:
56
Step-by-step explanation:
Write the word sentence as an inequality. Then solve the inequality. Eight times a number $n$ is less than 72
Answer:
8n < 72
n < 9
Step-by-step explanation:
Note that
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
for example : 2 < 3 means 2 is less than 3
3 >2 means 3 is greater than 2
8 times n = 8n
8n is less than 72, this can be represented by the equation : 8n < 72
to determine the value of n, divide both sides of the equation by 8
n < 9