Answer:
The length of one side of the octagon is 7.65 cm
Step-by-step explanation:
The parameters given are;
A regular octagon inscribed in a circle of radius, r, of 10 cm.
The length of each side is found from the isosceles triangle formed by the radius and one side of the octagon
The sum of interior angles in a polygon, ∑θ[tex]_i[/tex] = 180 × (n - 2)
Where;
n = The number of sides of the polygon
θ[tex]_i[/tex] = The interior angle of the polygon
For the octagon, we have;
n = 8, therefore;
∑θ[tex]_i[/tex] = 180 × (8 - 2) = 1080
Given that there are eight equal angles in a regular octagon, we have;
∑θ[tex]_i[/tex] = 8 × θ[tex]_i[/tex] = 1080
θ[tex]_i[/tex] = 1080/8 = 135°
The sum of angles at the center of the circle = 360
Therefore, the angle at the center (tip angle) of the isosceles triangle formed by the radius and one side of the octagon = 360/8 = 45°
The base angles of the isosceles triangle is therefore, (180 - 45)/2 = 67.5° = θ[tex]_i[/tex]/2
The length of the base of the isosceles triangle formed by the radius and one side of the octagon = The length of one side of the octagon
From trigonometric ratios, the length of the base of the isosceles triangle is therefore;
2 × r × cos(θ[tex]_i[/tex]/2) = 2×10 × cos(67.5°) = 7.65 cm
The length of the base of the isosceles triangle = 7.65 cm = The length of one side of the octagon.
Find the total cost, to the nearest cent, for a sweater that costs $22.95 with an additional 5.5% sales tax. Show your work.
Answer:
22.95×1.055≈$24.21
(3x-10) (2x-5) =? A. 6x^2 - 35x + 50 B. 6x^2 + 35x + 50 C. 6x^2 - 5x - 50 D. 6x^2 - 35x - 50
Answer:
[tex]\large \boxed{\sf \bf \ \ 6x^2-35x+50 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
[tex](3x-10)(2x-5)\\\\=3x(2x-5)-10(2x-5)\\\\=6x^2-15x-20x+50\\\\=\boxed{6x^2-35x+50}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
A is the correct answer
How would I answer this using a number line to find what the sum of
-2 + 2 =
Solution: in the picture
hope it helps^°^
PLEASE ANSWER!!!!!!
Which of the following is true? a) |−4| < 3 b) |−4| < |3| c) |−3| < −4 | d) −3| < |−4|
Answer:
The answer is D
Step-by-step explanation:
the first one is equal to the equation 4 < 3 because of absolute value, second 4 < 3, third 3 < -4, fourth -3 < 4
PLZZ HELPP!! On Tony's map, the distance from Saint John, NB to St. John's, NL is 21 cm. The actual distance between these two cities is 1050km. What is the scale of Tony's map?
Answer:
1/5 000 000
Step-by-step explanation:
1050km is equal to 105 000 000cm
105 000 000 ÷ 21= 5 000 000
So the scale is 1/5 000 000.
Carly is traveling to visit family. She drives x miles on the first day and y miles on the second day for a total of 800 miles. What are the domain and range of this relationship?
Answer:
The domain and range of this relationship is (-∞,∞) and (-∞,∞) respectively.
Step-by-step explanation:
We are given that Carly is traveling to visit family.
She drive distance on first day = x
She drive distance on second day = y
We are also given that Carly is travelling a total of 800 miles.
So,x+y=800
We are supposed to find domain and range of this relationship.
y=800-x
Domain : (-∞,∞)
Range:(-∞,∞)
Hence the domain and range of this relationship is (-∞,∞) and (-∞,∞) respectively.
Answer:
domain: 0 ≤ x ≤ 800
range: 0 ≤ y ≤ 800
Step-by-step explanation:
when the equation is graphed is it linear or nonlinear ??
Answer:
Nonlinear
Step-by-step explanation:
This is nonlinear because its parent function is y = [tex]x^{2}[/tex]. The parent function of a linear equation is y = x.
I hope this helps :))
Find the value of x.
Answer:
D. 15
Step-by-step explanation:
Both equations need the same end result because this is a square:
3x - 15 = 45 - x =
3x - 3x = 45 - x - 3x
0 = 45 - 4x
4x = 60
4x/4 = 60/4 =
X = 15
Check:
3(15) - 15 = 45 - 15
45 - 15 = 45 - 15
30 = 30
Write the geometric sequence in function notation.
7, 14, 28, 56, 112, ...
3
Ax) = (7). ()x-1
f(x) = (7) · (2)X-1
O AX) = (7) . (3)X-1
Rx) = (2) (+)*-1
Answer:
a(n) = 7*2^(n - 1)
Step-by-step explanation:
The first term of the given geometric sequence, 7, 14, 28, 56, 112, ... , is 7, and the common ratio is 2. Each new term is twice the previous term.
Thus the general formula for the geometric sequence becomes
a(n) = 7*2^(n - 1).
As a check, let's see whether this formula correctly predicts the fourth term (56): Here n = 4, and so a(4) = 7*2^(4 - 1) = 7*2^3 = 7*8 = 56. Yes.
Answer:
f(x) = (7) ∙ (2)x–1
Step-by-step explanation:
The first term in the sequence is 7, and the common ratio is 2. Using the explicit formula and writing it in function notation results in f(x) = (7) ∙ (2)x–1.
Nine and one-half less than four and one-half times a number is greater than 62.5. Which of the following represents the solution set of this problem?
(16, positive infinity)
(Negative 16, positive infinity)
(Negative infinity, 16)
(Negative infinity, Negative 16)
Answer:
{16, +infinity}
Step-by-step explanation:
Represent the number with n
Required
Find the solution set
From the question, we have that;
4½n - 9½ > 62.5
Convert all numbers to decimal
4.5n - 9.5 > 62.5
Add 9.5 to both sides
4.5n - 9.5 + 9.5 > 62.5 + 9.5
4.5n > 72
Multiply both sides by 2
2(4.5n) > 72 * 2
9n > 144
Multiply both sides by ⅑
⅑ * 9n > 144 * ⅑
n > 16
This implies that n ranges to infinity from positive 16;
Hence, the correct answer is {16, +infinity}
complete the table of values for y=-x^2+2x+1
Answer:
-1=-2
4=-7
Step-by-step explanation:
for x=-1
y=(-1^2)+(2*-1)+1
y=-1-2+1
y=-2
for x=1
y= (-1^2)+(2*1)+1
y= -1+2+1
y=2
for x=4
y=(-4^2)+(2*4)+1
y=-16+8+1
y=-7
help me please real quick
Answer:
D) [tex]360 m^{3}[/tex]
Step-by-step explanation:
Let's review the formula for finding the volume of a cube or rectangular prism.
[tex]V = (l)(h)(w)[/tex] - Basically saying "Volume = length × height × width".
In this case, you can consider 9 meters as the length, 5 meters as the height, and 8 meters as the width (but it doesn't really matter which dimensions are which since you are just multiplying them all together).
Now, let's multiply our dimensions together.
[tex]9 * 5 * 8 = 360[/tex]
That's your answer! Make sure to not forget your units (in this case, meters) cubed.
Hope that helps and maybe earns a brainliest!
Have a splendid day! <3
Please help ASAP!!!!!!!!
Answer:
Balance = $14,723.06
Step-by-step explanation:
Given:
Principal (P) = $15,000
Interest Rate (R) = 7.5%
Time (T) = ¹/12
Monthly payment = $185.49
Required:
Balance of the loan at the end of 3 months using the formula for simple interest.
SOLUTION:
[tex] I = \frac{P.T.R}{100*12} [/tex]
First Month:
Principal => $15,000
Add interest => [tex](\frac{15,000*7.5*1}{100*12} )[/tex] => $93.75
= $15,093.75
Less payment => $185.49
= $14,908.26
Second Month:
Principal => $14,908.26
Add interest => [tex](\frac{14,908.26*7.5*1}{100*12})[/tex] => $93.18
= $15,001.44
Less payment => $185.49
= $14,815.95
Third Month:
Principal => $14,815.95
Add interest => [tex](\frac{14,815.95*7.5*1}{100*12})[/tex] => $92.60
= $14,908.55
Less payment => $185.49
Balance = $14,723.065. Find the measures of the following. Round to the nearest whole number
Answer:
a - HT = 17
b - ∠T = 62
c - ∠H = 28
A circle has a radius of 26.85 inches. What is the circumference of this circle? Use 3.14 for pi. Round your final answer to the nearest tenth. Enter your answer as a decimal in the box. the first choose dropdown has :0.25 and 4 then is the scale factor an enlargement or not THE TRIANGLE ON THE LEFT IS 1.5 AND THERE IS AN ARROW GOING INTO A BIGGER TRIANGLE THAT IS 6
Answer:
Step-by-step explanation:
Circumference of the circle = 2 x pi x r
= 2 x 3.14 x 26.85
= 168.618 Inches
after rounding to nearest tenth, 168.6 inches
Answer:
168.6 inches
Step-by-step explanation:
The formula for finding the circumference of a circle is:
[tex]\pi r2[/tex] (Basically multiplying [tex]\pi[/tex] by the diameter since the radius is half the diameter)
Let's substitute and solve!
3.14(26.85 × 2) =
3.14 × 53.7 =
168.61800............but if we round to the nearest tenth, it will be 168.6 inches!
Hope that helps and maybe earns a brainliest!
Have a great day! > <
U
08.01) Which of the following statements shows a characteristic of a statistical question? (4 points) Select one: a. The question is focused. b. The distribution can be broken into categories. c. The question asks for a quantitative response. d. The question allows for surveys to be conducted
Answer:
the distribution can be broken into categories
Statement c shows a characteristic of a statistical question.
What is statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
So, based on the definition of statistics we can say.
1)Statistical data can be analysed.
2)Statistical data can be used to interpret many things.
3)Statistical data can forecast the results.
Out of the given statements, only statement c falls under the category of statistical statement.
Hence, statement c shows a characteristic of a statistical question.
To get more about statistics visit:
https://brainly.com/question/15525560
Find the measure of the remote exterior angle. m∠x=(197−5n)°m∠y=(6n+22)°m∠z=(n+7)°
A. 14
B. 91
C. 21
D. 127
Answer:
D. 127°
Step-by-step explanation:
The exterior angle (x) is the sum of the remote interior angles (y, z).
Setupx = y +z
(197 -5n) = (6n +22) +(n +7) . . . . . substituting the given expressions
SolutionEliminating parentheses and collecting terms, we have ...
197 -5n = 7n +29
168 = 12n . . . . . . . . . add 5n-29
14 = n . . . . . . . . . . divide by 12
Then the measure of remote exterior angle x is ...
m∠x = (197 -5(14))° = (197 -70)°
m∠x = 127°
plz help urgent ,plz have step by step explanation find a and b
Answer:
but i didn't understand the root 5 with b on the question
|5x + 1 over 2y2| What is the value of the expression above when x = 3 and y = 2? You must show all work and calculations to receive full credit.
Answer:
2
Step-by-step explanation:
The value of the expression |5x + 1 / 2y²| when x = 3 and y = 2 will be 2.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The expression is given below.
⇒ |5x + 1 / 2y²|
The value of the expression at x = 3 and y = 2, then we have
⇒ |5(3) + 1 / 2(2)²|
⇒ |15 + 1 / 2(4)|
⇒ |16 / 8|
⇒ 2
The value of the expression |5x + 1 / 2y²| when x = 3 and y = 2 will be 2.
More about the function link is given below.
https://brainly.com/question/5245372
#SPJ3
attachment help for question c no explanation only answer thank you
Answer:
Tablets.
Step-by-step explanation:
You didn't want an explanation so....here you go....no explanation.
Hope that helps and maybe earns a brainliest.
Have a great day!
Math Question (10 Points):
Answer:
x-axis
Step-by-step explanation:
Answer:
It is the x-axis
Step-by-step explanation:
In a graph, the horizontal part of it is called the x axis.
Here is an definition: horizontal axis of a system of coordinates, points along which have a value of zero for all other coordinates
Choose the property of real numbers that justifies the equation! Photo of questions are below
Answer:
Multiplicative Identity Property,Associative Property of Addition,Commutative Property of Multiplication,Zero Property of Multiplication
Step-by-step explanation:
The required properties for the given expression of the real numbers are multiplication property, associative property, commutative property, and property of zero multiplication.
Given that,
A number of expressions for the real number are given we have determined the corresponding properties for the arithmetic operation given.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements.
Here,
1.
n.1 = n
It is a unit multiplication property.
2.
(4 + b) + 7 = 4 + (b + 7)
it is associative property of real numbers.
3.
m.9 = 9.m
it is commutative property.
4.
0.c = 0
It is a property of zero multiplication.
Thus, the required properties for the given expression of the real numbers are multiplication property, associative property, commutative property, and property of zero multiplication.
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ2
Sally’s house is located at (5, −1) and her school is located at (−9, 7). Her best friend Molly lives at
the midpoint of Sally’s house and school. What coordinate represents Molly’s house?
A. (2, −3) B. (−2, 3) C. (3, −2) D. (−3, 2)
Answer:
B. (−2, 3)
Step-by-step explanation:
To find the midpoint of a segment, add the x-coordinates of the endpoints and divide by 2. Add the y-coordinates of the segments and divide by 2.
x: (5 + (-9))/2 = -2
y: (-1 + 7)/2 = 3
Midpoint: (-2, 3)
Answer: B. (−2, 3)
Answer:
b
Step-by-step explanation:
-9+5=-4÷2=-2
-1+7=6÷2=3
Jamaal spent x minutes today practicing his guitar and y minutes today on homework. If the total time he spent on both is 45 minutes or more, which inequality best represents his practice time?
x + y < 45
x + y > 45
x + y ≤ 45
x + y ≥ 45
Answer:
x + y ≥ 45
Step-by-step explanation:
This is because the total amount of minutes could be equal to 45, meaning your inequality sign has to have a line underneath it.
Additionally, x + y is greater than or equal to because the amount could be more than 45... therefore, 45 is not greater than x + y
Hi there! Hopefully this helps!
----------------------------------------------------------------------------------------------------------
If the total time he spent on both is 45 minutes or more, the answer is:
x + y ≥ 45.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Hints for next time
(≥ Means greater than or equal to.)
(≤ Means less than or equal to)
(> Greater than)
(< Less than)
These cones are similar. Find the surface
area of the smaller cone. Round to the
nearest tenth.
Answer:
33.3
Step-by-step explanation:
plsssssss help me!!!!!!!!!!!!!!!!!!!!!!! it is recommended that for every 8 square feet of surface, a pond should have 2 fish. a pond that has a surface of 72 square feet should contain how many feet?
What is h decreased by 20
Answer:
h minus 20
Step-by-step explanation:
4 cm, 5 cm, 20 cm
can the side lengths
form a triangle ?
Answer: No
Step-by-step explanation:
Because 4^2=16
5^2=25
25+16=41
41 squared =6.4031.....
6.4031 does not = 20
Answer: No, a triangle is not possible
The two smaller sides add to 4+5 = 9 which is not larger than 20. For a triangle to be possible, we need to be able to add 2 sides to make them longer than the third side. This is an application of the triangle inequality theorem.
What is the range of possible sizes for side x?
8.0
2.5
Please helpp!!
Triangle inequality theorem:
In any triangle, the length of any side must be:
less than the sum of the lengths of the other two sides.greater than the difference of the lengths of the other two sides.For the problem you have:
x must be greater than 8.0 - 2.5 and less than 8.0 + 2.5
5.5 < x < 10.5
Answer:
5.5<x<10.5
Step-by-step explanation:
Can someone help me with this math problem
Answer:
B. (m-1)(m-8)
Step-by-step explanation:
The factors of 8 (constant term) are
{(1,8), (2,4)}, from which we see that 1+8 = 9, the absolute value of the coefficient of the second term.
Therefore we can group the expression as
m^2 - 9m + 8
= m^2-m - (8m -8)
then factor each group
= m(m-1) - 8(m-1)
and factor out (m-1)
= (m-1)(m-8)
