Answer:
Part A) [tex]A_s=\frac{\pi r^{2}}{360^o}{\theta}[/tex]
Part B) option 1,option 4
Step-by-step explanation:
Part A) Derive the formula for the area of a sector
we know that
The area of circle is equal to
[tex]A=\pi r^{2}[/tex]
The area of circle subtends a central angle of 360 degrees
so
using proportion
Find out the area of a sector [tex]A_s[/tex] by a central angle of ∅ degrees
[tex]\frac{\pi r^{2}}{360^o}=\frac{A_s}{\theta}[/tex]
[tex]A_s=\frac{\pi r^{2}}{360^o}{\theta}[/tex]
Part B) Verify each case
case 1) we have
radius = 5 cm
angle = 120°
area = 26.2 cm 2
Find the area of the sector and then compare with the value of the given area
assume
[tex]\pi=3.14[/tex]
substitute the given values
[tex]A_s=\frac{(3.14)(5)^{2}}{360^o}{120^o}[/tex]
[tex]A_s=26.2\ cm^2[/tex]
so
The given value of area is correct
case 2) we have
radius = 4 cm
angle = 105°
area = 16.7 cm 2
Find the area of the sector and then compare with the value of the given area
assume
[tex]\pi=3.14[/tex]
substitute the given values
[tex]A_s=\frac{(3.14)(4)^{2}}{360^o}{105^o}[/tex]
[tex]A_s=14.7\ cm^2[/tex]
so
The given value of area is not correct
case 3) we have
radius = 6 cm
angle = 85°
area = 23.7 cm 2
Find the area of the sector and then compare with the value of the given area
assume
[tex]\pi=3.14[/tex]
substitute the given values
[tex]A_s=\frac{(3.14)(6)^{2}}{360^o}{85^o}[/tex]
[tex]A_s=26.7\ cm^2[/tex]
so
The given value of area is not correct
case 4) we have
radius = 7
angle = 75°
area = 32.1 cm 2
Find the area of the sector and then compare with the value of the given area
assume
[tex]\pi=3.14[/tex]
substitute the given values
[tex]A_s=\frac{(3.14)(7)^{2}}{360^o}{75^o}[/tex]
[tex]A_s=32.1\ cm^2[/tex]
so
The given value of area is correct
Raj has a $25 budget to spend on decorations for a party he has already spent $18.60 he now wants to get some helium balloons that’s cost $0.80 each write and solve an inequality to show the number of balloons the raj could buy
Answer:
The number of balloons Raj could buy is 8.
Step-by-step explanation:
Given:
Raj has a $25 budget to spend on decorations for a party.
He has already spent $18.60.
He wants to get some helium balloons that’s cost $0.80 each.
Now, to write and solve an inequality to show the number of balloons Raj could buy.
Let the number of balloons be [tex]x.[/tex]
Cost of each balloons = $0.80.
So, the total cost of balloons = [tex]0.80x.[/tex]
He already spent = $18.60.
Total budget Raj has = $25.
Now, to solve an inequality to show the number of balloons:
[tex]0.80x+18.60\leq 25[/tex]
Subtracting both sides by 18.60 we get:
[tex]0.80x\leq 6.40[/tex]
Dividing both sides by 0.80 we get:
[tex]x\leq 8.[/tex]
Therefore, the number of balloons Raj could buy is 8.
Jackie is thinking of one number and Adrian is thinking of another. Camila thought if I take these two numbers, they have a product of 567 and a difference of six. Jackie’s number is higher than Adrian’s. What are Jackie’s and Adrian’s numbers?
Answer:
Jackie: 27Adrian: 21Step-by-step explanation:
Integers with a product of 567 are ...
567 = 1·567 = 3·189 = 7·81 = 9·63 = 21·27
The last of these pairs of factors have a difference of 6, so they are the answers.
Jackie's number is 27; Adrian's number is 21.
_____
You could let "a" represent Adrian's number and write the equation ...
a(a +6) = 567
a^2 +6a +9 = 576 . . . . . complete the square
(a +3)^2 = 24^2 . . . . . . . write as squares
a = -3 +24 = 21 . . . . . . . . take the positive square root; subtract 3
Adrian's number is 21; Jackie's number is 27.
F^-1(4) when f(x) = 3x - 4/ 5
Answer: [tex]f^{-1}(4)=\frac{8}{5}[/tex]
Step-by-step explanation:
1. You need to find the Inverse function [tex]f^{-1}(x)[/tex]:
- Given the function f(x):
[tex]f(x) = 3x - \frac{4}{ 5}[/tex]
- Rewrite it with [tex]f(x)=y[/tex]:
[tex]y= 3x - \frac{4}{ 5}[/tex]
- Now you must solve for "x":
[tex]y+\frac{4}{ 5} = 3x\\\\(y+\frac{4}{ 5})(3)=x\\\\x=\frac{y}{3}+\frac{4}{15}[/tex]
- Now you must exchange the variables:
[tex]y=\frac{x}{3}+\frac{4}{15}[/tex]
- Then:
[tex]f^{-1}(x)=\frac{x}{3}+\frac{4}{15}[/tex]
2. Substitute [tex]x=4[/tex] into the Inverse function and then evaluate:
[tex]f^{-1}(4)=\frac{(4)}{3}+\frac{4}{15}\\\\f^{-1}(4)=\frac{8}{5}[/tex]
in the three stacks of books there are 15 books, 9 books and 9 books if the books were rearranged so that the stack had the same number of books how many books would be even?
Answer:
There would be 11 books in each stack, to have the same number.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Books in stack 1 = 15
Books in stack 2 = 9
Books in stack 3 = 9
2. If the books were rearranged so that the stack had the same number of books how many books would be even?
Total books = Books in stack 1 + Books in stack 2 + Books in stack 3
Total books = 15 + 9 + 9
Total books = 33
Total books/Number of stacks = Number of books per stack to be the same
33/3 = Number of books per stack to be the same
Number of books per stack to be the same = 11
Sally found 58 seashells on the beach, she gave Jason some of her seashells. She has 28 left. How many seashells did she give to Jason?
Sally gave 30 shells to Jason
Solution:
Given that, Sally found 58 seashells on the beach, she gave Jason some of her seashells
She has 28 left
To find: Number of sea shells she gave to Jason
From given,
Total number of shells she found = 58
Remaining shells = 28
Therefore,
Number of sea shells she gave to Jason = Total number of shells she found - Remaining shells
Number of sea shells she gave to Jason = 58 - 28 = 30
Thus Sally gave 30 shells to Jason
0.6 of it is 30
Find the number
Answer:
The number is 50.
Step-by-step explanation:
0.6x=30
x=30/0.6
x=50
if the origin is the midpoint of the line segment joined by the points (2,3) (x,y) find x and y
Answer:
(- 2, - 3 )
Step-by-step explanation:
Given the endpoints of a segment (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
[0.5(x₁ + x₂), 0.5(y₁ + y₂ ) ]
Here (x₁, y₁ ) = (2, 3) and (x₂, y₂ ) = (x, y) and the midpoint = (0, 0), thus
0.5(2 + x) = 0 , that is
2 + x = 0 ( subtract 2 from both sides )
x = - 2
0.5(3 + y) = 0, that is
3 + y = 0 ( subtract 3 from both sides )
y = - 3
Thus (x, y) = (- 2, - 3 )
what is the slope a ski run that rises 8 feet for every horizontal change of 72 feet
Answer:
the slope of the ski run is 9
Solve for x in the equation x squared minus 4 x minus 9 = 29. x = 2 plus-or-minus StartRoot 42 EndRoot x = 2 plus-or-minus StartRoot 33 EndRoot x = 2 plus-or-minus StartRoot 34 EndRoot x = 4 plus-or-minus StartRoot 42 EndRoot
Answer:
The correct answer is A. x = 2 +/- √42
Step-by-step explanation:
Let's solve for x the quadratic equation, this way:
x² - 4x - 9 = 29
x² - 4x - 38 = 0
Using the quadratic formula, we have:
x = [- (-4) +/- √ -4² - 4 * -38]/2
x = 4 +/- √ 16 + 152/2
x = 4 +/- √ 168/2
x = 4 +/- √ 4 * 42/2
x = 4 +/- 2 √42/2
x = 2 +/- √42
The correct answer is A. x = 2 +/- √42
Answer:
the answer is A on edg2020
Step-by-step explanation:
4. A Christmas promotion included a $2.5 mail-
promotion included a $2.5 mail-in rebate for the purchase of a 10-liter bome
K and a store coupon for $1.39 off a 5-liter bottle of vegetable oil. Jesse Gatling
bought one 10-liter bottle of milk for $33.00 and a 5-liter bottle of vegetan
$26.89. Calculate his total cost if an envelope costs $0.10 and a stamp costs $
5. An Apple iPod sells for $781.29 and has a mail-in rebate for
$55.00. Determine the cost after the rebate if an envelope
costs $0.13 and a stamp costs $0.40.
The answer is
Final answer:
To find the final cost of an Apple iPod after a mail-in rebate and the cost of mailing the rebate (envelope and stamp), subtract the rebate amount from the original price and add the mailing costs. The total cost after these calculations is $726.82.
Explanation:
Let's tackle the Apple iPod rebate calculation problem. An Apple iPod sells for $781.29 and has a mail-in rebate for $55.00. To calculate the cost after the rebate, you must also consider the costs of an envelope and a stamp, which are $0.13 and $0.40, respectively. The formula for the final cost after applying the mail-in rebate, including the expenses for an envelope and a stamp, is as follows:
Calculate the rebate price by subtracting the rebate amount from the original price: $781.29 - $55.00 = $726.29.
Add the costs of the envelope and stamp to the price after rebate: $726.29 + $0.13 + $0.40 = $726.82.
The final cost of the iPod after the rebate and additional costs is $726.82.
Find the value of x. Round to the nearest degree.
Select one:
a. 53
b. 37
c. 49
d. 39
Answer:
a. 53
Step-by-step explanation:
The side with length 15 is opposite the right angle, so it is the hypotenuse of the right triangle.
For angle x, the side measuring 12 is the opposite leg.
Our 3 items of interest are: angle, opposite leg, hypotenuse.
The trig ratio that relates the opposite leg to the hypotenuse is the sine ratio.
sin x = opp/hyp
sin x = 12/15
sin x = 0.8
Now we take the inverse sine of 0.8 to find the measure of the angle.
x = sin^(-1) 0.8 = 53 deg
Consider the Piece-Wise graph described by the following equation:
Determine the coordinates of the point on the graph where x=3.
(3, 1)
(3, 3)
(3, 5)
(3, 13)
Answer:
(3, 5 )
Step-by-step explanation:
when x = 3, that is x ≥ 3, thus
y = 2x - 1 = 2(3) - 1 = 6 - 1 = 5 ⇒ (3, 5 ) is the point on the graph
f(1)=−1.8 f(n)=f(n−1)⋅9 Find an explicit formula for f(n)
Answer:
f(1) = - 1.8
f(n) = f(1) x 9ⁿ⁻¹
Step-by-step explanation:
f(1) = - 1.8
f(n) = f(1) x 9ⁿ⁻¹
f(1) = - 1.8 x 9⁰ = -1.8
f(2) = - 1.8 x 9¹
f(3) = - 1.8 x 9²
check:
f(1)=−1.8
f(n)=f(n−1)⋅9
f(2) = f(1) x 9 = -1.8 x 9¹
f(3) = f(2) x 9 = (- 1.8 x 9) x 9 = -1.8 x 9²
Answer: f(n)= -1.8*9^n-1
Step-by-step explanation:
old mcdonald has 100 chickens and goats in the barnyard. Altogether, there are 284 feet. How many chickens and how many goats are in the barnyard?
Answer:
58 chickens, 42 goats
Step-by-step explanation:
there are a total of 100 chickens and goats
c + g = 100....c = 100 - g
there are 284 feet....chickens have 2 feet and goats have 4 feet
2c + 4g = 284
2(100 - g) + 4g = 284
200 - 2g + 4g = 284
-2g + 4g = 284 - 200
2g = 84
g = 84/2
g = 42 <===== goats
c + g = 100
c + 42 = 100
c = 100 - 42
c = 58 <==== chickens
Final answer:
To solve the problem, set up equations based on the number of feet each animal has, then use substitution to find there are 58 chickens and 42 goats in the barnyard.
Explanation:
How to Solve Problems Involving Numbers of Chickens and Goats
Old McDonald has 100 chickens and goats in the barnyard, and altogether, there are 284 feet. To find out how many chickens and how many goats are there, we can set up a system of equations based on the information given. A chicken has 2 feet and a goat has 4 feet. Let's assign the variable C to represent the number of chickens and G to represent the number of goats.
We are given two pieces of information which we will translate into two equations:
Equation 1: C + G = 100 (since there are 100 chickens and goats in total)
Equation 2: 2C + 4G = 284 (since chickens have 2 feet and goats have 4 feet)
To solve for C and G, we can multiply Equation 1 by 2 to align it with the coefficients of Equation 2:
2C + 2G = 200
Now, subtract this new equation from Equation 2 to solve for G:
(2C + 4G) - (2C + 2G) = 284 - 200
2G = 84
G = 42
With G known, we can substitute it back into Equation 1 to find C:
C + 42 = 100
C = 58
Therefore, there are 58 chickens and 42 goats in the barnyard.
The diagram shows several planes, lines, and points.
Which statement is true about line h?
O Line h intersects line fat two points, A and B.
Line h is the intersection of planes Rand T.
Line h intersects plane pat point C.
© Line h has points on planes R P, and T.
Answer:
The true statement is Line h has points on planes R, P, and T
Step-by-step explanation:
The rest of the question is the attached figure
According to the graph, we will check which option is true.
a. Line h intersects line f at two points, A and B (Wrong)
Because: h intersects line f at B only.
b. Line h is the intersection of planes R and T (Wrong)
Because: g is the intersection of planes R and T
c. Line h intersects plane P at point C (Wrong)
Because: h intersects plane P at point B
d. Line h has points on planes R, P, and T (True)
Because h has the point B on the plane P, h has the point A on the plane T
and the points of h on the plane R
Answer:
Line h has points on planes R, P, and T
Step-by-step explanation:
did the test
5 minus what equals 4.329
Final answer:
5 minus 0.671 equals 4.329.
Explanation:
The student is asking for the number that, when subtracted from 5, equals 4.329. To find this number, you subtract 4.329 from 5:
5 - x = 4.329
Solving for x, you subtract 4.329 from 5:
x = 5 - 4.329
x = 0.671
Therefore, 5 minus 0.671 equals 4.329. When dealing with subtraction, it's important to round the result correctly, just as with other operations such as addition, multiplication, and division.
5[8 (7 — 4) divided by 6]
What is the value of the expression?
Please please please answer!
Answer:
20
Explanation:
PEMDAS
Job A pays $28.59 per hour. Job
B pays $25.71 per hour, but has
health benefits. Lauren will need
to buy health insurance for $6650
per year if it's not a job benefit. If
Lauren expects to work 2,000
hours during the year, and
ignoring taxes, which job should
Lauren take to have more
spending cash?
Answer:
Job B
Step-by-step explanation:
Job A:
Job A pays $28.59 per hour.
Lauren expects to work 2,000 hours during the year, so Lauren can expect to be paid
[tex]\$28.59\times 2,000=\$57,180[/tex]
Job B:
Job B pays $25.71 per hour.
Lauren expects to work 2,000 hours during the year, so Lauren can expect to be paid
[tex]\$25.71\times 2,000=\$51,420[/tex]
Health insurance costs $6,650. Add health insurance to job B payment:
[tex]\$51,420+\$6,650=\$58,070[/tex]
Since [tex]\$58,070>\$57,180,[/tex] Lauren should take job B
Evaluate -|-8 - 2|
-6
-10
10
Answer:
-10
Step-by-step explanation:
Answer:
-6
Step-by-step explanation:
How would you solve 4n-2n=4?
Answer:
n = 2
Explanation:
Simplify both sides of the equation
4n − 2n = 4
4n + −2n = 4
(4n + −2n) = 4 (Combine Like Terms)
2n = 4
2n = 4
Divide both sides by 2
2n / 2 = 4 / 2
n = 2
4n-2n=4
4n-2n= 2n
2n=4
÷2
n=2
Which salt is the most common found in ocean water?
A.) calcium carbonate
B.) magnesium
C.) potassium
D.) sodium chloride
Answer:
sodium chloride
Step-by-step explanation:
sea salt is basically sodium chloride
Answer:
Sodium chloride is the most abundant salt
Step-by-step explanation:
What’s is the least common multiple of 5,4,3
Answer:
Step-by-step explanation:
The LCM of 5,4,3 is 5×4×3=60
2/5 times 25 help I got game day tomorrow
Answer:
10
Step-by-step explanation:
You are doing:
(2/5) * 25
You can do it two ways, first divide, then multiply, OR multiply, then divide.
In this case, I will multiply, then divide:
First, multiply:
(2 * 25)/5 = (50)/5
Next, divide:
50/5 = 10
10 is your answer.
~
What is solution of 8x-2y =1 and -4x+y = 3
Answer: it has no solution
Step-by-step explanation:
8x - 2y = 1 ..................... equation 1
-4x + y = 3 ...................... equation 2
solving the system of linear equation by substitution method . From equation 2 , make y the subject of the formula.
y = 3 + 4x .......................... equation 3
substitute equation 3 into equation 1 .
8x - 2(3 + 4x ) = 1
8x - 6 - 8x = 1
8x- 8x - 6 = 1
-6 = 1
this means that the equation has no solution
Which property is demonstrated in the equation 0×25=0 ?
if you get 17 out of 20 questions correct on your next test what percent of the test did you answer correctly?
Answer:
85%
Step-by-step explanation:
Just use a calculator to divide 17 by 20. That gives you .85. To convert into a percent, multiply by 100, giving you an 85%.
A trick I use to convert decimals into percents is to jut move the decimal point 2 spaces to the right.
You answered 85% of the test questions correctly.
To find the percentage of questions answered correctly, we can use the formula:
Percentage = (Number of questions answered correctly / Total number of questions) × 100
In this case, you answered 17 out of 20 questions correctly. Plugging these values into the formula:
Percentage = (17 / 20) × 100
Percentage = 0.85 × 100
Percentage = 85
Therefore, you answered 85% of the test questions correctly.
To know more about " Percentage. ." here
https://brainly.com/question/24877689
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Madison Middle School spends $750 per year on club activities. They spend at least twice the amount on after school activities. Write an inequality that represents how much they spend on after school activities
Answer:
x≥1500
Step-by-step explanation:
Finn bought 12 movie tickets. Student tickets cost $4, and adult tickets
cost $8. Finn spent a total of $60. Write a system of equations
to find the number of student and adult tickets Finn bought.
Answer:
x=9(student cost)
y=3(adult cost)
12=4x+8y
60=4x+8y
Answer:
x=9(student cost)
y=3(adult cost)
12=4x+8y
60=4x+8y
Step-by-step explanation:
What is the answer to the problem 1 + -4
Answer:
-3
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
cuz its like 4-1
Determine the slope of the line that passes through points (0, -4) and (-1,2).
6
-6
-1/6
1/6
Answer:
B) -6
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(2-(-4))/(-1-0)
m=(2+4)/(-1)
m=6/-1
m=-6
the answer is B, -6, because if you graph it the line goes down and it rises up 6