Given:
Radius of a circle = 21 m
Area of a sector of the circle = 27.72 m²
To find:
The angle at the center of the circle.
Solution:
The area of a second is:
[tex]A=\pi r^2\times \dfrac{\theta}{360^\circ}[/tex]
Where, r is the radius of the circle and [tex]\theta[/tex] is the central angle.
Putting [tex]\pi=\dfrac{22}{7},\ r=21,\ A=27.72[/tex] in the above formula, we get
[tex]27.72=\dfrac{22}{7}\times (21)^2\times \dfrac{\theta}{360^\circ}[/tex]
[tex]27.72=1386\times \dfrac{\theta}{360^\circ}[/tex]
[tex]27.72=3.85^\circ \times \theta[/tex]
[tex]\dfrac{27.72}{3.85^\circ }=\theta[/tex]
[tex]7.2^\circ=\theta[/tex]
Therefore, the central angle of the sector is [tex]7.2^\circ[/tex].
HELP PLEASE! for 20 points
Fifty-five petcent of people in a survey said that they do exercise on a fairly regular basis. If 12,000 people were sureveyed, how many of them exercised on a fairly regular basis? A. 5,000 B. 5,500 C. 6000 D. 6,600
Marco needs to climb up to the roof of his house. He placed his ladder so that the bottom of
the ladder was 4 feet away from the wall. If his ladder was 13 feet long, how high up was the
top of the ladder against the wall of the house? Round your answer to the nearest tenth.
Answer:
12.4 feet
Step-by-step explanation:
A ladder placed against the wall forms a right angle triangle
Hypotenuse ² = opposite ² + adjacent ²
Hypotenuse = 13 feet
Opposite = 4 feet
Adjacent = x
Hypotenuse ² = opposite ² + adjacent ²
13² = 4² + x²
169 = 16 + x²
169 - 16 = x²
153 = x²
Find the square root of both sides
√153 = √x²
12.369316876852 = x
x = 12.4 feet
Adjacent = x = 12.4 feet
A line that includes the point (2, 9) has a slope of 8. What is its equation in slope-intercept
form?
Answer:
y-8x+7=0
Step-by-step explanation:
slope(m)=8
using slope intercept form of equation of staright line we get
y=mx+b
y=8*x+b
y-8x=b ................ eq(i)
since the line include the point (2,9) it satisfies the euation,
here x=2 and y=9
equation: y-8x=b
9-8*2=b
9-16=-b
-7=b
substituting the value of b in eq(i) we get
y-8x=-7
y-8x+7=0 is a required equation of the line.
G
A right rectangular prism has a height of 15 meters, a length of 4 meters, and a width of 3 meters. Which expressions
show how to calculate the volume? Check all that apply.
Answer:
180m^3
Step-by-step explanation:
Given data
Height = 15m
Lenght= 4m
Width=3m
We know that the volume of a rectangular prism is expressed as
Volume= L*W*H
Substitute
Volume= 4*3*15
Volume= 180m^3
what is 4:6 as a percentage
Answer:
66.6667%
Step-by-step explanation:
The ratios a: B and B :c are equivalent to one another
Select all the statements that must be true
Answer:
Options (2) and (5)
Step-by-step explanation:
Given ratio is a : b and b : c
[tex]\frac{a}{b}=\frac{b}{c}[/tex]
[tex]\frac{b}{a}= \frac{c}{b}[/tex] [Option 2]
[tex]\frac{a}{b}=\frac{b}{c}[/tex]
b × b = a × c
b² = ac
If a = b,
b² = bc
b = c [Option 5]
Therefore, Options (2) and (5) are the correct options.
Dana enters a race where she has to cycle and run. She cycles a distance of 25km and then runs for 20km. Her average running speed is half of her average cycling speed. If dana completes the race in 5 hours, what is her average cycling speed !
Step-by-step explanation:
Let running speed = x.
So, cycling speed = 2x.
Total distance traveled = 20 + 25 = 45km
Time taken running = 20/x
Time taken cycling = 25/2c
Total time taken = 5 hours
So, 5 = 20/x + 25/2x
Solving this equation for x gives:
10x = 65. Thus x = 6.5
Since cycling speed = 2x, cycling speed = (6.5)(2)
So cycling speed is 13 km/h.
Hope it helps.
What are the coordinates of the point 1/6 of the way from a to b?
Answer:
B. (2, 6)
Step-by-step explanation:
Xp = 1 + (1/6 × (7-1)) = 1 + (1/6×6) = 1+1 = 2
Yp = 8 + (1/6 × (-4-8)) = 8+(1/6×(-12))
= 8+(-2) = 6
the coordinate => (2, 6)
Pls I need this before midnight (USA)
Answer:
I can’t post an image, but I’ll explain below
Step-by-step explanation:
Start at a point where the line crosses through a coordinate exactly, like (0,1), and find a second one. Draw a line from the first to the right until it’s over the second point, then go down to the second point. It should look like half of a rectangle. Just follow the lines of the graph :)
Please help thank you!
Answer:
24.
(-24 ÷
[tex] {6}^{2} [/tex]
16+8= 24
Use the x-coordinates A and C to calculate AC without counting
Will
Give BRIANLIST
Write the sentence as an equation use x to represent a number
“Six times the difference of 11 and a number is -72”
Answer:
6 × (11 - x) = -72 => x = 23
or
6 × (x - 11) = -72 => x = -1
Step-by-step explanation:
there are at least two possibilities, as the "difference between two numbers a and b can be excised as either a-b or b-a.
in any case, just following the sentence
Six times = 6 ×
difference of 11 and a number = 11 - x
is -72 = -72
so,
6 × (11 - x) = -72
and that is true for x = 23
but
the other direction is possible too
6 × (x - 11) = -72
and that is true for x = -1
At the market you can buy 5 bags of apples for $23.60. At the farm you can buy 7 apples for $32.76. Which is the better deal
Answer:
Market
Step-by-step explanation:
Market : 5 bags = $23.60
Farm : 7 apples = $32.76
Market = $23.60 ÷ 5
= $4.72 each BAG
Farm = $32.76 ÷ 7
= $4.68 each APPLE
Thus, market is the better deal because you will get 5 bags of apple for $4.72 for each bag.
Please help thanks this is due today!
D. [tex] ({ - 8})^{2} - 9 + ( - 7)[/tex] ✅
Step-by-step explanation:
[tex] {( - 32 \div4 })^{2} - 9 + ( - 7) \\ \\ = ({ - 8})^{2} - 9 +(- 7 )\\ \\=64-9-7\\\\ = 64 - 16 \\ \\ = 48[/tex]
Note:-
[tex]\sf\red{PEMDAS\: rule.}[/tex]
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
[tex]\sf\red{(+\:x\:-)\:=\:-}[/tex]
[tex]\sf\red{(-\:x\:-)\:=\:+}[/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
Please helpp I will mark brainliest!!<3
Step-by-step explanation:
x+4=12
In this equation, x is a unknown value,
x plus four is twelve.
So, it also represents four more than x is twelve.
What is the probability of an event that is certain?
Answer:
Nvm my answer is wrong
An event that is certain to happen has a probability of 1. An event that cannot possibly happen has a probability of zero. If there is a chance that an event will happen, then its probability is between zero and 1.
Runner A runs at 10 km/h due north. Runner B leaves the same spot and runs at 12 km/h due east. Find the distance and bearing of runner B from runner A after 30 minutes
Answer: [tex]7.81\ km[/tex]
Step-by-step explanation:
Given
Runner A runs towards North at speed of 10 km/h
Runner B runs towards East at speed of 12 km/h
After half hour, they covered a distance of
[tex]\Rightarrow d_a=10\times 0.5\\\Rightarrow d_a=5\ km[/tex]
[tex]\Rightarrow d_b=12\times 0.5\\\Rightarrow d_b=6\ km[/tex]
They are running in perpendicular direction to each other
So, the distance between them is given by
[tex]\Rightarrow d=\sqrt{d_a^2+d_b^2}\\\Rightarrow d=\sqrt{5^2+6^2}\\\Rightarrow d=\sqrt{61}\\\Rightarrow d=7.81\ km[/tex]
11
Select the correct answer.
The elimination method is ideal for solving this system of equations. By which number must you multiply the second equation to eliminate the
yavariable, and what is the solution for this system?
x + 3y - 42
2x-y-14
OA. Multiply the second equation by-3. The solution is x = 12. y - 9.
ов.
Multiply the second equation by-2. The solution is x-12. y = 10.
OC.
Multiply the second equation by 2. The solution is x - 15, y = 9.
OD
Multiply the second equation by 3. The solution is x - 12. = 10.
Reset
Next
Answer:
D. Multiply the second equation by 3. The solution is x = 12, y = 10
Step-by-step explanation:
Given:
x + 3y = 42 (first equation)
2x - y = 14 (second equation)
To solve by elimination, starting with elimination of the y-variable, multiply the second equation by 3 to get a third equation.
2x - y = 14 (2nd eqn.) × 3
6x - 3y = 42 (3rd equation)
Add the 3rd equation and the 1st equation together.
x + 3y = 42 (first equation)
6x - 3y = 42 (3rd equation)
7x = 84
7x/7 = 84/7
x = 12
To find y, substitute x = 12 in the first equation
x + 3y = 42 (first equation)
12 + 3y = 42
12 + 3y - 12 = 42 - 12
3y = 30
3y/3 = 30/3
y = 10
Solution is x = 12, y = 10
What is the product?
(x − 3)(2x2 − 5x + 1)
Answer:
5x2+20x−15
Step-by-step explanation:
Help me please
The question is in the picture above..
Consider the systems of equations:
y=4/5 x−3
y=4/5 x+1
Without graphing, determine and explain how many solutions you would expect this system of equations to have.
Answer:
no solutions; the lines are parallel
Step-by-step explanation:
The eqautions are in slope intercept form.
The slope of both lines is 4/5; therefor the lines are parallel
The y-intercept of one line is -3 and the other is 1
That means the parallelines never meet.
There are no solutions
There are no solutions for the system of equations y=4/5 x−3
and y=4/5 x+1
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The system of equations,
y=4/5 x−3
y=4/5 x+1
The equations are in slope intercept form.
As we observe the equations, the slopes of two equations is 4/5.
The slope of both lines is 4/5
Therefor the lines are parallel
The y-intercept of one line is -3 and the other is 1
That means the parallel lines never meet. There are no solutions
Hence there are no solutions for the system of equations y=4/5 x−3
and y=4/5 x+1
To learn more on slope intercept form click:
https://brainly.com/question/9682526
#SPJ2
please help with number 53!!!!
pretty please
Answer:
The sequence would be arithmetic. This is because an arithmetic sequence has a common number multiplying, adding, subtracting etc. The common rule for this set of numbers was x5. 9x5=45, 45x5=225 etc. We simply used this method with negative numbers, but the rule was still multiplying.
Happy learning!
--Applepi101 :)
Answer:
Arithmetic
Step-by-step explanation:
It has a constant difference between each number whilst Geometric usually has the same difference between each number
Tell whether the triangle with the given side lengths is a right triangle. Y/N question
Answer: need a picture of the traingle but if it's at a 90 degree angle on any sides then yes
Step-by-step explanation:
PLEASE HELP ME, THANK YOU!!
EXPLAIN YOUR ANSWER FOR BRAINLIEST
A prism with an volume of 148 cubic cm is dilated by a factor of 5.5.
The volume of the dilated prism is ___ cubic cm.
(this is just a word question)
Answer:
24623.5 cubic cm
Step-by-step explanation:
A prism with an volume of 148 cubic cm is dilated by a factor of 5.5.
This is calculated as:
Let the volume of the dilated prism = x
Hence:
x/148 = (5.5)³
Cross Multiply
x = 148 cm³ × 5.5³
x = 24623.5 cm³
The volume of the dilated prism is 24623.5 cubic cm.
(5x-3)=(3x+27) I dont understand
Answer:
x = 15
Step-by-step explanation:
(5x-3)=(3x+27)
Subtract 3x from each side
(5x-3x-3)=(3x-3x+27)
2x-3 = 27
Add 3 to each side
2x-3+3 = 27+3
2x= 30
Divide by 2
2x/2 = 30/2
x = 15
US
Find the median of the data.
The number of boys per classroom.
9, 2, 8, 6, 12, 2
Median: [?] boys
Enter the number that belongs in the green box.
Enter
Answer:
7 boys
Step-by-step explanation:
We must find the median of the data given. A median is the "middle number" of a set of numbers ordered in increasing value.
Step 1, ordering the numbers:
We will start by ordering the numbers from smallest to largest. We have:
2, 2, 6, 8, 9, 12
Step 2, finding the "middle number":
Well...notice how there is an even amount of numbers in the data set. We can't exactly find one "middle number". We can however, narrow the list down to two "middle numbers."
We have 6 and 8.
Step 3, taking the average:
To find the median, we will take the average of the two "middle numbers."
[tex]\frac{6+8}{2} =\\\frac{14}{2}=\\\fbox{7}[/tex]
The median is 7 boys.
I hope this helps! Let me know if you have any questions :)
37 + (-37) im looking for the answer
Answer:
0
Step-by-step explanation:
37 + (-37)
open the bracket
remember when u multiply the bracket - sign and + sign also gets multiplied and (-) * (+) is( -) . So
37 - 37
0
Match them BRAINLIEST IF CORRECT
Answer:
1/2 for the red card
1/52 for queen of hearts
1/4 for clubs
3/13
Step-by-step explanation:
the red card is 1/2 because the only other color is black
there is only one queen of hearts
it is one of four possible symbols
because that is the only one left
Math help please urgent
Answer:
16 m^2
Step-by-step explanation:
Area of triangle = (Base * Height) / 2
Area of triangle = ( 8 * 4 ) / 2
Area of triangle = 16