The area of the sector with a radius of 20 units and a central angle of 162° is 180π unit².
What is the sector of a circle?
A sector is the portion of a circle enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger is the major sector.
The radius of the sector =20 units
Central angle subtended by sector = 162° = 162π/180 radians
As we know the area of a sector= 0.5r²α
where r is the radius and α is the central angle.
So, the area of the given sector = 0.5*20²* 162π/180
The area of the given sector = 180π unit²
Therefore, The area of the sector with a radius of 20 units and a central angle of 162° is 180π unit².
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Answer:
its c
Step-by-step explanation:
Christopher opened a savings account with $1800 that pays no interest. He deposits an additional $90 each week thereafter. How much money would Christopher have in the account 42 weeks after opening the account?
Answer:
I think 5580
Step-by-step explanation:
You move the 1800 away for a bit so since it's 42 weeks you have to multiply 90 and 42 then add that to 1800.
When you use a (___________________ ), the money you spend is deducted
A credit card
B debit card
C deposit
D credit score
Answer:
B Debit Card
Step-by-step explanation:
When you use a debit card money comes out of your checking account
Answer:
a credit card
Step-by-step explanation:
because I think it makes sense
can someone help me? it’s due in a few hours
Answer:
cars value decreases in value exponentially
Step-by-step explanation:
cant really read it but say that the cars value decreases in value exponentially and compare that to however the other cars decrease in value over time
23.-28. In a manner similar to Example 1, (a) identify input and
output consistent with the general proportional model; (b) write
an equation for the model; (c) determine a numerical value for the
constant k; and (d) solve the problem.
24. The speed of a skidding car is directly proportional to the
square root of the length of the skid. On a snowy road, a car
with good brakes traveling at 40 mph would skid approxi-
mately 178 ft. If the skid marks of a similar car on a similar
road were 400 ft, how fast would this car be traveling?
24. If the skid marks of a similar car on a similar road were 400 ft, how fast would this car be
traveling?
The direct variation that of the speed to the skid length implies that the speed increases as the length increases
The car would be traveling at 59.96 mph
How to determine the speed of the skidding car?A direct variation that illustrates the speed of the skidding car is:
s = k√l
Where:
s represents the speed of the carl represents the length of the skidk represents the proportionality constantMake k the subject in s = k√l
k = s /√l
Rewrite as:
s₁ /√l₁ = s₂ /√l₂
Substitute known values
40 /√178 = s₂ /√400
Evaluate the square root of 40
40 /√178 = s₂ /20
Multiply both sides by 20
800 /√178 = s₂
Evaluate the quotient
s₂ = 59.96
Hence, the car would be traveling at 59.96 mph
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The number of students taking algebra increased 20% in one year. If
60 students are taking algebra this year, how many took algebra last
year?
Answer: 50 students
Step-by-step explanation:
You know that the number of students last year plus 20% of that number equals the number of students this year, which can be written as: x + 0.2x = 60 →
1.2x = 60 → x = 50 students :)
Answer: 50 students
Step-by-step explanation:
x + .2x = 60
1.2x = 60
x = 60/1.2
x = 50
Jasmine is trying to replace the flooring in her rectangular bedroom. When she measured the width and length of the floor, she found that the length is 5 ft. longer than the width. If the perimeter of the room is 50 ft., how much flooring will she need to replace the existing flooring in her room?
Answer:
150ft^2
Step-by-step explanation:
FINDING THE LENGTHS
50 = x + 5 + x + x + 5 + x
50 = 4x + 10
50 - 10 = 4x
40 = 4x
40/4 = x
10ft = x
AMOUNT OF FLOORING
area = l x b
= (10 + 5) x 10
= 15 x 10
= 150ft^2
If the slope of a line is zero the line must be a
line.
Answer:
Straight along the horizontal axis
Step-by-step explanation:
Hope this helped :)
What is the median age of a group of employees
whose ages are 32, 37, 30, 43, 29 and 31?
Find the volume of the prism in terms of y.
is there a value to y? if not, this is what I got:
Y^2 + 2y + 3
please show steps to solve the problem thank you
Answer:
65 total number of boys
Step-by-step explanation:
In the boys row there are 45 "Blue" boys and 20 "Orange" boys.
You can add these numbers up together to find the answer to this problem.
45 + 20 = 65
65 total number of boys
How much of a radioactive substance must be presented to decay to 80 grams in 12 years if the half-life of the substance is 7.6 years?
Answer:
Radioactive in half life is 51gram
Step-by-step explanation:
80grams:12years
X :7.6years
12x÷x=x
7.6×80÷12=51gram
Answer:
239 grams.
Step-by-step explanation:
Half life t(1/2) = ln 2 / k
So 7.6 = ln 2 / k
k = ln 2 / 7.6 = 0 0901204
N = No e^-kt
So after 12 years
80 = No / e^(-0.0901204*12)
No = 80 / e^(-0.0901204*12)
= 239.
A rectangle has length 1. 5 times the width, and perimeter 12 cm. What are the dimensions of
the rectangle?
Answer:
Length = 3.6
Width= 2.4
Step-by-step explanation:
A rectangle has length 1. 5 times the width, and perimeter 12 cm. What are the dimensions of
the rectangle?
So a rectangle has 2 longer sides and 2 shorter sides.
Knowing the length is 1.5 times the width
and perimeter of 12 centimeters.
The Perimeter is the adding of all the values around a shape. A rectangle has 4 sides so you add up all the sides.
1.5w+1.5w+w+w=12
5w=12
12/5=w
w=2.4
To figure the length just multiply 1.5*2.4=3.6
And That is how you solve it :)
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Write the equation of the line that passes through the points (-9,-9)(−9,−9) and (6,-7)(6,−7). Please help me
Answer:
y = (2/15) x -(117/15)
Step-by-step explanation:
To write the equation we should know the slope m and the y-intercept b .
m= (y2-y1)/(x2-x1)
For points (x1 = -9, y1 = -9) and (x2 = 6, y2 = -7)
m = (-7 - - 9)/(6 - - 9) = (-7 + 9)/(6 +9) = 2 / 15
The general equation of a line is
y= mx + b
Our equation is
y = (2/15) x +b
To find b, substitute one of the two points, we know are on the line, in our equation. For example, we can substitute point (-9,-9)
-9 = (2/15) (-9) +b , multiply -9 by 2/15
-9 = - (18/15) +b, add -18/15 on both sides
-9 + (18/15) = b, find common denominator and add
[(-9 ·15) +18]/15 = b , simplify
-117/15 = b
So our equation is:
y = (2/15) x -(117/15)
Solve the equation . 5x+17=42
Answer:
x = 5
Step-by-step explanation:
5x+17=42
5x + 17 - 17 = 42 - 17
Please help ASAP!!! Thank you!
Answer: 58 1/3 in^3.
Step-by-step explanation: To find the volume of a pyramid, you need to multiply the length, width, and height and divide it by 3. The length and width are both 5 and the height is 7, so the equation is 5 x 5 x 7. The answer to that is 175. Now, you have to divide 175 by 3, which is 58.33, or 58 1/3, which is your answer.
Let me know if this is right! :)
Determine the probability of choosing a pair need help
pls help
Triangle MNP with the vertices M(-6,-8) M(-1,-6) and P(-2,-8) in the line y= -5
Triangle MNP with the vertices M(-6,-8) N(-1,-6) and P(-2,-8) is reflected across the line y= -5 to give M'(-6, -2), N'(-1, -4) and P'(-2, -2)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Triangle MNP with the vertices M(-6,-8) N(-1,-6) and P(-2,-8) is reflected across the line y= -5 to give M'(-6, -2), N'(-1, -4) and P'(-2, -2)
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10. To calculate the area of a rectangle, you multiply the length by the width. If the
length of a rectangle is (2x + 1) and the width is (x - 1), what is the area of the
) -
rectangle?
A. 3x
B. 3x2 - 1
C. 2x2 - x - 1
D. X - 1
Answer:
Multiply those side lengths using the F.O.I.L method (first-outer-inner-last). Write it longhand then simplify if that’s what is needed.
(x+5)(x-5) = x^2 -5x + 5x -25
the -5x and + 5x cancel each other so it simplifies to x^2 - 25 units squared.
These cones are similar. find the surface
area of the smaller cone. round to the
nearest tenth.
2 cm
3 cm
surface area = [? ] cm2
surface area = 75 cm?
Answer:
33.3 is your answer
Step-by-step explanation:
The surface area of the smaller cone A₁ is approximately 33.3 cm² when rounded to the nearest tenth.
What is a cone?A cone is a three-dimensional geometric form with a flat base and a smooth, tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that link the base's points to the apex, which is a common point on a plane that does not include the base.
Two cones A₁ and A₂ are similar.
The radius of A₁ = 2 cm
radius of A₂ = 3 cm
The surface area of A₁ = ? cm²
surface area of A₂ = 75 cm²
Since the cones A₁ and A₂ are similar, their corresponding sides are proportional.
Specifically, the ratio of their radii is the same as the ratio of their surface areas. That is,
(radius of A₁) / (radius of A₂) = (surface area of A₁) / (surface area of A₂)
We can use this relationship to solve for the surface area of A₁:
(surface area of A₁) = (radius of A₁ / radius of A₂)^2 × (surface area of A₂)
Substituting the given values, we get:
(surface area of A₁) = (2/3)² × 75
(surface area of A₁) = 4/9 × 75
(surface area of A₁) ≈ 33.3 cm²
Therefore, (surface area of A₁) ≈ 33.3 cm²
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Dylan owns a bag that contains 7 blue marbles, 5 purple marbles, 12 red marbles, and 6 orange marbles. If he randomly pulls a marble from the bag, What is the probability of him pulling a red marble? What is the probability of him pulling a blue or purple marble?
Answer:
The probability of him pulling a red marble is 12 to 30. The probability of him pulling a blue or purple marble is also 12 to 30.
Step-by-step explanation:
7+5+12+6=30 (all colors)
12 to 30 red ones
7+5+12+6=30 (all colors) and
7+5=12 (blue + purple)
12 to 30 blue or purple
(h+1)^2=16 solve using square root property
Answer: h = 3
Step-by-step explanation:
(h+1)² = 16
h+1 = √16
h+1 = 4
h = 3
Hope this helped :)
Answer:
[tex]h=3, \ h=-5[/tex]
Step-by-step explanation:
[tex](h+1)^2=16[/tex]
[tex](h+1)^2=16[/tex]
[tex]\sqrt{(h+1)^2} = \±\sqrt{16}[/tex] <== you take the square root of both sides
[tex](h+1) = \±\ 4[/tex] <== you take the square root of both sides
[tex](h+1) = +\ 4, \ (h+1) = -\ 4[/tex] <== separate into 2 equations and solve
[tex]h+1 = 4, \ h+1 = -\ 4\\\\. \ -1 -1, \ \ \ \ -1\ \ \ \ -1\\\\h=3, \ h=-5[/tex]
Hope this helps!
 find the equation of the line that is parallel to the line Y equals 3X -6 and passes through the points (1 -8). Write the equation in point slope form
=====================================================
Parallel lines have the same slope.
So if the given line has a slope of 3, then the line parallel to it has the same slope (3)
Now, let's write the equation of the line in Point-Slope Form.
Remember, point-slope form looks like so:-
[tex]\bigstar{\underline{\boxed{\pmb{y-y1=m(x-x1)}}}[/tex]
Where
y₁ is the y-coordinate of the point that the line passes through
m is the slope
x₁ is the x-coordinate of the point that the line passes through
In this case,
y₁ is equal to -8
m is equal to 3
x₁ is equal to 1
Plug in the values:
[tex]\longrightarrow\sf{y-(-8)=3(x-1)}[/tex]
Simplify:
[tex]\longrightarrow\sf{y+8=3(x-1)}[/tex]
and we're done!
=========================================================
note:-Hope everything is clear; if you need any more explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
A school needs to buy new notebook and desktop computers for its computer lab. The notebook computers cost $300 each, and the laptop computers cost $350 each. How much would it cost to buy 18 notebooks and 12 desktop computers? How much would it cost to buy nn notebooks and dd desktop computers?
Answer:
$9,600
Step-by-step explanation:
notebook computer : $300
laptop computer : $350
18 x 300 = 5,400
12 x 350 = 4,200
4,200 + 5,400 = 9,600
There are 221 students on a field trip.
. Five students ride in a van.
. The rest of the students fill 6 buses.
Enter an equation that can be solved to find the number of students, s, that are on each bus. Enter your response in
the first response box.
Enter the number of students that are on each bus. Enter your response in the second response box.
The equation that models the students is a linear equation
The equation that models the number of students in each bus is 6x = 216, and the number of students in each bus is 36
How to determine the equation?The given parameters are:
Students = 221
Van = 5
The rest students = 6 buses
Start by calculating the number of students remaining:
Remaining students = 221 - 5
Remaining students = 216
Represent the number of students in each bus with x.
So, we have:
6 buses * x = Remaining students
This gives
6x = 216
Divide both sides by 6
x = 36
Hence, the equation that models the number of students in each bus is 6x = 216, and the number of students in each bus is 36
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Tony is flying from Los Angeles to Boston. His plane ticket costs $605 and the total flight distance is 3,052 miles. What is the cost per mile?
Answer:
AROUND $0.20 per mile
Step-by-step explanation:
605/3052 is around 0.198, which rounds to 0.20.
Find the value of 9u-2 given that -7u-7=7 ?
Answer:
-20
Step-by-step explanation:
when you solve: -7u-7=7, you get u= -2 and when you plug it in you get this equation 9(-2)-2=?
then you get -20
Hey there!
-7u - 7 = 7
ADD 7 to BOTH SIDES
-7u - 7 + 7 = 7 + 7
CANCEL out: -7 + 7 because it give you 0
KEEPs 7 + 7 because it help solve for the u-value
NEW EQUATION: -7u = 7 + 7
SIMPLIFY IT!
-7u = 14
DIVIDE -7 to BOTH SIDES
-7u/-7 = 14/-7
CANCEL out: -7/-7 because it give you 0
KEEP: 14/-7 because it give you the
u-value
NEW EQUATION: u = 14/-7
SIMPLIFY IT!
u = -2
SOLVING FOR : 9u - 2
9u - 2
= 9(-2) - 2
= -18 - 2
= -20
Therefore, your answer is: -20
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Helppppppppppppppppppp
Answer:
8/27
Step-by-step explanation:
It says to use V=s^3.
s is the the side length of the cube which is 2/3 in this case.
So to get your answer you have to do: (2/3)^3 or 2/3 x 2/3 x 2/3.
Which of the following is a defined term?
Angle
Line
Point
Plane
Answer:
C. Point is a defined term
Step-by-step explanation:
kleann
Can sombody solve this please. :)
144 x m - 309.6 = 50.4
Add 309.6 to both sides:
144 - 309.6 + 309.6 = 50.4 + 309.6
Simplify the arithmetic:
144 x m = 50.4 + 309.6
Simplify the arithmetic:
144 x m =360
m = 5/2
HELPP PLEASE!!!!!!!!!!!!!!!!!!!!!!
Answer:
Third one down |2s + 1| -3
Step-by-step explanation:
there is no value of s where it is valid