The function for the area of the circle if x is the radius of the circle and y is the area of the circle is y = πx².
What is area?An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely cover the surface of a closed figure.
Given:
The area of a circle is a function equal to the product of pi (pi) and the square of the radius (r),
The area of the circle can be written as shown below,
Area of circle = π × R²
Here π is a constant, R is the radius of the circle,
When we put the value of the radius, we will get the value of the area,
Hence, the radius is an independent function and the area is dependent on the value of R (dependent function),
Replace y with area and radius with x as shown below,
y = πx²
Thus, y = πx² is the function for the area of the circle.
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help someone plz
A student needs to make a rectangular cardboard piece that is 12 inches long. The area of the cardboard piece should be between 60 square inches to 300 square inches. The function f(w) relates the area of the cardboard, in square inches, to the width w in inches. Which of the following shows a reasonable domain for f(w)?
A: 2 ≤ w ≤ 5
B: 5 ≤ w ≤ 25
C: 25 ≤ w ≤ 60
D: 60 ≤ w ≤ 300
area = L x w
60 = 12 x w
w=60/12 = 5
300 = 12 x w
w = 300/12 = 25
so B is the correct answer
Answer:
Option B
[tex]5 \leq w \leq 25[/tex]
Step-by-step explanation:
Let
L------> the long of the cardboard piece
W-----> the width of the cardboard piece
The area of cardboard piece is equal to
[tex]A=L*W[/tex]
In this problem we have
[tex]L=12\ in[/tex]
so
[tex]A=12W[/tex]
[tex]f(W)=12W[/tex]------> equation A
[tex]f(W)\geq 60\ in^{2}[/tex] ------> inequality B
[tex]f(W)\leq 300\ in^{2}[/tex] ------> inequality C
Substitute equation A in the inequality B
[tex]12W\geq 60\ in^{2}[/tex]
[tex]W\geq 60/12[/tex]
[tex]W\geq 5\ in[/tex]
Substitute equation A in the inequality C
[tex]12W\leq 300\ in^{2}[/tex]
[tex]1W\leq 300/12[/tex]
[tex]1W\leq 25\ in[/tex]
The domain for the function f(W) is equal to the interval------> [tex][5,25][/tex]
25/150 in simplest form
Where is the answer to the expression 4 − 8 located on a horizontal number line? 4 units to the left of 4
4 units to the right of 4
8 units to the left of 4
8 units to the right of 4
I need the answer asap whoever answers first and gets it right gets brainliest
The temperature at 9 a.m. is 2 degrees. The temperature rises 3 more degrees by noon. Which expression describes the temperature at noon?
2 + 3
2 + (–3)
–2 + (–3)
–2 + 3
it starts at 2 degrees which is not a negative number and temperature rises so it isn't a negative number either
so it would be 2+3
An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is A, 2+3.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Given that the temperature at 9 a.m. is 2 degrees. Further, the temperature rises 3 more degrees by noon.
As two whole numbers are added together, the total quantity or sum of those values is obtained. Therefore, the expression that describes the temperature at noon is 2 + 3.
This is because the temperature is positive and after the temperature rises, the temperature will be added.
Hence, the expression that describes the temperature at noon is 2 + 3.
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what's the Least common multiple for 2,6,8?
Write the equation of a linear function in point-slope form and slope-intercept form for a line that passes through point A(3,-7) and has an undefined slope.
Find the height of a triangle with an area (A) of 35 square inches and base (b) of 7 inches. Use the formula for the area of a triangle, A=1/2bh
Height of the triangle is 10 inches
What is Triangle ?A triangle is a polygon with three edges and three vertices.
What is Area?Area is the quantity that expresses the extent of a region on the plane or on a curved surface.
Given,
Area of the triangle = 35 square inches
Base of the triangle = 7 inches
Area of the triangle = [tex]\frac{1}{2}bh[/tex]
where,
b is the base length and h is the height
Substitute the values in the equation
[tex]35=\frac{1}{2}(7)(h)\\ 35=3.5h\\h=\frac{35}{3.5}[/tex]
Height h = 10 inches
Hence, the height of the triangle is 10 inches
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Answer this please image below
Find the measure of angle AOE in the diagram below.
Help will be appreciated!
Answer:
We choose D
Step-by-step explanation:
Given that:
∠BOA = (3x -28) degrees ∠COD = (66 -x) degrees ∠BOC = 90 degreesAs we know that ∠BOA + ∠COD + ∠BOC= 180 degrees because AD is a straight line, so we have:
(3x -28) + (66-x) +90 = 180
<=> 2x = 52
<=> x = 26 degrees.
=> ∠BOA = 3*26 - 28 = 50 degrees
As we can see that, ∠BOA = ∠DOE (The properties of two straight lines intersect)
<=> ∠DOE = 50 degrees
Once again, the AD is a straight line, so we have:
∠DOE + ∠AOE = 180
<=> ∠AOE = 180 - ∠DOE
<=> ∠AOE = 180 - 50 = 130 degrees
We choose D
The dot plot below shows the hourly rate of some babysitters in a city: A number line is shown from 1 dollar to 7 dollars in increments of 1 dollar for each tick mark. The horizontal axis label is Dollar per hour. There are 2 dots above 4 dollars, 3 dots above 5 dollars, 3 dots above 6 dollars, and 2 dots above 7 dollars. The title of the line plot is Babysitting Rates. Which statement best describes the shape of the data? It is symmetric and has no gaps. It is not symmetric and has a peak at $7.00. It is a cluster from $1.00 to $7.00 and has no gaps. It is a cluster from $1.00 to $7.00 and has a peak at $6.00.
Answer:
D
Step-by-step explanation:
it did this test
need help, thank you!
2x+3y=5x−y
y=0
x=?
Answer:
X=4\3
Step-by-step explanation:
find the area of the circle with diameter of 11mm leaving answer in terms of pi
If matrix A has dimensions 3 x 2 and matrix B has dimensions 3 x 2, can matrix A and matrix B be multiplied?
Answer:
we can not multiply matrix A and B.
Step-by-step explanation:
We have been given that
dimension of matrix A = 3 x 2
dimension of matrix B = 3 x 2
Rule of multiplying two matrices:
Two matrix can be multiplied if the column of first matrix is equal to the row of second matrix.
column of first matrix = row of second matrix
Here, we have
Column of first matrix A = 2
Row of second matrix b = 3
Since,, column of matrix A ≠ Row of matrix B
Hence, we can not multiply matrix A and B.
if a polynomial has one root in the form a+√b , it has a second root in the form of a_√b
Answer:
a - √b
Step-by-step explanation:
If you solve the quadratic equation x² - 2ax + a² - b = 0 with the quadratic formula, it should yield the pair of conjugate radical roots.x = (1/2) [ 2a +/- √(4a² - 4(a² - b)] = a +/- (1/2)*√(4b) = a +/- √bx = a + √b, or x = a - √b, as expected.
factors of 212 like finding a common factor its really hard because the number is so high please please HELP ME!!!!!!!
Answer:
1.2..17.5
Step-by-step explanation:
i had been singing for the operpopitay
Please help :) :) :)
A motorboat
travels 222 km in 6 hours going upstream.
Rate = distance/time = 222/6 = 37 km/hr
----------------------
It travels 390 km going downstream in the same amount of time.
Rate = distance/time = 390/6 = 65 km/hr
---------
What is the rate of the boat in still water and what is the rate of the
current?
Equations:
Upstream: b-c = 37 km/hr
Downstrm: b+c = 65 km/hr
Add and solve
for "b":
(2)b = 102 km/hr
b = 51 km/hr (speed of the boat in still water)
-----
Solve for "c":
b+c = 65
51 + c = 65
c = 14 km/hr (speed of the current)
Eight states in the united states start with the letter M. What fractions of states in simplest form,begins with the leter M?
Stuart is buying a pair of jeans that regularly cost $40. They are on sale for 20% off. If the tax rate is 8%,what is the sale price of the jeans including tax?
A baseball was pitched at a speed of 75.2 miles per hour. a tennis ball was served at a speed 1.5 times faster than this. how much faster was the speed of the tennis ball than the speed of the baseball?
Answer:
75.2*1.5=112.8
112.8+75.2=188
188-75.2=112.8
Solve:
y^6 (y^5)
plz i put eleven idk why se says it's wrong :c
Use the law of cosines to find the missing third side
The missing third side BC is approximately 16.93 units. To use the Law of Cosines to find the missing third side (BC), we'll use the formula:
[tex]c^2 = a^2 + b^2 - 2ab * cos(C)[/tex]
where:
c is the side opposite angle C (BC in this case)
a and b are the known sides (AC and AB, respectively)
C is the angle opposite side c (angle BAC in this case)
Given values:
Angle BAC (C) = 54 degrees
AC (a) = 7.4
AB (b) = 15.8
Now, we can plug the values into the formula and solve for BC (c):
[tex]BC^2 = 7.4^2 + 15.8^2 - 2 * 7.4 * 15.8 * cos(54)[/tex]
To find cos(54), we can use a calculator:
[tex]cos(54 degrees) \approx 0.5878[/tex]
Now, we can continue the calculation:
[tex]BC^2 = 54.76 + 249.64 - 2 * 7.4 * 15.8 * 0.5878\\BC^2 = 54.76 + 249.64 - 17.44\\BC^2 = 286.96[/tex]
Now, find the square root of both sides to get the value of BC:
[tex]BC = \sqrt{286.96} \\BC \approx 16.93[/tex]
So, the missing third side BC is approximately 16.93 units.
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Determine the range of: f(x) = 13 - 20x - x^2 -3x^4. Also, find the max. And min. Values and state where those values occur
Ralph sold brownies for $0.27 a piece in order to earn money to buy baseball cards. If the cards cost $0.54 per pack, and if Ralph had no money left over after buying them, what is the least number of brownies he must have sold?
Daisy works at an ice-cream parlor. She is paid $10 per hour for the first 8 hours. She works for x hours in a day and x is greater than 8, the expression giving her net earnings for the day is
A. x(80+1.5)
B. (x-8)1.5
C. 80+15 (x-8)
D. (8)(15)(x-8)
the answer is option C
If f(x)=6x and g(x) = 4x+1, find ( f o g)(x)
Evaluate the expression : (0.4)^3=
The expression when evaluated, can be found to be 0. 064.
How to evaluate the expression ?( 0 . 4 ) ³ means raising the number 0. 4 to the power of 3 , which is the same as multiplying 0. 4 by itself three times. This is how the expression is evaluated.
Start with:
0 . 4 * 0 . 4 * 0 . 4
Calculate each multiplication step:
1st multiplication: 0 . 4 * 0 . 4 = 0 . 16
2nd multiplication: 0 . 16 * 0 . 4 = 0 . 064
So, when you multiply 0. 4 by itself three times ( 0 . 4 * 0 . 4 * 0 . 4), you get the result of 0 . 064.
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Jennifer can clean her room in 2 hours, while John can clean the same room in 5 hours. How many hours would it take for them to clean the room together?
7
10
seven tenths
ten sevenths
I think the answer is tenth sevenths but im not sure! Please Help ASAP
Answer: ten sevenths
Step-by-step explanation:
Given: Time taken by Jennifer to clean her room [tex]t_1= 2 \text[ hours}[/tex]
Time taken by John to clean same room [tex]t_2= 5\text[ hours}[/tex]
If they work together to clean the room , then the total time taken by them is given by :-
[tex]\dfrac{1}{t}=\dfrac{1}{t_1}+\dfrac{1}{t_2}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{1}{2}+\dfrac{1}{5}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{5+2}{10}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{7}{10}\\\\\Rightarrow\ t=\dfrac{10}{7}\text{ hours}[/tex]
A woman bought a dress at a discount of 16 2/3. If the woman paid 32.50, what was the original price of the dress
Five scouts took a white water rafting trip. The total cost of the trip was $721. Each person in the group received a student discount of $6. Write and solve an equation to find out how much each student paid before discount.
cost per student before discount = 721/5+6
721/5 = 144.20 +6 = 150.20
A peregrine falcon can fly 332 kilometers per hour. How many meters per hour can the falcon fly?