Answers
Answer:
[tex]\displaystyle r = 6 \ cm[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityGeometry
Volume of a Cone Formula: [tex]\displaystyle V = \frac{\pi}{3}r^2h[/tex]
r is radiush is heightStep-by-step explanation:
Step 1: Define
Identify variables
V = 120π cm³
h = 10 cm
Step 2: Solve for r
Substitute in variables [Volume of a Cone Formula]: [tex]\displaystyle 120\pi \ cm^3 = \frac{\pi}{3}r^2(10 \ cm)[/tex]Multiply: [tex]\displaystyle 120\pi \ cm^3 = \frac{10\pi}{3}r^2 \ cm[/tex][Division Property of Equality] Divide [tex]\displaystyle \frac{10\pi}{3} \ cm[/tex] on both sides: [tex]\displaystyle 36 \ cm^2 = r^2[/tex][Equality Property] Square root both sides: [tex]\displaystyle 6 \ cm = r[/tex]Rewrite: [tex]\displaystyle r = 6 \ cm[/tex]Answer:
Radius of cone is 6 cm
Step-by-step explanation:
[tex]\sf\small\underline\purple{Given:-}[/tex]
[tex]\sf{\leadsto Volume\:_{(cone)}=120π \:cm^3}[/tex]
[tex]\sf{\leadsto \: Height\:_{(cone)}=10 cm}[/tex]
[tex]\sf\small\underline\purple{To\: Find:-}[/tex]
[tex]\sf{\leadsto Radius\:_{(cone)}=?}[/tex]
[tex]\sf\small\underline\purple{Solution:-}[/tex]
To calculate the radius of cone . Simply by applying formula of volume of cone. As given in the question that height is 10 cm and it's volume is 120 π cm³.
[tex]\sf\small\underline\purple{Calculation\: begin:-}[/tex]
[tex]\sf{\leadsto Volume\:_{(cone)}=\dfrac{1}{3}\pi\:r^2\:h}[/tex]
[tex] \small \sf \leadsto volume \: of \: cone \: = \frac{1}{3} \pi \times r {}^{2} h \\ [/tex]
[tex] \small \sf \leadsto \: 120 π cm³ \: = \frac{1}{3} \times\pi r {}^{2} \times 10cm \\[/tex]
[tex] \small \sf \leadsto \: 120 π cm³ \: = \frac{10 \: \pi\: cm}{3} \: r {}^{2}[/tex]
[tex] \small \sf \leadsto \frac{ 120\pi \: cm {}^{3} \times 3}{10\pi \: cm} \: = r {}^{2} \\ \\ [/tex]
[tex] \small \sf \leadsto \frac{360\pi cm {}^{3} }{10\pi \: cm} = \: r {}^{2} \\ [/tex]
[tex]\small \sf \leadsto 36 \:cm {}^{2} = r {}^{2} [/tex]
[tex]\small \sf \leadsto \sqrt{36 \: cm {}^{2} } = \sqrt{r {}^{2} } [/tex]
[tex]\small \sf \leadsto6cm = r[/tex]
Related Questions
Siti bakes 55 vanilla cakes and 39 strawberry cakes. A box can hold 6 cakes. What is the smallest number of boxes needed to hold all the cakes?
Answers
Answer:
16
Step-by-step explanation:
total number of cakes baked=55+39=94 cakes
1 box can hold 6 cakes
let the number of box need to hold 94 cakes be x
:- 1 = 6 cakes
x = 94 cakes
cross multiply to get :
6x=94
divide both side by the coefficient of x i.e 6
6x/6=94/6
x= 15.7
because it a real object, the minimum nuber of boxes is 16
Find the midpoint of the segment
(-3,-1)
(-2,0)
(-2,-1)
(-3,0)
Answers
Question 24 Multiple Choice Worth 1 points)
(8.01 MC)
Two lines, A and B, are represented by equations given below:
Line A: y = x - 4
Line B: y = 3x + 4
Which of the following shows the solution to the system of equations and explains why?
0 (-3,-5), because the point satisfies one of the equations
0 (-3,-5), because the point lies between the two axes
(-4,-8), because the point satisfies both equations
(-4, -8), because the point does not lie on any axis
Answers
Given:
The system of equations is:
Line A: [tex]y=x-4[/tex]
Line B: [tex]y=3x+4[/tex]
To find:
The solution of given system of equations.
Solution:
We have,
[tex]y=x-4[/tex] ...(i)
[tex]y=3x+4[/tex] ...(ii)
Equating (i) and (ii), we get
[tex]x-4=3x+4[/tex]
[tex]-4-4=3x-x[/tex]
[tex]-8=2x[/tex]
Divide both sides by 2.
[tex]-4=x[/tex]
Substituting [tex]x=-4[/tex] in (i), we get
[tex]y=-4-4[/tex]
[tex]y=-8[/tex]
The solution of system of equations is (-4,-8).
Now verify the solution by substituting [tex]x=-4, y=-8[/tex] in the given equations.
[tex]-8=-4-4[/tex]
[tex]-8=-8[/tex]
This statement is true.
Similarly,
[tex]-8=3(-4)+4[/tex]
[tex]-8=-12+4[/tex]
[tex]-8=-8[/tex]
This statement is also true.
Therefore, (-4,-8) is a solution of the given system of equations, because the point satisfies both equations. Hence, the correct option is C.
how mamy times can you subtract 10 from a hundred?
Answers
You can substract 10 from 100 ten times :)
Answer:
10
Step-by-step explanation:
100 - 10 = 90 ( 1 )
90 - 10 = 80 ( 2 )
80 - 10 = 70 ( 3 )
70 - 10 = 60 ( 4 )
60 - 10 = 50 ( 5 )
50 - 10 = 40 ( 6 )
40 - 10 = 30 ( 7 )
30 - 10 = 20 ( 8 )
20 - 10 = 10 ( 9 )
10 - 10 = 0 ( 10 )
we subtract 10 from 100 10 times
help me please as soon as possible. I will mark you as the brainliest
Answers
1) 36
2) 143
3) 18
4) 12
5) 15
6) 108
7) 58
The key here is to perform direct substitution in each problem.
I'll do a quick working down here
1) 9(8-4)= 9*4 =36
2) 4(5*4)+7*9= 80+63 =143
3) 114-(3*8*4)= 114-96=18
4) 24/(1*2) = 24/2 = 12
5) 19 - (28/7) = 19- 4 = 15
6) 3 (6)^2 = 3*6*6= 108
7)49 - 3(3)^2 + (6)^2 = 49-27+36= 58
2. 4(5)(4)+7(9)= 80+63= 143
3. 114-3(8)(4)= 114-96= 18
4. 24/(2)(1)= 24/2= 12
5. 19-28/7= 19-4= 15
6. 3(6)^2= 18*18= 324
7. 49-9^2+ 6^2= 68
What is the value of this expression when g=-3.5?
8-12g-5
Answers
Answer:
45
Step-by-step explanation:
8-12(-3.5)-5
8+42-5
=45
Solve the system by substitution.
y = 7x– 45
Y = 2x
Answers
Answer:
(x,y)=(9,18)
Step-by-step explanation:
Determine the solution, if any, to the system of equations below. 8. 2y = 1 - 4x + y = 3 Show your work or explain how you got your answer.
Answers
Answer:
y=1/2 , x= -5/8
Step-by-step explanation:
⇒[tex]2y=1. -4x+y=3 : y=\frac{1}{2} \\\left \{ {{2y=1} \atop {-4x+y=3}} \right. \\ where: y=\frac{1}{2} \\-4x+\frac{1}{2}=3\\isolate for -4x+\frac{1}{2} =3: x=-\frac{5}{8} \\y=\frac{1}{2} : x=\frac{-5}{8}[/tex]
PLSSS ASAP 20 POINTS AND BRAINLIEST IF RIGHT!!!!!!
The graph of g is a translation 3 units down of the graph of f(x) = x2 + 1. What is the range of g?
A. all real numbers
B. g(x) ≥ −3
C. g(x) ≥ −2
D. g(x) ≥ −1
Answers
Answer:
All real number
Step-by-step explanation:
Is this ok
Answer:
C
Step-by-step explanation:
To translate something 3 units down subtract it by 3
which means our equation is
x²-2
From here it's pretty easy to see that the answer must be C
Please help, I need it due today and urgently! Please give a small explanation and an answer
Answers
Answer:
0=0 1=1 6<8
Since 6 < 8 0.16 < 0.18
so, the hummingbird weighs more than a nickel
Step-by-step explanation:
6 is less than 8 so therefore .16 is less than .18. The nickel weighs .18 and .16 is less than that.
A city planner wanted to place the new town library at site A. The mayor thought that it would be better at site B. 1. What transformations were applied to the building at site A to relocate the building to site B? 2. Did the mayor change the size or orientation of the library?
Answers
Answer:
you have to connect an image or provide further information
Step-by-step explanation:
What is the distance between the points (8, 12) and (1,3)? If necessary, round
your answer to two decimal places.
Answers
Answer:
13.03 units
using distance formula which is
root under
(X\/2-X\/1)^2 + (y\/2-y\/1)^2
What is the approximate circumference of a circle that has a diameter of 15 inches? A) 14 ft
B) 21.98 ft
C) 28 ft
D) 7 ft
Answers
Answer:
47 ft
Step-by-step explanation:
3.14 x 15
please help due tmr!!!
Answers
Answer:
y 4 4x + 2
y< 6 x+3
Step-by-step explanation:
Find the sine ,cosine and tangent ratios of
Answers
Step-by-step explanation:
Given that,
Hypotenuse, H = 13
Base, b = 12
Perpendicular, P = 5
[tex]\sin\theta=\dfrac{P}{H}\\\\\sin\theta=\dfrac{5}{13}[/tex]
[tex]\cos\theta=\dfrac{B}{H}\\\\\sin\theta=\dfrac{12}{13}[/tex]
and
[tex]\tan\theta=\dfrac{P}{B}\\\\=\dfrac{5}{12}[/tex]
Hence, this is the required solution.
Which expression is equivalent to 10k + 17 - 7j - 18 - 11k?
-8jk - 1
-7j - k - 1
-7j + k + 1
-8j - k
PLEASE HURRY !!!!
20 POINTS!!!
Answers
Answer:
-7j-k-1
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
An equivalent expression is an expression which is equal to 10k + 17 - 7j - 18 - 11k. You can expand or simplify an expression to make an equivalent expression. Combine like terms to form a new equivalent expression. Like terms are terms which have the same base or variable.
10k + 17 - 7j - 18 - 11k
10k -11k + 17 - 18 - 7j Move to group like terms together.
-k - 1 - 7j
Please help me please
Answers
Answer:
21
Step-by-step explanation:
If lines m and n are equal, line t intersects both of them at the exact same angle. This means that 6x+3=7x-19. Start moving the variables to one side. 3=x-19. Then move the numbers to the other side of the equation. x=21.
How many wax warmers will she make when she makes 77 candles
A.75
B.55
C.40
D.69
Answers
Each number on the right side is going up by 5, so 11 x 5 = 55
Answer: B. 55
Help... A store owner collected data about the number of customers who came to the store in a day, y, for several days compared to the high temperature for that day, x. He found that the correlation coefficient was −0.76.
Answers
Answer:
Decreased
Strong negative
Step-by-step explanation:
The correlation Coefficient is used to show the strength and type of relationship which exists between the dependent and independent variable. The correlation Coefficient value ranges from - 1, to 1. With values closer to either - 1 or 1 depicting a strong relationship while those closer to 0 represents weak relationship. And correlation Coefficient of 0 indicates that no relationship exiata at all. Depending in the sign, that is positive or negative, positive sign means positive relationship while a negative sign represents a negative association. Positive association is interpreted as, for every increase in A, Variable B also increase and vice versa. For negative association, When A increases, B decreases and vice versa
find the midpoint of the line segment with end coordinates of (2,1) and (4,5)
Answers
Answer:
(3,3)
Step-by-step explanation:
5 - 2x^2 = -15 solve the question using inverse operations
Answers
Answer:
x= √10 and x= -√10
Step-by-step explanation:
first look to isolate the term with the variable on one side
-5 +5 -2x² = -5 -15; subtract 5 from both sides(inverse of addition)
-2x² = -20; divide both sides by -2 (inverse of multiplication)
x² = 10; square root both sides (the inverse of raising to power of 2)
√x² =√10
x =±√10
Find the area of the circle if the square has an area of 900in^2. Give your answer in terms of 3.14 or pi
Answers
Answer:
450in^2
Step-by-step explanation:
square root of 900 is 30.
Each side of square is 30.
Each side of a triangle formed by drawing a radi in the square is 15 in.
The hypotenuse is 15[tex]\sqrt{2}[/tex] that is also the radius of the circle.
A= (15[tex]\sqrt{2}[/tex])^2 times pi = 450 in^2
A square has sides of length (2 a-b) metres. Write down an expression for the area of the square and simplify it
Answers
Answer:
A = 4a² - 4ab + b²
Step-by-step explanation:
The area (A) of a square is calculated as
A = s² ( s is the side length ) , so
A = (2a - b)² ← expand using FOIL
= (2a)² - 2ab - 2ab + (- b)²
= 4a² - 4ab + b²
what is the value of J
Answers
Answer:
Step-by-step explanation:
Since all 3 of these angle come off a straight line, they all add up to equal 180. Thus,
2j + 32 + 6j - 2 + 30 = 180 and
8j + 60 = 180 and
8j = 120 so
j = 15
What is the ratio of people who prefer pistachio to the people who prefer vanilla?
- 3/2
- 2/3
- 4/5
- 5/4
Answers
Answer:
3/2
Step-by-step explanation:
Answer:
2/3
Step-by-step explanation:
people who like pistachio = 24
people who like vanilla = 36
ration pf people who prefer pistachio to the peple who prefer vanilla = 24/36
=2/3
the difference between two number is 5. when the larger number is multiplied by 2, the sum of both the numbers is 7. Hence, represent graphically the simultaneous linear equations in two variables and state the type of solutions.
Answers
Step-by-step explanation:
let the larger number = a,
and the smaller one = b.
a - b = 5 ==> a = b+5
2a + b = 7
2(b+5) +b=7
2b+10+b=7
3b= 7-10
3b = -3
b = -1
a = -1+5 = 4
Is Is y=2x+7 proportional?
Answers
Answer:
no
Step-by-step explanation:
Proportional must go through (0,0)
0 = 2(0) +7
0 = 7
This is not true so this is not proportional
A real estate agent earns about a 6% commission on each house sold. How
much commission would an agent earn on a house that sold for $125,000?
Answers
Answer:
132'500
Step-by-step explanation:
It is like doing tax, you just needed to multiply your number by 0.6
Answer:
$ 7,500
Step-by-step explanation:
commission=6%
House price= $125,000
Commission=6/100 ×125,000
Commission= $ 7,500
pls solve quickly !!
Answers
Answer:
Options A
Step-by-step explanation:
Properties of the graph given for the function 'g',
y-intercept of the function 'g' → y = -4
Minimum value of g(x) → y = -4 (Value of the function at the lowest point)
Roots of g(x) → x = -2, 2
At x = 4,
g(4) = 11
Another function is,
f(x) = -x² - 4x - 4
= -(x² + 4x + 4)
= -(x + 2)²
Properties of the function f(x) = -(x + 2)²,
y-intercept (at x = 0) of the function 'f',
y = -(x + 2)²
y = -4
Since, leading coefficient of the function is (-1) therefore, graph will open downwards and the maximum point will be its vertex.
Maximum value of the function 'f' = Value of the function at the vertex
Coordinates of vertex → (-2, 0)
Therefore, maximum value of 'f' = 0
Roots (at y = 0) of the function 'f' → x = -2
At x = 4,
f(4) = -(4 + 2)²
= -36
Therefore, Options A will be the correct option.
find the volume of the rectangle
Answers
Answer:
3/16
Step-by-step explanation:
simply multiply all 3 numbers