Mathematics Middle School

PLEASE HELP ME!! A right circular cone has a radius of 6 inches and a volume of 180 cubic inches. What is the height of the cone? Please answer without using pi. Thank you

A. 5 in.
B. 15 in.
C. 25 in.
D. 90 in.

Answers

Answer 1
Volume of the cone = [tex] \frac{1}{3} \pi x^{2} h[/tex]

Given that the volume is 180 cubic inches
[tex] \frac{1}{3} \pi r^{2} h[/tex] = [tex]180[/tex] 

Given that the radius is 6m
[tex] \frac{1}{3} \pi 6^{2} h[/tex] = [tex]180[/tex] 

Evaluate 
[tex] \frac{1}{3} \pi (36) h[/tex] =  [tex]180[/tex] 
[tex] 12\pi h[/tex] =  [tex]180[/tex] 
[tex] h[/tex] =  [tex]180[/tex]  ÷ ([tex] 12 \pi [/tex])
[tex] h[/tex] = 4.77  ≈ 5 inches (Answer A)


Answer 2

Option B.The height of a cone is 15 inches.

To find the height of the cone, we will use the formula for the volume of a cone:

V = (1/3) * π * r² * h

We know the volume (V) is 180 cubic inches and the radius (r) is 6 inches.
We need to solve for the height (h).
First, let's plug in the known values:

180 = (1/3) * π * (6)² * h

180 = (1/3) * π * 36 * h

540 = π * 36 * h

540 / 36π = h

We can simplify this further, h = 15/π. Since we do not use π for the answer:

By rational observation of given options, B. 15 in. seems accurate.

Related Questions

What situation could this diagram represent?

Answers

Answer: B- Flipping two coins once


Step-by-step explanation:


B. Tossing Two Coins Once

I Got it Right i Promise

If a(x) is a polynomial function and b(x) is a polynomial function, then which of the following could be the sum of a(x) + b(x)?


A. ex + 2
B. x2 + 2x − log(x)
C. x6 − x4 + 9x
D. 5x² − 3x

Answers

The sum of two polynomial functions will also be a polynomial function. The exponents of the variables in the polynomial function are non-negative integers. Option A is an exponential function. Option B is a logarithmic function. 

The formatting is not proper in the options C and D. Only 1 option can be the correct answer.

If the options are:

[tex]C) x^{6} - x^{4} +9x \\ \\ D) 5x^{2} -3^{x} [/tex]

Then option C would be the correct answer as in option D variable is in the exponent which is against the definition of polynomial function.

If the options are:

[tex]C) x^{6} - x^{4} +9^{x} \\ \\ D) 5x^{2} -3x[/tex]

Then option D would be the correct answer as in option C variable is in the exponent which is against the definition of polynomial function.
Answer:
Options C and D are correct

Explanation:
We are given that both functions a(x) and b(x) are polynomial.
This means that adding them will also produce a polynomial function
polynomial a(x) + polynomial b(x) = polynomial c(x)

Now, let's check the given options:
Option A:
e² + 2
This is a exponential function. An exponential function is not a polynomial. Therefore, this option is incorrect

Option B:
x² + 2x - log(x)
This is a logarithmic function. A logarithmic function is not a polynomila.
Therefore, this option is incorrect

Option C:
x⁶ - x⁴ + 9x
This is a polynomial of the 6th degree.
Therefore, this option is correct

Option D:
5x² - 3x
This is a polynomial of the second degree.
Therefore, this option is correct

Based on the above, options C and D are both correct options

Hope this helps :)

PLZ HELP!
at the apple orchard workers were asked to put 100 apples in barrels. the following five were filled incorrectly. if the supervisor wrote +5 above a barrel, it meant that the barrel was 5 apples over, -5 meant that a barrel was 5 apples less than 100.
How many TOTAL apples are i the five barrels?
a -480 apples
b 498 apples
c 500 apples
d 520 apples

Answers

B.) four hundred ninety-eight, You would add the number of mistakes in the barrels, then subtract that from five hundred.

if a line is tangent to a circle at how many points does it interest the circle?

Answers

The intersection of a tangent to a circle and the circle is at exactly one point. Don't let a drawing fool you. In a drawing, it looks like there are several points of intersection, but keep in mind that a point has no dimensions, no length, width, or height, and a line has only length but no width. A drawing is just a representation of a point and a line, so we can see them.
If a line is tangent with a circle, it has one point in common with it.

Bill says that he can add 23 and 40 without regrouping. Is bill correct? How do you know?

Answers

He can because you can add it mentally. You can just have 23 in your head and count by adding 10 "4" times. 

Hope this helped☺☺
Yes because 23+40 equals to 63 without any twist or turns, it is a simple answer

Tony Hawk was the first skateboarder to do a “900,” a rotation of 900°. How many times did he rotate on the skateboard? times 8. Each arm of this pinwheel is the image of another arm rotated

Answers

1 complete circle = 360 degrees

900 / 360 = 2.5 rotations
900 / 360 = 2.5 rotations

an art easel with equal sides are opened and placed on a desk, classify the type of triangle formed by the easel and the desk

Answers

It would be an isosceles triangle, an easy way to remember this is to think of an ice cream cone (ISO ICE word play helps) because an ice cream cone has two long sides and one short one.

You and your friend are standing back to back. Your friend runs 20 feet forward and then 15 feet right. At the same time, you run 12 feet forward and then 9 feet right. You stop and throw a baseball to your friend, who catches it. How far did you throw the baseball

Answers

I think its 32 because he runs 20 you run 12 you ran right no forward or backward. hope this helps good luck

A cake recipe requires 1 2/3 cups of milk how many cups altogether are necessary to make 4 cakes

Answers

For four cakes you would need to multiply 4 times 1 2/3 which equals 
6 and 2/3
1 2/3*4=

5/3*4=

20/3=

6 2/3.

Hope this helped☺☺

A bag of fruit contains 3 apples, 2 oranges, 1 banana and 4 pears. What is the probability that I will pull out a banana first and a pear second?

Answers

1/2 if simplified. If you don't want it's simplified then it's 5/10
The probability of pulling out a banana is 1 out of 10 (which is not high) and of choosing a pear second is 4 out of 10 (which is higher)

Evaluate. 6+5|4-3^2| A. -19 C. 31 D. 55

Answers

Answer:

6 + 5|4 - 3²| =

6 + 5|4 - 9| =

6 + 5|-5| =

6 + 5(5) =

6 + 25 = 31

The correct answer is C.

if side a=22.3 and angle b=47 ,find c.
A.24.6
B.25.1
C.31.5
D. 32.9

Answers

Answer:

D. 32.9

Step-by-step explanation:

-(m-6)=3m+14 what is m

Answers

the answer is
[tex] - m + 6 = 3m + 14[/tex]
[tex] - 4m = 8[/tex]
[tex]m = - 2[/tex]

The area of a rectangular knitted blanket is 15x2-14x-8. What are the possible dimensions of the blanket? Use factoring.

Answers

The answer for that equation would be 2-5x and 3x +4

Final answer:

The area of a rectangular blanket is 15x² - 14x - 8, and by factoring this expression, we find the possible dimensions to be (5x + 2) units by (3x - 4) units. The variable x represents a dimension and must be a positive value so that the actual dimensions are also positive.

Explanation:

The student is asking about the possible dimensions of a rectangular knitted blanket whose area is given by the polynomial 15x² - 14x - 8. To find the dimensions of the blanket, we need to factor this quadratic expression. Factoring is the process of breaking down a complex expression into simpler ones that, when multiplied together, give the original expression.

Let's factor the given expression:

Find two numbers whose product is 15 (coefficient of x²) multiplied by -8 (constant term) and whose sum is -14 (coefficient of x). These numbers are -20 and +6.Rewrite the middle term (-14x) using the numbers found: 15x² - 20x + 6x - 8.Factor by grouping: (15x² - 20x) + (6x - 8) = 5x(3x - 4) + 2(3x - 4).The expression can now be factored as (5x + 2)(3x - 4).

The factored form suggests that the rectangle's dimensions could be (5x + 2) units by (3x - 4) units, where x is a variable representing one of the dimensions. However, since the values of x need to make physical sense in the context of a blanket's size, x will need to be a positive value such that (5x + 2) and (3x - 4) are also positive.

What is the area of the triangle in this coordinate plane? 9.0 units² 14.0 units² 16.5 units² 24.5 units² A graph with a triangle drawn on it

Answers

I took the test, the correct answer is 16.5 units²

A function is a relationship that maps__.
A) many inputs to many outputs or one input to one output
B) many inputs to many outputs or many inputs to one output
C) one input to many outputs or one input to one output
D) one input to one output or many inputs to one output

Answers

Solution:

A function is always a relation but a relation is not always a fucntion.

For example

we can make a realtion of student roll number and their marks obtained in mathematics.

So we can have pairs like (a,b), (c,d)..etc.

Its a realtion but it may not be function. Because function follows that for same input there should not be diffrent output, aslo there could be many inputs to one output in the case of constant function . But this doesn't holds a necessary condition in case of relation.

Because two diffrent students with two diffrent Roll number may have same marks.

Hence the foolowing options holds True in case of a function.

A) many inputs to many outputs or one input to one output.

D) one input to one output or many inputs to one output.

Answer:

The correct answer is D. A function is when an input has one output. An input can only have one output but an output can have multiple inputs. Hope this helps!

Jeremiah built a box that was 5 inches long by 6 inches wide by 7 inches high .he started filling it up with 1 cube.he realized quickly that he did not have nearly enough cubes to fill the box .can he still figure out how many cubes it will hold?

Answers

To determine the number of cubes he needs to fill the box (this is assuming the cubes are 1 in cubes, he would need to calculate the volume of the box. To find the volume he would multiply the length by the width by the height. This would be 5 in x 6 in x 7 in. The volume is 210 cubic inches, so he could fill it with 210 one inch cubes.

write the equation of the parabola below

Answers

Answer:
Equation is: y = 0.5x² + 0.5x - 3

Explanation:
general form of the parabola is:
y = ax² + bx + c

Now, we will need to solve for a, b and c.
To do this, we will simply get points from the graph, substitute in the general equation and solve for the missing coefficients.

First point that we will use is (0,-3). 
y = y = ax² + bx + c
-3 = a(0)² + b(0) + c
c = -3

The equation now becomes:
y = ax² + bx - 3

The second point that we will use is (2,0):
y = ax² + bx - 3
0 = a(2)² + b(2) - 3
0 = 4a + 2b -3
4a + 2b = 3
This means that:
2b = 3 - 4a
b = 1.5 - 2a ...........> I

The third point that we will use is (-3,0):
y = ax² + bx - 3
0 = a(-3)² + b(-3) - 3
0 = 9a - 3b - 3
9a - 3b = 3 ...........> II

Substitute with I in II and solve for a as follows:
9a - 3b = 3
9a - 3(1.5 - 2a) = 3
9a - 4.5 + 6a = 3
15a = 7.5
a = 7.5 / 15
a = 0.5

Substitute with the value of a in equation I to get b as follows:
b = 1.5 - 2a 
b = 1.5 - 2(0.5)
b = 0.5

Substitute with a and b in the equation as follows:
y = 0.5x² + 0.5x - 3

Hope this helps :)

What is the volume of this right triangular prism?


A.)144.2 cm3
B.)164.8 cm3
C.) 288.4 cm3
D.) 1153.6 cm3

Answers

You’re answer is B, you just have to multiply all of the sides together and then add your sums.

Hope this helps:)
The volume =0.5* Length * width * height
                     = 0.5* 7 *4* 10.3 =144.2 cm3

Simplify each expression. Select the correct answer from the drop-down menu.

−6(3i)(−2i) =

2(3 − i)(−2 + 4i) =

Answers

-6(3i)(-2i)= -36

2(3-I)(-2+4i)= -4 + 28i



the answer is:

−6(3i)(−2i) = -36

2(3 − i)(−2 + 4i) = -4+28i

2i(4 − 5i) = 10+8i

hope this helps! :o)

round 49,953 to the nearest hundred

Answers

The correct answer is 50,000
49,953 to the nearest hundred would be 50,00. This would be because the 9 would round to 10 and since 10 ins't a one digit number the number becomes 50,000. 

Two sides of a triangle measure 20 cm and 30cm. What is the third side?

Answers

Hi there!

It depends on what angles there are, and how many degrees are in each angle. In order to figure this problem out, you need to know at least one angle ;)

Hope this helps!
I think the measure of the third side is 11 cm.

Hope this helped☺☺

In a dog show, there will be a gold, a silver, and a bronze medal awarded. There are
5 finalists. In how many different ways can the 3 medals be awarded?

Answers

Answer
60 ways

Explanation
In permutation the order really matters unlike combination where order does not matter.
The question wants you to find how many time you can choose 3 out of 5 with order.
This means we should find 5 permutation 3.

5P3=5!/3!
=(5×4×3×2×1)/(3×2×1)=5×4 
                                     =60 

Answer:

60 ways

Step-by-step explanation:

There are five finalist and 3 medals.

For getting the first medal, there are 5 choices, any of the finalist can get that.

For getting the second medal, we are left with 4 choices.

For getting the third medal we are left with 3 choices.

Hence, the number of ways 3 medals can be awarded are:

5×4×3=60 ways

Write an equition that expresses y in terms of x

Answers

y = 5x + 2

y on the left side is expressed in terms of x on the right side.

A three dimensional object was sliced parallel to its base and the result was a triangular cross-section.The same shape resulted from slicing the object perpendicular to its base.What three dimensional object fits this description?

Answers

Answer:

The answer is below!

Step-by-step explanation:

Final answer:

A cone is the three-dimensional shape that gives a triangular cross-section when sliced either parallel or perpendicular to its base.

Explanation:

The three-dimensional shape that fits the description of producing a triangular cross-section when sliced both parallel and perpendicular to its base is a cone.

A cone is a solid that has a circular base and a single vertex. When a cone is sliced parallel to its base, the cross-section is a circle. When a cone is sliced perpendicular to its base, the cross-section is a triangle, specifically a right triangle. The right triangle results from the slice passing through the vertex and the base of the cone.

Learn more about Cone here:

https://brainly.com/question/10670510

#SPJ11

PLEASE NEED HELP WITH A-D

Answers

a.
4(d+3c)

b.
6(3x+5y)

c.
7(3a+4y)

d.
8(3f + 7g)
Hello there! I can help you! For this question, we write this in distributive property by finding the GCF of both terms. As far as we see for all 4 of them, there are no like variables, and we find the GCF, just like we would for constants. When you find the GCF, be sure to divide each terms by the GCF, and then place the GCF outside the parenthesis. If you solve this correctly, here are your answers:

a. 4(a + 3e)

b. 6(3x + 5y)

c. 7(3a + 4y)

d. 8(3f + 7g)

Pls help me lots of points

Answers

3 Treats total: 2 m&ms and 1 hershey's bar


Answer:

2 m&ms and 1 hershey's bar

Step-by-step explanation:

Going against the current, a boat takes 7 hours to make a 120 mile trip. When the boat travels with the current on the return trip, it takes 4.5 hours. If x is the speed of the boat is still water and y is the speed of the current, which of the following system of equations could be used to solve the problem?

Answers

The system of equations that could be used to solve the problem is 7(x - y) = 120; 4.5(x + y) = 120. option A

which of the following system of equations could be used to solve the problem?

If

x is the speed of the boat is still water

y is the speed of the current

7(x - y) = 120

4.5(x + y) = 120

Therefore, the system of equation can be rewritten as;

7x - 7y = 120

4.5x + 4.5y = 120

Complete question:

Going against the current, a boat takes 7 hours to make a 120 mile trip. When the boat travels with the current on the return trip, it takes 4.5 hours. If x is the speed of the boat is still water and y is the speed of the current, which of the following system of equations could be used to solve the problem?

A. 7(x - y) = 120; 4.5(x + y) = 120

B. 7(x + y) = 120; 4.5(x + y) = 120

C. 7(x - y) = 120; 4.5(x - y) = 120

D. 7(x + y) = 120; 4.5(x + y) = 120

PLEASE HELP!!!! SOLVE: |2x+1|+|3x−4|=5

Answers

i have no idea what the lines mean :(
2x+1+3x-4=5
5x-3=5 Group like terms
5x=8 Add 3 to the end to isolate x
x=1.6 Divide 8 by 5
Hope this helped 

What is the value of G in the center and how do you solve it?

Answers

first solve:
7 + 3c = -11 --> c = -6
-9 - a/4 = 5 --> a = -56
b/5 +9 = 6 --> b = 75

second, solve:
a/f = -7 --> substitute -56 in for a --> -56/f = -7 --> f = 8
b/e = 3 --> substitute 75 in for b --> 75/e = 3 --> e = 25
3 = c/d --> substitutie -6 in for c --> 3 = -6/d --> d = -2

third solve:
g = d+e+f --> substitute -2 in for d, 25 in for e, and 8 in for f.
g = -2 + 25+8 
g = 31
Lets find out d first:

3 = c/d => d = c/3

7+3c = -11 => 3c = -11 - 7 => 3c = -18 => c = -18/3 => c = -6.

Now d = c/3 => d = -6/3 => d = -2.

Lets now find out e:

b/e = 3 => e = b/3

b/5 + 9 = 6 => b = (6-9)*5 => b = -15

Now e = b/3 => e = -15/3 = -5

Now we need to find f:

a/f = -7 => f = a/-7

-9 - a/4 =5 => a= (-9-5)*4 = -56

Now f = a/-7 => f = -56 / -7 = 8

So g = d + e + f
= (-2) + (-5) + 8
= 1
Therefore g = 1
Other Questions
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They are so successful they can triple in size every few months by molting when they outgrow their exoskeletons. They start out as nymphs, able to capture only prey that is smaller than they are. They end their lives about a year later becoming predators that can take down prey as large as hummingbirds. Finally, they are very personable, as far as insects go. They have a large, triangular-shaped head with large eyes. This alien-like appearance makes them quite cute. When you come across them in the garden, you can tell right away they are aware of you. They follow your movements as if to assess if you are either something to eat or something that will eat them. The little ones will accept rides on your finger if you are gentle. But be carefulthey can jump surprisingly far even when small. If they think your freckle is prey, you may be surprised to find a mantis on your nose. As far as predatory insects go, the mantis is one of the most impressive. 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