Mathematics High School

The area of the base of a pyramid is 15 cm2.

If the height of the pyramid is 4 cm, what is the volume of the pyramid?

20 cm3 60 cm3 120 cm3 180 cm3

Answers

Answer 1
The volume of any prism is equal to its base times its height. V = Bh
A figure such as a pyramid or cone has 1/3 of the volume of the prism which contains it. V = Bh/3

In the case of our pyramid here...
B = 15√3 cm²
h = 4 cm
Plug these into our formula...
V = Bh/3 = (15√3)(4)/3 = (60√3)/3 = 20√3 cm³
Hope this helps...
Answer 2
For a rectangular pyramid:
V = L*W*H/3 or B*H/3
V = (15*4)/3
V = 60/3
V = [tex] 20^{3} [/tex]

Related Questions

Child development
What have researchers learned about the relationship between longer childhoods and brain development?

Answers

Researchers have learned that the longer the childhood, the more learning the child can do. Like Gopnik says that we humans aren’t good at anything in particular, but good at learning about many different environments and are learning to do more than one thing unlike chickens."
Final answer:

Longer childhoods are closely linked to brain development, enhancing cognitive abilities by allowing more complex neuronal connections and greater adaptation to environmental stimuli. Extended brain development is also associated with increased brain plasticity, leading to better adaptability and higher complex problem-solving skills.

Explanation:

Research has found a significant relationship between longer childhoods and brain development. Humans have one of the longest childhoods among species, a period during which our brains continue to develop and mature significantly. This extended period of growth allows for more complex neuronal connections and adaptation to environmental stimuli, thus enhancing cognitive abilities.

A long childhood provides ample opportunities for learning and skill acquisition, and it is during this period that the brain is especially receptive to picking up new information. More prolonged brain development during childhood also tends to be associated with increased brain plasticity, meaning the brain's ability to change and adapt as a result of experiences. This plasticity aids in the formation of our identities and equips us to handle complex tasks and challenges as we grow.

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What is a 401(k) plan? an investment plan offered by an insurance company a retirement plan offered by employers a personal retirement plan

Answers

It is retirement plan in which you donate a certain amount of your paycheck to your retirement and you decide the contribution percentage
a retirement plan offered by employers

A pool is being drained at a rate of 120 gallons per minute.What is this rate in quarts per hour?

Answers

There are 4 quarts in 1 gallon, so a rate of 120 gallons per minute converts to 4 x 120 = 480 quarts per minute. To find the per hour rate, we simply multiply our per minute rate by 60, obtaining 480 x 60 = 28800 quarts per hour.

Express terms in i square root -40

Answers

[tex]\bf \sqrt{-40}\implies \sqrt{-1\cdot 40}\implies \sqrt{-1}\cdot \sqrt{40}\implies i\cdot \sqrt{4\cdot 10} \\\\\\ i\cdot \sqrt{2^2\cdot 10} \implies 2i\sqrt{10}[/tex]

Why is it important to simplify rational expressions before multiplying or dividing? How do you determine that a rational expression is in simplest form?

Answers

Simplifying rational expressions will make the further calculations easier since the variables to work with will usually be smaller.

To determine that a rational expression is in simplest form we need to make sure that the numerator and the denominator have no common variables.

It is important for us to simplify rational expressions before multiplying or dividing because it makes our calculations easier.

The rational expression is in its simplest form when there is no common factor between the numerator and the denominator.

What is a rational number?

A rational number is a number that can be written in the form of p/q where q is not equal to zero.

We have,

Some examples of rational numbers are:

38/44 or 39/63

We can divide this rational number into a decimal number but it is easier for us if we can simplify it in its simplest form.

There is no common factor between numerator and the denominator in its simplest form.

The simplest form of 38/44.

= 38/44

= 2 x 19 / 2 x 22

= 19/22

The simplest form of 39/62 is

= 39/63

= 3 x 13 / 3 x 21

= 13/21

Thus,

It is important for us to simplify rational expressions before multiplying or dividing because it makes our calculations easier.

The rational expression is in its simplest form when there is no common factor between the numerator and the denominator.

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Select "Growth" or "Decay" to classify each function.

Function Growth Decay
y=200(0.5)^2t
y=1/2(2.5)^t/6
y=(0.65)^t/4


Which equation can be used to find the solution of (1/3)^d−5 = 81 ?

A. −d−5=4

B. d + 5 = 4

C. d−5=4

D. −d+5=4

Answers

1. The growth rate equation has a general form of:

y = A (r)^t

The function is growth when r≥1, and it is a decay when r<1. Therefore:

y=200(0.5)^2t                    --> Decay

y=1/2(2.5)^t/6                  --> Growth

y=(0.65)^t/4                       --> Decay

 

2. We rewrite the given equation (1/3)^d−5 = 81

 

Take the log of both sides:

(d – 5) log(1/3) = log 81

d – 5 = log 81 / log(1/3)

d – 5 = - 4

 

Multiply both sides by negative 1:

- d + 5 = 4

So the answer is D

HELP WITH SOLVING SYSTEMS WITH THREE VARIABLES, WILL MEDAL




-x -y -z = -8
-4x + 4y + 5z = 7
2x + 2z = 4

I'm not sure how to work this out.

Answers

Equation 1)  -x - y - z = -8
Equation 2)  -4x + 4y + 5z = 7
Equation 3)  2x + 2z = 4

Solving for three variables is quite similar to solving for two variables. Just like when solving for two variables, you look for like variables & solve them one-by-one. So, let's get started! :)

Multiply ALL of equation 1 by four.

1)  4(-x - y - z = -8)

Simplify.

1)  -4x - 4y - 4z = -32

Both equations 1 & 2 have the same three variables (x, y, z), so, we must look at these equations together.

1)  -4x - 4y - 4z = -32
2)  -4x + 4y + 5z = 7

Add these equations together, and create a fourth equation.

4)  -8x - z = -25

Now, notice how both equations 3 & 4 have the same two variables (x, z).

So, we must look at these equations together.

3)  2x + 2z = 4
4)  -8x - z = -25

Multiply ALL of equation 4 by 2.

4)  2(-8x - z = -25)

Simplify.

4)  -16x - 2z =-50
3)  2x + 2z = 4

Now, add the equations together, so that we can solve for x.

-14x = -42

Divide both sides by -14.

x = 3

Now, plug in 3 for x into our 3rd equation.

3)  2x + 2z = 4

3)  2(3) + 2z = 4

Simplify.

6 + 2z = 4

Subtract 6 from both sides.

2z = 4 - 6

Simplify.

2z = -2

Divide both sides by 2.

z = -1

Now, plug in -1 for z & 3 for x in our 1st equation.

1)  -x - y - z = -8

-(3) - y - (-1) = -8

Simplify.

-3 - y + 1 = -8

Simplify.

-2 - y = -8

Add 2 to both sides.

-y = -8 + 2

Simplify.

-y = -6

Divide both sides by -1.

y = 6

SO :

x = 3, y = 6, z = -1

~Hope I helped!~

HELP! A daycare purchases two type of snacks, granola bars and fruit rolls. One week, they purchase 10 packs of granola bars and 6 packs of fruit rolls for a total of 152 snacks. The next week, they purchase 7 packs of granola bars and 12 packs of fruit rolls for a total of 200 snacks. How many snacks are in one pack of granola bars and one pack of fruit rolls?

Answers

10x+6y=152
5x+3y=76
7x+12y=200
-20x-12y=-304
-13x=-104
x=8
40+3y=76
3y=36
y=12
There are 8 granola bars in a pack and 12 fruit rolls in a pack

Answer: The number of granola bars in one pack = 8

The number of fruit rolls in one pack = 12

Step-by-step explanation:

Let x be the number of granola bars in each pack and y be the number of fruit rolls in each pack .

Then according to the question we have the following system of equations :

[tex]10x+6y=152.....................(1)\\7x+12y=200.......................(2)[/tex]

Multiply equation (1) by 2 we get

[tex]20x+12y=304......................(3)[/tex]

Subtract equation (2) from equation (3), we get

[tex]13x=104\\\\\Rigtarrow x=8[/tex]

Substitute x=8 in (1), we get

[tex]10(8)+6y=152\\\\\Rightarrow6y=152-80\\\\\Rightarrow\ 6y=72\\\Rightarrow y=12[/tex]

Hence, the number of granola bars in one pack = 8

The number of fruit rolls in one pack = 12

How many centimeters is a piece of paper that measures 12 inches? centimeters?

Answers

Well, there are 2.54 centimeters in an inch, so if you multiply 12 by 2.54, you get 30.48, which would be how many centimeters there are in 12 inches. Hope this helps!

Which improper fraction is equal to the mixed number 4 7/9 btw its a mixed number fraction

A. 37/9
B. 47/9
C. 43/9
D. 20/9

plz help asap

Answers

the answer is C 100% positive

Bailey writes the expression g2 + 14g + 40 to represent the area of a planned school garden in square feet. If g = 5, what are the dimensions of the school garden?

Answers

[tex] 5^{2} + 14(5) + 40 [/tex]
[tex] 25 +70 + 40[/tex]
135

[tex] \frac{135}{15} =9[/tex]

15 feet by 9 feet
(5x2)=10 (14x5)=70 40=40 10+70+40=120

Which statements are true about the ordered pair (−4, 0) and the system of equations? {2x+y=−8x−y=−4
Select each correct answer.

The ordered pair (−4, 0) is a solution to the first equation because it makes the first equation true.

The ordered pair (−4, 0) is a solution to the second equation because it makes the second equation true.

The ordered pair (−4, 0) is not a solution to the system because it makes at least one of the equations false.

The ordered pair (−4, 0) is a solution to the system because it makes both equations true.

Answers

Selections (a, b, d) are the most correct answers. To begin, 2x is equal to -8 when x is (-4). Adding 0 to this (for y) gives -8, which is the answer for the first equation. Doing the same for the second equation gives (-4 - 0) = -4, which shows that the second equation is also correct. Since both equations are satisfied by this ordered pair, it shows that the pair (-4,0) is a solution to the entire system.

How to find the values of the six trigonometric functions for 180?

Answers

I like to imagine a triangle in place of the negative x axis of the unit circle where  the opposite side = 0, the adjacent is -1 and the hypotenuse = 1.
so sin 180 = 0/1 = 0, cos 180 = -1/1 = -1   and tan 180 = -0/-1 = 0.
Then the other ratios are csc is 1/0 = indeterminate, sec = 1/-1 = -1 and cot is indeterminate.

factor completely: x^3+8x^2+7x

Answers

there's an x in all terms so factor that out first.

x(x^2 + 8x + 7)

now it's x multiplied by a typical parabolic equation. factor this normally by seeing what multiplies to give 7 and adds to give 8.

x(x + 7)(x + 1)

Trisha needs 4 yards of fabric to do a project. If she already has of a yard of fabric, what is the minimum amount of fabric she must buy to be able to complete her project? A. 3 5/6 B.4 1/12 C.4 1/6

Answers

the answer would be A.

Answer:

The answer is A. OR   3 5/6

Directions: Use a proportion to solve the problem.

Emily weighs six times as much on Earth as she does on the Moon. If her weight is ninety pounds on earth, what would her weight be on the moon?

Answers

so, since she weights 6 times more on earth, say for every lb on the moon  is 6lbs on earth then.

now, if 1lb on the moon is 6lbs on earth, how much is 90 earth lbs on the moon?

[tex]\bf \begin{array}{ccll} moon&earth\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 1&6\\ m&90 \end{array}\implies \cfrac{1}{m}=\cfrac{6}{90}\implies \cfrac{1\cdot 90}{6}=m[/tex]

One third of the sum of two consecutive odd integers is five less than the smaller integer

Answers

1/3(x + (x+2)) = x - 5

Your answer is 17, 19

Tom is deciding whether or not he should become a member gym to use their basketball courts. The membership cost is $135. Members pay $2 to rent out the basketball courts. Non-members can rent the court also, but they have to pay $11 each time. how many times would Tom need to rent the court in order for it be cheaper to be a member than a non member?

Answers

Final answer:

Tom would need to rent the basketball court 15 times for the gym membership to be more cost-effective than paying the non-member rental fee.

Explanation:

To determine how many times Tom would need to rent the basketball court to make the membership cheaper than being a non-member, we can set up a cost equation and find the breakeven point. Let's assume that Tom rents the court x times. For a non-member, the cost is $11 each time, which results in 11x dollars. For a member, the cost includes the one-time membership fee of $135 plus $2 each time the court is rented, summing to 135 + 2x dollars.

To find the breakeven point, we equate the two costs and solve for x:

11x = 135 + 2x

9x = 135

x = 135 / 9

x = 15

Thus, Tom would need to rent the court 15 times for the membership cost to be cheaper than paying as a non-member.

When writing the slope as a fraction which numner goes on top?

Answers

The number that goes on top is the number that represents your move on the Y axis of a graph from the point so up or down. 

The number goes on top tells line changes in the y direction and how much it rises.

what is slope?

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

As, The top number indicates how much the line rises or moves in the y direction.

Given that the number is a 1 and is positive, we can infer that the line rises or moves up by one.

Hence, line changes in the y direction and how much it rises.

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11. Solve for the value of x in the triangle shown below. Show your work! (1 point for equation, 1 point for answer)

Answers

3 inside angles need to = 180, since it is a right triangle, the bottom left angle = 80 so the other 2 angles need to equal 90 degrees

 so you have:

(8x+2) + (9x+3) = 90

 combine like terms to get:

17x+5 = 90

subtract 5 from both sides:

17x = 85

 divide both sides by 17

x = 85/17 = 5

x = 5

As Marta built a square fence around her garden, she wondered how much she would have to pay if she increased the length of each side of the fence by the same number of meters. Each meter of fence costs 3 dollars. Which of the following functions best describes the additional amount of money Marta will have to spend, in dollars, if she increases each side of the fence by m meters?

Answers

Given that as Marta built a square fence around her garden, she wondered how much she would have to pay if she increased the length of each side of the fence by the same number of meters.

Suppose the she increases each side of the fence by m meters, then the total increase to the four sides of the square is given by 4m.

Given that each meter of fence costs 3 dollars, therefore, the function that best describes the additional amount of money Marta will have to spend, in dollars, if she increases each side of the fence by m meters is given by C = 12m.

What is the measure of MOP?

Answers

Answer:

(C) [tex]{\angle}MOP=61^{\circ}[/tex]

Step-by-step explanation:

Given: It is given that angle MON is a straight angle and OP is bisects angle MOQ.

To find: The measure of the angle MOP.

Solution: It is given that angle MON is a straight angle and OP is bisects angle MOQ.

Thus, using the straight line property, we get

[tex]{\angle}MOP+{\angle}POQ+{\angle}QON=180^{\circ}[/tex]

[tex]2{\angle}MOP+{\angle}QON=180^{\circ}[/tex]

Substituting the given values, we get

[tex]2{\angle}MOP+58^{\circ}=180^{\circ}[/tex]

[tex]2{\angle}MOP=122^{\circ}[/tex]

[tex]{\angle}MOP=61^{\circ}[/tex]

Hence, option (C) is correct.

Answer: C - 61°

Step-by-step explanation: edge

Which ordered pairs are solutions to the inequality y−4x≥−5 ?

Select each correct answer.

(5, −2)

(1, −1)

(−4, 2)

(4, 0)

(−2, 1)

Answers

(1,-1) (-4,2) (-2,1) are all correct answers because when you plug them in to the eqaution they keep the eqaution correct

The ordered pairs that satisfy the given inequality is required.

The points that are solutions are [tex](-4,2),(-2,1),(1,-1)[/tex]

The given inequality is [tex]y-4x\geq -5[/tex]

Let us substitute each point in the inequality

[tex](5,-2)[/tex]

[tex]y-4x\\ =-2-4\times 5\\ =-22\ngeq -5[/tex]

[tex](1,-1)[/tex]

[tex]-1-4\times 1\\ =-5\geq -5[/tex]

[tex](-4,2)[/tex]

[tex]2-4\times -4\\ =18\geq -5[/tex]

[tex](4,0)[/tex]

[tex]0-4\times 4=-16\ngeq -5[/tex]

[tex](-2,1)[/tex]

[tex]1-4\times -2=7\geq -5[/tex]

The points that are solutions are [tex](-4,2),(-2,1),(1,-1)[/tex]

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Hadlee got 18 out of 20 questions correct on her math quiz. What percent of the questions did she get right?

Answers

It would be a 90%. In the calculator 18 is what percent of 20.
To find percents.  

First divide -----> 18/20 = 0.9

Then multiply by 100 or move decimal 2 places to the right.

----> 0.9 * 100 = 90

Answer: 90%


Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.

6 less than the product of 3 and a number.

Answers

The product of three and a number means 3 times x.

6 less than a number means you subtract 6.

3x - 6

Hope this helps!

The algebraic expression representing the words "6 less than the product of 3 and a number" is shown as 3x - 6.

What is an algebraic expression?

An algebraic expression is a combination of terms separated by mathematical operations (+, -, *, /).

A term is a combination of numerals and variables where variables are raised to integral powers.

How to solve the question?

In the question, we are asked to write the algebraic expression that represents the words "6 less than the product of 3 and a number".

Assuming the number to be x.

We first try to make the terms.

The term that will be formed using the words the product of 3 and a number is 3 * x = 3x.

The term using the word 6 is 6.

Now, to complete the expression, we combine the terms.

The words less than implies the difference. Thus the expression can be written as 3x - 6.

Thus, the algebraic expression representing the words "6 less than the product of 3 and a number" is shown as 3x - 6.

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Use your calculator to evaluate the limit of x equals 1 to 3 of e raised to the x squared power, dx. Give your answer to the nearest integer.

Numerical Answers Expected!

Answers

The integral of e raised to x squared dx to the limit from 1 to 3 translating in equation we get
∫1-3 e^(X^2) dx.

Solving using scientific calculator, we have  1443.082471 or simply 1443.

ANSWER: 1443

Point F is on circle C.



What is the length of line segment GF?

a.12.5 units
b.15.0 units
c.17.5 units
d.20.0 units

Answers

The answer was D. "20.0 units"

Answer:

GF = 20  units .

Step-by-step explanation:

Given  : A circle ,Point F is on circle C.

To find : What is the length of line segment GF.

Solution : We have given  A circle ,Point F is on circle C.

In circle we can see in triangle GCE

EC = CF = 7.5

GE = 10.

By the Pythagorean theorem :

GC²  = EG²+ EC².

Plugging the values

GC²  = 10²+ 7.5².

GC²  = 100 + 56 .25.

GC²  = 156.25.

Taking square root.

GC = 12.5 units.

Radius of circle CF = 7.5 units .

GF = GC +CF.

GF = 12.5 + 7.5

GF = 20  units .

Therefore, GF = 20  units .

Which of the following phrases could represent the expression k - 4?
A.a number subtracted from four
B.four less a number
C.a number decreased by four
D.a number less than four

Answers

c a number decreased by 4
Salutations!

There are two phrases that can represent the expression [tex]k - 4[/tex]

→ Four less a number

or

→ A number decreased by four.

Bot option B and C are correct.

Hope I helped (:

Have a great day!

Which is cheaper for a $56 item that cost $9.25 to ship, a $15 off coupon off the cost or free shipping

Answers

the answer would have to the 15 dollars off the price
The $15 dollar coupon. You'll save about $6

The line passing through the points (-7,4) and (-23,y) is parallel to a line that has a slope of -5/8. What is the value of y?

Answers

two lines that are parallel to each other, will have the same slope.

so if this line is parallel to another with a slope of -5/8, the slope of this line is also -5/8 then.  We also know that it passes through -7, 4 and -23, y, let's do some checking.

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -7}}\quad ,&{{ 4}})\quad % (c,d) &({{ -23}}\quad ,&{{ y}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{y-4}{-23-(-7)}\implies \cfrac{y-4}{-23+7} \\\\\\ \cfrac{y-4}{-16}=\boxed{-\cfrac{5}{8}}\implies 8y-32=80\implies 8y=112 \\\\\\ y=\cfrac{112}{8}\implies y=14[/tex]
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