The height of one square pyramid is 12 m. A similar pyramid has a height of 6 m. The volume of the larger pyramid is 400 m3. Determine each of the following, showing all your work and reasoning.

Scale factor of the smaller pyramid to the larger pyramid in simplest form

Ratio of the areas of the bases of the smaller pyramid to the larger pyramid

Ratio of the volume of the smaller pyramid to the larger

Volume of the smaller pyramid

Answers

Answer 1

[tex]\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &Sides&Area&Volume\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array} \\\\ -----------------------------\\\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\ [/tex]

[tex]\bf \cfrac{smaller}{larger}\qquad \cfrac{\stackrel{height}{6}}{\stackrel{height}{12}}\implies \cfrac{1}{2}\impliedby \textit{scale factor of the pyramids}\\\\ -------------------------------\\\\ \cfrac{smaller}{larger}\qquad \cfrac{h}{h}=\cfrac{\sqrt{base}}{\sqrt{base}}\implies \cfrac{1}{2}=\sqrt{\cfrac{base}{base}}\implies \left( \cfrac{1}{2} \right)^2=\cfrac{base}{base} \\\\\\ \cfrac{1^2}{2^2}=\cfrac{base}{base}\implies \cfrac{1}{4}=\cfrac{base}{base}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \cfrac{smaller}{larger}\qquad \cfrac{h}{h}=\cfrac{\sqrt[3]{volume}}{\sqrt[3]{volume}}\implies \cfrac{1}{2}=\sqrt[3]{\cfrac{volume}{volume}} \\\\\\ \left( \cfrac{1}{2} \right)^3=\cfrac{volume}{volume} \implies \cfrac{1^3}{2^3}=\cfrac{volume}{volume}\implies \cfrac{1}{8}=\cfrac{volume}{volume}\\\\ -------------------------------\\\\ \cfrac{smaller}{larger}\qquad \cfrac{1}{8}=\cfrac{\stackrel{volume}{v}}{\stackrel{volume}{400}}\implies \cfrac{1\cdot 400}{8}=v[/tex]

Related Questions

Simplify (x3+ 8x + 5) − (2x2− 3x − 12). −x2+ 11x + 17 x3− 2x2+ 11x + 17 −x2+ 5x − 7 x3− 2x2+ 5x − 7

Answers

x^3 + 8x + 5 - (2x^2 - 3x - 12) =
x^3 + 8x + 5 - 2x^2 + 3x + 12 =
x^3 - 2x^2 + 11x + 17 <===

Please help!!

4) Use the figure below to answer parts A and B. Show your work. (4 Points)

A.)Explain, in words, a series of rigid motions that would map ∆MJS onto ∆DWP.

B.)Write the ordered-pair rule for each transformation in the sequence

Answers

Part A:

The series of rigid motions that would map ∆MJS onto ∆DWP are:

a.) A rotation of 90 degrees about the point J in the clockwise direction.
b.) A translation of 1 units to the right and 5 units up.

Part B:

The ordered-pair rule for each transformation in the sequence are:

a.) R (J, 90 degrees)
b.) (x, y) → (x + 1, y + 5)

what is f(-5) if f(x) equals |2x-1|+10?

Answers

|2(-5) - 1| + 10
|-10-1| + 10
|-11| + 10
11 + 10
21 is your answer

Hope this helped!

Answer:

The value of the function for f(-5) is 21.

Step-by-step explanation:

Consider the provided function.

[tex]f(x)=|2x-1|+10[/tex]

We need to find the value of the function for f(-5).

Substitute the value of x=-5 in the above function.

[tex]f(-5)=|2(-5)-1|+10[/tex]

[tex]f(-5)=|-10-1|+10[/tex]

[tex]f(-5)=|-11|+10[/tex]

The absolute value of -11 is 11.

[tex]f(-5)=11+10[/tex]

[tex]f(-5)=21[/tex]

Hence, the value of the function for f(-5) is 21.

Mayumi is constructing a line through point P that is perpendicular to RS←→. A horizontal line segment R S and a point P are drawn. The point P is above the horizontal line segment R S. She places her compass on point P to construct an arc. What must be true about the width of the compass opening when Mayumi draws the arc? It must be greater than 12RS. It must be equal to PS . It must be wide enough so that the arc intersects RS←→ in two points. It must be equal to PR .

Answers

Width of the compass should be more than the smallest space between P and RS, so that it cuts RS at two distinct points. Therefore, it must be wide enough so that the arc intersects RS←→ in two points. The photo is attached so that you can understand it more.

Hola fellow K12 kiddos!

Correct answer:

It must be wide enough so that the arc intersects RS←→ in two points.

3(x−7)=6(x−10)
Solve For X
3x-21=6x-60

Answers

3(x-7)=6(x-10)
3x-21=6x-60
3x-21+21=6x-60+21
3x=6x-39
3x-6x=6x-39-6x
-3x=-39
-3x/-3=-39/-3
x=13

Hello,

Let's look at the equation: 3(x−7)=6(x−10). Let's distribute the 3 and 6 to the parenthesis. After you distribute, the equation should look like:
3x - 21 = 6x - 60. Then add 21 to both sides and that should leave you with
3x = 6x - 39. Let's then get 6x to the other side by subtracting 6x to both sides. That'll leave you with -3x = -39, then divide each side by -3 to get x by itself. The equation would now be: x = 13. Hope this helps =).

Brainly use a matrix to find the solution to the system of equations -8x-8y=-16 6x-9y=-108

Answers

We want to use a matrix to solve
-8x - 8y = -16
6x - 9y = -108

Before solving, simplify the equations as follows:
Divide the first equation by -8 to obtain
x + y = 2 (1)
Divide the second equation by 3 to obtain
2x - 3y = -36 (2)

In matrix form, the equations are
[tex] \begin{bmatrix}1&1\\2&-3\end{bmatrix} \begin{\bmatrix} x\\y\end{bmatrix}=\begin{bmatrix}2 \\ -36 \end{bmatrix}[/tex]

The determinant of the matrix is
D = (1)(-3) - (1)(2) = -5

Use Cramer's Rule.
[tex]x = \frac{1}{D} det(\begin{bmatrix}2&1\\-36&-3 \end{bmatrix} ) = \frac{1}{-5} (-6+36) = -6[/tex]
Similalrly,
[tex]y= \frac{1}{-5} det(\begin{bmatrix} 1&2\\2&-36\end{bmatrix} ) = \frac{1}{-5}(-36-4) =8[/tex]

Answer: (-6, 8) or x = -6, y = 8

My number has nine digits it is evenly divisible by 100 the value of one of the digits is 700,000 the digit in the millions place is both even and prime the digit in the hundreds place is the temperature at which water freezes the digit in the ten millions place is triple the number in the millions place the digit in the thousands place is the number of fluid ounces in a cup the digit in the hundred millions place is a special number because it is a factor of every number.

Answers

Let's go for it:
Nine digits: nnn,nnn,nnn

Divisible by 100 = last two digits are 00
hundred thousands place = 7
one millions place is even and prime = 2 [the only prime even number]
hundreds place = 0 [water freezes at 0 °C]
Ten millions place is triple one millions place = 6 [2x3]
one thousands place = 8 [8 ounces in one cup]
Hundred millions place = 1 [only number that's a factor of every number]

162,708,000

Write a linear model for the cost of tickets based on the number of tickets a fan buys.

Answers

y = mx + b

y = 2x + 7

You have 120 pieces of fabric to make a blanket. Each piece of fabric is a square with a side length of 6 inches. you can use as many pieces of fabric as possible to create a square blanket. What is the area of the blanket? How many pieces of fabric or left over. How many more pieces of fabric what you need to increase the size of the blanket

Answers

Area of blanket = 25 sq ft Pieces left over = 20 Need 1 more piece to make the blanket 5.5 ft on edge. Since you want a square blanket, the first step is to calculate the square root of 120, which is 10.95. Since you cannot use a fractional piece of cloth, that means the final blanket will have 10 squares of cloth per edge. What is the area of the blanket? Since there's 10 pieces of cloth per edge and each piece of cloth is a 6 inch square, each edge is 5 feet long. So the total area is 5 * 5 = 25 square feet. How many pieces of fabric is left over? Since there's 10 pieces of cloth per edge, the total number of pieces used will be 10 * 10 = 100. So the number of pieces left over will be 120 - 100 = 20 How many pieces of fabric do you need to increase the size of the blanket? Since the current size is 10x10, the next larger size is 11x11 which means a total of 121 pieces of fabric is needed. Of those 121 pieces, 100 is already being used for the blanket, so you need to add 121 - 100 = 21 pieces of fabric to the blanket. You already have 20 pieces available, so you only need to get 21 - 20 = 1 more piece to make the blanket larger.

Martin drew a pair of perpendicular lines and a pair of parallel lines.which of these statements best compares the pairs of perpendicular and parallel lines?

Answers

You need to post the statements

How to write 0.924 in two other forms

Answers

Hi there!

Your question:

How to write 0.934 in two other forms?

My answer:

Since 0.924 is a decimal, the two other ways are going to be a fraction and a percent. To make it a fraction you are going to find out what it's out of. in this case, it's 1,000.

The answer is: 924/100 and 92.4%

What is the value for x?
Enter your answer in the box.

Answers

A is equal to C
73=8y-7
+7
80=8y
y=10
73+73=146
180-146=34
6x+4=34
-4
6x=30
x=5

x=5
y=10

5=x. angles a and c are equivalent, so you just add them together and subtract from 180, then solve for x plugging in difference of the two.

Suppose A and B are points. How many lines contain both A and B?

Answers

One and only one line contains both A and B (assuming, that A and B do not overlap)

Point A and point B should both contain one line

Find the 40th term of the following arithmetic sequence:16,6,-4,-14

Answers

Let the 40th number be x
(x-16)/(-10) + 1 = 40
x-16 = 39(-10)
x = -390 + 16
x = -374

The 40th number in the sequence is -374

TWO EASY QUESTIONS 8TH GRADE MATH
9. Complete the missing steps in the paragraph proof of Theorem 3-8.
11. Solve for the value of x in the triangle shown below. Show your work! (1 point for equation, 1 point for answer)

Answers

9.
<2 and <6 are right angles by the definition of perpendicular lines.
Since corresponding angles are congruent, m || n.

11.
In a triangle, the measures of the three angles add to 180 degrees.
If one angle is a right angle, then that angle measures 90 degrees. The other two angle measures plus 90 degrees add to 180 degrees, so the other two angle measures add to 90 degrees. In a right triangle there is a right angle and two other angles that are complementary.

Now look at your problem.
One angle is a right angle.
The other two angles are complementary, so their measures add to 90 deg.

8x + 2 + 9x + 3 = 90

17x + 5 = 90

17x = 85

x = 5

is the choice vertical angle theorem correct?

Answers

Unfortunately it is incorrect. You should instead go for the Alternate Exterior Angle Theorem

Angle 2 and angle 7 are on opposite or alternate sides of the transversal cut. They are also exterior because they are on the outside of the train tracks (think of line a and line b as the metal rail of the train tracks). If a || b, then the alternate exterior angles are congruent, which applies to angle 2 and angle 7. Also it applies to angle 1 and angle 8.

Multiply or divide as indicated 10x^5/2x^2

Answers

To perform the following operation, make sure to do the division parts separately and place them back together in the final answer.

10/2 and x^5/x^2

5 and using the exponential laws of division X ^m/X^n = X ^ m-n

The second part evaluates to X^3.

Putting the terms together we get the final answer, which is 5x^3.

Final answer:

The expression [tex]10x^5/2x^2[/tex] simplifies to [tex]5x^3[/tex] by dividing the coefficients (10/2) to get 5 and subtracting the exponents (5 - 2) in [tex]x^5[/tex] and[tex]x^2[/tex]to get 3.

Explanation:

To solve the given expression, [tex]10x^5/2x^2[/tex], you would first divide the coefficients and then deal with the bases (x) separately.

The coefficients (numbers without variables), 10 and 2, divide to give you: 10/2 = 5.

For the part that includes x, [tex]x^5/x^2[/tex], you subtract the lower exponent from the higher exponent because when you divide powers with the same base you subtract the exponents. So 5 - 2 = 3.

Thus, the final answer is: [tex]5x^3[/tex].

Learn more about Mathematics here:

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A train travels 128 km in 2 hours and 30 minutes. What is its average speed in km/min?

Answers

1 hour = 60 minutes

2 hours = 120 minutes +30 = 150 minutes total

128 / 150 = 0.853 km/min

1/4 (4r - 8) = r - 2

Answers

Solve for r.

Use distributive property.

4/4r - 8/4 = r - 2

4/4 can be written as 1 and -8/4 can be written as -2.

r - 2 = r - 2

You have an infinite amount of solutions.

Hope this helps!

The current diameter of a tree trunk is 10 inches. the trunk diameter increases at a rate of 2 inches per year. an insect burrows into the trunk and lays its eggs in the secondary xylem, 1 inch out from the center of the tree. how far from the center will the dormant eggs be located in two years?

Answers

The answer is 1 because tree trunks grow wider because of cell divisions that occur only in the vascular and cork cambia (both located underneath the bark). Secondary xylem (wood) remains in place once it is formed. Therefore, the eggs will remain in their current position (1 inch out from the center).

the answer would be "1".

Which set of integers is a pythagorean triple?
a. 2, 3, 6
b. 3, 4, 5
c. 4, 5, 9
d. 5, 7, 12?

Answers

H^2 = P^2 + B^2

a. 6^2 = 2^2 + 3^2
36 = 4 + 9
36 = 13
Therefore this is not a Pythagorean triple

b.5^2 = 4^2 + 3^2
25 = 16 + 9
25 = 25
Therefore this is a phythagorean triple

A scale model of a merry-go-round and the actual merry-go-round are similar.
a. How many times greater is the base area of the actual merry-go-round than the base area of the scale model? Explain. The ratio of the corresponding lengths is : 1. So, the ratio of the areas is : 1 and the base area of the actual merry-go-round is times greater than the base area of the scale model.
b. What is the base area of the actual merry-go-round in square feet? The base area of the actual merry-go-round is square feet.

Answers

Final answer:

The base area of the actual merry-go-round is the same as the model due to the 1:1 scale. Without further information, the actual base area of the merry-go round cannot be calculated.

Explanation:

To understand this, we need to know a key principle of scale models. In a scale model, when the ratio of the lengths is 1:n, the ratio of the areas is square of that, or 1:n2. Hence, if the scale of models is 1:1 as given, the base area of the actual merry-go-round is equal to the base area of the scale model, meaning the ratio is also 1:1.

For part b, without the specific measurements of the base area of the scale model or the scale used, it is impossible to calculate the base area of the actual merry-go-round in square feet. We need one or the other to make this calculation.

Learn more about Scale Models here:

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Final answer:

The base area of the actual merry-go-round is 16 times greater than the base area of the scale model. The base area of the actual merry-go-round in square feet can be calculated using the base area of the scale model.

Explanation:

The base area of the actual merry-go-round is 16 times greater than the base area of the scale model. This is because the ratio of the corresponding lengths is 1:4, so the ratio of the areas is 1:16.

To find the base area of the actual merry-go-round in square feet, you will need to know the base area of the scale model in square feet. If you provide the base area of the scale model, I can help you calculate the base area of the actual merry-go-round.

Learn more about scale models here:

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Solve for x.

x+8-3=19

Answers

x + 8 - 3 = 19

x + 5 = 19

x + 5 (-5) = 19 (-5)

x = 14

hope this helps

x is 14.

Do the problem backwards.

19 - 8 + 3 = x

11 + 4 = x

14 = x

Hank's pickup can travel 42 miles on 3 gallons of gas. How many gallons will Hank's pickup need to travel 28 miles?

Answers

2 gallons of gas

hope it helps

brainliest pls

Answer:

The person is right it's 2 gallons of gas to travel 28 miles

Step-by-step explanation:

Solve each system by substitution {4p+2q=8 and q=2p+1} {x+6y=2 and 5x+4y=36}

Answers

4p +2q = 8
Q=2p+1

4p +2(2p + 1)=8
4p + 4p + 2=8
8p = 6
P=3/4

Substituting p=3/4 into the first equation
4(3/4) +2q =8
3+2q =8
2q=5
Q=5/2

The transitive property of equality states that:

if a = b, then b = a
if a = b, then ac = bc
if a = b and b = c, then a = c
if a = b and c = c, then a + b = b + c

Answers

the transitive property of equality states that if a = b, then b = c, then a = c.

hope that helps, God bless!

Answer: The correct option is

(C) if a = b and b = c, then a = c.

Step-by-step explanation: We are given to select the correct statement for the transitive property of equality.

We know that

if x, y and z are three real numbers, then the transitive property of equality states that

if x = y and y = z, then x = z.

So, for reals a, b and c, the property states that

if a = b and b = c, then a = c.

Option (C) is CORRECT.

Evaluate the expression for x = –3

Answers

Kinda confused of the question

Solve for y, give the slope and y intercept 5y=20, -y + 3=15x, y +1/3x=17

Answers

[tex]5y=20[/tex] Equation

[tex]y=4[/tex] Divide by 5 on both sides

[tex]5(4)=20[/tex] Plug in for y

[tex]20=20[/tex] Simplify

y=4
slope= 0
y-intercept= 4

[tex]^{-}y+3=15x[/tex] Equation

[tex]^{-}y=15x-3 [/tex] Subtract 3 from both sides

[tex]y=-15x+3[/tex] Divide both sides by -1

[tex]- (^{-}15x+3) +3=15x[/tex] Plug in for y

[tex]15x-3+3=15x[/tex] Distribute -1 into the parenthesis

[tex]15x=15x[/tex] Further simplified

y= -15x+3
slope= -15
y-intercept= 3

[tex]y+ \frac{1}{3}x=17 [/tex] Equation

[tex]y=^{-}\frac{1}{3}x+17 [/tex] Subtract 1/3x from both sides

[tex](^{-}\frac{1}{3}x+17 )+\frac{1}{3}x =17[/tex] plug in for y

[tex]17=17 [/tex] Simplify

y= -1/3x+17
slope= -1/3
intercept= 17

Help I can’t answer this math question!!!

Answers

I hope this will help you
The probability is 6 out of 16

if kyra cuts a 12" string into 3/4 strips for her art project , how many strips will she have
A) 9
B) 12
C) 15
D) 16

Answers

The answer is D) 16, I divided

Answer:

Kyra will have 16 strips of 3/4".

Step-by-step explanation:

This is a case of a division where we have to divide the 12" string in pieces of 3/4", this is:

[tex]NumberStrips=12/\frac{3}{4} =16[/tex]

Kyra will have 16 strips of 3/4".

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