Consider the three triangular pyramids.

Pyramid 1
Pyramid 2
Pyramid 3

Triangular pyramid 1. The base has a base of 12 meters and height of 2 meters. The height of the pyramid is 10 meters.

Triangular pyramid 2. The base has a base of 6 meters and height of 4 meters. The height of the pyramid is 10 meters.

Triangular pyramid 3. The base has a base of 12 meters and height of 4 meters. The height of the pyramid is 5 meters.

Which statement about their volumes is true? (Recall the formula V = one-third B h.)

O All three pyramids have the same volume.
O All three pyramids have different volumes.
O Only pyramids 1 and 2 have the same volume.
O Only pyramids 1 and 3 have the same volume.

Answers

Answer 1

9514 1404 393

Answer:

  (a) All three pyramids have the same volume

Step-by-step explanation:

The triangular base has an area of ...

  B = 1/2bh . . . . where b is the base of the triangle and h is its height.

The volume of the pyramid is ...

  V = 1/3BH . . . . where B is the area of the base, and H is the height of the pyramid.

Combining these equations gives ...

   V = 1/3(1/2bh)H = 1/6bhH

__

Pyramid 1 volume

  V1 = 1/6(12 m)(2 m)(10 m) = 40 m³

Pyramid 2 volume

  V2 = 1/6(6 m)(4 m)(10 m) = 40 m³

Pyramid 3 volume

  V3 = 1/6(12 m)(4 m)(5 m) = 40 m³

All three pyramids have the same volume.


Related Questions

I will give brainliest if correct!!! Please show work so I know how to do it. :)
12. Let logb(3) = 0.5646, logb(4) = 0.7124, and logb(5) = 0.8271. Using these values, evaluate logb(5/3).
A. 0.1518
B. 1.4649
C. 1.2138
D. 0.2625
E. 0.5341
F. 2.6252

Answers

Answer:

.2625

Step-by-step explanation:

logb(3) = 0.5646, logb(4) = 0.7124, and logb(5) = 0.8271

logb(5/3)

We know that logx ( y/z) = logx (y) - logz (z)

logb ( 5) - logb(3)

0.8271 - 0.5646

.2625

Answer:

F. 2.6252

Step-by-step explanation:

0.8271 - 0.5646

Can someone please help me

Answers

Answer: B. 4 × 10⁻⁵

Step-by-step explanation:

0.00003762 = 3.762 × 10⁻⁵ ≈ 4 × 10⁻⁵

Answer:

b

Step-by-step explanation:

[tex]4 \times {10}^{ - 5} = 4 \times \frac{1}{100000} [/tex]

find two consecutive whole number such that five times the greater number makes 59 hint let the number be x and x + 1​

Answers

Answer:

Step-by-step explanation:

Let the smaller number = x

Let the larger number = x + 1

5*(x + 1) = 59

You can do this. The problem says that when the larger number is multiplied by 5, you get 59. You are also told that the numbers are whole numbers. 59 divided by 5 leaves a remainder which is not a whole number.

15 points f (x) = 1/x+5 -1. Find the inverse of (x) and its domain.

Answers

Answer:

D

Step-by-step explanation:

[tex]f(x)=\frac{1}{x+5} -1\\let~f(x)=y\\y=\frac{1}{x+5} -1\\flip~x~and~y\\x=\frac{1}{y+5} -1\\x+1=\frac{1}{y+5} \\y+5=\frac{1}{x+1} \\y=\frac{1}{x+1} -5\\f^{-1}(x)=\frac{1}{x+1} -5\\x+1\neq 0\\x\neq -1[/tex]

Find the area to the left of z = 0.25.
A. 0.6012 B. 0.5987 C. 0.4013 D.0.3988

Answers

Answer:

.5987

Step-by-step explanation:

Use a ztable and find .25 (pic below)

40 points Please help!!!
What is the volume of this regular prism?
48.55 cubic inches
55.8 cubic inches
9.7 cubic inches
24.28 cubic inches

Answers

Answer:

V = 24.28 in ^3

Step-by-step explanation:

The area of the base is

A =5/2 × s × a  where s is the side length and a is the apothem

A = 5/2 ( 2.13) * .87

A = 4.63275

The volume is

V = Bh  where B is the area of the base and h is the height

V = 4.63275 ( 5.24)

V =24.27561 in^3

Rounding to the  hundredth

V = 24.28 in ^3

The square root of 0.25 is 0.5 which is a greater number. Give another number whose square root is larger than the number and explain why.

Answers

Answer:

Another example of a number who's square root is greater than the number is  [tex]\sqrt{0.49}[/tex] which is 0.7

Step-by-step explanation:

This square root is larger than the number because it is a decimal. When you multiply a decimal by a decimal, the decimal point becomes greater. For example: 0.7 multiplied by 0.7 equals 0.49 which has 2 decimal places, while 0.7 only has one.

Can someone help me with this math homework please!

Answers

1. a= 19

2.2 ( second option)

3.C

4D

A chair which was produced at a cost of Rs 450 was sold at a profit of 22%. What was the profit?​

Answers

Answer:

RS 99

Step-by-step explanation:

%p = p/cp ×100

22 = p/450 × 100

22 = 100p/450

cross multiply

22 × 450 =100p

9900 = 100p

100p =9900

p = 9900/100

p = 99

9 is subtracted from 5 times 3 and 10 is added

Answers

Answer:

-16

Step-by-step explanation:

9 - 5 x 3 + 10
9 - 15 + 10
9 - 25
-16
9-5 times 3= -6 +10=4

George has opened a new store and he is monitoring its success closely. He has found that this store’s revenue each month can be modeled by r(x)=x2+6x+10 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars. He has also found that his expenses each month can be modeled by c(x)=x2−4x+5 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars. What does (r−c)(4) mean about George's new store?

Answers

Answer:

(r - c)(4), is the profit made in George's new store after 4 months which is $4,500

Step-by-step explanation:

The given parameters for George's store are;

The amount of revenue George makes each month, r(x) = x² + 6·x + 10

The expenses each month, c(x) = x² - 4·x + 5

Where;

x = The number of months the store has opened the doors

r(x) and c(x) are measured in hundreds of dollars

The amount of profit from the store, P = Revenue - Expenses

Therefore, the profit made on a given month, x, is P(x), which is found as follows;

P(x) = r(x) - c(x) = (r - c)(x)

Therefore, (r - c)(4) = P(4), is the profit realized from George's new store, after 4 months

(r - c)(4) = 4² + 6·4 + 10 - (4² - 4·4 + 5) = 45

Answer:

The new store will have a profit of $4500 after its fourth month in business.

Step-by-step explanation:

I took the quiz

1,4,9 find the fifth pattern​

Answers

Answer:

1, 4, 9, 16, 25

Step-by-step explanation:

The pattern increases by an odd number. It can be seen that;

for the first pattern

1²=1

for the second pattern

2²=4

for the third pattern

3²=9

for the forth pattern

4²=16

for the fifth pattern

5²=25

Please I need help someone answer asap

Answers

Answer:

C -2,-1

Step-by-step explanation:

I pulled up a graph of a circle. -2, -1 is outside the circle

Find the discernment and the numbers of the number of real roots for this equation.
x^2+3x+8=0

Answers

Answer:  2 distinct complex solutions (ie non real solutions).

Work Shown:

The given equation is in the form ax^2+bx+c = 0, so

a = 1, b = 3, c = 8

Plug those into the formula below to find the discriminant

D = b^2 - 4ac

D = 3^2 - 4(1)(8)

D = -23

The discriminant is negative, so we get two nonreal solutions. The two solutions are complex numbers in the form a+bi, where a & b are real numbers and [tex]i = \sqrt{-1}[/tex]. The two solutions are different from one another.

Answer:

Discriminant: -23

Number of real roots: 0

Step-by-step explanation:

For a quadratic in standard form [tex]ax^2+bx+c[/tex], the discriminant is given by [tex]b^2-4ac[/tex].

In [tex]x^2+3x+8[/tex], assign:

[tex]a\implies 1[/tex] [tex]b\implies 3[/tex] [tex]c\implies 8[/tex]  

The discriminant is therefore:

[tex]3^2-4(1)(8)=9-32=\boxed{-23}[/tex]

For any quadratic:

If the discriminant is greater than 0, the quadratic has two real rootsIf the discriminant is equal to 0, the quadratic has one real rootIf the discriminant is less than 0, the quadratic as no real roots

Since the quadratic in the question has a discriminant less than 0, there are no real solutions to this quadratic.

Jessica ate 7 /10 of her orange before lunch and 1/10 of her orange after lunch. How much of her orange did she eat?

Answers

Answer:

8/10

Step-by-step explanation:

which of the following equations have complex roots?

Answers

9514 1404 393

Answer:

  B.  3x² +2 = 0

Step-by-step explanation:

The equation of A has a couple of real roots. We're pretty sure there are complex numbers that will satisfy this equation, but we don't know how to find them. (We suspect a typo, and that the equation is supposed to be 2x² +1 = 7x, which has only real roots.)

__

The equation of B can be rewritten as ...

  x² = -2/3

This will have complex roots.

__

The discriminants of both equations C and D are positive, so those have only real roots.

  2x² -5x -1   ⇒   d = (-5)² -4(2)(-1) = 33

  3x² -6x -1   ⇒   d = (-6)² -4(3)(-1) = 48

Please help me Find PA.

Answers

PO is 5 by using Pythagorean theorems and it forming a 3,4,5 triangle so PA is PO + OA so it is 8

Given g (n) = 3n + 2, f (n) = 2n^2 + 5
Find g (f (2))

a)8
b)41
c)133
d)21

Answers

Answer:

g(f(2)) = 41

b)41

Step-by-step explanation:

g(f(2)) = 41

f(2)= 2(2²) + 5 = 13

So g(f(2)) → g(n = 13)

g(n = 13)→ 3(13) + 2 = 41

Given: -1/2 x > 6.

Choose the solution set.

A. {x | x R, x > -12}
B. {x | x R, x > -3}
C. {x | x R, x < -3}
D. {x | x R, x < -12}

Answers

SoLuTiOn彡

Given: -1/2 x > 6

Solving It:-

-1/2 x > 6

x > -6×2

x > -12

So The Correct Solution Set Will Be

A. {x | x R, x > -12}

Hope This Helps You

If
f(x) = x2 + 2x - 4
and
g(x) = 3x + 1
Find
f(g(x)) = [? ]x2 + [ ]+х

Answers

Answer:

f(g(x)) = 9x^2 +12x -1

Step-by-step explanation:

f(g(x)) means you replace the x in f(x) with g(x), which is 3x + 1:

(3x+1)^2 + 2(3x+1) - 4

then expand and simplify:

(3x+1)(3x+1) + 6x+2 - 4

9x^2+6x+1 + 6x+2 - 4

and then collect all like terms:

9x^2

6x + 6x = 12x

1 + 2 - 4 = -1

Need help with this!!! 8 points!!!

Answers

Answer:

The answers is 369 and 577... good luck. ♥️♥️♥️

which of the following are exterior angles?

Answers

Answer:

A, B, E

Step-by-step explanation:

Exterior angles are angles that are outside the shape. In this case, angle 4, 3 and 2 are exterior angles.

Complete this equations,( show your work).

* I re-wrote some of the questions below them so u can read ' em better. ty​

Answers

Answer:

21 is: [tex]\frac{4}{9}[/tex] x + [tex]\frac{31}{72}[/tex]

22 is: 4 [tex]\frac{39}{44}[/tex]

23 is:[tex]\frac{1}{4}[/tex] x + [tex]\frac{31}{72}[/tex]

24 is:  [tex]\frac{-2}{11}[/tex] x + [tex]\frac{7}{11}[/tex]

Step-by-step explanation: Hope this helps and good luck mark brainliest if u want :)

Find the line’s slope and a point on the line
Y-4=-3/4(x+5)

Answers

Answer:

The slope is -3/4 and a point on the line is (-5,4)

Step-by-step explanation:

This equation is in point slope form

y -y1 = m(x-x1)

where m is the slope and (x1,y1) is a point on the line

Y-4=-3/4(x+5)

Y-4=-3/4(x -  -5)

The slope is -3/4 and a point on the line is (-5,4)

help please like PLEASE ASAP

Answers

Answer:

1/5^5

Step-by-step explanation:

Flip the equation into a fraction.

:>

I think the answer is 1/5^5

WILL GIVE BRAINLIEST, HELP QUICK!!

Answers

The answer is A

It is A because it is 4 units squares away so it has to be A.

Hope this helps :))))

Answer:

the answer is 5 units

Step-by-step explanation:

You can look at the location of B and C and see that the line goes from 2 to -2 which is 5 units apart. -2, -1, 0, 1, 2

What is the simplest version of 9/16×4/18​

Answers

Answer:

1/8

Step-by-step explanation:

9/16 * 4/18

Rewriting

9/18 * 4/16

9/18 = 1/2   and 4/16 = 1/4

1/2 * 1/4

1/8

Answer:

[tex]\frac{1}{8}[/tex]

Step-by-step explanation:

[tex]\frac{9}{16}[/tex] x [tex]\frac{4}{18}[/tex] = [tex]\frac{(9)(4)}{(16)(18)}[/tex]

[tex]\frac{(9)}{(18)}[/tex] = [tex]\frac{1}{2}[/tex]

[tex]\frac{4}{16}[/tex] = [tex]\frac{1}{4}[/tex]

[tex]\frac{(1)(1)}{(2)(4)}[/tex] = [tex]\frac{1}{8}[/tex]

Find the equation of the line passing through the point (-3.6, 2.1) and parallel
to the line 4.9x + 5.4y = 3

Answers

Answer:

y = -4.9/5.4x - 1.17

Step-by-step explanation:

First let's convert the equation to standard form of y = mx + b.

4.9x + 5.4y = 3

Subtract 4.9x from both sides.

5.4y = -4.9x + 3

Divide each term by 5.4.

y = -4.9/5.4x + 0.56

If two lines are parallel to each other, they have the same slope slopes.

The first line is y = -4.9/5.4x + 0.56. Its slope is -4.9/5.4. A line parallel/perpendicular to this one will also have a slope of -4.9/5.4.

Plug this value (-4.9/5.4) into your standard point-slope equation of y = mx + b.

y = -4.9/5.4x + b

To find b, we want to plug in a value that we know is on this line: in this case, it is (-3.6, 2.1). Plug in the x and y values into the x and y of the standard equation.

2.1 = -4.9/5.4(-3.6) + b

To find b, multiply the slope and the input of x (-3.6)

2.1 = 3.27 + b

Now, subtract 3.27 from both sides to isolate b.

-1.17 = b

Plug this into your standard equation.

y = -4.9/5.4x - 1.17

This equation is parallel/perpendicular to your given equation (y = -4.9/5.4x + 0.56) and contains point (-3.6, 2.1)

Hope this helps!

y=x+5 y=-2x-4 I need help with this problem will you help me?

Answers

Answer:

x = - 3, y = 2

Step-by-step explanation:

Given the 2 equations

y = x + 5 → (1)

y = - 2x - 4 → (2)

Substitute y = x + 5 into (2)

x + 5 = - 2x - 4 ( add 2x to both sides )

3x + 5 = - 4 ( subtract 5 from both sides )

3x = - 9 ( divide both sides by 3 )

x = - 3

Substitute x = - 3 into either of the 2 equations and evaluate for y

Substituting into (1)

y = - 3 + 5 = 2

Find the value of x.

A. 99
B. 9
C. 90
D. 11
ILL GIVE BRAINLIEST

Answers

Answer:

B) 9

Step-by-step explanation:

Because there's a square between the 2 angles, that means these angles are complementary (angles that add up to 90°). So:

5x - 9 + 6x = 90

11x - 9 = 90

11x = 90 + 9

11x = 99

x = 9

Answer:

B.9

Step-by-step explanation:

The way to solve this is by noticing that these angles are complementary(they add up to 90 degrees). So you add the equations together and equal them to 90. 5x-9+6x=90.Then you solve to find that x=9.

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