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3 years ago

be rectangular prism and rectangular pyramid have the same volume. determine the value of x, the height of the pyramid.

Mathematics

1 answer:

Marina CMI [18]3 years ago

7 0

ANSWER

$x= 9 \: in$

EXPLANATION

The volume of a rectangular prism is given by the formula,

$V = l \times b \times h$
We substitute the dimensions to obtain,

$V = 6 \times 3 \times 12 \: {in}^{3}$

The volume of the rectangular pyramid is,

$V = \frac{1}{3} \times 6 \times 12 \times x \: {in}^{3}$

Equating the two volumes gives,

$\frac{1}{3} \times 6 \times 12 \times x = 6 \times 3 \times 12$

We divide through by 6×12 to get,

$\frac{x}{3}=3$

We solve for x to obtain,

$x = 3 \times 3$

$x = 9 \: in$

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How do i solve x squared = 4x -5

ICE Princess25 [194]

Answer:

x = 2 ±i

Step-by-step explanation:

x^2 = 4x-5

Subtract 4x from each side

x^2 - 4x = 4x-5 -4x

x^2 - 4x= -5

Complete the square

Take the coefficient of the x term, divide by 2 and square it

-4/2 =2 2^2 =4

Add 4 to each side

x^2 -4x+4 = -5 +4

The left side is (x-coefficient of the x term/2)^2

(x-2)^2 = -1

Take the square root of each side

sqrt((x-2)^2) = sqrt(-1)

x-2 = ±i

Add 2 to each side

x-2+2 = 2 ±i

x = 2 ±i

6 0

3 years ago

Triangle EFG is dilated by a scale factor of 3 centered at (0, 1) to create triangle E'F'G'. Which statement is true about the d

jolli1 [7]

Answer:

Segment EH and segment E prime H prime both pass through the center of dilation (A)

The complete question related to this found on brainly (ID:16812154) is stated below:

Triangle EFG is dilated by a scale factor of 3 centered at (0, 1) to create triangle E'F'G'. Which statement is true about the dilation?

E(0,5) F(1,1) G(-2,1) H(0,1)

a) segment EH and segment E prime H prime both pass through the center of dilation.

b)The slope of segment EF is the same as the slope of segment E prime H prime.

c) segment E prime G prime will overlap segment EG. segment

d) EH ≅ segment E prime H prime.

Step-by-step explanation:

∆EFG = Original image

∆EFG is dilated to give ∆E'F'G'

∆E'F'G' = New image

Scale factor = 3

Center of dilation = (0,1) = H(0,1)

Coordinates ∆EFG : E(0,5) F(1,1) G(-2,1)

To determine the statement that is true about the dilation from the options,

First we would make a diagram on the coordinates of ∆EFG and center of dilation (H).

Find attached the diagram.

Length GF = 3unit

Length G'F' = 3×scale factor = 9unit

Length EH = 4unit

Length E'H' = 4×scale factor = 12unit

Then we would move 3units to the left on same line from G to get the coordinate of G'(mark the point).

Also move 3units to the right on same line from F to get the coordinate of F'(mark the point).

Both of these give length of G'F' = 9unit

Now move 8units to the top from E to get the coordinate of E'(mark the point).

From this you get length E'H' = 12unit

Draw lines connecting the three points to get ∆E'F'G'

See diagram for better understanding

From the diagram, EH and E'H' both pass through (0,1). The other options are wrong.

Therefore, Segment EH and segment E prime H prime both pass through the center of dilation (A)

5 0

3 years ago

Select the correct answer. Fredrick manages a band and sings lead vocals. The band charges $700 per concert. Fredrick receives $

Kisachek [45]

Answer:

A. $105

Step-by-step explanation:

Given

total charge= $700 per concert

solution

If Fredrick receives $175 of that money, the balance will be

$700-$175= $525

The balance will be shared by the 5 members

Hence each of them will take

525/5=$105

7 0

3 years ago

List five rational numbers between -4/5 and -2/3 . Please tell by step by step explaintion

attashe74 [19]

9514 1404 393

Answer:

-0.67, -0.68, -0.69, -0.70, -0.71

Step-by-step explanation:

There are an infinite number of ways to do this.

Perhaps the simplest is to do it in decimal.

-4/5 = -0.8

-2/3 = -0.666... (repeating 6)

Any negative decimal number between these values will do. For example, ...

-0.67, -0.68, -0.69, -0.70, -0.71

If you want to choose fractions that are evenly spaced between the given values, you can find their difference, then divide that difference into 6 parts (1 more than the number of numbers you need).

-2/3 -(-4/5) = 4/5 -2/3 = (12 -10)/(5·3) = 2/15 . . . . length of interval

1/6 of this difference is ...

(1/6)(2/15) = 2/90 = 1/45

The interval end point nearest 0 is ...

-2/3 = -30/45

so the 5 intermediate values will be that value with -1/45 repeatedly added:

-31/45, -32/45, -33/45 = -11/15, -34/45, -35/45 = -7/9

_____

Additional comment

The fractions we came up with could be referred to as "5 arithmetic means between -2/3 and -4/5." There is nothing in the problem statement suggesting the values need to be evenly spaced.

When doing this in decimal, you can obtain a new value simply by adding more digits to the decimal fraction:

-0.68, -0.685, -0.6853, -0.68531, -0.799

7 0

2 years ago

8/10x 1 3/5 =? would be what?

Aleonysh [2.5K]

8/10 x 1 3/5 = ?
first u need to find the mixed fraction is 8/5: 1 3/5 = 8/5
8/10 x 8/5 = 64/50
64/50 in simplest form: 32/25
32/25 equals to 1 7/25
so the answer is 1 and 7/25

6 0

3 years ago