How many of the small cubes with the edge length of 1/4 centimeter does it take to make a prism with the width of 1 3/4 cm, length of 1 1/4 cm and height of 3/4 cm?

Answer:   The square side lengths are  1 cm, 5 cm, and 11 cm.

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Explanation:

Refer to the diagram below.

Define the following areas

It doesn't really matter how you set up the labels, or what letters you pick, as long as you stay consistent.

We're told that "The areas of the overlapping zones are 2 cm², 5 cm², and 8 cm²", so let's make

Furthermore, we are told that "The total area of ​​the non-overlapping area of ​​the squares is 117 cm²" which means A+B+C = 117

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Refer to the diagram. For now, focus on the upper right square. It has regions A, E, and F. The area of this square is A+E+F

Similarly, the area of the left-most square is D+B+E

The area of the bottom-most square is C+F+D

Add up the expressions we found and we get

(A+E+F)+(D+B+E)+(C+F+D) = A+B+C+2D+2E+2F

This represents the sum of all three square areas even if we peeled the squares apart to not overlap.

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Let's plug in A+B+C = 117

We get

A+B+C+2D+2E+2F

117+2D+2E+2F

Now plug in D = 2, E = 5, and F = 8

117+2(2)+2(5)+2(8)

117+4+10+16

117+30

147

The sum of the three square areas is 147 square cm.

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Now we have to do a bit of trial and error. We're looking for ways to break up 147 such that it is a sum of three squares.

In other words, we want to find integers m,n,p such that m^2+n^2+p^2 = 147

Let's try subtracting off 121

147-121 = 26

I picked 121 since it's the largest perfect square just smaller than 147

Repeat this process, but do so for 25 since 25 is smaller than 26

26-25 = 1

We can see that

1 + 25 + 121 = 147

1^2 + 5^2 + 11^2 = 147

One solution is m = 1, n = 5, p = 11. There may be other solutions. Keep in mind that m,n,p are positive whole numbers.

So we got a bit lucky with our trial and error process. If we didn't find such a triple, we'd have to try other possible combos of squares until we get the right match.

Because 1^2 + 5^2 + 11^2 = 147, this means the squares' side lengths are 1, 5, and 11.

Answer: -18

Step-by-step explanation:

Answer:

Here’s the answer

Step-by-step explanation:

Answer:

i am pretty sure it is D

Step-by-step explanation:

Answer:

Its C.) 11x^5 - 6x^2 - 9x + 12

Step-by-step explanation:

ejenuwitee

=D

=P

Answer:

12. 20 ft

13. 4.5

Step-by-step explanation:

12. (29x29)-(21x21)=400

sq root 400= 20

13. (2x2)+(4x4)= 20

sq root 20= 4.5

Answer:

A. $2.89(m)=$40

B. 13 songs

Step-by-step explanation:

$2.89(m)=$40

m=$40/$2.89

m=13.84

She can download a maximum of 13 songs

Check:

$2.89 (13 songs)=$37.57

$40-$37.57=$2.43 left on her gift card

m=13.84, check that 0.84 of the cost of a song is left over 0.84*$2.89=$2.43

Answer:

13 songs

Step-by-step explanation:

40 divided by 2.89 is 13.84. DO NOT ROUND TO 14

So its a maximum of 13 songs, otherwise it will cost 40.46 for 14 songs

Answer:

b

Step-by-step explanation:

Answer:B

Step-by-step explanation:

Answer:

34

Step-by-step explanation:

Answer:

34 just subtract

Step-by-step explanation:

Answer:

[tex] slope (m) = -5 [/tex]

Step-by-step explanation:

The slope can be calculated using two points, (2, 60) and (4, 50) as shown below:

[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} [/tex], where,

[tex] (2, 60) = (x_1, y_1) [/tex]

[tex] (4, 50) = (x_2, y_2) [/tex]

Plug in the values into the equation

[tex] slope (m) = \frac{50 - 60}{4 - 2} [/tex]

[tex] slope (m) = \frac{-10}{2} [/tex]

[tex] slope (m) = -5 [/tex]

Answer:

x=6

Step-by-step explanation:

Answer:

x=-11

Step-by-step explanation:

3+3x=6=-24

3x+9=-24

3x=-33

x=-11

Answer:

x = -11

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define Equation

3 + 3(x + 2) = -24

Step 2: Solve for x

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Here we see that -24 does indeed equal -24.

∴ x = -11 is the solution to the equation.

Answer:

The measure of <FDE is 18°

Answer:

2^2 = 4

Step-by-step explanation:

2*2 = 4

Answer:

36:56

Step-by-step explanation:

Answer: C 34:55

Step-by-step explanation:

start with 6:8 that’s the first one multiply by 9 on each side you get 54:72 so that’s the same and then 6:8 divide by 2 and you get 3:4 but for 36:56 you’d have to multiply by 6 and that would give you 36:48 not 36:56

Answer: Steve's bedroom has the greater area.

Step-by-step explanation: The formula for area is Area = Length x Width.

So all you have to do to figure this out is multiply the Width of the rooms by the length.

So Steve's room is 12ft X 13ft = 156ft

Ricardo's room is 8ft X 14ft = 112ft

156ft > 112ft

Steve's room has a greater area.

Answer:

-3/5

Step-by-step explanation:

So first, you have to find out the two points :

(-1,-1), and (4,-4)

Next, you have to put into this formula:

y1-y2/x1-x2

The y values in our points are -4 and -1, and our x values are 4 and -1. Lets now substitute:

-4-(-1)/4-(-1)

Now simplify: -4+1/4+1, and solve and you will get -3/5 as the slope

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Hope you do well on your assignment!

Answer:

1/4 yards squared

Step-by-step explanation:

Area of a rectangle equals length times width.

1/3 x 3/4 = 3/12, or 1/4

Answer:

It would be 1/4 and if not try 3/12

Step-by-step explanation:

I hope this helped

Answer:

say what

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

Answer:

x=1.2

Step-by-step explanation:

You're given

x + y + z = 165

7x = n

n = y - 9

n = 9 + z

and you want to find xyz.

Solve the last three equations for x, y, and z :

7x = n   →   x = n/7

n = y - 9   →   y = n + 9

n = 9 + z   →   z = n - 9

Substitute x, y, and z into the first equation and solve for n :

n/7 + (n + 9) + (n - 9) = 165

n/7 + 2n = 165

n + 14n = 1155

15n = 1155

n = 77

Now solve for x, y, and z :

x = 77/7 = 11

y = 77 + 9 = 86

z = 77 - 9 = 68

Then the product is

xyz = 11 • 86 • 68 = 64,328

The product of the three numbers is 8,192,040. The sum of three numbers x, y, z is 165: x + y + z = 165

The problem states:

1. When the smallest number x is multiplied by 7, the result is n: 7x = n

2. The value n is obtained by subtracting 9 from the largest number y: n = y - 9

3. The value n is also obtained by adding 9 to the third number z: n = z + 9

Now, let's proceed to find the values of x, y, z, and n:

From equation (2), we can express x in terms of n:

x = n/7

Now, substitute the value of x in equation (1):

(n/7) + y + z = 165

From equation (3), we can express y in terms of n:

y = n + 9

Now, substitute the value of y in the equation above:

(n/7) + (n + 9) + z = 165

From equation (4), we can express z in terms of n:

z = n - 9

Now, substitute the value of z in the equation above:

(n/7) + (n + 9) + (n - 9) = 165

Combine the terms with n:

3n/7 = 165

To isolate n, multiply both sides by 7/3:

n = 165 * (7/3)

n = 385

Now, we have the value of n, which is 385. To find the values of x, y, and z, substitute n back into the respective equations:

x = n/7 = 385/7

≈ 55

y = n + 9 = 385 + 9

= 394

z = n - 9 = 385 - 9

= 376

Now, we have the values of x, y, z, and n:

x = 55,

y = 394,

z = 376,

n = 385

To find the product of the three numbers, simply multiply them:

Product = x * y * z

= 55 * 394 * 376

≈ 8,192,040

So, the product of the three numbers is 8,192,040.

To know more about three numbers:

https://brainly.com/question/30269736

#SPJ2

Answer:

45 Tulips

Step-by-step explanation:

63/7=9

Tulips: Roses=5:2

Tulips=9x5=45

Roses=9x2=18

Answer:

24$

Step-by-step explanation:

15%=0.15

160*0.15=24

Answer:

10,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

Answer:

36/90%=40

Step-by-step explanation:

40 points in total

Answer: 25

Step-by-step explanation: When you divide exponents with the same base, you can subtract the exponents. It becomes 5^4-2, which is 5^2, which is 25

Answer:

is it 4 3/5 it might be

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

Answer: Each shelf is 2ft

Step-by-step explanation:

16 = (2 x 4) + 4s

16 = 8 + 4s

8 = 4s (subtract 8 from both sides)

8/4 = 4s/4 (divide both sides by 4)

2 = s

Answer:

Yes

Step-by-step explanation:

Answer:

divide 15 into 82 to get 5 is the first step

Step-by-step explanation:

Answer:

The answer is A, ¨Divide 15 into 82 to get 5.¨

Step-by-step explanation:

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