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3 years ago

What is the volume of a cube with a side length that measures 112 ft?

Mathematics

2 answers:

anzhelika [568]3 years ago

4 0

Answer:

1,404,928 is the volume

Aleonysh [2.5K]3 years ago

3 0

Answer:

1,404,928 is the volume of a cube with a side length that measures 112 ft

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Please help problem 3 and 4 show work find the value of x, y and z

ratelena [41]

Answer:

Step-by-step explanation:

The altitude to the hypotenuse of a right triangle create two smaller triangles, all of which are similar to the original. This means corresponding sides are proportional.

3. Using the above relationship, ...

short-side/hypotenuse = 8/y = y/(8+23)

y^2 = 8·31

y = 2√62

long-side/hypotenuse = z/(8+23) = 23/z

z^2 = 23·31

z = √713

short-side/long-side = 8/x = x/23

x^2 = 8·23

x = 2√46

_____

4. The picture is fuzzy, but we think the lengths are 25 and 5. If they're something else, use the appropriate numbers. Using the same relations we used for problem 3,

y = √(5·25) = 5√5 . . . . . . . = √(short segment × hypotenuse)

z = √(20·25) = 10√5 . . . . . = √(long segment × hypotenuse)

x = √(5·20) = 10 . . . . . . . . . = √(short segment × long segment)

3 0

3 years ago

A^2 + b^2 + c^2 = 2(a − b − c) − 3. (1) Calculate the value of 2a − 3b + 4c.

Verdich [7]

Answer:

$2a - 3b + 4c = 1$

Step-by-step explanation:

Given

$a^2 + b^2 + c^2 = 2(a - b - c) - 3$

Required

Determine $2a - 3b + 4c$

$a^2 + b^2 + c^2 = 2(a - b - c) - 3$

Open bracket

$a^2 + b^2 + c^2 = 2a - 2b - 2c - 3$

Equate the equation to 0

$a^2 + b^2 + c^2 - 2a + 2b + 2c + 3 = 0$

Express 3 as 1 + 1 + 1

$a^2 + b^2 + c^2 - 2a + 2b + 2c + 1 + 1 + 1 = 0$

Collect like terms

$a^2 - 2a + 1 + b^2 + 2b + 1 + c^2 + 2c + 1 = 0$

Group each terms

$(a^2 - 2a + 1) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0$

Factorize (starting with the first bracket)

$(a^2 - a -a + 1) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0$

$(a(a - 1) -1(a - 1)) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0$

$((a - 1) (a - 1)) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0$

$((a - 1)^2) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0$

$((a - 1)^2) + (b^2 + b+b + 1) + (c^2 + 2c + 1) = 0$

$((a - 1)^2) + (b(b + 1)+1(b + 1)) + (c^2 + 2c + 1) = 0$

$((a - 1)^2) + ((b + 1)(b + 1)) + (c^2 + 2c + 1) = 0$

$((a - 1)^2) + ((b + 1)^2) + (c^2 + 2c + 1) = 0$

$((a - 1)^2) + ((b + 1)^2) + (c^2 + c+c + 1) = 0$

$((a - 1)^2) + ((b + 1)^2) + (c(c + 1)+1(c + 1)) = 0$

$((a - 1)^2) + ((b + 1)^2) + ((c + 1)(c + 1)) = 0$

$((a - 1)^2) + ((b + 1)^2) + ((c + 1)^2) = 0$

Express 0 as 0 + 0 + 0

$(a - 1)^2 + (b + 1)^2 + (c + 1)^2 = 0 + 0+ 0$

By comparison

$(a - 1)^2 = 0$

$(b + 1)^2 = 0$

$(c + 1)^2 = 0$

Solving for $(a - 1)^2 = 0$

Take square root of both sides

$a - 1 = 0$

Add 1 to both sides

$a - 1 + 1 = 0 + 1$

$a = 1$

Solving for $(b + 1)^2 = 0$

Take square root of both sides

$b + 1 = 0$

Subtract 1 from both sides

$b + 1 - 1 = 0 - 1$

$b = -1$

Solving for $(c + 1)^2 = 0$

Take square root of both sides

$c + 1 = 0$

Subtract 1 from both sides

$c + 1 - 1 = 0 - 1$

$c = -1$

Substitute the values of a, b and c in $2a - 3b + 4c$

$2a - 3b + 4c = 2(1) - 3(-1) + 4(-1)$

$2a - 3b + 4c = 2 +3 -4$

$2a - 3b + 4c = 1$

7 0

4 years ago

Solve the equation -4 + 4a = 12 for a.

WARRIOR [948]

Hello there! The answer to your question is a = 4.

To solve for a in the equation -4 + 4a = 12 you want to isolate, or separate, a from all of the equation's other values.

Our first step is to add 4 to both sides so the 4 cancels out on the left side.

-4+4 + 4a = 12+4

4a = 16

Next, we divide both sides by 4 to finish isolating a.

4/4a = 16/4

a = 4

Want to verify that this is correct? Place the value we found for a (4) into the equation in place of a and if it comes out as a true statement, the answer is correct.

-4 + 4(4) = 12

-4 + 16 = 12

12 = 12

Since 12 is in fact equal to 12, i can guarantee you that i have provided you with the correct answer. I hope this helps & have a great rest of your day! :)

6 0

3 years ago

Read 2 more answers

Someone help please and please make sure it’s right :)

Anuta_ua [19.1K]

Answer:

Step-by-step explanation:

5x + 5 = 4x + 16 ( being alternate angles)

5x - 4x = 16 - 5

x = 11

Hope it will help :)

6 0