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3 years ago

The dimensions of a box are x, 2x, and 3x. Each dimension is increased by 3. Calculate the volume of the box.

Mathematics

2 answers:

Tema [17]3 years ago

6 0

Answer:

The volume of the box would be 6x³+33x²+54x+27.

Step-by-step explanation:

The new dimensions of the box would be (x+3), (2x+3), and (3x+3). Since the volume of a rectangular prism are calculated by multiplying the length, width, and depth, we can just multiply all three of these dimensions together to come up with the answer.

Using foil on the first two terms originally you get (x+3)×(2x+3)= 2x²+3x+6x+9 which can be simplified to 2x²+9x+9.

Then you multiply this equation by (3x+3). (2x²+9x+9)×(3x+3)= 6x³+6x²+27x²+27x+27x+27 which can be simplified to 6x³+33x²+54x+27.

NISA [10]3 years ago

4 0

Answer:

6x³+33x²+54x+27

Step-by-step explanation:

dimensions are now:

x+3, 2x+3, 3x+3

Volume

V=lwh
V= (x+3)(2x+3)(3x+3)=
3(x+1)(x+3)(2x+3)=
3( x² + 4x+3)(2x+3)=
3(2x³+11x²+18x+9)=
6x³+33x²+54x+27

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Write an equation, and solve. Round your answer to the nearest cent.

VashaNatasha [74]

Answer:

The cost of 16 oz of granola should be $16.16

Step-by-step explanation:

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3 years ago

Convert 150 meters per second into miles per day

statuscvo [17]

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3 years ago

1. What are the solutions (coordinate points) to the system of equations?

Leto [7]

Question 1

The given system of equations is:

$y = {x}^{2} + 5x + 6 \\ y = 3x + 6$

Equate the two equations:

${x}^{2} + 5x + 6 = 3x + 6$

Rewrite in standard form:

${x}^{2} + 5x - 3x + 6 - 6 = 0$

${x}^{2} + 2x = 0$

$x(x + 2) = 0$

$x = 0 \: or \: x = - 2$

When we put x=0, in y=3x +6, we get:

$y = 3(0) + 6 = 6$

One solution is (0,6)

When we put x=-2, into y=3x+6, we get:

$y = 3( - 2) + 6 = 0$

Another solution is (-2,0)

The solutions are; (0,6) and (-2,0)

Question 2:

The function is

$f(x) = {x}^{6} - {x}^{4}$

Let us put x=-x,

$f( - x) = {( - x)}^{6} - {( - x)}^{4}$

This gives:

$f( - x) = {x}^{6} - {x}^{4}$

We can observe that:

$f(x) = f( - x)$

This is the property of an even function.

Question 3:

The given function is

$f(x) = {x}^{2} + 3x - 2$

The average rate of change of f(x) from x=a to x=b is given as:

$\frac{f(b) - f(a)}{b - a}$

This is the slope of the secant line connecting the two points on f(x)

From x=2 to x=6, the average rate of change

$= \frac{f(6) - f(2)}{6 - 2} \\ = \frac{ {6}^{2} + 3 \times 6 - 2 - {2}^{2} - 3 \times 2 + 2 }{4} \\ = \frac{36 + 18 - 4 - 6}{4} \\ = \frac{44}{4} \\ = 11$

The average rate of change is 11

3 0

3 years ago

F(x)=3x+2 and g(x)=-2x-4, find h(x)= f(x)-g(x)

Katena32 [7]

substitute for your equation;

h(x) = f(x) - g(x)

h(x) = (3x + 2) - (-2x -4)

h(x) = 3x + 2 + 2x + 4 (minus and minus = addition)

h(x) = 3x + 2x + 2 + 4 (combine like terms)

h(x) = 5x + 6

Hope that helps! :D

8 0

3 years ago

10+2b-4+5b <br> = ( )b+( ) help please!!!

bagirrra123 [75]

The solution is (7)b+(6)

Hope it helps!

3 0

3 years ago

Read 2 more answers