All categories

2 years ago

Find the dimensions of the box described.

Mathematics

1 answer:

Rina8888 [55]2 years ago

5 0

The dimensions of the box are 6 inches, 12 inches and 10 inches

Step-by-step explanation:

There is a box, with dimensions length, width and height

The length is twice as long as the width
The height is 4 inches greater than the width
The volume is 720 cubic inches

We need to find its dimensions

Assume that the width of the box is x

∵ The width of the box is x

∵ The length is twice as long as the width

- Twice means times 2

∴ The length of the box = 2(x) = 2x

∵ The height is 4 inches greater than the width

- 4 inches greater means add 4

∴ The height of the box = x + 4

∵ The volume of the box = length × width × height

∵ length = 2x , width = x , height = x + 4

∴ The volume of the box = (2x) × (x) × (x + 4)

∵ (2x) × (x) = 2x²

∵ 2x²(x + 4) = (2x²)(x) + (2x²)(4) = 2x³ + 8x²

∴ The volume of the box = 2x³ + 8x²

∵ The volume of the box is 720 inches³

∴ 2x³ + 8x = 720

- Subtract 720 from both sides

∴ 2x³ + 8x² - 720 = 0

- Use your calculator to solve the equation and find the value of x

∴ x = 6

∴ The width of the box = 6 inches

∴ The length of the box = 2(6) = 12 inches

∴ The height of the box = 6 + 4 = 10 inches

The dimensions of the box are 6 inches, 12 inches and 10 inches

Learn more:

You can learn more about volume in brainly.com/question/12497249

#LearnwithBrainly

You might be interested in

Please help me someone !!

adelina 88 [10]

Answer:

$6^{\frac{-1}{3}}$

Step-by-step explanation:

put them both in exponential form and then since they are both base 6, you can add the exponents.

$6^{\frac{1}{6}} *6^{\frac{-3}{6} }$

4 0

2 years ago

What is the sum of 20x^2-10x-30

ivann1987 [24]

Answer:

The sum of the roots is 0.5

Step-by-step explanation:

<u><em>The correct question is</em></u>

What is the sum of the roots of 20x^2-10x-30

we know that

In a quadratic equation of the form

$ax^{2} +bx+c=0$

The sum of the roots is equal to

$-\frac{b} {a}$

in this problem we have

$20x^{2} -10x-30=0$

$a=20\\b=-10\\c=-30$

substitute

$-\frac{(-10)} {20}=0.5$

<u><em>Verify</em></u>

Find the roots of the quadratic equation

The formula to solve a quadratic equation is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

$a=20\\b=-10\\c=-30$

substitute

$x=\frac{-(-10)\pm\sqrt{-10^{2}-4(20)(-30)}} {2(20)}$

$x=\frac{10\pm\sqrt{2,500}} {40}$

$x=\frac{10\pm50} {40}$

$x=\frac{10+50} {40}=1.5$

$x=\frac{10-50} {40}=-1$

The roots are x=-1 and x=1.5

The sum of the roots are

$-1+1.5=0.5$ ----> is ok

5 0

2 years ago

What solution is 2x+6=6+2x?

Reptile [31]

Answer:

Step-by-step explanation:

2x + 6 = 6 + 2x

4 + 6 = 6 + 4

10 = 10

8 0

1 year ago

Find thetwo consecutive integers whose product is 24

malfutka [58]

Answer:

There is no solution to this equation that is an integer for x.

Step-by-step explanation:

x is the first integer, and x+1 the second

$x(x+1) = 24\\x^{2} + x - 24 =0\\$

$x = \frac{-1+\sqrt{1^{2}+4*24}}{2} =\frac{-1+\sqrt{97}}{2}\\x = \frac{-1-\sqrt{1^{2}+4*24}}{2} =\frac{-1-\sqrt{97}}{2}$

5 0

2 years ago

The rabbit population, y, in hundreds of rabbits, in an area x years since 1990 can be determined using this function: y = -0.1x

IrinaVladis [17]

Y=-0.1x^2+50

This is a quadratic with a negative acceleration of -0.2, a velocity of -0.2x, and an initial value of 50.

The rabbit population is decreasing rapidly, perhaps due to the area in which they live being developed or by the introduction of a predator population...

5 0

2 years ago