What are the solutions to the equation 3(X -4)(X +5) =0

A box has a volume of 192 cubic inches, a length that is twice as long as its width, and a height that is 2 inches greater than

ruslelena [56]

Answer:

Therefore the dimension of the cuboid is 8 inches×4 inches ×6 inches.

Step-by-step explanation:

Cuboid : A cuboid is a three dimension shape. The length ,breadth and height of a cuboid are not same.

A cuboid has 6 faces.
A cuboid contains 8 vertices.
A cuboid contains 12 edges .
The total surface area of a cuboid is

= 2(length×breadth+breadth×height+length×height) square units

The dimension of a cuboid is written as length×breadth×height.

The volume is( length×breadth×height) cubic units

Given that the volume of the box is 192 cubic inches.

Let x inches be the width of the cuboid.

Since the length is twice as long as its width.

Then length = 2x inches

Again height is 2 inches longer than width.

Then height = (x+2) inches.

Therefore the volume of the cuboid is

$=[x\times 2x\times (x+2)]$ cubic inches

$=[2x^2(x+2)]$ cubic inches

$=(2x^3+4x^2)$ cubic inches

According to the problem,

$2x^3+4x^2=192$

$\Rightarrow 2x^3+4x^2-192=0$

$\Rightarrow 2(x^3+2x^2-96)=0$

$\Rightarrow (x^3+2x^2-96)=0$

$\Rightarrow x^3-4x^2+6x^2-24x+24x-96=0$

$\Rightarrow x^2(x-4) +6x(x-4)+24(x-4)=0$

$\Rightarrow (x-4)(x^2+6x+24)=0$

Therefore x=4

Since the all zeros of x²+6x+24 =0 is negative.

Therefore breadth = 4 inches

length=(2×4) inches=8 inches

and height = (4+2)inches = 6 inches.

Therefore the dimension of the cuboid is 8 inches×4 inches ×6 inches.

8 0

2 years ago

245. 202, 254, 245, 276 Write the values from least to greatest Mean Median: Mode:

Burka [1]

Answer:

The values from least to greatest would be 202, 245, 245, 254, 276

The mean would be 244.4

The median would be 245

The mode would be 245

Step-by-step explanation:

To find the mean, you add all the numbers together and divide that sum by the number of numbers. In this case, you add all the numbers together and you get 1222. Next, you divide that by 5 because there are 5 numbers. To find the median, you order the numbers from least to greatest and find the middle number. For this question, the answer would be 245. Lastly, to find the mode you look for the number that appears the most. In this case it's 245.

7 0

3 years ago

Winnie wrote the following riddle.I am a number between 60 and 100.My ones digit is two less than my tens digit.I am a prime num

Kazeer [188]

Answer:

79

Step-by-step explanation:

60<xy<100

y -2 =x

if it is prime

y cannot be even

so y could be 1,3,5,7,9

x would then be 9,1,3,5,7

but to be between 60 and 100

x must be 7 or 9

so the number must be 79 or 57

57 is not prime so

the number is 79

5 0

2 years ago

How to isolate scalars from a matrix

I am Lyosha [343]

The technique of matrix isolation involves condensing the substance to be studied with a large excess of inert gas (usually argon or nitrogen) at low temperature to form a rigid solid (the matrix). The early development of matrix isolation spectroscopy was directed primarily to the study of unstable molecules and free radicals. The ability to stabilise reactive species by trapping them in a rigid cage, thus inhibiting intermolecular interaction, is an important feature of matrix isolation. The low temperatures (typically 4-20K) also prevent the occurrence of any process with an activation energy of more than a few kJ mol-1. Apart from the stabilisation of reactive species, matrix isolation affords a number of advantages over more conventional spectroscopic techniques. The isolation of monomelic solute molecules in an inert environment reduces intermolecular interactions, resulting in a sharpening of the solute absorption compared with other condensed phases. The effect is, of course, particularly dramatic for substances that engage in hydrogen bonding. Although the technique was developed to inhibit intermolecular interactions, it has also proved of great value in studying these interactions in molecular complexes formed in matrices at higher concentrations than those required for true isolation.

3 0

2 years ago

If f (x) = x2 – 2x, find: f(6) = [?]

Alexxx [7]

Answer:

f(6) = 24

Step-by-step explanation:

f(x) = x^2 - 2x

Let x = 6

f(6) = 6^2 - 2(6)

= 36 - 12

= 24

6 0

1 year ago