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Ann [662]
3 years ago
10

Small squares with sides 4 cm were cut from each of the corners of a square piece of cardboard. Then it was folded into an open-

top box. Find the original dimensions of the square piece of cardboard if the volume of this box is 144 cm3.
Mathematics
1 answer:
melomori [17]3 years ago
3 0
Let the length and width of the square board be x  cm, when 4 cm are cut of from the corner, the dimensions of the box will be:'
length=(x-8) cm
width=(x-8) cm
height=x cm
thus the volume will be:
4(x-8)(x-8)=144 
4(x^2-16x+64)=144
this can be written into:
x^2-16x^2+64=36
solving the above gives us:
x=2 or x=14
when x=2, the dimensions will be negative. Thus we take x=14 cm, the original dimensions are 14 cm by 14 cm


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antoniya [11.8K]
The answer should be A.
7 0
3 years ago
If f(x)=x^3-12x^2+35x-24f(x)=x 3 −12x 2 +35x−24 and f(8)=0f(8)=0, then find all of the zeros of f(x)f(x) algebraically.
Neporo4naja [7]

Answer:

The zeros of f(x) are: (x - 1), (x - 3) and (x - 8)

<em></em>

Step-by-step explanation:

Given

f(x)=x^3-12x^2+35x-24

f(8) = 0

Required

Find all zeros of the f(x)

If f(8) = 0 then:

x = 8

And x - 8 is a factor

Divide f(x) by x - 8

\frac{f(x)}{x - 8} = \frac{x^3-12x^2+35x-24}{x - 8}

Expand the numerator

\frac{f(x)}{x - 8} = \frac{x^3 - 4x^2 -8x^2 + 3x + 32x - 24}{x - 8}

Rewrite as:

\frac{f(x)}{x - 8} = \frac{x^3 - 4x^2 + 3x - 8x^2 +32x - 24}{x - 8}

Factorize

\frac{f(x)}{x - 8} = \frac{(x^2 - 4x + 3)(x - 8)}{x - 8}

Expand

\frac{f(x)}{x - 8} = \frac{(x^2 -x - 3x + 3)(x - 8)}{x - 8}

Factorize

\frac{f(x)}{x - 8} = \frac{(x - 1)(x - 3)(x - 8)}{x - 8}

\frac{f(x)}{x - 8} = (x - 1)(x - 3)

Multiply both sides by x - 8

f(x) = (x - 1)(x - 3)(x - 8)

<em>Hence, the zeros of f(x) are: (x - 1), (x - 3) and (x - 8)</em>

7 0
3 years ago
The price of a coat was reduced from $40 to $30. By what percentage was the price of the coat reduced?
Liula [17]

Answer:

The percentage that the coat was reduced is 25%.

Step-by-step explanation:

A percentage is always out of a factor of 100.

40 x 2.5 = 100

30 x 2.5 = 75

75/100 = 3/4

1/4 is missing, which is the percentage.

1/4 = 0.25, or 25%

Hope This Helps!

4 0
3 years ago
Read 2 more answers
Help meeeeeeee please :(.
vodomira [7]

Answer:

x^{3} -5x^{2} -6x +8 \frac{-2}{x + 3}

Step-by-step explanation:

            x^{3} -5x^{2} -6x +8 \frac{-2}{x + 3}

x + 3 / x^{4} - 2x^{3}-21x^{2} -10x +22

         -(x^{4} + 3x^{3})

                 -5x^{3} -21x^{2} -10x +22

                 -(-5x^{3} -15x^{2})

                              -6x^{2} -10x +22

                            -(-6x^{2} -18x)

                                            8x +22

                                          -(8x + 24)

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4 0
3 years ago
Which model shows the correct factorization of x2 – x – 2?
Murljashka [212]

Answer: The correct factors are

(x-1) and (x+2)

Step-by-step explanation:

Step one :

To factorize the equation

x²– x – 2=0

First we look for numbers that when multiplied will result to the constant term and when added will result to the second term (1x, - 2x)

Step two :

We replace the second term with these factors we have

x²–(x-2x)–2=0

x²–x+2x–2=0

Factoring the expression we have

x(x–1)+2(x–1)=0

Hence the factors will be

(x-1) and (x+2)

8 0
3 years ago
Read 2 more answers
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