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3 years ago

The total surface area of a cube is 96cm2, find its volume.

Mathematics

1 answer:

Setler [38]3 years ago

6 0

Answer:

$\huge\boxed{V=64cm^3}$

Step-by-step explanation:

The formula of a surface area of a cube:

$SA=6a^2$

The formula of a volume of a cube:

$V=a^3$

We have

$SA=96cm^2$

Calculate the edge length (<em>a</em>).

$6a^2=96$ <em>divide both sides by 6</em>

$a^2=16\to a=\sqrt{16}\\\\a=4(cm)$

Calculate the volume of a cube:

$V=4^3=64(cm^3)$

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Point-lope form for the line that pae through the point (1, –1) and ha a lope of 4

max2010maxim [7]

Answer is
Point-slope form: y + 1 = 4(x -1)
Assuming you wanted
Slope-intercept form: y = 4x -5

Step by step

y - - 1 = 4(x -1)

y + 1 = 4(x -1)

y + 1 = 4x -4

y = 4x -5

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1 year ago

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3 years ago

Write a quadratic equation given the roots -1/3 and 5, show your work

Travka [436]

$\boxed{(x - a)(x - b) = 0}$

The equation above is the intercept form. Both a-term and b-term are the roots of equation.

$x = - \frac{1}{3} \\ x = 5$

These are the roots of equation. Therefore we substitute a = - 1/3 and b = 5 in the equation.

$(x + \frac{1}{3} )(x - 5) = 0$

Here we can convert the expression x+1/3 to this.

$x + \frac{1}{3} = 0 \\ 3x + 1 = 0$

Rewrite the equation.

$(3x + 1)(x - 5) = 0$

Simplify by multiplying both expressions.

$3 {x}^{2} - 15x + x - 5 = 0 \\ 3 {x}^{2} - 14x - 5 = 0$

<u>Answer</u><u> </u><u>Check</u>

Substitute the given roots in the equation.

$3 {(5)}^{2} - 14(5) - 5 = 0 \\ 75 - 70 - 5 = 0 \\ 75 - 75 = 0 \\ 0 = 0$

$3( - \frac{1}{3} )^{2} - 14( - \frac{1}{3}) - 5 = 0 \\ 3( \frac{1}{9} ) + \frac{14}{3} - 5 = 0 \\ \frac{1}{3} + \frac{14}{3} - \frac{15}{3} = 0 \\ \frac{15}{3} - \frac{15}{3} = 0 \\ 0 = 0$

The equation is true for both roots.

<u>Answer</u>

$\large \boxed {3 {x}^{2} - 14x - 5 = 0}$

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2 years ago

There are twenty cards labeled from 1 to 20 in a bag. A card is randomly selected from the bag.

AveGali [126]

If you are asking for the probability of getting a certain card you have a 1/ 20th chance

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3 years ago

The graph shown below expresses a radical function that can be written in the form f(x)= a(x + k)^1/n +C. What does the graph te

MAXImum [283]

Answer:

C. <em>c</em> is less than zero

Step-by-step explanation:

The parent radical function y=x^(1/n) has its point of inflection at the origin. The graph shows that point of inflection has been translated left and down.

<h3>Function transformation</h3>

The transformation of the parent function y=x^(1/n) into the function ...

f(x) = a(x +k)^(1/n) +c

represents the following transformations:

vertical scaling by a factor of 'a'
left shift by k units
up shift by c units

<h3>Application</h3>

The location of the inflection point at (-3, -4) indicates it has been shifted left 3 units, and down 4 units. In the transformed function equation, this means ...

k = 3
c = -4

The graph says the value of c is less than zero.

<em>Additional comment</em>

Apparently, the value of 'a' is 2, and the value of n is 3. The equation of the graph seems to be ...

f(x) = 2(x +3)^(1/3) -4

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2 years ago