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3 years ago

What is the factored form of 30x + 24

Mathematics

1 answer:

Cloud [144]3 years ago

3 0

Answer:

6(5x+4)

Step-by-step explanation:The first step is, you multiply 6x5=30 then, pair it with the x which is 30x next, multiply 6x4=24 but u keep the 24 u dont have to pair a variable with it. Finally, put it all together and it equals 30x+24.

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The width of a container is 5 feet less than its height. Its length is 1 foot longer than its height. The volume of the containe

juin [17]

The height of container is 8 feet

Solution:

Let "w" be the width of container

Let "l" be the length of container

Let "h" be the height of container

The width of a container is 5 feet less than its height

Therefore,

width = height - 5

w = h - 5 ------ eqn 1

Its length is 1 foot longer than its height

length = 1 + height

l = 1 + h ---------- eqn 2

The volume of container is given as:

$v = length \times width \times height$

Given that volume of the container is 216 cubic feet

$216 = l \times w \times h$

Substitute eqn 1 and eqn 2 in above formula

$216 = (1 + h) \times (h-5) \times h\\\\216 = (h+h^2)(h-5)\\\\216 = h^2-5h+h^3-5h^2\\\\216 = h^3-4h^2-5h\\\\h^3-4h^2-5h-216 = 0$

Solve by factoring

$(h-8)(h^2+4h+27) = 0$

Use the zero factor principle

If ab = 0 then a = 0 or b = 0 ( or both a = 0 and b = 0)

Therefore,

$h - 8 = 0\\\\h = 8$

Also,

$h^2+4h+27 = 0$

Solve by quadratic equation formula

$\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

$\mathrm{For\:} a=1,\:b=4,\:c=27:\quad h=\frac{-4\pm \sqrt{4^2-4\cdot \:1\cdot \:27}}{2\cdot \:1}$

$h = \frac{-4+\sqrt{4^2-4\cdot \:1\cdot \:27}}{2}=\frac{-4+\sqrt{92}i}{2}$

Therefore, on solving we get,

$h=-2+\sqrt{23}i,\:h=-2-\sqrt{23}i$

Thus solutions of "h" are:

h = 8

$h=-2+\sqrt{23}i,\:h=-2-\sqrt{23}i$

"h" cannot be a imaginary value

Thus the solution is h = 8

Thus the height of container is 8 feet

8 0

3 years ago

What percent of 33 is 34

Viktor [21]

11.22 is 33% of 34 if that is what youre asking

3 0

3 years ago

Read 2 more answers

y = x2 - 6x - 8 Complete the square in the quadratic equation in order to write the equation in vertex form.

Airida [17]

Answer:

y = (x-3)^2 - 17

Step-by-step explanation:

To complete the square, take the middle term bx and divide it in two. Then take the square.

x^2 - 6x - 8 has bx = -6x. Take -6/2 = -3. Square -3^2 = 9.

Now to finish completing the square add 9 and subtract 9 from one side.

y = x^2 - 6x - 8

y = (x^2 - 6x +9) -9 - 8

y = (x-3)^2 - 17

8 0

3 years ago

What is the probability of getting heads, tails, and heads, in that order, when flipping a coin? Are these events dependent or i

leonid [27]

The possiblities that exist:

H, H, H
H, H, T
H, T, H <----
H, T, T
T, H, H
T, H, T
T, T, H
T, T, T

The answer is 1/8. Now the problem that you gave us isn't dependent upon anything, so more specifically the answer is 1/8 independent.

Nothing has actually happened therefore no odds have been decreased or increased.

6 0

3 years ago

How do I solve 4/9+9/2 and write my answer as a mixed number?

jenyasd209 [6]

9 has factors of 3*3.

2 is prime, so no factors.

from those two denominators, we can get the LCD of hmmm simply their product, namely 18.

$\bf \cfrac{4}{9}+\cfrac{9}{2}\implies \stackrel{\textit{using the LCD of 18}}{\cfrac{(2)4+(9)9}{18}}\implies \cfrac{8+81}{18}\implies \cfrac{89}{18}\implies 4\frac{17}{18}$

now, recall that, to get the mixed fraction, we divide 89 ÷ 18, the quotient goes up front, the "4", and the remainder is the one atop, the "17".

8 0

3 years ago