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Vesna [10]
3 years ago
6

What is 10x² if value of x is 2?​

Mathematics
1 answer:
zvonat [6]3 years ago
8 0

Answer:

Step-by-step explanation:

20

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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

<em><u>Solution:</u></em>

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

<em><u>The volume of container is given as:</u></em>

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

<em><u>Thus solutions of "h" are:</u></em>

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
Multiple Choice
Zanzabum

A) Answer: A. 22.5 cm, 30 cm, and 37.5 cm


Setting the unity measurement as x, the three sides will be 3·x, 4·x, and 5·x. The sum of the three sides will be (3 + 4 + 5)·x = 12·x; this corresponds to the perimeter, therefore:

12·x = 90 cm


We can solve for x:

x = 90 / 12 = 7.5 cm


Hence, the sides will be:

7.5 · 3 = 22.5 cm

7.5 · 4 = 30 cm

7.5 · 5 = 37.5 cm


This situation is represented in option A (which is also the only option whose sides add up to 90).



B) Answer: C. never true


We have:

6 + 8x - 9 = 11x + 14 - 3x


Bring all the terms with x on the left, by subtracting from both sides 11x and -3x, and all the numbers on the right by subtrcting from both sides 6 and -9:

6 + 8x - 9 - 11x - (-3x) - 6 - (-9) = 11x + 14 - 3x - 11x - (-3x) - 6 - (-9)


Cancel out the opposite terms from each side:

8x - 11x + 3x = 14 - 6 + 9


Combine likely terms:

0x = 17


Now you should ask yourself: what number multiplied by zero gives 17 as a result? The answer is none because a number multiplied by zero always equals zero.


Hence, the statement is never true.


C) Answer: r \leq \frac{1}{5}


We have:

5r + 4 ≤ 5


Subtract 4 from both sides:

5r + 4 - 4 ≤ 5 - 4


Combine likely terms:

5r ≤ 1


Divide both sides by 5:

\frac{5r}{5} \leq \frac{1}{5}

r \leq \frac{1}{5}


To graph the set of solutions, you need to set:

y₁ = 5x + 4 and

y₂ = +5


Plot these two lines:

y₂ is a horizontal line at a height of 5;

y₁ is a line passing through (0, 4) and (1, 9)


The set of solutions will be the part of the graph in which y₁ lies underneath y₂ (see picture attached), that happens for x \leq \frac{1}{5}.





4 0
3 years ago
Read 2 more answers
What is the volume of a sphere that has a radius of 12 mm?
ycow [4]

Answer:

452.16

Step-by-step explanation:

πr^2 ... then substitute the numbers accordingly!

7 0
3 years ago
Please help! thanks yall &lt;3 NO LINKS
Bess [88]

Answer:

x = 20

Step-by-step explanation:

5 0
2 years ago
In a large population, 3% of the people are heroin users. A new drug test correctly identifies users 93% of the time and correct
kari74 [83]

Answer:

(a) The probability tree is shown below.

(b) The probability that a person who does not use heroin in this population tests positive is 0.10.

(c) The probability that a randomly chosen person from this population is a heroin user and tests positive is 0.0279.

(d) The probability that a randomly chosen person from this population tests positive is 0.1249.

(e) The probability that a person is heroin user given that he/she was tested positive is 0.2234.

Step-by-step explanation:

Denote the events as follows:

<em>X</em> = a person is a heroin user

<em>Y</em> = the test is correct.

Given:

P (X) = 0.03

P (Y|X) = 0.93

P (Y|X') = 0.99

(a)

The probability tree is shown below.

(b)

Compute the probability that a person who does not use heroin in this population tests positive as follows:

The event is denoted as (Y' | X').

Consider the tree diagram.

The value of P (Y' | X') is 0.10.

Thus, the probability that a person who does not use heroin in this population tests positive is 0.10.

(c)

Compute the probability that a randomly chosen person from this population is a heroin user and tests positive as follows:

P(X\cap Y)=P(Y|X)P(X)=0.93\times0.03=0.0279

Thus, the probability that a randomly chosen person from this population is a heroin user and tests positive is 0.0279.

(d)

Compute the probability that a randomly chosen person from this population tests positive as follows:

P (Positive) = P (Y|X)P(X) + P (Y'|X')P(X')

                  =(0.93\times0.03)+(0.10\times0.97)\\=0.1249

Thus, the probability that a randomly chosen person from this population tests positive is 0.1249.

(e)

Compute the probability that a person is heroin user given that he/she was tested positive as follows:

P(X|positive)=\frac{P(Y|X)P(X)}{P(positive)} =\frac{0.93\times0.03}{0.1249}= 0.2234

Thus, the probability that a person is heroin user given that he/she was tested positive is 0.2234.

6 0
3 years ago
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