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Cerrena [4.2K]
2 years ago
12

Which statement below is always true?

Mathematics
2 answers:
Pepsi [2]2 years ago
4 0

The answer is <u><em>Choice B</em></u>

<u><em>Step-by-step explanation:</em></u>

Parallel lines never intersect

Lines that are skew don't have to intersect

Transversal lines intersect other lines

STatiana [176]2 years ago
3 0

Answer:

The answer is <u>B. Two parallel lines lie in the same plane.</u>

Step-by-step explanation:

  • <u>Parallel lines never cut (intersect) or meet each other, and they lie on the same plane. </u>
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What is the square root of 45600 in fraction​
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Answer:

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Step-by-step explanation:

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A company’s profit in dollars is modeled by the equation p(x) = –0.5x2 + 100x, where x represents the number of units sold.
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Answers:

a. The company needs to sell 100 units to reach the maxmum profit.

b. The company's maximum profit is $5,000.

Solution:

a. How many unit does the company need to sell to reach the maximum profit?

p(x)=-0.5x^2+100x

This is a quadratic equation, and its graph is a parabola vertical (because the veriable "x" is square). Comparing with the general form:

p(x)=ax^2+bx+c; a=-0.5, b=100, c=0

a=-0.5<0 (negative), then the parabola opens downward, and it has a maximimun value (maximum profit) at its vertex.

We can find the abscissa of the vertex (units that the company needs to sell to reach the maximum profit using the following formula:

x=-b/(2a)

Replacing b by 100 and a by -0.5 in the formula above:

x=-100/[2(-0.5)]

x=-100/(-1)

x=100

The company needs to sell 100 units to reach the maximum profit.


b. What's the company's maximum profit?  

To determine the maximum profit we substitute the value of "x" obrained in part "a" in the quadratic equation:

x=100→p(100)=-0.5(100)^2+100(100)

p(100)=-0.5(10,000)+10,000

p(100)=-5,000+10,000

p(100)=5,000

The company's maximum profit is $5,000.

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