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3 years ago

Mr. Nice's backyard has an area of 225 square feet. What is the length of one side of his backyard?

Mathematics

1 answer:

Fittoniya [83]3 years ago

7 0

Answer:

C. 15 feet

Step-by-step explanation:

Area formula

A = l²

225 = l²

l = √225

l = √15²

l = 15 feet

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in an election about 500,000 people voted in all what could be the exact number of people who voted in the election

salantis [7]

It can be any number from 450000 to 549999. This is due to the fact that when figures like this are reported they are either rounded up or down.

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3 years ago

29. Consider the diagram below. Solve for x

Flauer [41]

Answer:

x = 76

Step-by-step explanation:

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3 years ago

How many times larger is 3×108 than 3×102?

Vinvika [58]

Answer: 120

Step-by-step explanation:

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3 years ago

why does the multiplication property of equality not allow us to divide both sides of an equation by zero

AlladinOne [14]

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3 years ago

Giving 100 points.

Nitella [24]

Answer:

1. Cost per customer: 10 + x

Average number of customers: 16 - 2x

$\textsf{2.} \quad -2x^2-4x+160\geq 130$

3. $10, $11, $12 and $13

Step-by-step explanation:

Given information:

$10 = cost of buffet per customer
16 customers choose the buffet per hour
Every $1 increase in the cost of the buffet = loss of 2 customers per hour
$130 = minimum revenue needed per hour

Let x = the number of $1 increases in the cost of the buffet

Part 1

Cost per customer: 10 + x

Average number of customers: 16 - 2x

Part 2

The cost per customer multiplied by the number of customers needs to be at least $130. Therefore, we can use the expressions found in part 1 to write the inequality:

$(10 + x)(16 - 2x)\geq 130$

$\implies 160-20x+16x-2x^2\geq 130$

$\implies -2x^2-4x+160\geq 130$

Part 3

To determine the possible buffet prices that Noah could charge and still maintain the restaurant owner's revenue requirements, solve the inequality:

$\implies -2x^2-4x+160\geq 130$

$\implies -2x^2-4x+30\geq 0$

$\implies -2(x^2+2x-15)\geq 0$

$\implies x^2+2x-15\leq 0$

$\implies (x-3)(x+5)\leq 0$

Find the roots by equating to zero:

$\implies (x-3)(x+5)=0$

$x-3=0 \implies x=3$

$x+5=0 \implies x=-5$

Therefore, the roots are x = 3 and x = -5.

Test the roots by choosing a value between the roots and substituting it into the original inequality:

$\textsf{At }x=2: \quad -2(2)^2-4(2)+160=144$

As 144 ≥ 130, the solution to the inequality is between the roots:

-5 ≤ x ≤ 3

To find the range of possible buffet prices Noah could charge and still maintain a minimum revenue of $130, substitute x = 0 and x = 3 into the expression for "cost per customer.

[Please note that we cannot use the negative values of the possible values of x since the question only tells us information about the change in average customers per hour considering an increase in cost. It does not confirm that if the cost is reduced (less than $10) the number of customers increases per hour.]

Cost per customer:

$x =0 \implies 10 + 0=\$10$

$x=3 \implies 10+3=\$13$

Therefore, the possible buffet prices Noah could charge are:

$10, $11, $12 and $13.

8 0

1 year ago