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3 years ago

Which property of equality is represented? 2(x + 3y) = 2(x + 3y)

Mathematics

1 answer:

shepuryov [24]3 years ago

6 0

Answer:

Identical Property

Step-by-step explanation:

2.x + 2.3y2. = 2.x + 2.3y2.

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Find the midpoint of the line segment joining the points P1 and P2.

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Formula for midpoint between two points is M(x,y)

x=(x1+x2)/2 and y=(y1+y2)/2

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x=(m+0)/2=m/2 and y=(b+0)/2=b/2 M(m/2,b/2)

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3 years ago

If one rectangular solid with dimensions of 6 x 6 x10 millimeters is stacked on top of an identical rectangular solid so that th

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3 years ago

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Walter walked 15.5 block from his house to work. It took him 35 minutes. What is his rate in blocks per hour

Sonbull [250]

For this case we first calculate the rate in blocks per minutes.
rate = (15.5) / (35) = 0.443 blocks per minutes.
Then, we can go to blocks per hour.
Remember: 1h = 60min.
rate = 0.443 * (1/60) = 0.00738 blocks per hour.
answer
his rate in blocks per hour is 0.00738 blocks per hour.

6 0

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:

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