Angle A and B are supplementary. Angle A has a measure of 5x+10. Angle B has a measure of 70. What is the value of x?

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

Which of the following statements are never true? Select all that apply. Three points are coplanar Two planes meet in exactly on

statuscvo [17]

Answer: Two planes meet in exactly one point

Two lines meet at exactly two points

Step-by-step explanation:

From the given statements there are two statements which are never true :-

1) Two planes meet in exactly one point .

Since when two line meets , they either meet at one point or infinite points (coincidence) , thus its impossible that they will meet at exactly two points.

2) Two lines meet at exactly two points

Since when two planes meet , the intersection of two plane always make a line not a point. Thus its impossible.

7 0

2 years ago

Help plz I need help

makkiz [27]

B. The answer would be B because inscribed means inside the circle. All the points in the angle touch the side of the circle.

Hope I could help!!!!!
Good luck!!!!

8 0

2 years ago

Please answer 1-5 i give brainlesit

Klio2033 [76]

1. 5 and E, 6 and F, 7 and D, 8 and A, 9 and G

5 0

2 years ago

Read 2 more answers

I need some help on this thanks!!! -

Alexxandr [17]

Answer:

The 4th option, 10g + 24 = t

Step-by-step explanation:

It costs 24 dollars per month no matter what.

$10 * the amount of GB you want

Add those two values to get the total cost per month.

In this case you want 5 GB, so substitute the g in the equation for 5. You will get:

10 * 5 +24 = t

50 + 24 = t

74 = t

So it costs 74 dollars per month to get 5 GB.

3 0

2 years ago