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3 years ago

1. What must be multiplied to (x + 1) to obtain (x2 + 4x + 3)?

Mathematics

1 answer:

andriy [413]3 years ago

8 0

Answer:

$1. x + 3 \\ 2.125 {x}^{3} \\ 3.2\pi(x + 7) \\ 4.12x + 11 \\ 5.4{a}^{2} - 16 \\ 6.4 {x}^{2} + 32x - 12$

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If it snows on game day there is a 32% chance the Jets will win. If it does not snow on game day there is a 41% chance the jets

marysya [2.9K]

a) It is Win with snowfall OR Win without snowfall = 32% + 41% = 73% b) It is Snowfall on game day AND Win = 29% * 32% = 9.28% c) It is 32% * 29% / 73% = 12.71 %

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3 years ago

Find the perimeter of the polygon PQR shown in the graph

DaniilM [7]

Answer:

Step-by-step explanation:

After u calculate the measure of each side by using formula

$\sqrt{(xB - xA )^2 + (yB - yA)^2}$

U should calculate the sum of all sides of this polygon

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3 years ago

What is ordered pair?

lions [1.4K]

12y - 7x = 5......(1 , ?)....when x = 1....so we sub 1 in for x
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12y - 7 = 5
12y = 5 + 7
12y = 12
y = 12/12
y = 1........so ur y value is 1....and ur ordered pair is (1,1) <==

3 0

3 years ago

A student desk has an area of 15/16 square meters. The width of the desk is 5/4 meters. What is the length of the desk in meters

olga_2 [115]

For this case, the first thing we are going to do is model the desk as a rectangle.
The area of the rectangle is given by:
A = w * l
Where,
w: width
l: length
Clearing we have:
l = A / w
Substituting values:
l = (15/16) / (5/4)
Rewriting we have:
l = (15/16) * (4/5)
Simplifying we have:
l = (3/4) m
Answer:
The length of the desk in meters is:
l = (3/4) m

7 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:

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

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

Therefore, the possible buffet prices Noah could charge are:

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

8 0

2 years ago