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11111nata11111 [884]

3 years ago

4

A bank sends its customers an e-mail when their accounts fall below -$10. Which inequality models this situation? A) a<-10 B)

a>-10 C) a≥-10 D) a≤-10

2 answers:

Vedmedyk [2.9K]3 years ago

5 0

Hello! Below is under the amount, not equal to. Therefore, C and D are eliminated. B represents a greater than symbol, so that one is out. A shows a less than symbol and is the inequality we are looking for. The answer is A.

Svetach [21]3 years ago

3 0

Answer:

<−10

Step-by-step explanation:

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Factor j²-13j+42 <br><br> The Factored Expression =

Ymorist [56]

Answer:

(j - 7)(j - 6)

Step-by-step explanation:

${j}^{2} - 13j + 42 \\ = {j}^{2} - 7j - 6j + 42 \\ = j(j - 7) - 6(j - 7) \\ = (j - 7)(j - 6) \\ are \: required \: factors$

8 0

3 years ago

Read 2 more answers

trasher [3.6K]

X squared +14=9x
Square both sides and you get
X+14=3x subtract 14 from both sides
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X=3x-14 subtract 3x

-2x=-14 divide negative 2
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7 0

3 years ago

Help, i keep failing this quiz.

Ray Of Light [21]

Answer:

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Step-by-step explanation:

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7 0

3 years ago

Giving 100 points.

Nitella [24]

Answer:

1. <u>Cost per customer</u>: 10 + x

<u>Average number of customers</u>: 16 - 2x

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

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

Step-by-step explanation:

<u>Given information</u>:

$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

<u>Part 1</u>

<u></u>

<u>Cost per customer</u>: 10 + x

<u>Average number of customers</u>: 16 - 2x

<u>Part 2</u>

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

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

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

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

<u>Part 3</u>

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.

<u>Test the roots</u> 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 <u>solution</u> to the inequality is <u>between the roots</u>:

-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 <em>increase </em>in cost. It does not confirm that if the cost is reduced (less than $10) the number of customers <em>increases </em>per hour.]

<u>Cost per customer</u>:

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

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

Therefore, the possible buffet prices Noah could charge are:

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

8 0

2 years ago

Write the expression in interval notation

Ludmilka [50]

If we have a less than (or less than or equal to) sign with an absolute value, that indicates a conjunction where values can be expressed as an interval. The absolute value will be less than the number to the right, but it will also at the same time be greater than the negative of the number to the right. Don't forget that absolute value is a distance measurement, and the distance from the origin to -4 is 4 units, just like the distance from the origin to +4 is 4 units. Our particular absolute value will look like this: $\left[\begin{array}{ccc}x-6\end{array}\right] \leq 4$ and $\left[\begin{array}{ccc}x-6\end{array}\right] \geq -4$ . Solving the first absolute value we have that $x \leq 10$ and the second one is $x \geq 2$ . In interval notation we need to put x between the 2 inequality signs, which will look like this: $2 \leq x \leq 10$ . And there you go!

3 0

3 years ago