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2 years ago

Solve the formula a(m+r) -t=s for a.

Mathematics

1 answer:

devlian [24]2 years ago

4 0

9514 1404 393

Answer:

a = (s +t)/(m +r)

Step-by-step explanation:

Add t, then divide by the coefficient of 'a'.

$a(m+r)-t=s \qquad\text{given}\\\\a(m+r)=s+t \qquad\text{add $t$}\\\\\boxed{a=\dfrac{s+t}{m+r}} \qquad\text{divide by $m+r$}$

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3 years ago

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Dennis_Churaev [7]

-7.5x = -5.61 - 0.39

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3 years ago

The probability of rolling an even number with a six-sided number cube

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Equally likely

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2 years ago

Read 2 more answers

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

WILL MARK YOU BRAINLIEST

anzhelika [568]

Answer:The area is 14306. 625 cm.

Step-by-step explanation:

To find the area of the circle, we will need to find the diameter and find the radius.

So we know the circumference is 423.9 m and we know to get the circumference, you will need to multiply pie by the diameter .

so now we need divide the circumference by pie to find the diameter.

423.9/ 3.14 = 135 so 135 is the diameter.

To find the radius we need to divide the diameter by 2.

135/2 = 67.5

Now is time to find the area which uses the formula A= nr^2

A = 3.14 * 67.5^2

A = 14306. 625

5 0

3 years ago

Solve the formula a(m+r) -t=s for a.​

Solve the formula a(m+r) -t=s for a.