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3 years ago

Answer the Question below (45 points)

Mathematics

1 answer:

iren [92.7K]3 years ago

8 0

3x-5=-6x+13 : Given

3x=-6x+18 : Addition property of Equality

9x=18: Subtraction property of Equality

x=2: Division Property of Equality

Step-by-step explanation:

We need to give justification to each step

Step 1:

3x-5=-6x+13

This is the question given, which we need to solve and find value of x.

Justification: Given

Step 2:

Adding 5 on both sides of the equation using addition property of equality.

3x-5+5=-6x+13+5

Simplifying

3x=-6x+18

Justification: Addition property of Equality

Step 3:

Adding 6x on both sides of the equation

3x+6x=-6x+18+6x

9x=18

Justification: Subtraction property of Equality

Step 4:

Divide both sides of the equation by 9, to find the value of x using division property of equality

9x/9=18/9

x=2

Justification: Division Property of Equality

Keywords: Solving Equations

Learn more about Solving Equations at:

#learnwithBrainly

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A total of $12,000 is invested in two corporate bonds that pay 7.5% and 9% simple interest. The invest wants an annual interest

nlexa [21]

Answer:

$13,200

Step-by-step explanation:

You need to use the simple interest formula

I = P * r * t

I = Interest accrued

P = Principal amount invested

r = Interest rate you need to divide by 100 to get it in decimal form

t = time, in years if you are given a partial year, divide the months by 12

P = $12,000

r = 7.5% = .075

t = 1

But, because we want I to equal $990 then I is

I = $990

So we ignore our P and instead solve for the P that will give us the desired result.

I = P * r * t

$990 = P * .075 * 1

$990 = P.075 Divide each side by .075

$990/.075 = P.075/.075

$990/.075 = P

$13,200 = P

So, to earn an annual interest income of $990, $13,200 will have to be invested in the 7.5% bond.

6 0

3 years ago

Is the relation a function?

Margaret [11]

No; a domain value has two range values.

x = -2 then y = 1 and 2

they would form a vertical line, which tells us that it's not a function

8 0

3 years ago

Aaron gives an estimate of 2 for the quotient in a division problem his teacher says his estimate is reasonable if the divisor i

viva [34]

B because it's the closest to 8

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3 years ago

A motel owner observes that when a room is priced at $60 per day, all 80 rooms of the motel are occupied. For every $3 rise in t

Zinaida [17]

Answer:

a) p(x) = 300 - 3

b) P(x) = -3 x² + 285 x

c) Price of per room per day = $ 157.5

when Number of rooms occupied , x = 47.5

Step-by-step explanation:

Given - A motel owner observes that when a room is priced at $60 per day, all 80 rooms of the motel are occupied. For every $3 rise in the charge per room per day, one more room is vacant. Each occupied room costs an additional $15 per day to maintain.

To find - a) Find the demand function, expressing p, the price charged for each room per day, as a function of x, the number of rooms occupied.

b) Find the profit function P(x).

c) Find the price of per room per day the motel should charge in order to maximize its profit.

Proof -

Let

(x, y) be the point

where x represents number of rooms occupied

and y represents price of room per day.

Now,

Given that,

a room is priced at $60 per day, all 80 rooms of the motel are occupied.

So, point becomes (80, 60)

And given that For every $3 rise in the charge per room per day, one more room is vacant.

So, point becomes (79, 63)

Now, we have two points (80, 60), (79, 63)

Let us assume that,

p(x) be the price charged for each room per day

Now,

By using point - slope formula , we get

p -60 = $\frac{(63 - 60}{(79 - 80)} (x - 80)$

⇒p -60 = (-3)(x-80)

⇒p-60 = 240 -3 x

⇒p(x) = 240 + 60 -3 x

⇒p(x) = 300 - 3 x

Given that,

Each occupied room costs an additional $15 per day to maintain.

Let C(x) be the cost function,

Then C(x) =15 x

now,

Revenue function,

R(x) =x*p

= x*(300 -3 x )

= 300 x - 3 x²

⇒R(x) = 300 x - 3 x²

Now,

We know

Profit function = Revenue function - Cost function

⇒P(x) = R(x)-C(x)

⇒P(x) = (300 x -3 x²) -15 x

⇒P(x) = -3 x² + 285 x

P'(x) = -6 x +285

For Maximize profit , Put P'(x) = 0

⇒-6 x+ 285 =0

⇒6 x= 285

⇒x = $\frac{285}{6}$

⇒x= 47.5

∴ we get

Maximize profit is when price, p = 300 - 3x

= 300 -3(47.5)

= $157.5

⇒Price of per room per day = $ 157.5

when Number of rooms occupied , x = 47.5

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consider the function represented by the equation 16b = 4r - 12. write the equation in function notation, where b is the indepen

katovenus [111]

When you write a function in the form $y=f(x)$ , y is the dependent variable, and x is the independent variable.

So, if b is the independent variable, it means that we have to solve the expression for r.

To do so, we perform the following steps: start with

$16b = 4r - 12$

Add 12 to both sides

$16b+12 = 4r$

Divide both sides by 4:

$4b+3 = r$

So, we wrote the expression in the form $r = f(b) = 4b+3$ , which means that r is the dependent variable and b is the independent variable, as requested.

4 0

3 years ago