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4 years ago

Which expression represents 12x³-6x²+2x ÷2x in simplest form?

Mathematics

1 answer:

Elden [556K]4 years ago

5 0

Answer:

x^2 (12 x - 5)

Step-by-step explanation:

Simplify the following:

12 x^3 + (2 x x)/2 - 6 x^2

(2 x x)/2 = 2/2×x x = x x:

12 x^3 + x x - 6 x^2

x x = x^2:

12 x^3 + x^2 - 6 x^2

x^2 - 6 x^2 = -5 x^2:

12 x^3 + -5 x^2

Factor x^2 out of 12 x^3 - 5 x^2:

Answer: x^2 (12 x - 5)

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You have $10 to go bowling with your friends. You need to rent shoes for $4. Each game (g) costs $3. Write and solve an equation

dexar [7]

Answer:

The equation is: x = (y - $4) / g

Where x is the number of games you can play;

y is the amount you have

and g is the cost of each game

You can play only 2 games

Step-by-step explanation:

From the question, you have $10 to go bowling and you need to rent shoes for $4. Hence, after renting the shoes, you will have $10 - $4 left, that is you will have $6 left. To determine the number of games you can play, that will be the amount you have left after renting shoes divided by the cost of each game.

Let the number of games you can play be x games

and the amount you have be y

and the cost of each game be g

Hence,

x = (y - $4) / g

From the question,

y = $10

and g = $3

∴ x = ($10 - $4)/ $3

x = $6 / $3

x = 2

Hence, you can play only 2 games

6 0

3 years ago

Find the amount budgeted for food on a salary of $19,300 if the food budget is 13%.

kvv77 [185]

The amount of the food budget is $2,509 as it is 13% of $19,300.

4 0

3 years ago

Four brothers each bought two hot dogs and a bag of chips at the football concession stand. If the bag of chips was $1.25, and t

IRISSAK [1]

Items bought in total:
4 brothers X two hot dogs and one bag of chips=
4X3=
12.

Hot dogs- x, chips- y.
4y + 8x= $18.20

Chips= $1.25 each so
4($1.25) + 8x= $18.20
5 + 8x= $18.20
8x= $18.20-5
8x= $13.20
x= $13.20/8 [13.20 divided by 8]
x= $1.65

This means that one hot dog= $1.65.

If you’re unsure what to write as the answer I’d suggest that you put all the working out down in your copy/notes.

3 0

3 years ago

A bacteria culture starts with 12,000 bacteria and the number doubles every 50 minutes.

Vlada [557]

Answer:

a) $y=12000(2)^{\frac{t}{50}}$

b) Approx. 27,569 bacteria

c) About 103 minutes

Step-by-step explanation:

This will follow exponential modelling with form of equation shown below:

$y=Ab^{\frac{t}{n}}$

Where

A is the initial amount (here, 12000)

b is the growth factor (double, so growth factor is "2")

n is the number of minutes in which it doubles, so n = 50

Substituting, we get our formula:

$y=Ab^{\frac{t}{n}}\\y=12000(2)^{\frac{t}{50}}$

To get number of bacteria after 1 hour, we have to plug in the time into "t" of the formula we wrote earlier.

Remember, t is in minutes, so

1 hour = 60 minutes

t = 60

Substituting, we get:

$y=12000(2)^{\frac{t}{50}}\\y=12000(2)^{\frac{60}{50}}\\y=12000(2)^{\frac{6}{5}}\\y=27,568.76$

The number of bacteria after 1 hour would approximate be <u>27,569 bacteria</u>

<u></u>

To get TIME to go to 50,000 bacteria, we will substitute 50,000 into "y" of the equation and solve the equation using natural logarithms to get t. Shown below:

$y=12000(2)^{\frac{t}{50}}\\50,000=12,000(2)^{\frac{t}{50}}\\4.17=2^{\frac{t}{50}}\\Ln(4.17)=Ln(2^{\frac{t}{50}})\\Ln(4.17)=\frac{t}{50}*Ln(2)\\\frac{t}{50}=\frac{Ln(4.17)}{Ln(2)}\\\frac{t}{50}=2.06\\t=103$

After about 103 minutes, there will be 50,000 bacteria

4 0

3 years ago

What is true about the relationship between alternate interior angles?

svet-max [94.6K]

The Alternate Interior Angles theorem states, if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. A theorem is a proven statement or an accepted idea that has been shown to be true.

6 0

3 years ago

Which expression represents 12x³-6x²+2x ÷2x in simplest form?​

Which expression represents 12x³-6x²+2x ÷2x in simplest form?