Give a real life example of two variables that very directly

Greatest common factor of five

arsen [322]

Answer:

GCF(greatest common factor) of 5 is 5.

6 0

3 years ago

What is the difference of the two polynomials? (9x2 + 8x) – (2x2 + 3x) 7x2 + 5x 7x2 + 11x 11x2 + 5x 11x2 + 11x

Anuta_ua [19.1K]

we have

$(9x^{2}+8x)-(2x^{2}+3x)$

Step 1

Eliminate the parenthesis

$(9x^{2}+8x)-(2x^{2}+3x)=9x^{2}+8x-2x^{2}-3x$

Step 2

Group terms that contain the same variable

$9x^{2}-2x^{2}+8x-3x$

Step 3

Combine like terms

$7x^{2}+5x$

therefore

the answer is

$7x^{2}+5x$

5 0

3 years ago

Read 2 more answers

Assume that cigarettes cost $7 per pack and consider a 21 year old college student smoker who smokes 15 packs of cigarettes per

stepladder [879]

Answer:

The answer is $57657.6

Step-by-step explanation:

First, you must determine the amount of money the student saves per month. To do this, the number of cigarette packages she smokes is multiplied by the price she pays for them.

Per month: 15 packs*$7 each packet=$105

This means that per month she save $ 105.

Now you must determine the amount of money saved per year, knowing that in a year there are 12 months. Therefore, you make a simple rule of three: If in a month you save $ 105, how much money do you save in 12 months?

Per year: $\frac{105*12months}{1 month} =1260$

This means that per year she save $ 1260. And she each month invests the amount she would have spent on cigarettes in a savings plan that averages a 4% annual return. This means that in addition to saving $ 1260 per year, she gets 4% annually. For this you must first know how much 4% equals. For that you must keep in mind that to obtain a percentage in decimals, you must divide by 100. Then 0.04 represents 4%.

Now, to get the annual return of the savings plan you multiply the percentage by the amount invested in the plan. And to determine the total amount of money she save in a year with this plan, you add the amount invested plus the annual return. All this is:

0.04*$1260+$1260=$1310.4

This means that finally per year she save $ 1310.4 with the annual return.

You know that between 65 and 21 years of age of the student, there is a difference of 44 years, obtained by calculating 65 years minus 21 years. Then you can make a simple rule of three to determine the amount of money saved during those 44 years:if in one year the student save $1310. 4, how much money do she save in 44 years?

$\frac{1310.4*44 years}{1 year} =57657.6$

So, finally,  she will have saved $ 57657.6 by the time she is 65

5 0

3 years ago

Two chemicals A and B are combined to form a chemical C. The rate, or velocity, of the reaction is proportional to the product o

koban [17]

Answer: 17.6 grams

Step-by-step explanation:

As the problem tells us, the velocity of the reaction is proportional to the product of the quantities of A and B that have not reacted, so from this we get the next equation:

V = k[A][B]

where [A] represents the remaining amount of A, and [B] represents the remaining amount of B. To solve this equation we have to represent it through a differential equation, which is:

dx/dt = k[α - a(t)][β - b(t)] (1)

where,

k: velocity constant

a(t): quantity of A consumed in instant t

b(t): quantity of B consumed in instant t

α: initial quantity of A

β: initial quantity of B

Now we need to define the equations for a(t) and b(t), and for this we are going to use the law of conservation of mass by Lavoisier, with which we can say that the quantity of C in a certain instant is equal to the sum of the quantities of A and B that have reacted. Therefore, if we need M grams of A and N grams of B to form a quantity of M+N of C, then we can say that in a certain time, the consumed quantities of A and B are given by the following equations:

a(t) = ( M/M+N) · x(t)

b(t) = (N/M+N) · x(t)

where,

x(t): quantity of C in instant t

So for this problem we have that for 1 gram of B, 2 grams of A are used, therefore the previous equations can be represented as:

a(t) = (2/2+1) · x(t) = 2/3 x(t)

b(t) = (1/2+1) · x(t) = 1/3 x(t)

Now we proceed to resolve the differential equation (1) by substituting values:

dx/dt = k[α - a(t)][β - b(t)]

dx/dt = k[40 - 2x/3][50 - x/3]

dx/dt = k/9 [120 - 2x][150 - x]

We use the separation of variables method:

dx/[120-2x][150-x] = k/3 · dt

We integrate both sides of the equation:

∫dx/(120-2x)(150-x) = ∫kdt/9

∫dx/(15-x)(60-x) = kt/9 + c

Now, to integrate the left side of the equation we need to use the partial fraction decomposition:

∫[1/90(120-2x) - 1/180(150-x)] = kt/9 + c

1/180 ln(150-x/120-2x) = kt/9 + c

(150-x)/(120-2x) = Ce^{20kt}

Now we resolve by taking into account that x(0) = 0, and x(5) = 10,

for x(0) = 0 , (150-0)/(120-0) = Ce^{20k(0)} , C = 1.25

for x(5) = 10 , (150-10)/(120-(2·10)) = 1.25e^{20k(5)} , k ≈ 113 · 10^{-5}

Now that we have the values of C and k, we have this equation:

(150-x)/(120-2x) = 1.25e^{226·10^{-4}t}

and we have to clear by x, obtaining:

x(t) = 150 · (1 - e^{226·10^{-4}t} / 1 - 2.5e^{226·10^{-4}t})

Therefore the quantity of C that will be formed in 10 minutes is:

x(10) = 150 · (1 - e^{226·10^{-4}(10)} / 1 - 2.5e^{226·10^{-4}(10)})

x(10) ≈ 17.6 grams

8 0

3 years ago

A store gave away 6700 candy canes to 83 kids how many candy canes did each child get round to nearest tenth

hammer [34]

Answer:

80.7 candy canes/child

Step-by-step explanation:

6700 divided by 83=80.722

3 0

2 years ago