What is another way to write 9x200?

Suppose that we wish to expand (x + y + z)17. what is the coefficient of x 2 y5z10

Delvig [45]

We use the trinomial theorem to answer this question. Suppose we have a trinomial (a + b + c)ⁿ, we can determine any term to be:

[n!/(n-m)!(m-k)!k!] a^(n-m) b^(m-k) c^k

In this problem, the variables are: x=a, y=b and z=c. We already know the exponents of the variables. So, we equate this with the form of the trinomial theorem.

n - m = 2
m - k = 5
k = 10

Since we know k, we can determine m. Once we know m, we can determine n. Then, we can finally solve for the coefficient.

m - 10 = 5
m = 15

n - 15 = 2
n = 17

Therefore, the coefficient is equal to:

Coefficient = n!/(n-m)!(m-k)!k! = 17!/(17-5)!(15-10)!10! = 408,408

6 0

2 years ago

AT&T has a family plan of four lines for $125 and additional lines are $15 each per month. If Jason wants to spend at most $

denis-greek [22]

Given:

Cost of four lines = $125

Cost of each additional line = $15

Jason wants to spend at most $200 per month on cell phone expenses.

To find:

The inequality for the given situation.

Solution:

Let $x$ be the number of additional line.

Cost of one additional line = $15

Cost of $x$ additional line = $\$15x$

Total cost = Fixed cost + Addition cost

= $125+15x$

It is given that Jason wants to spend at most $200 per month on cell phone expenses. It means the total cost must be less than or equal to 200.

$125+15x\leq 200$

Therefore, the correct option is C.

8 0

2 years ago

Andre and Diego were each trying to solve 2x+6=3x−8. Describe the first step they each make to the equation. The result of Andre

Oksi-84 [34.3K]

Answer:

Andre subtracted 3x from both sides
Diego subtracted 2x from both sides

Step-by-step explanation:

Andre

Comparing the result of Andre's work with the original, we see that the "3x" term on the right is missing, and the x-term on the left is 3x less than it was. It is clear that Andre subtracted 3x from both sides of the equation.

__

Diego

Comparing the result of Diego's work with the original, we see that the "2x" term on the left is missing, and the x-term on the right is 2x less than it was. It is clear that Diego subtracted 2x from both sides of the equation.

_____

Comment on their work

IMO, Diego has the right idea, as his result leaves the x-term with a positive coefficient. He can add 8 and he's finished, having found that x=14.

Andre can subtract 6 to isolate the variable term, and that will give him -x=-14. This requires another step to get to x=14. Sometimes minus signs get lost, so this would not be my preferred sequence of steps.

As a rule, I like to add the opposite of the variable term with the least (most negative) coefficient. This results in the variable having a positive coefficient, making errors easier to avoid.

3 0

1 year ago

Tara owes $14,375 in credit card debt. The interest accrues at a rate of 5.3%. She is also borrowing $570 each month for rent fr

siniylev [52]

Answer:

$(f + g)(t) = f(t) + g(t) = 14375 (1 + \frac{5.3}{100})^{t} + 6840t$