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tensa zangetsu [6.8K]
3 years ago
8

What is the product of the polynomials below?

Mathematics
1 answer:
Alexeev081 [22]3 years ago
5 0
Hope this helps you.

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Marsha deposited 7,500 into a savings account 3 years ago. The simple interest rate is 5%. How much money did Marsha earn in int
Ludmilka [50]

Answer:

$1,125 in interest.

Step-by-step explanation:

We need the formula of I = P * i * t where P is the total principle, i is the rate of interest per year, and t is the total time in years.

So we have

P = $7,500

i = 5%

t = 3 years

I = 7500 * 0.05 * 3

I = 1,125 (Interest)

Now we need to find the amount using A = P + I

A = 7,500 + 1,125

A = 8,625

Therefore $8,625 is our total. While our interest is $1,125.

8 0
2 years ago
For integers a, b, and c, consider the linear Diophantine equation ax C by D c: Suppose integers x0 and y0 satisfy the equation;
Dmitrij [34]

Answer:

a.

x = x_1+r(\frac{b}{gcd(a, b)} )\\y=y_1-r(\frac{a}{gcd(a, b)} )

b. x = -8 and y = 4

Step-by-step explanation:

This question is incomplete. I will type the complete question below before giving my solution.

For integers a, b, c, consider the linear Diophantine equation

ax+by=c

Suppose integers x0 and yo satisfy the equation; that is,

ax_0+by_0 = c

what other values

x = x_0+h and y=y_0+k

also satisfy ax + by = c? Formulate a conjecture that answers this question.

Devise some numerical examples to ground your exploration. For example, 6(-3) + 15*2 = 12.

Can you find other integers x and y such that 6x + 15y = 12?

How many other pairs of integers x and y can you find ?

Can you find infinitely many other solutions?

From the Extended Euclidean Algorithm, given any integers a and b, integers s and t can be found such that

as+bt=gcd(a,b)

the numbers s and t are not unique, but you only need one pair. Once s and t are found, since we are assuming that gcd(a,b) divides c, there exists an integer k such that gcd(a,b)k = c.

Multiplying as + bt = gcd(a,b) through by k you get

a(sk) + b(tk) = gcd(a,b)k = c

So this gives one solution, with x = sk and y = tk.

Now assuming that ax1 + by1 = c is a solution, and ax + by = c is some other solution. Taking the difference between the two, we get

a(x_1-x) + b(y_1-y)=0

Therefore,

a(x_1-x) = b(y-y_1)

This means that a divides b(y−y1), and therefore a/gcd(a,b) divides y−y1. Hence,

y = y_1+r(\frac{a}{gcd(a, b)})  for some integer r. Substituting into the equation

a(x_1-x)=rb(\frac{a}{gcd(a, b)} )\\gcd(a, b)*a(x_1-x)=rba

or

x = x_1-r(\frac{b}{gcd(a, b)} )

Thus if ax1 + by1 = c is any solution, then all solutions are of the form

x = x_1+r(\frac{b}{gcd(a, b)} )\\y=y_1-r(\frac{a}{gcd(a, b)} )

In order to find all integer solutions to 6x + 15y = 12

we first use the Euclidean algorithm to find gcd(15,6); the parenthetical equation is how we will use this equality after we complete the computation.

15 = 6*2+3\\6=3*2+0

Therefore gcd(6,15) = 3. Since 3|12, the equation has integral solutions.

We then find a way of representing 3 as a linear combination of 6 and 15, using the Euclidean algorithm computation and the equalities, we have,

3 = 15-6*2

Because 4 multiplies 3 to give 12, we multiply by 4

12 = 15*4-6*8

So one solution is

x=-8 & y = 4

All other solutions will have the form

x=-8+\frac{15r}{3} = -8+5r\\y=4-\frac{6r}{3} =4-2r

where r ∈ Ζ

Hence by putting r values, we get many (x, y)

3 0
3 years ago
brooklyn bought 8 bags of the same dog food. She has a $5 coupon. She spent $91. How much was each bad of dog food?
blsea [12.9K]

Answer:

$12

Step-by-step explanation:

Hi there!

What we know:

  • Brooklyn bought 8 bags of dog food
  • Brooklyn also used a $5 coupon
  • The total was $91

Therefore, 8 × (cost of 1 bag) - 5 = 91

Form an equation with x as the cost of 1 bag of dog food:

8 × (cost of 1 bag) - 5 = 91

8x-5=91

Add 5 to both sides

8x-5+5=91+5\\8x=96\\

Divide both sides by 8

\frac{8x}{8} = \frac{96}{8} \\x=12

Therefore, 1 bag of dog food costs $12.

I hope this helps!

5 0
3 years ago
Are the expressions 2(3x - 6) and 6x + 12 are equivalent? Explain your reasoning.
zvonat [6]

Answer:

The two expressions are not equivalent

Step-by-step explanation:

2(3x-6) = 6x-12 which is not equal to 6x+12 because of the positive and

negative signs

5 0
3 years ago
Read 2 more answers
Seema is travelling to Guernsey. She travels a distance of 3,800 km by plane to London and then another 400 km to Guernsey. Both
slava [35]

9514 1404 393

Answer:

  4 hours 40 minutes

Step-by-step explanation:

The appropriate relation is ...

  time = distance/speed

  time = (3800 km)/(900 km/h) +(400 km)/(900 km/h) = (38+4)/9 h

  = 14/3 h = 4 2/3 h

Seema's flight time is 4 hours 40 minutes.

__

2/3 of 60 minutes is 40 minutes

4 0
2 years ago
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