Determine the solution for the system of equations: y = -2x + 1 3x - 2y = 5 A. (1, -1) B. (-1, 1) C. (-1, 0) D. No Solution

A woman earns $ 1,350 in interest from two accounts in one year. If she has three times as much invested at 7% as she does at 6%

VashaNatasha [74]

Answer:

The woman invested $15,000 at 7% interest rate and $5,000 at 6% interest rate.

Step-by-step explanation:

We are given the following in the question:

Let x be the interest earned from 7% interest rate and y be the interest earned from 6% interest rate.

The woman invested has three times as much invested at 7% as she does at 6%.

Thus, we can write the equation:

$x = 3y$

The total interest is $1,350.

Thus, we can write the equation:

$1350 = \dfrac{7x}{100} + \dfrac{6y}{100}\\\\7x + 6y = 135000$

Solving the two equations by substitution method:

$7(3y) + 6y = 135000\\27y = 135000\\y = 5000\\x = 3(5000) = 15000$

Thus, she invested $15,000 at 7% interest rate and $5,000 at 6% interest rate.

8 0

3 years ago

When writing twenty-one-and-a-half-trillion in scientific notation, what is the exponent needed on the base ten?

Nat2105 [25]

1 trillion is 10^9.

Thus, 21 1/2 trillion is 21 1/2 times 10^9, or 2.15 times 10^10

Hope this helps. If not, ask for clarification.

5 0

3 years ago

Read 2 more answers

What is 8(2x-3)-6x if x = 3

KengaRu [80]

8(2x - 3)-6x

First, replace all the x's with 3s. Simplfy 2 × 3 to 6. / Your problem should look like: 8 × (6 - 3) - 6 × 3
Second, simplify 6 - 3 to 3. / Your problem should look like: 8 × 3 - 6 × 3
Third, simplify 8 × 3 to 24. / Your problem should look like: 24 - 6 × 3
Fourth, simplify 6 × 3 to 18. / Your problem should look like: 24 - 18
Fifth, simplify 24 - 18 to get 6. / Your problem should look like: 6

Answer: 6

4 0

2 years ago

Which statement about the randomization for the matched pairs design is correct? For each participant, the nutritionist should f

nikklg [1K]

Answer:

it is A

For each participant, the nutritionist should flip a coin. If the coin lands on heads, the participant will be assigned to exercise during the first month and drink energy drinks during the second month. If the coin lands on tails, the participant will be assigned to drink energy drinks during the first month and exercise during the second month.

Step-by-step explanation:

i just finished the test

6 0

2 years ago

Please help I'm confused. It's finding a function

shepuryov [24]

Easy, that is the slope from (2,f(2)) to (3,f(3))

remember that the slope between the points (x1,y1) and (x2,y2) is
(y2-y1)/(x2-x1)

find f(2) and f(3)
f(2)=2²+6(2)+5=4+12+5=21
f(3)=3²+6(3)+5=9+18+5=32

so the slope from (2,21) to (3,32) is (32-21)/(3-2)=11/1=11

answer is 11

3 0

3 years ago