The set of all solutions of the inequality

Suppose your friend's parents invest $20000 in an account paying 7% compounded annually. What will the balance be in 7 years

Greeley [361]

The balance will be: <span>$500,637.91

</span>

3 0

2 years ago

Read 2 more answers

How would you solve these 2 maths problems?

sweet-ann [11.9K]

Answer:

see explanation

Step-by-step explanation:

(9)

Expand and simplify right side and compare coefficients of like terms on left side.

(x - 2)(x² + ax + b) + c

= x³ + ax² + bx - 2x² - 2ax - 2b + c

= x³ + x²(a - 2) + x(b - 2a) - 2b + c

compare with

x³ + 2x² - 3x + 4

x² terms

a - 2 = 2 ( add 2 to both sides )

a = 4

x terms

b - 2a = - 3 ← substitute a = 4

b - 8 = - 3 ( add 8 to both sides )

b = 5

constant terms

- 2b + c = 4 ← substitute b = 5

- 10 + c = 4 ( add 10 to both sides )

c = 14

Thus a = 4, b = 5 and c = 14

-------------------------------------------------

(10)

Since both functions cross the x- axis at - 2 then (- 2, 0) satisfies both, that is

f(- 2) = $(-2)^{4}$ + a(- 2)³ + b(- 2)² + 36(- 2) + 144 = 0, that is

- 16 - 8a + 4b - 72 + 144 = 0

- 8a + 4b + 56 = 0

- 8a + 4b = - 56 → (1)

and

g(- 2) = $(-2)^{4}$ + (a + 3)(- 2)³ - 23(- 2)² + (b + 10)(- 2) + 40 = 0, that is

- 16 - 8(a + 3) - 92 - 2(b + 10) + 40 = 0

- 16 - 8a - 24 - 92 - 2b - 20 + 40 = 0

- 8a - 2b - 112 = 0

- 8a - 2b = 112 → (2)

Subtract (1) from (2) term by term

- 6b = 168 ( divide both sides by - 6 )

b = - 28

Substitute b = - 28 into (2)

- 8a + 56 = 112 ( subtract 56 from both sides )

- 8a = 56 ( divide both sides by - 8 )

a = - 7

Thus a = - 7 and b = - 28

5 0

3 years ago

Reggie, Alvin, and Jose are member of a relay running team. Reggie finished his leg of the race 2.45 seconds faster than Alvin a

lorasvet [3.4K]

From the given, we expressed the time that each of the team members ran in mathematical expression.

Reggie = 57.12 seconds
Alvin = 57.12 + 2.45 seconds = 59.57 seconds
Jose = 57.12 - 3.81 seconds = 53.31 seconds
We then sum up all the time we calculate to determine the total time for the team. The answer is therefore 170 seconds.

8 0

2 years ago

A pilot was scheduled to depart at 4:00 pm, but due to air traffic, her departure has been delayed by 15 minutes. Air traffic co

Sladkaya [172]

Answer:

y = (1/2)x + 15

Step-by-step explanation:

First, we need to identify the parts of the problem that we already know:

1) The pilot was originally scheduled to depart at 1600 (4:00 pm).

2) The pilot's departure was delayed by 15 minutes.

3) the traffic control approved a new flight plan that would allow the pilot to travel to her destination two times faster than her original flight plan.

For the problem's sake, let us pretend that the pilot's original flight plan was going to take two hours. Had he/she left at 4:00 pm, the pilot would have landed at 6:00 pm.

With a delay of 15 minutes, the duration of the flight would still remain constant, so the pilot would arrive at their destination two hours later, at 6:15 pm.

With the new flight plan, the pilot's travel time would be cut in half, so it would be 1/2 of x (time, in minutes, of original flight). Thus, her new flight time would only be one hour (60 minutes).

So, now we have to subtract 1/2 from the original flight time, as well as adding the 15 minute delay for departure. Now we can create a formula:

y = (1/2)x + 15

Y equals the total amount of time (in minutes) that it would take for the plane to leave. We divide x (total time of original flight) by 2, because her new flight plan will be twice as fast. Then we have to take into account the extra 15 minute delay!

8 0

3 years ago

Cos 200. Cos 115- Sin 200. Sin 115=

Harrizon [31]

Cos 200= -0.939692621. cos 115-sin200=-0.080598118 Sin 115=0.906307787

6 0

3 years ago