Coffee with sugar and milk added to it can contain up to calories. To consume a maximum of 600 mg if caffeine per day, how many

Answer:

A sum of $12,000 should be allocated at an interest rate of 5.25%, while $13,000 should be put in at 4%.

Step-by-step explanation:

Recall that

The simple interest formula is given by

where

I represents the total interest earned,

P is the initial investment,

r stands for the interest rate, and

t is the number of time periods.

Define

x as the amount invested at 5.25%,

and (25,000 - x) as the amount put in at 4%.

From the problem,

Plugging these into the formula:

Now, isolate x:

Hence, investing $12,000 at 5.25% and $13,000 at 4% meets the required interest condition.

Answer:

dV(t)/dt = kV(t)

Step-by-step explanation:

The annual change in the car's value, represented by dV(t)/dt, has a proportional relationship with V(t), the car's current value.

dV(t)/dt ∝ V(t)

dV(t)/dt = kV(t)

This may be a bit awkward to explain in writing, so please bear with me:)

You are given the equations. Begin by focusing on ad = 11.6. Treating variables normally, this reads as a times d = 11.6.
From that, d = 11.6/a by dividing both sides by a.

With d expressed, substitute (11.6/a) into cd = 6.7. Then isolate c by multiplying both sides by a/11.6, yielding c = (6.7a)/11.6.

Now that c is known, insert (6.7a)/11.6 for c in bc = 8.3. The algebra becomes a bit messy, but solving for b gives approximately 14.3705 / a. Since you need ab, multiply both sides by a, and rounding to one decimal place produces ab = 14.4

Response:

x² + -6x = -13

Detailed breakdown:

8x² - 48x = -104

Rearranging gives us x² - 6x = -13

I can assist you a bit; here’s what I got correct.