The graphs of the function f (given in blue) and g (given in red) are plotted above. Suppose that u(x)=f(x)g(x) and v(x)=f(x)/g(

The interest rate equals 25%

Explanation:

Provided data:

Principal amount, P = $2,000

Total amount, A = $2500

Duration, t = 1 year

Interest rate, r =?

We understand:

Substituting the known values gives:

Thus, the interest rate is 25%

Answer:

Part A:

x+y= 95

x = y+25

Part B: 35 minutes

Part C: No

Step-by-step explanation:

• Part A:

Eric spends a total of 95 minutes daily playing basketball and volleyball combined.

x+y= 95

Where:

x =minutes Eric plays basketball

y = minutes he allocates to volleyball

He dedicates 25 minutes more to basketball compared to volleyball.

x = y+25

Equations are:

x+y= 95

x = y+25

• Part B:

Substituting x=y+25 into the first equation yields:

(y+25) + y =95

Solving for y

y+25+y =95

25+2y=95

2y=95-25

2y=70

y = 70/2

y = 35 minutes

Part C: No

If x = 35

x+y= 95

35+y =95

y= 95-35

y = 60 minutes

Inserting y=60 into the other equation:

x = y+25

35 = 60+25

35 ≠85

The original price stands at $450.

Step-by-step explanation:

Step 1:

Given information, Discount%, D% = 30 and Selling Price, SP = $315

Step 2:

Formulate the equation for determining the Original Price

Selling Price (SP) = Original Price (OP) - Discount (D)

Discount (D) = Original Price (OP) * (D%/100)

Step 3:

Plug in the known values into the formula

315 = OP - D

D =

D = 0.3 OP

Step 4:

Insert the value of D back into the initial equation

315 = OP - 0.3 OP

315 = OP (1 - 0.3) = 0.7 OP

A resulting Original Price of OP = 315/0.7 = $450

Tara's total expense for watching the movie amounts to $50.50