Minato drove 390 miles. Part of the drive was along local roads, where his average speed was 20 mph, and the rest was along a hi

Answer:

The function decreases across all real numbers x where x < 1.5.

Step-by-step explanation:

We have

This represents an upward-opening vertical parabola

The vertex denotes a minimum point

The vertex is located at (1.5,-6.25)

We know that

The function is decreasing within the interval ----> (-∞, 1.5) x < 1.5

This means----> the function is continuously decreasing for all real x values under 1.5

Conversely, the function is increasing within the interval ----> (1.5, ∞) x> 1.5

Thus, for all real x values greater than 1.5, the function is increasing

Check the attached figure for further clarification

Therefore

The true statement is

The function decreases across all real numbers x where x < 1.5.

Answer:

The amount of ovens that must be produced in a week to earn a $1610 profit is 70.

Step-by-step explanation:

Given:

A small-appliance manufacturer determines the profit P (in dollars) from producing x microwave ovens weekly by the formula:

with 0 ≤ x ≤ 200.

The target profit is $1610

So, set P = 1610, then solve for x:

Multiply both sides by 10:

Next, factor the quadratic:

Solving for x gives:

Since x=230 is outside the domain 0 ≤ x ≤ 200, we discard it.

Hence, the valid solution is x=70.

Therefore, to achieve a $1610 profit, the manufacturer must produce 70 ovens weekly.

Answer:

13%

Detailed breakdown:

Information provided:

• MP = 2080
• Discount = d%
• VAT = (d-2)%
• Cost = 1997.84

Applying the discount:

• 2080 - d% = 2080*(1 - 0.01d)

Including VAT:

• 2080*(1 - 0.01d) + (d - 2)%
• 2080*(1 - 0.01d) * (1 + (d -2)/100)
• 2080*(1 - 0.01d) * (0.98 + 0.01d) = 1997.84
• (1 - 0.01d)(0.98 + 0.01d) = 1997.84/2080
• 0.98 + 0.01d - 0.0098d - 0.0001d² = 0.9605
• - 0.0001d² + 0.0002d + 0.98- 0.9605 = 0
• 0.0001d²- 0.0002d - 0.0195 = 0
• d² - 2d + 195 = 0

Solving this quadratic equation yields:

• d = 15

Therefore

• VAT rate = 15 - 2 = 13%