Explanation

Explanation

Explanation

To find the slope of the tangent to the parabola y = 2x^2 - 13x + 5, we need to find the derivative of y with respect to x.

dy/dx = 4x - 13

We want to find if there is a point where the slope of the tangent is -1.

4x - 13 = -1

4x = 12

x = 3

Now, we need to find the corresponding y-coordinate.

y = 2(3)^2 - 13(3) + 5

y = 18 - 39 + 5

y = -16

So, the point of tangency is (3, -16).

The equation of the tangent line is:

y - (-16) = -1(x - 3)

y + 16 = -x + 3

y = -x - 13

Explanation

Explanation

Calculation:

• Current total age = 80 years

• Three years ago, each person was 3 years younger.

• Since there are three people, the total reduction in age is $3\times 3=9$ years.

So, the total of their ages three years ago is:

$$\mathrm{<b><font\; color="\#0000ff">80</font></b>}<b><font\; color="\#0000ff">-</font></b>\mathrm{<b><font\; color="\#0000ff">9</font></b>}<b><font\; color="\#0000ff">=</font></b>\mathrm{<b><font\; color="\#0000ff">71</font></b>}\text{<b><font color="\#0000ff"> years</font></b>}$$

Explanation

Explanation

Explanation

"Exorbitantly" means excessively or unreasonably high, which fits well in the sentence:

"Fares are exorbitantly high in this city."

Explanation

The Current Ratio = Current Assets ÷ Current Liabilities.

It evaluates a company’s liquidity and its ability to pay short-term debts.

Explanation

The Income Statement reports a company’s revenues, expenses, and net profit or loss over a specific period.

It reflects the company's operational performance during that time.