A farmer is having problems with birds eating her crops. She tries putting up different numbers of scarecrows to keep the birds

Answer: D. 45 inches, 75 inches

Step-by-step explanation:

To resolve this inquiry, we first need to divide the board's total length by the number of segments forming the two sections.

Given the ratio of 3:5, one section consists of 3 segments and the other of 5, making a total of 8 segments.

120 divided by 8 equals 15 inches for each segment.

Next, we multiply the length of each segment by how many segments each section has (3 and 5).

15 times 3 equals 45 inches.

15 times 5 equals 75 inches.

Answer:

The ratio   corresponds to the tangent of ∠I.

Step-by-step explanation:

Let’s revisit the trigonometric ratios:

• sin Ф =  
• cos Ф =  
• tan Ф =  

For triangle HIJ

∵ m∠J = 90°

- The hypotenuse is the side opposite the right angle.

So, HI is the hypotenuse.

∵ HJ = 3 units

∵ IH = 5 units

- We’ll apply the Pythagorean Theorem to solve for HJ.

∵ (HJ)² + (IJ)² = (IH)²

∴ 3² + (IJ)² = 5²

∴ 9 + (IJ)² = 25

- Subtract 9 from both sides.

∴ (IJ)² = 16

- Taking the square root on both sides gives:

∴ IJ = 4 units

To determine the tangent of ∠I, identify the sides that are opposite and adjacent to it.

∵ HJ is opposite to ∠I

∵ IJ is adjacent to ∠I

- Utilizing the rule of tan above:

∴ tan(∠I) =

∴ tan(∠I) =

The ratio indicates the tangent of ∠I.

Response:

, indicating the amount of earnings per working hours, designated as x

Detailed Explanation:

We have two distinct functions to analyze:

This function delineates the earnings based on units of x

Then the second function is

which illustrates the quantity of gallons of ice cream produced by Barrett each hour, with x representing the hours worked.

Our aim is to determine the composite function

resulting from substituting the output of as input for . Within this framework, the function signifies the amount of money accrued per number of working hours, x.

By substituting g(x) into the x variable of f(x), we obtain: