What is the cost of r grapefruits, if each grapefruit costs s?

Answer:

One input(x-value) can only have one output(y-value) in order to be a function.

Step-by-step explanation:

Final answer:

One-to-one functions yield unique outputs for each input. Many-to-one functions can yield the same output for different inputs. The term one-to-many does not typically apply to functions, and a relation is not a function if one input yields multiple outputs. To answer the question specifically about Item 2, additional information or a visual representation is needed.

Explanation:

To determine the type of a function or relation, we need to understand what it means for a function to be one-to-one, many-to-one, one-to-many, or not a function.

A function is one-to-one (also known as injective) if every element of the range corresponds with exactly one element of the domain. In simpler terms, no two different inputs (x-values) yield the same output (y-values).

A function is many-to-one if there are at least two elements in the domain associated with the same value in the range. This means, two or more different inputs (x-values) can yield the same output (y-value).

The term one-to-many typically does not apply to functions in the strictest mathematical sense. Functions by definition associate one, and only one output with each input.

Lastly, a relation is not a function if at least one element in the domain is associated with more than one value in the range. That is, there is atleast one input (x-value) that yields more than one output (y-value).

Without further specific information or visual representation (like a graph) of Item 2, it's difficult to definitively state what type of relation or function it is.

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Answer:

sin(A-B) = 24/25

Step-by-step explanation:

The trig identity for the differnce of angles tells you ...

sin(A -B) = sin(A)cos(B) -sin(B)cos(A)

We are given that sin(A) = 4/5 in quadrant II, so cos(A) = -√(1-(4/5)^2) = -3/5.

And we are given that cos(B) = 3/5 in quadrant I, so sin(B) = 4/5.

Then ...

sin(A-B) = (4/5)(3/5) -(4/5)(-3/5) = 12/25 + 12/25 = 24/25

The desired sine is 24/25.

The work done by the man against gravity in climbing to the top is 16740 lb-ft

What is work done against gravity?

The work done against gravity relies on the height of the object and the weight at which the object is changing.

From the given information:

Taking the vertical y-axis when y = 0, then:

• The weight of the paint w(y) becomes;

w(0) = 20 lb

w(90) = 20 - 8 = 12 lb

Provided that the paint leaks steadily, the function of y i.e. w(y) can be expressed as a linear function in the form:

w(y) = a + by ---- (1)

Thus;

• w(0) = a = 20

• w(90) = 20 + 90b = 12
• b = (12 - 20)/90
• b = -4/45

From equation (1)

w(y) = 20 - 4y/45

The total weight becomes;

w = w(y) + the man's weight

w = 20 - 4y/45 + 170

w = 190 - 4y/45

Therefore, the work done against gravity is computed as:

W = ∫ w dy

where;

• y varies from 0 to 90

W = 16740 lb-ft

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You'll need 2 more lines to complete this two column proof.

---------------------

Line 4

For the "statement" portion, you'll say something like

The reason for this statement is "transitive property"

We're basically combining lines 1 and 3 to form this new line.

The transitive property is the idea that if A = B and B = C, then A = C. We connect the statements like a chain.

---------------------

Line 5

The statement is what you want to prove since this is the last line.

So the statement is

The reason is "converse of corresponding angles theorem"

As you can probably guess, this theorem says "If two corresponding angles are congruent, then the lines are parallel".

Final answer:

To prove that lines P and Q are parallel based on congruent angles, utilize the geometric understanding that if a transversal intersects two parallel lines, the corresponding angles are congruent. Given that angle 1 is congruent to angle 2, we can infer that the lines forming these angles (P and Q) are parallel.

Explanation:

To prove that the lines P and Q are parallel using the fact that angle 1 is congruent to angle 2, you will utilize the concept of congruent angles. When two parallel lines are intersected by a transversal, the corresponding angles are congruent. Therefore, if we know that angle 1 is congruent to angle 2, we can say the lines forming these angles are parallel.

Here are the steps:

1. Identify the given congruent angles (angle 1 and angle 2).
2. Identify the lines that form these angles, which are lines P and Q in this case.
3. Remember, by the corresponding angles postulate, if a transversal intersects two parallel lines, then the corresponding angles are congruent.
4. We have given that angle 1 is congruent to angle 2. So, the lines forming these angles, P and Q, are parallel.

This process uses reasoning of the geometry and reviews the core concept of parallel lines and transversals in proving that P is parallel to Q.

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Answer:

C

Step-by-step explanation: