A hallway measuring 90 feet x 7 feet requires 1/2 a fluid oz of cleaning solution per sq ft. How much cleaning solution is needed to clean the hallway?

Answer: Both P(x) has a factor (x+2) and P(x) has an x-intercept of -2

Explanation: if a polynomial has a factor (x-a) it means its form can be written as:

(x-a)*(rest of polynomial)=0

and thus "a" is a root because the entire expression becomes 0 when x=a. In this case a=-2

An x-intercept is a point on the curve intersecting the x axis with coordinates (a, 0) where a is one of the roots. As shown above x=-2 will make the expression 0, so y=0 for x=-2. In other words there is a point (-2,0), which means -2 is the x-intercept.

Final answer:

The graph has a positive slope, is non-proportional, and has a y-intercept of 2. The slope represents the rate of change between the x and y variables. The y-intercept represents the value of y when x is 0. The graph shows a relationship where y increases by a constant rate of 3 for every one unit increase in x.

Explanation:

A. The graph has a positive slope. It is non-proportional as the points do not lie on a straight line. The y-intercept is 2.

B. The slope of the graph represents the rate of change between the x and y variables. In context, it means that for every unit increase in x, y increases by 3 units.

C. The y-intercept of the graph represents the value of y when x is 0. In context, it means that when x is 0, y is equal to 2.

D. The graph of the line is showing a relationship between x and y variables, where y increases by a constant rate of 3 for every one unit increase in x, starting from a y-value of 2 when x is 0.

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Final answer:

In a graph, the slope describes the rate of change, and the y-intercept is where the line intersects the y-axis. A positive pitch rises from left to right, while a negative one falls. A proportional graph reflects a constant rate of change, while a non-proportional one shows a non-constant rate of change.

Explanation:

We need to know the specifics of the graph to explain the components you've asked about. A positive slope on a chart is represented by a line that rises from left to right, while a negative slope descends from left to right. The value of the pitch can be determined by the rise over run (change in y / change in x).

A graph is proportionalif the line passes through the origin (0,0) and has a constant slope. If it doesn't, it's considered non-proportional, meaning the change rate is unstable.

The y-intercept is the point where the line intersects with the y-axis. In the context of an equation, it's the value of 'y' when 'x' equals zero.

A graph's slope depicts the change rate between the two variables. The y-intercept typically represents the starting value or the value of 'y' when 'x' has yet to apply. Finally, the overall graph of a line shows the relationship between two variables, represented in a way that changes in one variable correspond with a change in another.

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Applying the properties of a rhombus and the Pythagorean Theorem, the length of one side of the rhombus is: 14.9

Recall:

• The diagonals of a rhombus bisect each other at right angles, thereby forming 4 right triangles.

• Half of a diagonal and half of the other diagonal make up a right triangle.

Thus, given:

• EG = 22 (diagonal)
• FH = 20 (diagonal).

Find the length of one side using Pythagorean theorem as shown below:

• Substitute

Therefore, applying the properties of a rhombus and the Pythagorean Theorem, the length of one side of the rhombus is: 14.9

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