In graphs of linear relationships, you can always determine a proportional linear relationship by observing where the line crosses the y axis. If the line crosses through the origin, then the relationship is proportional. This means that the independent data(in this case time) can be multiplied by a constant factor to always get it's related dependent piece of data.

From the graph you might notice some data points for Gary: At 2mins he completes 1.5 knots or the ordered pair (2, 1.5). We see another data point at 4mins he completes 3 knots or the ordered pair (4,3). How about the ordered pair (6, 4.5)? Notice that if I multiply the "x" coordinate of all these ordered pairs by 0.75, I get the "y" coordinate. Or maybe another way to look at it, the "y" coordinate of each point on the line divided its corresponding "x" coordinate will always produce the same number, 0.75. This number, 0.75, is called the constant of proportionality.

So, the answer to this problem is choice "D"

Summary: To identify proportional linear relationship from a graph, look for the line that goes through the origin. To find the constant of proportionality, determine the coordinates of a convenient point on the line and divide the y coordinate by the x .

5 0

3 years ago

A can of beans has surface area 332 cm squared. Its height is 10 cm. What is the radius of the circular top? (Hint: The surface

In-s [12.5K]

Answer:

The radius of can is approximately 3.82 cm.

Step-by-step explanation:

We are given the following in the question:

Surface area of can = 332 square cm

Height of can = 10 cm

We have to find the radius of circular top.

Formula:

Surface area of can = Surface area of cylinder

$2\pi r(r + h) = 332\\2\pi r(r + 10) = 332\\\\r^2 + 10r = \dfrac{332}{2\pi}\\\\r^2 + 10r - 52.82 = 0\\\text{Using quadratic formula}\\\\r = \dfrac{-10\pm \sqrt{100 - 4(-52.82)}}{2}\\\\r = -13.82, 3.82$

Since, the radius cannot be negative.

The radius of can is approximately 3.82 cm.

5 0

3 years ago

Mr. Jamieson plans to put some 3-pound math books in a box that can hold 26 pounds or less. The inequality 3b ≤ 26 describes the

solniwko [45]

Answer:

b ≤ 26/3

Step-by-step explanation:

All we have to do is divide both sides by 3

3x/3 ≤ 26/x

x ≤ 8.67

7 0

3 years ago