All categories

2 years ago

This graph shows a proportional relationship.

Mathematics

1 answer:

Alisiya [41]2 years ago

5 0

Answer:

The constant of proportionality is:

k = 5/4

Step-by-step explanation:

We know that when y varies directly with x, we get

y ∝ x

y = kx

k = y/x

where 'k' is called the constant of proportionality

From the graph, it is clear that the point (2/5, 1/2) passes through the line which represents the direct relationship.

so we have the point (2/5, 1/2), and

x = 2/5

y = 1/2

so substituting x = 2/5 and y = 1/2 in the equation

k = y/x

k = [1/2] / [2/5]

k = [1 × 5 ] / [2 × 2 ]

k = 5/4

Therefore, the constant of proportionality is:

k = 5/4

You might be interested in

Homework Progress 107 / 285 A sequence has three terms. Its term-to-term rule is multiply by 6 and then add 13 a)

____ [38]

Answer:

It's C

Step-by-step explanation: I took the test and got it wrong

8 0

2 years ago

20. What is the volume, in terms of r, for a cylindrical

inysia [295]

Step-by-step explanation:

Volume of cylindrical container

$= \pi {r}^{2} h \\ \\ = 3.14 \times ( {3.25)}^{2} \times 10 \\ \\ = 3.14 \times 10.5625 \times 10 \\ \\ = 331.6625 {cm}^{3} \\ \\ \approx \: 331.66 \: {cm}^{3}$

4 0

3 years ago

Which statements about the system are true?

Kruka [31]

2 Answers:

B) The lines are parallel
C) The lines have the same slope.

Parallel lines always have equal slope, but different y intercepts.

==========================================================

Explanation:

Let's solve the second equation for y

3y - x = -7

3y = -7+x

3y = x-7

y = (x-7)/3

y = x/3 - 7/3

y = (1/3)x - 7/3

The equation is in y = mx+b form with m = 1/3 as the slope and b = -7/3 as the y intercept. We see that the first equation, where y was already isolated, also has a slope of m = 1/3. The two equations of this system have the same slope. Choice C is one of the answers.

However, they don't have the same y intercept. The first equation has y intercept b = -4, while the second has b = -7/3. This means that they do not represent the same line. They need to have identical slopes, and identical y intercepts (though the slope can be different from the y intercept of course) in order to have identical lines. So we can rule out choice D and E because of this.

Because the two equations have the same slope, but different y intercepts, this means the lines are parallel. Choice B is the other answer.

Parallel lines never touch or intersect, which in turn means there is no solution point. A solution point is where the lines cross. We can rule out choice A.

I recommend using your graphing calculator, Desmos, GeoGebra, or any graphing tool (on your computer or online) to graph each equation given. You should see two parallel lines forming. I used GeoGebra to make the graph shown below.