Answer:
The relationship is linear, and of the form:
(last option in the list of possible answers)
Step-by-step explanation:
Yes, the relationship is linear. Such can be clear by examining if the rate of change when using different pairs of x,y coordinates. Notice for example that when you do the difference between consecutive y-values of the table, you always get "5":
10-5 = 5
15-10 = 5
20-15 = 5
and the respective differences between consecutive x-values of the table, always render "4":
5-1 = 4
9-5 = 4
13-9 = 4
This tells us that the associated rates of change are constant and equal to "5/4".
This is then the slope of the line that joints all of those points.
Now, in order to find a point-slope form for this line one can use the first pair (1, 5) for the point we want the line to go through, and apply the general slope-point for a line knowing that the slope m = 5/4, and that we can use the point (1, 5) as the particular point to define it:
, which is in fact the last option given in the choice of answers.
Given:
- Max and Jack have 86 stamps
- If Max gives away 36 stamps, they have the same number of stamps
To Find:
The number of stamps Max needs to give to Jack so that they have the same number of stamps.
Answer:
Max needs to give Jack 18 stamps so that they have the same number of stamps.
Step-by-step explanation:
Let x denote the number of stamps Max has, and y denote the number of stamps Jack has.
Given that they have 86 stamps in total, the following equation is true
![x+y=86](https://tex.z-dn.net/?f=x%2By%3D86)
Now, if Max was to give away 36 stamps, then Max and Jack would have the same number of stamps. So,
![x-36=y](https://tex.z-dn.net/?f=x-36%3Dy)
Let us rewrite the first equation as
![x+y=86\\\\y=86-x](https://tex.z-dn.net/?f=x%2By%3D86%5C%5C%5C%5Cy%3D86-x)
We have thus got two values of y interms of x. So, putting
in
![y=86-x](https://tex.z-dn.net/?f=y%3D86-x)
we have,
![x-36=86-x\\\\2x=86+36\\\\2x=122\\\\x=61](https://tex.z-dn.net/?f=x-36%3D86-x%5C%5C%5C%5C2x%3D86%2B36%5C%5C%5C%5C2x%3D122%5C%5C%5C%5Cx%3D61)
Using
we have,
So, Max has 61 stamps and Jack has 25 stamps.
Max has 36 more stamps than Jack. So, we see that if Max gives 36/2 = 18 stamps to Jack, they will both have equal stamps. That is, both Max and Jack will then have 43 stamps each.
Answer: She will earn $15 excluding the one-time credit during the year.
Step-by-step explanation:
Since we have given that
Amount Sandra gain = $210
Gain included a one time per year credit
Amount of that one time per year credit = $30
Her equation becomes,
![14(x+30)=210](https://tex.z-dn.net/?f=14%28x%2B30%29%3D210)
To project how money x her investment account will earn during the year
We need to find the amount that Sandra's account will earn during the year, excluding the one time credit
So, our equation becomes,
![14x=210\\\\x=\frac{210}{14}\\\\x=\$15](https://tex.z-dn.net/?f=14x%3D210%5C%5C%5C%5Cx%3D%5Cfrac%7B210%7D%7B14%7D%5C%5C%5C%5Cx%3D%5C%2415)
Hence, She will earn $15 excluding the one-time credit during the year.