Hi there!
The way that an infinite number of solutions is achieved is when the two equations, when solved together, get an answer which is just a number equal to the same number. To do this, first substitute 6x-b in for y in the second equation.
Now, we see that b needs to be equal to -3 when multiplied by -1/2. When both sides are divided by -1/2, b becomes equal to 6. Thus, b must be 6.
Check work:
Thus, as they are equal to each other, the answer is correct. b = 6.
Hope this helps!
Given:
The expression is .
To find:
The shows the correct way to use the rule ""multiply by the reciprocal"" for the given expression.
Solution:
According to the rule "multiply by the reciprocal", if a,b,c,d are four number, then
We have,
It can be written as
Using the rule "multiply by the reciprocal", we get
Therefore, the correct option is D.
Firts we need to find the rate of change, or in other words, the slope of the line.
Question 1:
a)
For this we can take two points in the form (years, salary). Then we can define as year 0 the year when Gary starts to work. In this year the salary is $58,550. The first point is (0, $58,550)
The next point we can take is at the year 10, when the salary of Gary will be $71,950. The second point is (10, $71,950)
b) Now that we have the two points, we can use the slope formula to get the rate of change. The slope formula is, for two points A and B:
In this case, we can call the points A(0, $58,550) and B(10, $71,950). Using the formula:
c) "The rate of change in Gary's salary is $1340 per year."
Question 2:
a) The slope intercept form of a line is:
Where:
y is the output of the function.
x is the input of the function. (we provide the function with a value for x and the function give us a value of y)
m is the slope of the line. We calculate it in question 1.
x1 is the x coordinate of a point we choose.
y1 is the y-coordinate of the same point of x1.
In this case, we know:
m = 1340;
And we can take the point (0, $58,550), thus:
x1 = 0
y1 = 58,550
b) Now we need to use all this values and use the slope-intercept form:
And solve to get:
Question 3:
a) Now we have a equation for the salary, we can use this to find the salary in 13 years. We just need to replace x = 13 in the equation:
B) The salary of Gary in 13 years will be $75,970.