First, find the slope of the initial line;
m=(y₁-y₂)/(x₁-x₂)
m=(4-0)/(11-8)
m=4/3
If two lines are parallel, the slope is the same although the intercept can differ.
If this parallel lines passes through the point (4, 5);
y=(4/3)x+c <-- plug in coordinates to solve for c
5=(4/3)(4)+c
(15/3)=16/3+c
(15/3)-(16/3)=c
-1/3=c
Therefore, the final equation should be y=4/3x-1/3
Hope I Helped :)
Answer: Choice B
a_n = 10(1/2)^(n-2) is the nth term
average rate of change = -35/3
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Explanation:
Each time x increases by 1, y is cut in half. For instance, going from (2,10) to (3,5) shows this.
If we want to go in reverse, decreasing x by 1 will double the y value. So (1,20) is another point and (0,40) is another. We'll be using (0,40) and (3,5) because we want the average rate of change from x = 0 to x = 3. I'm using x in place of n here.
Use the slope formula to find the slope of the line through (0,40) and (3,5)
m = (y2-y1)/(x2-x1)
m = (5-40)/(3-0)
m = -35/3
The negative slope means the line goes downhill as you read it from left to right. The average rate of change from n = 0 to n = 3 is -35/3
The nth term of this geometric sequence is 20(1/2)^(n-1) since 20 is the first term (corresponds to n = 1) and 1/2 is the common ratio. Your teacher has done a bit of algebraic manipulation to change the n-1 into n-2. This means the 20 has to change to 10 to counterbalance.
In other words, 20(1/2)^(n-1) is equivalent to 10(1/2)^(n-2) when n starts at n = 1.
Answer:
Use y + x = 3 and solve for either x or y.
Step-by-step explanation:
Substitution is a method to solve a system of equations by substituting an expression from one equation into the other.
To begin, first solve one equation by isolating for one variable. Choose the equation which will have the least number of steps to do so.
y + x = 3 can be solve for x or y by subtracting the other variable. Since this only requires one step use this equation. Either variable can be used.
C. -7.25 + 0.5(n)
Let's plug in some numbers
Let n = 2
-7.25 + 0.5(2) = -6.25
Let n = 3
-7.25 + 0.5(3) = -5.75
All the numbers match up when you substitute a whole number, therefore it is C.
Let's check one last one, if n=4
-7.25 + 0.5(4) = -5.25
Let's check to see if this is true.
-5.75 - 0.5 = -6.25
The -5.75 and the -6.25 are all numbers given for the equation. (in your picture)
Answer:
Step-by-step explanation:
60 miles per hour
Since d=rt, r = d/t = 420 miles/7 hours = 60 miles per hour.
