Answer:
The number of terms in the sequence is 9
Step-by-step explanation:
We want to get the number of terms
Mathematically, we have the formula for the sum of terms in an arithmetic sequence as
a represents the first terms, and i represent the last term
Answer:
r = 5
Step-by-step explanation:
Solving radical equations often results in extraneous solutions. These can be avoided by using a graphing calculator for the solution.
<h3>Graph</h3>The attached shows that the value of r that makes both sides of the equation have the same value is r = 5.
<em>Check:</em>
√(5·5 -9) -3 = √(5 +4) -2 ⇒ 4 -3 = 3 -2 . . . true
<h3>Analytical solution</h3>Solution of an equation like this is typically done by isolating the radical expressions, then squaring the equation.
We can add 3, square the equation, then isolate the radical and square again:
Trying these values in the original equation, we get ...
√((5(9/4) -9) -3 = √(9/4 +4) -2 ⇒ 1.5 -3 = 2.5 -2 . . . . . false
√(5(5) -9) -3 = √(5 +4) -2 ⇒ 4 -3 = 3 -2 . . . . . true
The solution is r = 5.
Answer:
A
Step-by-step explanation:
<u />
From inspection of the graph, we can see that every time the x-value increases by 10, the y-value increases by 1000.
So, the employee earns an additional $1000 for every 10 units sold.
To calculate how much the employee earns for every 1 unit sold, divide $1000 by 10:
1000 ÷ 10 = 100
Therefore, the employee earns an additional $100 for every one unit sold.
<u />
<u>Proof</u>
This can be proved by calculating the slope (gradient) of the graph:
where and
are two points on the line
When picking the two points, remember that the <u>y-values are in </u><u><em>thousands</em></u><u> </u><u>of dollars.</u>
<u />
Two points on the line:
(0, 30000) and (20, 32000)
Substituting these into the formula:
Therefore, the employee earns an additional $100 for every one unit sold.
