Answer:
Step-by-step explanation:
The sum of an infinite geometric series is expressed according to the formula;
where;
a is the first term of the series
r is the common ratio
If the sum of an infinite geometric series is three times the first term, this is expressed as
Substitute into the formula above to get the common ratio r;
open the parenthesis
subtract 3 from both sides
<em>Hence the common ratio of this series is </em><em></em>
Given that the number of tickets that are sold for $5 is (3t+2) tickets.
The number of tickets that are sold for $7 is (2t+5) tickets.
We need to determine the expression that represents the total number of tickets sold and the simplified expression.
<u>Total number of tickets sold:</u>
The expression for (3t+2) tickets sold for $5 is given by
The expression for (2t+5) tickets sold for $7 is given by
The expression for the total number of tickets sold is given by
Thus, the expression that represents the total number of tickets sold is
<u>Simplified expression:</u>
We need to simplify the expression
Hence, let us multiply the terms within the bracket.
Thus, we get;
Adding the like terms, we have,
Thus, the simplified expression is
Answer:
(1.13, 7.74) and (-4.13, 18.26)
Step-by-step explanation:
This can be solved in two ways: mathematically and graphically.
<u>Graphing</u>
Plot both lines and find where they intersect. See the attachment.
The intersection points are (1.13, 7.74) and (-4.13, 18.26)
<u>Mathematical</u>
y + 2x = 10
y = 10 - 2x
y = 3x² + 7x - 4
10 - 2x = 3x² + 7x - 4
3x² + 9x - 14 = 0
Solve this using the quadratic equation:
x = 1.13 and -4.13
Use these two values of x to find y:
y = 10 - 2x
y = 10 - 2(1.13)
y = 7.74
y = 10 -2x
y = 10 -2(-4.13)
y = 18.26
The two points are:
(1.13, 7.74) and (-4.13, 18.26)
