Answer:
x = 7 and x = 5
Step-by-step explanation:
12x - 35 = x²
x² - 12x + 35 = 0
(x - 7)(x - 5) = 0
x = 7 and x = 5
The appropriate choice is ...
D: Function 1 shows a greater rate of change, because Maddy spends $20 each month and Caitlin spends $18 each month.
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Each time the month number in Function 1 goes up by 1, the account balance goes down by $20. Each time the month number in Function 2 goes up by 1, the account balance goes down by $18. Once you have figured out that $20 is more than $18, you know the first two answers cannot be right. The third answer is wrong because Caitlin cannot (and does not) spend -$18 each month.
<u>Part A</u>
x² + 5x + 4 = 0
x = <u>-(5) +/- √((5)² - 4(1)(4))</u>
2(1)
x = <u>-5 +/- √(25 - 16)</u>
2
x = <u>-5 +/- √(9)</u>
2
x = <u>-5 +/- 3</u>
2
x = <u>-5 + 3</u> U x = <u>-5 - 3</u>
2 2
x = <u>-2</u> x = -<u>8</u>
2 2
x = -1 x = -4
<u>Part B</u>
4x² - 12x + 5 = 0
x = <u>-(-12) +/- √((-12)² - 4(4)(5))</u>
2(4)
x = <u>12 +/- √(144 - 80)</u>
8
x = <u>12 +/- √(64)</u>
8
x = <u>12 +/- 8</u>
8
x = <u>3 +/- 2</u>
2
x = <u>3 + 2</u> U x = <u>3 - 2</u>
2 2
x = <u>5</u> x = <u>1</u>
2 2
x = 2.5 x = 0.5
<u>Part C</u>
2x² - 10x + 3 = 0
x = <u>-(-10) +/- √((-10)² - 4(2)(3))</u>
2(2)
x = <u>10 +/- √(100 - 24)</u>
4
x = <u>10 +/- √(76)</u>
4
x = <u>10 +/- 2√(19)</u>
4
x = <u>5 +/- √(19)</u>
2
x = 2.5 <u>+</u> 0.5√(19)
x = 2.5 + 0.5√(19) U x = 2.5 - 0.5√(19)