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Polynomials, Quadratics, Linear Equations and Word Problems

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1.Simplify -i^4: answers a.-1 b.1 c.i d.-i
2.Types of Equations
Solve by factoring: x4 - 9x2 = 0. answers a.1, -1, 3, -3 b.0, 3, -3 c.9, -9 d.3, -3
3. Two-Dimensional Coordinate System and Graphs;
Find the midpoint of the line segment with endpoints (-4, 8) and (7, 2).
a.(3/2, 5) b(-11/2, 3) c.(11/2, -3) d.(3/2, 3)
4.Introduction to Functions
Given f(x) = 3x2 + x and g(x) = 8, find f(-1) and g(2). answer
a.f(-1) = 4; g(2) = 2 b.f(-1) = 2; g(2) = 2 c.f(-1) = 2; g(2) = 8 d.f(-1) = 4; g(2) = 8
5.The length of a rectangle is 4 feet less than twice the width of the rectangle. If the perimeter of the rectangle is 136 feet, find the length of the rectangle.
a.44 feet b.24 feet c.52 feet d. 16 feet
6.An elementary school class is selling candles to raise money to go on a field trip. The profit made by selling x candles is Profit = 1.25x - 45. How many candles must be sold to make a profit of $200? answers;
a.244 candles b.4 candles c.124 candles d.196 candles
Polynomial Division and Synthetic Division
8.Find the real zeros of the polynomial function P(x) = x(x - 1)(3x + 5).
9.Find the real zeros of the polynomial function P(x) = (x + 4)(x - 6)(x + 1)3.

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Polynomials, Quadratics, Linear Equations and Word Problems are investigated. The response received a rating of "5" from the student who posted the question.

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1. answer is b. 1 since i^2=-1, i^4=(-1)^2=1
2. x^4-9x^2=x^2(x^2-9)=x^2*(x-3)(x+3)
So, four roots are x=0, or x=0, or x=3, or, x=-3. So, answer is b.
3. Using a formula for midpoint below
So, we get

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  • MA, Shandong Univ.
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  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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