Answer:
A) x = {5, 7}
B) The solutions make the equation true.
Step-by-step explanation:
<u>Part A</u>:
To solve this by factoring, you need to find factors of 35 that have a sum of -12. Since 35 is the product of two primes, the search is a short one.
35 = (-1)(-35) = (-5)(-7)
The corresponding sums are -36 and -12, so the latter factor pair is the one we want. Since the coefficient of x^2 is 1, we can use these numbers directly in the binomial factors:
x^2 -12x +35 = (x -5)(x -7) = 0
The zero product rule tells us this product is zero only when one of the factors is zero:
x -5 = 0 ⇒ x = 5
x -7 = 0 ⇒ x = 7
The two solutions are x=5 and x=7.
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<u>Part B</u>:
The solutions from part A are the x-intercepts of the graph of the quadratic expression. They are the values of x that make the quadratic expression be zero. That is, they are the values of x that make the equation true.
Point slope: y - y1 = m(x - x1), m is the slope
first picture
points (-4,-1) and (3,-3)
the slope between these points is
slope = (-3 - 1)/( 3 - (-4) ) = -2/7
if (x1, y1) = (-4, -1), then the slope-point form is
y + 1 = -2/7(x + 4)
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second picture (horizontal line)
from the graph, the slope is 0 because there is no rise for a horizontal line.
if (x1, y1) = (-2, 1), then the point slope form is
y - 1 = 0(x + 2)
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third picture
from the graph, we have points (-2,2) and (2,-2) on the line. the slope is
slope = (-2 - 2)/(2 - (-2) ) = -1
if (x1, y1) = (-2,2), then point slope form is
y - 2 = -1(x + 2)
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fourth picture
if points (-2,-1) and (2,1) are on the graph, then slope is
slope = (1 - (-1) ) / (2 - (-2) ) = 1/2
with (x1, y1) = (-2,-1), the point slope form is
y + 1 = 1/2(x + 2)
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fifth picture
we have points (-1,-2) and (1,2). the slope is
slope = (2 - (-2) ) / (1 - (-1) ) = 2
with (x1, y1) = (1,2), the point slope form is
y - 2 = 2(x - 1)
Question #1 = <span>the amount of snow that falls each hour
question #2 = the starting amount of snow
algebra sucks, keep up the good work
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