This is a problem of Difference-of-squares. We know that for a difference of squares
the factorization is given by:
To learn this you need to remember that a <em>difference</em> means <em>subtraction.</em> So applying those concepts we can solve this problem step by step.
Applying distributive property:
Applying distributive property again:
Simplifying:
<em>The correct answer is C</em>
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Hi there
Let x be the number of miles Karly biked
Dory biked 11 times as many miles as Karly, therefor, Dory = 11x
The total number of miles back by both is 156
The equation will be:
11x + x = 156
Before we can get the number of miles Dory biked, we must first get the number of miles
Karly biked represented by x.
Get the x
12x = 156
12x/12 = 156/12
<span>x = 13 </span>
Karly = x = 13 miles biked
Dory = 11x = 11(13) = 143 miles biked
to check:
11x + x = 156
11(13) + 13 = 156
143 + 13 = 156
<span>156 = 156
i hope it helps have a nice day:)
</span>
Answer:
1. shifts the graph right 2 units
2. y = -2(x -3)² +7
Step-by-step explanation:
1) Replacing x with x-h in any function shifts the graph h units to the right. Here, you have replaced x with (x-2), so the graph will be shifted 2 units to the right.
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3) The vertex form of the equation of a parabola is ...
y = a(x -h)² +k . . . . . . . . for vertex (h, k) and vertical scale factor 'a'
Here, the vertex is (h, k) = (3, 7), and the parabola opens downward. This tells us the sign of 'a' is negative.
The graph is not so clear that it is easy to read the value of 'a' directly from it, but there are several clues.
The zeros of the above function are found at h±√(k/a). This graph shows the zeros to be located such that √(7/a) is slightly less than 2. This means the magnitude of 'a' will be slightly more than 7/2² = 1.75. The y-intercept of the function is 7-9a. It is less than -7, but probably more than -14. This puts bounds on 'a':
-14 < 7-9a < -7
-21/9 < -a < -14/9 ⇒ -2.33 < -a < -1.56
If we assume that 'a' is an integer value, we have bounded its magnitude as being between 1.75 and 2.33, so a=-2 is a reasonable choice.
The equation of the graph may be ...
y = -2(x -3)² +7
To get the largest area, the length and the width have to be as close as possible, if not the same.
Given Perimeter = 176 unit.
Length = 176 ÷ 4 = 44 units
Area = Length x Width
Area = 44 x 44 = 1936 units²
1936 units² is the largest possible area, given that the perimeter is 176 units. The dimension being 44 by 44
Answer:
m = -100
Step-by-step explanation:
(1/5)m -12 = -32
add 12 on both sides
(1/5)m = -20
multiply both sides by 5
m = -100
