Answer:
x = 3 . . . or . . . x = 4
Step-by-step explanation:
The factored form is ...
(x -3)(x -4) = 0
The zero product rule tells you the solutions are the values of x that make the factors be zero:
x = 3
x = 4
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Comment on factoring
When the leading coefficient is 1, the coefficient of the x-term is the sum of the constants in the binomial factors, and the constant term is their product. You can see this by multiplying out the generic case:
(x +a)(x +b) = x^2 +(a+b)x + ab
What this means is that when you're factoring, you're looking for factors of the constant that add up to give the coefficient of the x-term. Here, the x-term is negative and the constant is positive, so both factors will be negative.
12 = -1×-12 = -2×-6 = -3×-4
The sums of these factor pairs are -13, -8, -7. Clearly, the last pair of factors of 12 will be useful to us, since that sum is -7. So, the binomial factors of our equation are ...
(x -3)(x -4) = 0
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If the leading coefficient is not zero, the method of factoring is similar, but slightly different. Numerous videos and web sites discuss the method(s).
9514 1404 393
Answer:
(b) x +2y = 8
Step-by-step explanation:
The only offered line that includes the given point is ...
x +2y = 8
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We can check the other choices:
x + 2y = 2 +2(3) = 2+6 = 8 . . . matches B (not A)
2x +y = 2(2) +3 = 4+3 = 7 . . . . not a choice
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<em>Getting there from scratch</em>
The standard form equation for a line can be written from ...
(y2 -y1)x -(x2 -x1)y = constant
(-4 -0)x -(4 -(-4))y = constant . . . . using the given points (-4, 0) and (4, -4)
-4x -8y = constant
For standard form, we need the leading coefficient to be positive, and we need common factors removed. We can get there by dividing by -4.
x +2y = constant
The value of the constant will be whatever it takes for the given point to lie on the line. For (x, y) = (2, 3) to be a solution, we must have ...
x +2y = (2) +2(3) = constant = 8
The desired line has the equation ...
x +2y = 8
9514 1404 393
Answer:
(3) y = (x -3)²
Step-by-step explanation:
Try the first value of x in each function:
(1) y = 3² -3 ≠ 0
(2) y = (3 +3)² ≠ 0
(3) y = (3 -3)² = 0 . . . . . . matches the table value for f(3)
(4) y = 3² +3 ≠ 0
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The only viable choice is (3).
Sides:6.7,9.3,9.5
Tell me if that helps
Answer:
$1.10
Step-by-step explanation:
We have been that Alex went to the grocery store and bought 5 avocados. He paid $10 and received $4.50 in change.
First of all, we will find amount paid for 5 avocados by subtracting $4.50 from $10.
Now, we will divide $5.50 by 5 to find cost of each avocado.
Therefore, the cost of each avocado is $1.10.
