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).
Answer:
About 152 pieces of candy
Step-by-step explanation:
Set up equal proportions to solve for the $5.99 bag.
We know that 24 pieces = .99, so
Make sure to keep the pieces on top, and the dollars on bottom (or vice versa). If your units are messed up, it will not work.
Cross-multiply.
25(5.99) = .99x
Simplify.
149.75 = .99x
Divide both sides by .99.
x = 151.26 = about 151 pieces of candy
Answer:
The percentage decrease is 27%
Step-by-step explanation:
To find the percent decrease, first find the difference in the two costs.
$205,000 - $149,650 = $55,350
Now divide that number by the original cost.
$55,350/$205,000 = 27%
<span>The geese are required to make a 5000 meter journey. For every 500 meters they travel forward they are blown back 50 meters. Therefore rather than traveling forward 500 meters, they travel forward only 450 meters. Presumably this happens during the whole course of each section of the flight, so when they travel fractions of the distance they are blown back in the same proportion. Since each 450 meter gain requires 3 minutes, and it will take 11.11111 450 meter sections of flight, it will take 33.333333 minutes. Since they leave at 11:30, they will arrive at 12:03 and roughly twenty seconds.</span>
Answer:
(x+2)^2=-1
Step-by-step explanation:
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