Trust me: You must know how to do this basic factoring yourself.
x^2 -5x - 6 factors into (x-6)(x+1). Note how I got that: -6 is the product of 1 and -6, and -6 + 1 = -5.
You could also factor this by grouping:
x^2 -5x - 6 = x(x-6) + 1(x-6). Note how the middle terms combine to produce -5x and how (x-6) is a factor common to both terms; this leaves (x+1). So the factors are (x-6)(x+1).
Answer:
D -2x-6
Step-by-step explanation:
Y= -2x² + 32x -12
Take the derivative, and set it equal to zero. We are finding where the slope equals zero (the peak of the parabola)
y'= -4x + 32
0 = -4x + 32
4x=32
x=8
The maximum is at the point x=8. Plugging into the original equation:
y= -2x² + 32x -12
y= -2(8)² + 32(8) -12
y= 116
The maximum is at point y=116
Keep in mind what maximum means. It is the largest value for y that the function has. That means that the range, or all possible y-values, is
y ≤ 116.
Therefore, the answer is A) Max: 116, range: y ≤ 116
Answer:
46.9 times
Step-by-step explanation:
First, we can calculate how many feet it takes to run around the field. To find the perimeter of a rectangle, we can use the formula
2* length + 2 * width. With the length being 450 and the width being 225 here, we can say that
2*450 + 2 * 225 = 1350 feet
Therefore, Andrew runs 1350 feet each time he runs around the field. Next, we need to figure out how much 1350 feet goes into 12 miles as we want to find how many times Andrew runs around the field to get to 12 miles. This can be represented by
12 miles/1350 feet
One thing that we can do here is multiply the fraction by 1 to keep it the same. Because 1 mile = 5280 feet, we can say that
1 mile/5280 feet = 1 = 5280 feet/1 mile. Therefore, it would be safe to multiply
12 miles/1350 feet by 1 = 5280 feet/1 mile. Note that feet is on the bottom in the first fraction (12 miles/1350 feet) and on the top in the second (5280 feet/1 mile) so they will cancel out. Similarly, miles are on top in the first and bottom in the second. We then have
12 miles/1350 feet * 5280 feet/1 mile =63360/1350 ≈ 46.9
Where’s the graph? I will need it if I can help.
