Answer:
c. f(x)=x(x+2)(x-1)(x-4)
Step-by-step explanation:
Where it says "as x goes to negative infinity" then "y goes to infinity" (that's the part with the infinity symbols) that means the graph is going up at it's left end. This curve is a quartic (4th degree) which means its left and right ends are kind of parabola-ish, but the middle is not the neat u-ish, v-ish shape of a parabola; it's more like a wonky, noodle-ish wavy affair. Anyway, LIKE a parabola when the beginning of the equation is positive, the two ends point up. That's what's happening here and so we can eliminate b. and d. as potential answers.
Since -2, 0, 1, 4 are zeros (which are solutions...and also x-intercepts) we can find the factors of the function.
If x = -2
ADD 2 to both sides.
x + 2 = 0
This means (x+2) is a factor.
This is enough info to select answer c. but let's verify the other factors.
If x = 1
SUBTRACT 1 from both sides.
x - 1 = 0
Thus means (x - 1) is a factor.
If x = 4
SUBTRACT 4 from both sides.
x - 4 = 0
(x - 4) is a factor.
You can see c. has all these factors as well as x, because x=0 already, so x is a factor too.
I think of this as a working backwards problem, bc usually you have to factor and solve. This one, you have solutions (which are zeros and x-intercepts) and work backwards to find factors and multiply them together to find the function.
Turn it into slope-intercept form.
2y = -x + 14
y = -x/2 + 7
The slope is -1/2.
Perpendicular lines have slopes that are opposite reciprocal, so the slope of the perpendicular line is 2.
Answer:
6 miles
Step-by-step explanation:
2 hours can be made into 1 hour by dividing by 2. In order to keep the ratio, you also have to divide the miles by 2, giving you 6.
2:12
1:6
Answer:
56 cups of water
Step-by-step explanation:
Katrina drinks 0.5 gallons of water per day
We have 7 days in a week, hence, the number of gallons of water she drinks per week is calculated as:
1 day = 0.5 gallons
7 days = x
Cross Multiply
1 day × x = 7 days × 0.5 gallons
x = 7 days × 0.5 gallons/1 day
x = 3.5 gallons
Note that 16 cups = 1 gallon
The number of cups of water she drinks per week is
1 gallon = 16 cups
3.5 gallons = x
Cross Multiply
1 gallons × x = 3.5 gallons × 16 cups
x = 3.5 gallons × 16 cups/1 gallons
x = 56 cups
Therefore, Katrina drinks 56 cups of water in a week
Number one is correct and so is two