Answer:
D: y = 3x² - 5x - 2
Step-by-step explanation:
The general form of a quadratic equation is: y = ax² + bx + c
c is the y-intercept
We are given the point (0, -2) which is the y-intercept, so we can rewrite our general form into
y = ax² + bx - 2
We can create a system of equations to solve for a and b. We are given two points.
Equation 1: Take the first point (-2, 20) and plug it into our general equation...
20 = a(-2)² + b(-2) - 2
20 = 4a - 2b - 2
22 = 4a - 2b (add 2 to both sides)
11 = 2a - b (divide both sides by 2 since every coefficient is even)
Equation 2: Take the point (1, -4) and plug it into the general equation
-4 = a(1)² + b(1) - 2
-4 = a + b - 2
-2 = a + b
Now we have our 2 equations:
11 = 2a - b
-2 = a + b
Since the coefficients of b are already have opposite signs, add the two equations together (elimination method)
Now we have
9 = 3a now solve for a...
3 = a (divide by 3 on both sides)
If a = 3, then
-2 = 3 + b
-5 = b
Our equation is
y = 3x² - 5x - 2
Answer:
x> -1/2
Step-by-step explanation:
Natalia walked her dog 7 miles.
Work:
1 2/5 x 5 = 35/5 which is 7
Answer:
Step-by-step explanation:
The given triangle is a right triangle. This means that one can use right-angle trigonometry to solve the triangle. The right angle trigonometric ratios are a set of ratios that relate the sides and angles of a triangle. These ratios are as follows,
Bear in mind, the names (opposite) and (adjacent) change depending on the angle of reference. However, the side (hypotenuse) refers to the side opposite the right angle, this side doesn't change depending on the reference angle.
In this problem, one is given the measure of an angle, and the measure of the hypotenuse, the problem asks one to solve for the side opposite the given angle measure. It would make the most logical sense to use the ratio of sine (sin) to do this.
Substitute,
Inverse operations,
