There is only one real root, at x=-2, so the polynomial describing this parabola has factors of (x+2) with multiplicity 2. The y-intercept tells you the vertical stretch is 1.
The factorization is y = (x +2)².
Answer:
y=3/-1x+4
Step-by-step explanation:
Okay so first thing you need to know is that if there is an ordered pair (x, y) where x is 0, your y-intercept is your y. For example, your problem has (0, 4) your x is 0 and your y is 4. Therefore your y-intercept is 4 which is the b. To find your mx, or slope, you need to do (y2-y1)/(x2-x1). Your y2 will be your y in your second ordered pair and your y1 will be in your y in the first ordered pair. Same for your x. So, (4-1)/(0-1) which equals 3/-1. 3/-1 is your slope. So, your answer in slop intercept form is: y= 3/-1x+4. You could also try y= -3x+4 if that makes you more comfortable.
I know this is long this is my first time doing this lol.
Company A would because it is the least with the lowest slope since it is not increasing very fast
Answer:
Union and Intersection
Step-by-step explanation:
We know that the algebra of sets define the properties and laws of the sets.
The basic operations of sets are,
Union, Intersection, Complement of a set and Equality of sets.
Since, the operations addition, subtraction, multiplication and division are the basic arithmetic operations of numbers.
i.e. they are not in the algebra of sets.
So, we get that out of the given options, the operations in algebra of sets are Union and Intersection.
Answer:
System A has 4 real solutions.
System B has 0 real solutions.
System C has 2 real solutions
Step-by-step explanation:
System A:
x^2 + y^2 = 17 eq(1)
y = -1/2x eq(2)
Putting value of y in eq(1)
x^2 +(-1/2x)^2 = 17
x^2 + 1/4x^2 = 17
5x^2/4 -17 =0
Using quadratic formula:
a = 5/4, b =0 and c = -17
Finding value of y:
y = -1/2x
System A has 4 real solutions.
System B
y = x^2 -7x + 10 eq(1)
y = -6x + 5 eq(2)
Putting value of y of eq(2) in eq(1)
-6x + 5 = x^2 -7x + 10
=> x^2 -7x +6x +10 -5 = 0
x^2 -x +5 = 0
Using quadratic formula:
a= 1, b =-1 and c =5
Finding value of y:
y = -6x + 5
y = -6(\frac{1\pm\sqrt{19}i}{2})+5
Since terms containing i are complex numbers, so System B has no real solutions.
System B has 0 real solutions.
System C
y = -2x^2 + 9 eq(1)
8x - y = -17 eq(2)
Putting value of y in eq(2)
8x - (-2x^2+9) = -17
8x +2x^2-9 +17 = 0
2x^2 + 8x + 8 = 0
2x^2 +4x + 4x + 8 = 0
2x (x+2) +4 (x+2) = 0
(x+2)(2x+4) =0
x+2 = 0 and 2x + 4 =0
x = -2 and 2x = -4
x =-2 and x = -2
So, x = -2
Now, finding value of y:
8x - y = -17
8(-2) - y = -17
-16 -y = -17
-y = -17 + 16
-y = -1
y = 1
So, x= -2 and y = 1
System C has 2 real solutions
