When you have a bunch like this, I find it easiest to graph them.
The numbers of real solutions are ...
2
0
2
1
I know you know how to use Desmos to graph these. You can also write a little spreadsheet program to compute the discriminant b^2 -4ac, or do it the hard way.
1^2 -4(-3)(12) = 145 . . . positive, so 2 solutions
(-6)^2 -4(2)(5) = -4 . . .. negative, so 0 solutions
7^2 -4(1)(-11) = 93 . . . .. positive, so 2 solutions
(-8)^2 -4(-1)(-16) = 0 . .. zero, so 1 solution
Answer:
This means that f(x)→∞ as x→−∞ and f(x)→∞ as x→∞.
Step-by-step explanation:
Since the leading term of the polynomial (the term in a polynomial which contains the highest power of the variable) is x4, then the degree is 4, i.e. even, and the leading coefficient is 1, i.e. positive.
This means that f(x)→∞ as x→−∞ and f(x)→∞ as x→∞.
Answer: 1 foot
Step-by-step explanation:
because 1 foot is equivalent to 12 inches
Answer:
<em>(-3, -1)</em>
Step-by-step explanation:
Given the system of equation
y=1/3x-2
y=-3x – 12
Since both equations are y values, we will equate then=m to each other as shown;
1/3x - 2 = -3x - 12
x/3 + 3x = -12 + 2
(x+9x)/3 = -10
x+9x = -30
10x = -30
x = -30/10
x = -3
Substitute x = 3 into equation 1;
From 1: y=1/3x-2
y=1/3(3)-2
y = 1 - 2
y = -1
<em>Hence the required solution (x, y) is (-3, -1)</em>
-3 because it shows the value right there