Answer:
The solution is (8, -1).
Step-by-step explanation:
2x + 4y = 12..........(1)
y = 1/4x – 3 ..........(2)
Substitute y = x - 3 in equation (1):
2x + 4(1/4x - 3) = 12
2x + x - 12 = 12
3x = 24
x = 8.
Now substitute for x in equation (2):
y = 1/4 *8 - 3
y = -1.
Answer: -2-8= -10
4+1 = 5 (the negative switches to a positive)
Your slope equals -10/5. You can look at this in a fraction for when you might use it later in point slope or slope intercept form, or you can just simplify it to -2. It might also be helpful to remember the numerator as the rise and the denominator as run, or “rise over run” if you need to graph it.
Slope = -10/5 or -2
Step-by-step explanation:
Slope, often referred to as the variable “m” can be found by solving y2-y1/x2-x1. You can do it the opposite way, though make sure the y-values are on the top.
B) 14 is the correct answer
OK. These problems are easy if you know the quadratic formula,
and they're impossible if you don't.
Here's the quadratic formula:
When the equation is in the form of Ax² + Bx + C = 0
then x = [ -B plus or minus √(B²-4AC) ] / 2A
I'm sure that formula is in your text or your study notes,
right before these questions. You should cut it out or
copy it, and tape it inside the cover of your notebook.
Then, you'll always have it when you need it, until
you have it memorized and can rattle it off.
The first question says 3x² + 5x + 2 = 0
Is this in the form of Ax² + Bx + C = 0 ?
Yes ! A=3 B=5 C=2
so you can use the quadratic formula to solve it.
x = [ -B plus or minus √(B²-4AC) ] / 2A
= [ -5 plus or minus √(5² - 4·3·2) ] / 2·3
= [ -5 plus or minus √(25 - 24) ] / 6
= [ -5 plus or minus √1 ] / 6
x = -4 / 6 = -2/3
and
x = -6 / 6 = -1 .
_______________________________________
The second question says
4x² + 5x - 1 = 0
Is this in the form of Ax² + Bx + C = 0 ?
Yes it is ! A=4 B=5 C= -1
so you can use the quadratic formula to solve it.
x = [ -B plus or minus √(B²-4AC) ] / 2A
Now, you take it from here.
