First we need to find where the 2 graphs intercept.
x^2 + 3 = - (x^2 - 4x + 4) + 7
x^2 + 3 = -x^2 + 4x + 3
2x^2 - 4x = 0
2x(x - 2)
x = 0 , 2. are x coordinates of the 2 intercepts.
Remember (a²-b²)=(a-b)(a+b)
solve for a single variable
solve for y in 2nd
add y to both sides
x²-7=y
sub (x²-7) for y in other equaiton
4x²+(x²-7)²-4(x²-7)-32=0
expand
4x²+x⁴-14x²+49-4x²+28-32=0
x⁴-14x²+45=0
factor
(x²-9)(x²-5)=0
(x-3)(x+3)(x-√5)(x+√5)=0
set each to zero
x-3=0
x=3
x+3=0
x=-3
x-√5=0
x=√5
x+√5=0
x=-√5
sub back to find y
(x²-7)=y
for x=3
9-7=2
(3,2)
for x=-3
9-7=2
(-3,2)
for √5
5-7=-2
(√5,-2)
for -√5
5-7=-2
(-√5,-2)
the intersection points are
(3,2)
(-3,2)
(√5,-2)
(-√5,-2)
Answer
Good question!
A. false. Even though 5 is usually greater than 2, in this case it is less because it is negative and positives are always greater than negatives.
B. true. Just like the last question, positives are always greater than negatives and even though 8 is usually greater than 3, in this case the 3 is a negative so it is less.
C. true. Think about which number is closer to the number line. When we are talking about negative numbers, the number closer to the number line is greater.
D. false. Same concept as the last question where -12 is closer to the number line than -12.5 so -12 is actually greater.
If you have any additional questions feel free to ask me or your teacher so you can really master what you're learning. :)
Answer: 0.50
Step-by-step explanation:
ap ex
The equation in the form y = mx + b is y = 0.35x + 36.
<h3>How to represent a linear equation?</h3>
The equation formed from the expression is a linear equation and should be expressed in the slope intercept form.
y = mx + b
where
Therefore,
y = mx + b
where
- x = the number of monthly minutes used
- y = the total monthly of the Next fell plan
using the coordinates, let's find m
(470, 200.5)(590, 242.5)
Hence,
m = 242.5 - 200.5 / 590 - 470
m = 42 / 120
m = 0.35
Therefore,
y = 0.35x + b
200.5 = 0.35(470) + b
200.5 - 164.5 = b
b = 36
Finally, the equation in the form y = mx + b is y = 0.35x + 36.
learn more on linear equation here: brainly.com/question/24223023
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