Hi there! Hopefully this helps!
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<em>Remember: When the numerator and denominator both are positive integers or both are negative integers, it is a positive rational number. When either the numerator or the denominator is a negative integer, it is a negative rational number.</em>
(-1/-3) Positive Rational Number.
(+1/-3) Negative Rational Number.
(-2/+3) Negative Rational Number.
(+1/+3) Positive Rational Number.
(+2/-3) Negative Rational Number.
(-1/+3) Negative Rational Number.
(-2/-3) Positive Rational Number.
(+2/+3) Positive Rational Number.
f(x) = (x - 4)^2 - 1
g(x) = -(1/4) ( x - 4)^2 + 4
both the x and y values have to be the same. Start with the y values
f(x) = g(x)
(x - 4)^2 - 1 = -(1/4) (x - 4)^2 + 4 Add 1 to both sides.
(x - 4)^2 = -(1/4) (x - 4)^2 + 5 Add 1/4(x - 4)^2 to both sides.
(5/4) (x - 4)^2 = 5 Divide by 5/4 on both sides.
(x - 4)^2 = 5//(5/4)
(x - 4)^2 = (5/1)//5/4 Invert the second fraction and multiply
(x - 4)^2 = 5/1 * 4/5
(x - 4)^2 = 4 The 5s cancel
(x - 4)^2 = 4 Take the square root of both sides.
(x - 4) = +/- 2 Add 4 to each answer. Start with +2 on the right.
x - 4 + 4 = 2 + 4
x = 4 + 2 = 6
The x value that makes f(x)- g(x) = 0 is x = 6 The point is (6,3) answer.
Answer C.
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You do not need this next part. It is just for completeness.
x - 4 = - 2
x = 4 -2
x = 2
What are the y values for these 2 x values?
y = (x - 4)^2 - 1
y = (6 - 4)^2 - 1
y = 4 - 1
y = 3
The point where f(x) - g(x) = 0 is (6,3) <<<<<< Answer 1
The second point is
y = (x - 4)^2 - 1
y = (2 - 4)^2 - 1
y = (-2)^2 - 1
y = 4 - 1
y = 3
The second point is (2,3). Answer 2
Note the y values are the same. You might expect that.
Answer:
The ordered pair that makes an equation true is called a solution
a)solution
b) not a solution
c) solution
d) solution
e)not a solution
f) not a solution
g) solution
h) not a solution
Step-by-step explanation:
The first number in an ordered pair is x, the second one is y
Plug in the numbers to x and y respectively
I'll give two examples so you know how to solve it
a) y=3x+1
-5=3(-2)+1
make sure you use pemdas (multiply first)
-5=-6+1
add
-5=-5
this is true (meaning it is a solution)
b) 6=3(-3) +1
6=-9+1
6 = -8
this is NOT true (not a solution)
If you have any questions feel free to ask
You have to find what x is to do all of them
Answer:
C
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = 
with (x₁, y₁ ) = (0, 6) and (x₂, y₂ ) = (4, 0) ← 2 points on the line
m = 
= 
= - 
, then
y = - x + c
the line crosses the y- axis at (0, 6 ) ⇒ c = 6
y = - x + 6 ← equation in slope- intercept form
multiply through by 2 to clear the fraction
2y = - 3x + 12 ( add 3x to both sides )
3x + 2y = 12 ← equation in standard form
