D-7<span>≤ 3
add 7 to both sides
d</span><span>≤10</span>
Distance formula : d = sqrt (x2 - x1)^2 + (y2 - y1)^2
(3,8)(-7,11)
d = sqrt (-7 - 3)^2 + (11 - 8)^2
d = sqrt (-10^2) + (3^2)
d = sqrt (100 + 9)
d = sqrt 109
d = 10.44
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mid-point formula : ((x1 + x2) / 2 , (y1 + y2) / 2)
(-9,5)(21,-7)
midpoint = ((-9 + 21)/2 , (5 + (-7)/2)
= ((12/2) , (-2,2))
= (6, -1) <==
=======================
(-8,7)(-9,11)
midpoint = ((-8 + (-9) / 2, (7 + 11)/2 )
= (-17/2, 18/2)
= (-8.5, 9) <==
======================
(8,y)(-11,6).....midpoint = (-1.5/5)
midpoint = ((8 + (-11)/2, (y + 6)/2)
= (-3/2), (4 + 6)/2
= (-1.5,5)
y = 4 <==
======================
slope = (y2 - y1) / (x2 - x1)
(3,-6)(6,12)
slope = (12 - (-6) / (6 - 3) = (12 + 6) / 3 = 18/3 = 6 <==
======================
(x,10)(-4,8)...slope = 2/3
y = mx + b
slope(m) = 2/3
(-4,8)...x = -4 and y = 8
sub and find b
8 = 2/3(-4) + b
8 = -8/3 + b
8 + 8/3 = b
24/3 + 8/3 = b
32/3 = b
equation is : y = 2/3x + 32/3 or 3y = 2x + 32
when y = 10
3(10) = 2x + 32
30 - 32 = 2x
-2 = 2x
-2/2 = x
-1 = x <===
=================
(9,0)(3,y)...slope = 1/2
y = mx + b
slope(m) = 1/2
(9,0)...x = 9 and y = 0
sub and find b
0 = 1/2(9) + b
0 = 9/2 + b
-9/2 = b
equation is : y = 1/2x - 9/2 or 2y = x - 9
sub in 3 for x and solve for y
2y = 3 - 9
2y = -6
y = -6/2
y = -3 <==
=================
(8,7)(11,7)...notice how the y values are the same. This means it is a horizontal line. A horizontal line has a slope of 0.
====================
sorry...not too good with the picture graphs
Answer:
1: B
2: H
3. C or D (it's hard to tell, especially without an equation)
4. J
5. A
6. G
7. B
Step-by-step explanation:
1:
f(x) - g(x)
(x^2 + 8x) - (3x - 5) Distribute the negative
x^2 + 8x - 3x + 5 Combine like terms
x^2 + 5x + 5
2:
f(g(x))
Plug g(x) into f(x)
(2x - 1)^2 - 3
Immediately we can see that there will be a 4x^2 (because 2x times 2x = 4x^2) so we know the answer will be H because that's the only option with 4x^2
3:
The line starts at -4 on the x axis and goes infinitely to the right so everything greater than (and maybe equal to) -4.
On the y axis, the line starts at 0 and goes infinitely up so everything greater than (and maybe equal to) 0.
4:
To find the inverse of a function:
<em>f(x) -> y</em>
<em>Switch x and y</em>
<em>Solve for y again</em>
x = 3 +5y
x-3 = 5y
(x-3)/5 = y
5:
If option A were inverse functions, h(x) would be
x = 2y + 9
x - 9 = 2y
(x-9)/2 = y
Which could also be written as (1/2)x - 9/2 or (1/2)x - 4.5 but not (1/2)x - 9
6:
As y approaches -1, x approaches 1. Going the other direction,
As y approaches positive infinity, x approaches positive infinity.
7:
The number inside directly affecting the x moves the function left and right (left is positive, right is negative). The number outside moves the function up and down. So (x + 4) moves it left 4 and the +1 moves it up 1.
