Answer:
<em>k = - 7.5 </em>
Step-by-step explanation:
Slope "m" of a line through points
( 
, 
)
( 
, 
)
is m = 
Slopes of perpendicular lines are opposite reciprocal: 
= - 1
~~~~~~~~~~~~~~~
The slope of a line through points (0, 7) and (2, 10)
= 
= 
Slope of perpendicular line through points (3, 5) and (k, 12) is = 
or = 
=
2(k - 3) = - 21
k - 3 = - 10.5
<em>k = - 7.5</em>
Step-by-step explanation:
Howdy, did you do a, b, and c by yourself? Because there are some slight issues, so I'll do my best to explain.
a. 3x+5x
We know that x=2, so we can substitute 2 in for x right now, or we can combine like terms.
3x and 5x both have the variable x so we can add them easily to get 8x. If you substitute in 2, you're just multiplying 8×2, which is 16.
b. 5z+4z+z
Again, since
we know that z=-3, we can substitute in now, or we can combine like terms first. 5z, 4z, and z all have the variable x, we addition is easy. 5+4+1=10, so you'll have 10z. Substitute in -3 for z, and you're just multiplying 10×-3=-30
c. 3x+6+5x
This is trickier since 6 doesn't have the variable x. So to combine like terms means to only add 3x and 5x. So the equation will turn out looming like 8x+6. now substitute in 2 for x and you get
8(2)+6
16+6
22
d. 8y+8-4y
Combine like terms
4y+8
substitute in 5 for y
4(5)+8
20+8
28
e. 5z-4z+z
combine like terms
z+z
2z
substitute -3 for z
2(-3)
-6
f. 3x+6+5x-2
combine like terms
(so that's 3x+5x and 6-2)
8x+4
substitute in 2 for x
8(2)+4
16+4
20
g. 8y+8-4y-3
combine like terms
8y-4y+8-3
4y+5
substitute in 5 for y
4(5)+5
20+5
25
h. 5z-4z+z-3z
combine like terms
-z
substitute in -3 for z
-(-3)
double negatives make a positive
3
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