Answer:
y = -x - 8
Step-by-step explanation:
Midpoint of the line:
x = (x1 + x2)/2 = (-8 + -4)/2 = -12/2 = -6
y = (y1 + y2)/2 = (-5 + 1)/2 = -4/2 = -2
so midpoint is (-6,-2)
Slope of the line: Slope m = (y2-y1)/(x2-x1)
m = (-1 - -5)/(-4 - -8) = (-1 + 5)/(-4 + 8) = 4/4 = 1
Perpendicular lines have slopes that are negative reciprocals of one another
so slope of the perpendicular line is -1/1 is -1
y = mx + b
y = -x + b
Using (-6,-2)
-2 = -(-6) + b
-2 = 6 + b
b = -8
so y = -x - 8
9514 1404 393
Answer:
range: 5 ≤ f(x) ≤ 205
Step-by-step explanation:
You can put the extreme values of x in this linear function to see its range:
f(0) = 4·0 +5 = 5
f(50) = 4·50 +5 = 205
The range is 5 ≤ f(x) ≤ 205.
Answer:
75/16 or 4 11/16
Step-by-step explanation:
The first answer is an improper fraction, and the second answer is a mixed number...
A+bi is a complex number
(3+2i)(a+bi)=17+7i
remember
i²=-1
so
expand and solve
a is the ral part
bi is the imaginary part
ok so
if Ac+Be=dc+fe where c=c and e=e then A=d and B=f
(3+2i)(a+bi)=17+7i
expand/distribute/FOIL
3a+2ai+3bi+2bi²=17+7i
3a+2bi+2ai+2bi=17+7i
3a-2b+2ai+2bi=17+7i
real parts are 3a-2b
imaginary is 2ai+2bi
so
3a-2b=17 and
2ai+2bi=7i
we need to solve
2nd equation, divide both sides by i
2a+2b=7
multiply by -1 and add to other equation
3a+2b=17
<u>-2a-2b=-7 +</u>
1a+0b=10
a=10
subsitue
2a+2b=7
2(10)+2b=7
20+2b=7
2b=-13
b=-13/2
the complex number is
10-(13/2)i or
10-6.5i
1.425 gallons of apple juice are in one container
I got this because if she starts with 6 gallons and she’s left with 0.3 gallons, you would need to subtract 6 by 0.3 (6-0.3=5.7). So now you know how much is in 4 bottles. Now you need divide 5.7 by 4 to find out how much is in each container (which is 1.425).
