X=hours master worked
y=hours apprentice worked
62x+40y=492
if master worked 3hours more than apprntice
x=3+y
sub 3+y for x
62(3+y)+40y=492
expand
186+62y+49y=492
186+102y=492
minus 186 both sides
102y=306
divide both sides by 102
y=3
sub back
x=3+y
x=3+3
x=6
master electrician worked 6 hours
6*62=372
master electrician earned $372
Answer: x = 3.4
Step-by-step explanation: took the test and got it right. if you need help on this kind of work u can use things like (graphing gens) or math to help you more.
Answer:
The ans is in the picture with the steps how i got it
(hope this helps can i plz have brainlist :D hehe)
Step-by-step explanation:
Answer:
Alternate Interior Angles
Step-by-step explanation:
Since they are inside the parallel lines, Alternate Exterior Angles and any other similar theorems can be ruled out.
Since they are on opposite sides of each other, Corresponding Angles and any other similar theorems can be ruled out.
Since they are far apart from each other, Supplementary Angles, Adjacent Angles, Vertical Angles, and any other similar definitions can be ruled out.
Therefore, we are left with Alternate Interior Angles.
Step-by-step explanation:
let us give all the quantities in the problem variable names.
x= amount in utility stock
y = amount in electronics stock
c = amount in bond
“The total amount of $200,000 need not be fully invested at any one time.”
becomes
x + y + c ≤ 200, 000,
Also
“The amount invested in the stocks cannot be more than half the total amount invested”
a + b ≤1/2 (total amount invested),
=1/2(x + y + c).
(x+y-c)/2≤0
“The amount invested in the utility stock cannot exceed $40,000”
a ≤ 40, 000
“The amount invested in the bond must be at least $70,000”
c ≥ 70, 000
Putting this all together, our linear optimization problem is:
Maximize z = 1.09x + 1.04y + 1.05c
subject to
x+ y+ c ≤ 200, 000
x/2 +y/2 -c/2 ≤ 0
≤ 40, 000,
c ≥ 70, 000
a ≥ 0, b ≥ 0, c ≥ 0.
