t=2w-1
OPTION A is the correct answer...
Answer:
x=2/5, y=-24/5. (2/5, -24/5).
Step-by-step explanation:
y=-2x-4
y=1/2x-5
----------------
-2x-4=1/2x-5
-2x-1/2x-4=-5
-4/2x-1/2x=-5+4
-5/2x=-1
5/2x=1
x=1/(5/2)
x=2/5
y=1/2(2/5)-5
y=1/5-5
y=1/5-25/5
y=-24/5
Answer:
subtract 6 from 27 the divide by 3
Step-by-step explanation:
Mom drove for 11 hours.
Dad drove for 3 hours.
<u>Step-by-step explanation</u>:
- Total distance = 895 miles
- Mom drove a speed of 65 mph
- Dad drove a speed of 60 mph
Let 'x' be the number of hours drove by mom.
Let 'y' be the number of hours drove by dad.
x + y = 14 ---------------(1)
65x + 60y = 895 ---------(2)
Multiply eq(1) by 60 and subtract eq(2) from (1),
60x + 60y = 840
-(<u>65x + 60y = 895</u>)
<u> -5x = -55 </u>
x = 55/5
x = 11
∴ Mom drove for 11 hours.
Substitute x=11 in eq(1)
11+y = 14
y = 3
∴ Dad drove for 3 hours.
This is a problem you need to solve using logs. When you use logs you can "pull" the exponents down in front of the log to get a new equation that looks like this: 2x^3 + x^2 log 81 = 6x - 3 log 27. Now divide both sides by log 81 and 6x - 3 simultaneously to get (2x^3 + x^2)/(6x - 3) = (log 27)/(log 81). If you do the log math on the right side you get .75. Now multiply both sides by 6x-3 to get 2x^3+x^2 = .75(6x-3). If you distribute that out on the left side you'll get 2x^3+x^2=4.5x-2.25. Now move everything over to the left side and set the whole thing equal to 0: 2x^3+x^2-4.5x+2.25=0. When you solve for x, you are in essence factoring, so do this by grouping: x^2(2x+1)-2.25(2x+1). Now finally factor out the 2x+1 to get (2x+1)(x^2-2.25). You're not done yet though cuz you need to solve each of those for x: 2x+1=0, and x= -1/2; x^2=2.25, and x=+/- 1.5. So all the values for x here are -1/2, 1.5, and -1.5
