Answer: 25
Step-by-step explanation:
Both lines are being cut by the same transversal so to solve for x, make both equations equal to each other
2x+10 = 3x-15
To isolate x, do the inverse operations (for any side chosen)
Do the inverse operations to move -15 and isolate 3x
Add 15 to 10 (10+15=25)
You now have 2x+25=3x
Now, do the same to combine the x values together
25=3x-2x
You now have 25=1x
Divide by 1 on both sides
25=x
Answer:
at least $500,000 in sales
Step-by-step explanation:
Answer:
[see below]
Step-by-step explanation:
Randy first won 12 points on Monday. He earned as twice as many on Tuesday.
12 * 2 = 24
Randy scored 24 points Tuesday.
Randy earned 3 more points than Tuesday's points the next day.
24 + 3 = 27
Randy earned 27 points Wednesday.
12 + 24 + 27 = 63
Randy should earn a total of 63 points for the 3 days.
Hope this helps.
SOLUTION:
A box has a square base of side x and height y where x,y > 0.
Its volume is V = x^2y and its surface area is
S = 2x^2 + 4xy.
(a) If V = x^2y = 12, then y = 12=x^2 and S(x) = 2x^2 C 4x (12=x2) = 2x2 + 48x^-1. Solve S'(x) = 4x - 48x-2 = 0 to
obtain x = 12^1/3. Since S(x/) ---> infinite as x ---> 0+ and as x --->infinite, the minimum surface area is S(12^1/3) = 6 (12)^2/3 = 31.45,
when x = 12^1/3 and y = 12^1/3.
(b) If S = 2x2 + 4xy = 20, then y = 5^x-1 - 1/2 x and V (x) = x^2y = 5x - 1/2x^3. Note that x must lie on the closed interval [0, square root of 10]. Solve V' (x) = 5 - 3/2 x^2 for x>0 to obtain x = square root of 30 over 3 . Since V(0) = V (square root 10) = 0 and V(square root 30 over 3) = 10 square root 30 over 9 , the
maximum volume is V (square root 30 over 3) = 10/9 square root 30 = 6.086, when x = square root 30 over 3 and y = square root 30 over 3 .
5. 90 + 54 = 144 flowers
6. 250 - 106 = 144 balls
