Answer:
first one answer is 0 second one answer is 2
Answer:
3.81 inches
Step-by-step explanation:
πr² + 100 = π(r+3)²
divide by π and simplify:
r² + (100/π) = r² + 6r + 9
100/π = r² + 6r + 9
31.8309886184 - 9 = r² +6r
r² = 6r - 22.8309886184
0 = 6r - 22.8309886184
22.8309886184 = 6r
divide by 6:
3.80516476973 ≈ 3.81 inches
9514 1404 393
Answer:
- 2 6/11 days
- 1 2/3 hours
Step-by-step explanation:
1. Add the rates in terms of houses per day.
1/4 + 1/7 = (7+4)/28 = 11/28
Then the time required in terms of days per house is the reciprocal of this:
28/11 = 2 6/11 . . . . days to paint a house, working together
__
2. Each hour, the vehicles separate by 55 -40 = 15 miles. Then the time required for a separation of 25 miles is ...
time = distance/speed = (25 mi)/(15 mi/h_ = 5/3 h = 1 2/3 h
The vehicles will be separated by 25 miles after 1 2/3 hours.
Answer:
-x³ + 3x² - 14x + 12
Step-by-step explanation:
Area of outer rectangle = (x² + 3x - 4) * (2x - 3)
= (x² + 3x - 4) * 2x + (x² + 3x - 4) * (-3)
=x²*2x + 3x *2x - 4*2x + x² *(-3) + 3x *(-3) - 4*(-3)
=2x³ + 6x² - 8x - 3x² - 9x + 12
= 2x³ + <u>6x² - 3x²</u> <u>- 8x - 9x</u> + 12 {Combine like terms}
= 2x³ + 3x² - 17x + 12
Area of inner rectangle = (x² - 1)* 3x
= x² *3x - 1*3x
= 3x³ - 3x
Area of shaded region = area of outer rectangle - area of inner rectangle
= 2x³ + 3x² - 17x + 12 - (3x³ - 3x)
= 2x³ + 3x² - 17x + 12 -3x³ + 3x
= 2x³ - 3x³ + 3x² - 17x + 3x + 12
= -x³ + 3x² - 14x + 12
Find the rate of change, (y2-y1)/(x2-x1), from the data given...
(2.16-1.26)/(12-7)=0.18
(1.26-0.72)/(7-4)=0.18
Since the rate is constant, this is a linear equation of the form y=mx+b. Furthermore, since 0 pencils cost 0, b=0, so the cost of the pencils is simply the number of pencils times 18 cents...
c(p)=0.18p (cost with respect to pencils is 0.18 times the number of pencils)
