1/3=2/6
2/3=4/6
3/6 is between 2/6 and 4/6
.25(16x + 12) + 2x = 33
The first step is to distribute the .25 to what's inside the parentheses!
((16x*.25) +(12*.25)) + 2x = 33
Simplify...
4x + 3 +2x = 33
Add like terms...
6x + 3 = 33
Subtract three from both sides
6x + 3 - 3 = 33 - 3
Simplify
6x = 30
Divide each side by six
6x/6 = 30/6
Simplify
x = 5
That's your answer; x = 5! Hope this helped :)
H(t) = -16t² + 60t + 95
g(t) = 20 + 38.7t
h(1) = -16(1²) + 60(1) + 95 = -16 + 60 + 95 = -16 + 155 = 139
h(2) = -16(2²) + 60(2) + 95 = -16(4) + 120 + 95 = -64 + 215 = 151
h(3) = -16(3²) + 60(3) + 95 = -16(9) + 180 + 95 = -144 + 275 = 131
h(4) = -16(4²) + 60(4) + 95 = -16(16) + 240 + 95 = -256 + 335 = 79
g(1) = 20 + 38.7(1) = 20 + 38.7 = 58.7
g(2) = 20 + 38.7(2) = 20 + 77.4 = 97.4
g(3) = 20 + 38.7(3) = 20 + 116.1 = 136.1
g(4) = 20 + 38.7(4) = 20 + 154.8 = 174.8
Between 2 and 3 seconds.
The range of the 1st object is 151 to 131.
The range of the 2nd object is 97.4 to 136.1
h(t) = g(t) ⇒ 131 = 131
<span>It means that the point where the 2 objects are equal is the point where the 1st object is falling down while the 2nd object is still going up. </span>
Part A.
Using the Pythagorean theorem,
PR² = PQ² +QR²
PR² = (14 ft)² +(6 ft)² = 196 ft² +36 ft² . . . . substitute the given numbers
PR² = 232 ft² . . . . . . . . . . . . . . . . . . . . . . . .find the sum
PR = √(232 ft²) ≈ 15.23 ft . . . . . . . . . . . . . take the square root
The length of rod PR is 15.23 ft.
Part B.
Using the Pythagorean theorem,
PR² = PQ² +QR²
(16 ft)² = (14 ft)² +QR² . . . . . . . substitute the given numbers
256 ft² -196 ft² = QR² . . . . . .. subtract 14²
60 ft² = QR² . . . . . . . . . . . . . . find the sum
√(60 ft²) = QR ≈ 7.75 ft . . . . . take the square root
The new height QR is about 7.75 ft.
The answer is D. This is because when you take 10.65 and subtract 9.95 from it you get 0.07. If you take this number and continuously add to 9.95 you get the numbers provided in the chart. We'll also notice that the 0.07 is only added after 10 minutes of talking (10,20,30,etc.).
