48 divide by 4 sides = 12
12 x 12 = 144cm squared
Answer:Your left hand side evaluates to:
m+(−1)mn+(−1)m+(−1)mnp
and your right hand side evaluates to:
m+(−1)mn+(−1)m+np
After eliminating the common terms:
m+(−1)mn from both sides, we are left with showing:
(−1)m+(−1)mnp=(−1)m+np
If p=0, both sides are clearly equal, so assume p≠0, and we can (by cancellation) simply prove:
(−1)(−1)mn=(−1)n.
It should be clear that if m is even, we have equality (both sides are (−1)n), so we are down to the case where m is odd. In this case:
(−1)(−1)mn=(−1)−n=1(−1)n
Multiplying both sides by (−1)n then yields:
1=(−1)2n=[(−1)n]2 which is always true, no matter what n is
Step-by-step explanation:
For a quadratic equation y = ax² + bx + c, the vertex (the maximum or minimum point) is at x = -b/(2a).
1) y = -0.5t² + 2t + 38
The maximum is at:
t = -2 / (2 × -0.5)
t = 2
The maximum height is:
y = -0.5(2)² + 2(2) + 38
y = 40
The coordinates of the vertex are (2, 40). That means the missile reaches a maximum height of 40 km after 2 minutes.
2) y = -4.9t² + 12t + 1.6
The maximum is at:
t = -12 / (2 × -4.9)
t = 1.22
The maximum height is:
y = -4.9(1.22)² + 12(1.22) + 1.6
y = 8.95
The coordinates of the vertex are (1.22, 8.95). That means the missile reaches a maximum height of 8.95 m after 1.22 seconds.
3) y = -0.04x² + 0.88x
The maximum is at:
x = -0.88 / (2 × -0.04)
x = 11
The maximum height is:
y = -0.04(11)² + 0.88(11)
y = 4.84
The maximum height of the tunnel is 4.84 meters.
The maximum width is when y = 0.
0 = -0.04x² + 0.88x
0 = -0.04x (x − 22)
x = 22
The maximum width is 22 feet.
Answer: n = 75; p = 30
Explanation: (a) 5p + 4n = 450 where p is for pen and n is for notebook.
(b) 10p + 3n = 525
We can use the elimination method to solve these two equations.
1. Multiply the first equation by 2 so that 10p will cancel out:
2(5p + 4n = 450)
- 10p + 3p = 525
10p + 8n = 900
- 10 p + 3n = 525
5n = 375
2. Divide by 5 to get n alone: n = 75
3. Plug 75 into the first equation: 5p + 4(75) = 450
5p + 300 = 450
4. Subtract 300 from 450: 5p = 150
5. Divide by 5 to get p alone: p = 30
We can test if this is correct by plugging our answers into the second equation:
10(30) + 3(75) = 525
300 + 225 = 525
525 = 525
This is a true statement, which means that our answers are correct.
Answer:
y=2x-1
Step-by-step explanation:
use slope formula
the substitute into slope intercept form
