y = 19
x = 4(19) + 21(19) = 76 + 399 = 475
3(475) × 7
1425 × 7
9975 <--- answer.
Hope this helped!
Nate
Answer:
503
Step-by-step explanation:
For an arithmetic sequence, the n-th term is found by
To find 
(the common difference) we can simply subtract one of the terms by the last, for example:
The common difference must be the same throughout the entire sequence, so we can do it once more just to be sure:
We also have to know that 
stands for the first term of the sequence, which in this case is 311.
Now that we know this, let's find the 32nd term
Good luck!
The simple way of calculating a perimeter is to add all of the sides.
For a rectangle this would equal 2 x length + 2 x width
P = 2(6x + 3) + 2(-2x - 5)
= 12x + 6 - 4x - 10
= 8x - 4
At a higher level both the length and width must be greater than zero (= zero is a trivial rectangle)
6x + 3 > 0
6x > -3
x > -0.5
-2x - 5 > 0
2x + 5 < 0 (multiplying by -1 reverses the inequality)
2x < -5
x < -2.5
This rectangle cannot exist as x cannot be < -2.5 and > -0.5 at the same time!
There are 5 solutions for this system.
x^2 + 4y^2 = 100 ____1
4y - x^2 = -20 ____2
Add both 1 & 2 together. x^2 gets cancelled
4y^2 + 4y = 80 (send 80 to the other side and divide by 4)
Then equation the becomes : y^2 + y -20 =0
Now factorise the equation: (y+5) (y-4) = 0
Solve for y : y = -5 and y = 4
Using the values of y to find the values of x. From equation 1:
x^2 = 100 - 4y^2 x = /100 - 4y^2 (/ means square root) Replace values of y
y = -5, x = /100 - 4(-5)^2 = /100 - 100 = 0
y = 4, x = /100 - 4(4)^2 = / 100 - 64 = /36 = -6 or 6
Thus we have 6 solutions y = -5, 4 and x = -6, 0, 6
Answer: 134 miles
Step-by-step explanation:
f(m) = 16.95 + 0.92m
140.23 = 16.95 + 0.92m
0.92m = 140.23 - 16.95
0.92m = 123.28
m = 123.28/0.92
m = 134 miles
