Let S = number of small yogurts ($2 each).
Let M = number of medium yogurts ($3 each)
Let L = number of large yogurts ($5 each)
Total yogurts is 27, therefore
S + M + L = 27
Total revenue generated is $98, therefore
2S + 3M +5L = 98
There are five more large yogurts than small yogurts, therefore
L = S + 5, or
-S + L = 5
These three equations may be written as the matrix equation
[ 1 1 1 | |S| |27|
| 2 3 5 | |M| = |98|
| -1 0 1 | |L| | 5|
The determinant of the matrix is
D = 3 - (2+5) + 3 = -1.
Solve with Cramer's Rule to obtain
S = -[27*3) - (98-25) - 15]
= 7
M = -[(98-25) - 27(2+5) + (10+98)]
= 8
L = -[15 - (10+98) + 27(3)]
= 12
Answer: 7 small, 8 medium, 12 large yogurts.
1) the form of the equation may be written as y = A(X - Xo)(X - X1)
Where Xo and X1 are the two roots of the equation.
2) We can fix the system of coordinates so that the vertex is in the middle of the gate => Xo = - 40 and X1 = +40
=> y = A (X + 40) (X - 40) = A (X^2 - 1600)
3) The height, at X = 0 is 25
=> A(0 - 1600) = 25
=> -1600A = 25 => A = -25 / 1600 = - 1/64
4) The equation is y = - [1/64] (X^2 - 1600)
5) You can present it in different equivalent forms.
Some of those other forms are:
1) - 64y = (x^2 - 1600)
2) x^2 = - 64y + 1600
3) X^2 = - 64 (y - 25)
<span>–1 + 6(–1 – 3x) > –39 – 2x.
</span>-1-6-18x>-39-2x
-7-18x>-39-2x
-18x>-32-2x
-16x>-32
x<2
B. x<2
