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.
Answer:
AB=2.775
BC=5.55
CA=6.475
Step-by-step explanation:
Since midpoints split their sides in half, we can see that the triangle MNK formed by the midpoints will be half the perimeter of the triangle ABC. Since P of MNK = 7.4, we know that the perimeter of ABC = 7.4 * 2, which is 14.8. Now we can split the 14.8 so that it follows the ratio.
3+6+7=16
14.8/16=0.925
AB=0.925*3=2.775
BC=0.925*6=5.55
CA=0.925*7=6.475
Answer:
$4080
Step-by-step explanation:
We have the amount she will pay back, but first, we need to find the Interest accrued.
Simple Interest is given as:

where P = principal
R = rate
T = time taken (in years)
Therefore, the interest on $3,000 at 9% simple interest for 4 years is:

I = $1080
Therefore, the amount she will pay back is:
$3000 + $1080 = $4080
The lines y=x+2 and y=x are parallel, because they have the same slope.