Answer:
A
Step-by-step explanation:
This explanation mostly depends on what you're learning right now. The first way would be to convert this matrix to a system of equations like this.
g + t + k = 90
g + 2t - k = 55
-g - t + 3k = 30
Then you solve using normal methods of substitution or elimination. It seems to me that elimination is the quickest method.
g + t + k = 90
-g - t + 3k = 30
____________
0 + 0 + 4k = 120
4k = 120
k = 30
No you can plug this into the first two equations
g + t + (30) = 90
g + t = 60
and
g + 2t - (30) = 55
g + 2t = 85
now use elimination again by multiplying the first equation by -1
g + 2t = 85
-g - t = -60
_________
0 + t = 25
t = 25
Now plug those both back into one of the equations. I'll just do the first one.
g + (25) + (30) = 90
g = 35
Therefore, we know that Ted spent the least amount of time on the computer.
The second method is using matrix reduction and getting the matrix in the row echelon form, therefore solving using the gauss jordan method. If you would like me to go through this instead, please leave a comment.
Answer:
Step-by-step explanation:
The attached photo shows the diagram of quadrilateral QRST with more illustrations.
Line RT divides the quadrilateral into 2 congruent triangles QRT and SRT. The sum of the angles in each triangle is 180 degrees(98 + 50 + 32)
The area of the quadrilateral = 2 × area of triangle QRT = 2 × area of triangle SRT
Using sine rule,
q/SinQ = t/SinT = r/SinR
24/sin98 = QT/sin50
QT = r = sin50 × 24.24 = 18.57
Also
24/sin98 = QR/sin32
QR = t = sin32 × 24.24 = 12.84
Let us find area of triangle QRT
Area of a triangle
= 1/2 abSinC = 1/2 rtSinQ
Area of triangle QRT
= 1/2 × 18.57 × 12.84Sin98
= 118.06
Therefore, area of quadrilateral QRST = 2 × 118.06 = 236.12
A. The number of fabric-pattern-color combinations is 4 * 13 * 9 = 468
B. P(1st choice) = no of novels / total books = 3/6 = 1/2
P(2nd choice) = no of remaining novels/ total remaining books = 2/5
P(both novels) = 1/2 * 2/5 = 1/5 (without replacement assumed)
C. P(1st choice) = no of biographies / total books = 2/6 = 1/3
P(2nd choice) = no of remaining biographies/ total remaining books = 1/5
P(both biographies) = 1/3 * 1/5 = 1/15 (without replacement assumed)
D. P(1st choice) = no of history books / total books = 1/6
P(2nd choice) = no of novels/ total remaining books = 3/5
P(a history, then a novel) = 1/6 * 3/5 = 1/10 (without replacement assumed)
It would be list f. Each serving(1)serves16 so 2 servings serve 32 and so on.
It is answer choice A because you have to take the the GCF of each number which is 2x. Then if you were to divide the numbers by 2x you would put those numbers in the brackets.
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