Gonzalez Manufacturing 30,000. Part of the money was borrowed at 6%, part at 8%, and part at 10%. The annual interest was $2440,
and the total amount borrowed at 6% and 8% was twice the amount borrowed at 10%. Use Gaussian elimination or Gauss-Jordan elimination to find the amount borrowed at each rate.
How much money was borrowed at 6%?
How much money was borrowed at 8%?
How much money was borrowed at 10%?
How much money was borrowed at 6%?
How much money was borrowed at 8%?
How much money was borrowed at 10%?
1 answer:
Answer:
8,000 at 6%; 12,000 at 8%; 10,000 at 10%
Step-by-step explanation:
Let a, b, c represent the amounts borrowed at 6%, 8%, 10%, respectively. Then the problem statement gives rise to three equations:
... a + b + c = 30,000 . . . . . the total borrowed
... a + b - 2c = 0 . . . . . . . . . . the relationship between the quantities
... .06a +.08b + .10c = 2440 . . . . the total interest charge
_____
Subtracting the second equation from the first, it becomes
... 3c = 30,000
... c = 10,000 . . . . . divide by 3 . . . [equation 4]
Subtracting 0.06 times the first equation from the third, we have
... .02b +.04c = 640
Multiplying [equation 4] by 0.04 and subtracting from this, we get
... .02b = 240
... b = 12,000 . . . . divide by 0.02 .
Substituting for b and c into the first equation, we find ...
... a + 22000 = 30000
... a = 8000
Then the amounts are ...
- 8000 was borrowed at 6%
- 12000 was borrowed at 8%
- 10000 was borrowed at 10%
_____
Most graphing calculators are capable of solving matrix problems such as this one. The attachment shows a TI-84 solution.
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The answer is 23.3
Is that the answer of d
Is that the answer of d
Answer:
F is E reflected across the y-axis; only the signs of the x-coordinates of F and E are different.
Step-by-step explanation:
The question is incomplete. Here is the complete question.
" Points F and E on the coordinate grid below show the positions of two midfield players of a soccer team:
Coordinate grid shown from negative 4 to positive 4 on x-axis and negative 4 to positive 4 on y-axis. From the origin, point E is 1.5 units to the left and 3 units up. From the origin, point F is 1.5 units to the right and 3 units up.
Which statement best describes the relationship between the positions of the two midfield players? (1 point)
Based on the coordinate of E;
The value on the x axis is -1.5 since the point is 1.5unitsTO THE LEFT from the origin(-ve x-axis acts towards the left in space). The value on the y-axis will be +3units since its 3units UP(+ve y axis acts upward).
The E coordinates will therefore be (-1.5, 3)
Similarly, for coordinate F:
If from the origin, point F is 1.5 units TO THE RIGHT, then the x-axis will be +1.5 (x-axis is positive towards the right) and +3 units up(+ve y axis acts upward).
The F coordinate will therefore be;
(1.5, 3).
From both coordinates, it can be seen that both x axis are of the same value but different signs. This means that the points E and F will act in the opposite side of the y-axis and a reflector of each other.
Based on the explanation above, it can be concluded that "F is E reflected across the y-axis; only the signs of the x-coordinates of F and E are different."
