6) The solution of the system of linear equations is (x, y, z) = (2, 5, 3).
11) The average depth of the water is 0.35 kilometers.
12) The dollar value of the deposit after 10 years is $ 1205.85.
13) Three horses need a consumption of 930 pounds of hay for the month of July.
14) The circle with equation x² + y² + 8 · y + 8 · y + 28 = 0 has a radius of 2.
15) Anna has a mean time of 7.39 minutes.
How to analyze algebraic equations
In this question we must analyze and resolve on algebraic equations such as linear equations or conic sections. 6) We must use algebra properties to solve on the system of linear equations. First, we clear x in the first equation:
x = y - z
Then, we apply it in the two remaining equations:
- 5 · (y - z) + 3 · y - 2 · z = - 1
2 · (y - z) - y + 4 · z = 11
- 2 · y + 3 · z = - 1
y + 2 · z = 11
Second, we clear y in the second expression and we substitute into the first expression:
y = 11 - 2 · z
- 2 · (11 - 2 · z) + 3 · z = -1
- 22 + 7 · z = - 1
z = 3
y = 5
x = 2
The solution of the system of linear equations is (x, y, z) = (2, 5, 3).
11) There is a function of the speed of a tsunami in terms of the average depth of the water. The former variable is known and we need to clear d in the formula to find the missing value:
145 = 356 · √d
d = (145 / 356)²
d = 0.345 km
The average depth of the water is 0.35 kilometers.
12) The compound interest model is shown below:
C' = C · (1 + r / 100)ˣ (1)
Where:
- C' - Initial capital
- C - Current capital
- r - Interest rate
- x - Number of periods
If we know that C = 500, r = 4.5 and x = 20, then the resulting capital after 10 years is:
C' = 500 · (1 + 4.5 / 100)²⁰
C' = 1205.85
The dollar value of the deposit after 10 years is $ 1205.85.
13) The situations indicates a direct variation as the amount of hay is directly proportional to the number of days. Hence, we have the following linear model for the hay consumption of one horse:
y = m · x (2)
y = 10 · x
Where:
- m - Hay consumption rate, in pounds per day.
- x - Time, in days.
- y - Consumed hay, in pounds.
The total consumption of three horses during July is equal to the product of the number of horses and consumed hay by one horse during one month:
y' = 3 · [10 · (31)]
y' = 930
Three horses need a consumption of 930 pounds of hay for the month of July.
14) There is the general equation of the circumference and we must transform it into its vertex form to find information about the radius. This can done by algebraic procedures:
x² + y² + 8 · y + 8 · y + 28 = 0
(x² + 8 · y) + (y² + 8 · y) = - 28
(x² + 8 · y + 16) + (y² + 8 · y + 16) = 4
(x + 4)² + (y + 4)² = 2²
The circle with equation x² + y² + 8 · y + 8 · y + 28 = 0 has a radius of 2.
15) We need to sum all the times described in the table and divide it by the number of data to find the mean time for a 1-kilometer race:
x = (7.25 + 7.40 + 7.20 + 7.10 + 8.00 + 8.10 + 6.75 + 7.35 + 7.25 + 7.45) / 10
x = 7.39
Anna has a mean time of 7.39 minutes.
To learn more on algebraic functions: https://brainly.com/question/12178721
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