Answer:
Herman's final position is -3 feet relative to the ground level.
Step-by-step explanation:
As given:
Herman starts out on a rung that is 6 feet under ground ,climbs up 14 feet,then climbs down 11 feet.
The initial position is 6 feet(negative value) under ground, then up 14 feet (plus value)and down again 11 feet(negative value).
We take positive value when position is above the initial level and negative when the position is below the level.
The final position relative to ground level is:
=
Therefore, Herman's final position is -3 feet relative to the ground level.
The cost of one doughnut is $0.75 and the cost of one cookie is $0.60.
The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Alexandra buys two doughnuts and three treats at a donut shop and is charged $3.30. Brianna buys five doughnuts and two treats at a similar shop for $4.95. Every one of the doughnuts and treats has a similar cost.
Assume 'x' is the cost of doughnuts and 'y' is the cost of one cookie. Then the equations are given as,
2x + 3y = 3.30 ...1
5x + 2y = 4.95 ...2
Multiply equation 1 by 5 and equation 2 by 2, then we have
10x + 15y = 16.50 ...3
10x + 4y = 9.90 ...4
Subtraction equation 2 from equation 1, then we have
15y - 4y = 16.50 - 9.90
11y = 6.60
y = $0.60
Then the value of 'x' is given as,
2x + 3(0.60) = 3.30
2x + 1.80 = 3.30
2x = $1.50
x = $0.75
The expense of one donut is $0.75 and the expense of one treat is $0.60.
More about the solution of the equation link is given below.
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-2x+6y=3
16. Tell whether the lines for each pair of equations are parallel perpendicular or neither
Y=-1/5x+6
-2x+10y= 5
Answer:
Step-by-step explanation:
15. The given lines are
Y=-3x+7 & -2x+6y=3 or, 6y = 3 + 2x or, .
The slope of the first line is -3 and the slope of the second line is [Comparing with the standard form of equation of straight line y = mx + c, where m is the slope of the straight line].
Two straight lines will said to be perpendicular to each other, if the product of its slopes will be equal to -1.
Since, , the equations are perpendicular with respect to each other.
16. The lines are and -2x + 10y = 5 or, 10y = 5 + 2x or, .
As per the question number 15, it is clear that these equations are not perpendicular.
Here, the slope of the first one is and the slope of the second one is .
The values are same with different sign. Hence, these equations are not parallel too.