Jace is making a water play table from a triangular table top. He sketched a dotted line to show where he wants to add a circula
2 answers:
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Answer:
His parents should invest $15,278.16 to reach this goal ⇒ 4th answer
Step-by-step explanation:
* Lets explain how to solve the problem
- Derrick will need $39,500 in 10 years for college tuition
∴ The future amount is $39,500
∴ The time for investment is 10 years
- P is the money his parents invest now at 9.5% annual interest,
compounded daily
∴ The rate is 9.5% per year compounded daily
- The formula of the compounded interest is:
, where
# A is the future value of money
# P is the value of investment
# r is the rate of interest in decimal
# t is the time of investment
# n is the period of the time
∵ A = $39,500
∵ t = 10
∵ r = 9.5/100 = 0.095
∵ n = 365 ⇒ compounded daily
- Lets use the formula above to find P
∴
∴
- Divide both sides by 2.58539
∴ P = $15278.16
∴ His parents should invest $15,278.16 to reach this goal
Part 1)
We have two lines: y = 2-x and y = 8x+4
Given two simultaneous equations that are both required to be true.
the solution is the points where the lines cross
Which is where the two equations are equal
Thus the solution that works for both equations is when
2-x = 8x+4
because
where that is true is where the two lines will cross and that is the common point that satisfies both equations.
Part 2) Make tables to find the solution to 2−x = 8x+4. take the integer values of x between −3 and 3
see the attached table
The table shows that none of the integers from [-3,3] work because in no case does
<span>2-x = 8x+4
</span>
To find the solution we need to rearrange the equation to the form x=n
2-x =8x+4
8x+x=2-4
9x=-2
x=-2/9
The only point that satisfies both equations is
where
x = -2/9
Find y:
y = 2-x = 2 - (-2/9) = 2 + 2/9 = 20/9
Verify we get the same in the other equation
y = 8x+4 = 8(-2/9) + 4 = 20/9
Thus the only actual solution, being the point where the lines cross,
is the point (-2/9, 20/9)------> (-0.22,2.22)
Part 3) how can you solve the equation 2−x = 8x+4 graphically?
<span>The point on the graph where the lines cross is the solution to the system of equations
</span>
using a graph tool
see the attached figure
the solution is the point (-0.22,2.22)
We have two lines: y = 2-x and y = 8x+4
Given two simultaneous equations that are both required to be true.
the solution is the points where the lines cross
Which is where the two equations are equal
Thus the solution that works for both equations is when
2-x = 8x+4
because
where that is true is where the two lines will cross and that is the common point that satisfies both equations.
Part 2) Make tables to find the solution to 2−x = 8x+4. take the integer values of x between −3 and 3
see the attached table
The table shows that none of the integers from [-3,3] work because in no case does
<span>2-x = 8x+4
</span>
To find the solution we need to rearrange the equation to the form x=n
2-x =8x+4
8x+x=2-4
9x=-2
x=-2/9
The only point that satisfies both equations is
where
x = -2/9
Find y:
y = 2-x = 2 - (-2/9) = 2 + 2/9 = 20/9
Verify we get the same in the other equation
y = 8x+4 = 8(-2/9) + 4 = 20/9
Thus the only actual solution, being the point where the lines cross,
is the point (-2/9, 20/9)------> (-0.22,2.22)
Part 3) how can you solve the equation 2−x = 8x+4 graphically?
<span>The point on the graph where the lines cross is the solution to the system of equations
</span>
using a graph tool
see the attached figure
the solution is the point (-0.22,2.22)