The equation that models the balance y after x is y = -145x + 1400
<h3>How to find the equation?</h3>
given that
Zachary uses a payment plan to buy a PC for $1,400. His balance was $820 four months after he made the computer purchase. His amount was $240 eight months after he made the computer purchase.
Assume it has to do with developing an equation that represents this loan as a function of time. Use the loan amount as Y and the time as X.
Now Put that in the standard format:
Y = mX + b
according to the question
at x = 0 then y = 1400
at x = 4 then y = 820
at x = 8 then y = 240
now find the slope
points are (4,820) & (8,240)
slope = -145
now the equation is y = -145x + b
Let x = 4 & y = 820
then
820 = -145(4) + b
820 = 580 + b
b = 820 + 580
b = 1400
finally the equation is
y = -145x + 1400
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Answer:
Step-by-step explanation:
Given
Required
Find f(g(-4))
First, calculate f(g(x))
We have:
Substitute:
Open bracket
Substitute for
Step-by-step explanation:
3x contains a variable x, hence 3x is algebraic expression.
Answer:
<h2>BD = DC</h2>
Step-by-step explanation:
A perpendicular bisector is a line segment that goes form a vertex to its opposite side. The important characteristic is that a perpendicular bisector intersects the opposide at the mid point and with a right angle, that's why is called perpendicular and bisector.
So, Andrew can conclude that side BC is divide equally, that is, BD = DC.
Therefore, the right answer is the second choice.
Answer: The min value of Q is Q = 84 and it happens when x = 4 and y = 3
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Explanation:
x+y = 7 turns into y = 7-x after subtracting x from both sides
Replace y with 7-x in the other equation to get
Q = 3x^2 + 4y^2
Q = 3x^2 + 4( y )^2
Q = 3x^2 + 4(7-x)^2
Q = 3x^2 + 4(49 - 14x + x^2)
Q = 3x^2 + 196 - 56x + 4x^2
Q = 7x^2 - 56x + 196
We have a function with one variable. Graphing 7x^2-56x+196 produces a parabola in which the vertex point is what we're after
Anything in the form p(x) = ax^2+bx+c will have a vertex (h,k) such that
h = -b/(2a)
k = p(h)
Let's find the x coordinate of the vertex
h = -(-56)/(2*7)
h = 4
Use this to find the y coordinate of the vertex
k = p(h)
p(x) = 7x^2-56x+196
p(h) = 7h^2-56h+196
p(4) = 7(4)^2-56(4)+196
p(4) = 84
The vertex is the lowest point in this case (since a = 7 is positive) and the vertex is (4,84)
Therefore, the minimum value of Q is Q = 84 and this happens when x = 4 and y = 3. Recall that y = 7-x.
We can see that,
Q = 3x^2 + 4y^2
Q = 3(4)^2 + 4(3)^2
Q = 3(16) + 4(9)
Q = 48 + 36
Q = 84
Which helps us verify we have the right Q value.