Answer: To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect. The two lines intersect in (-3, -4) which is the solution to this system of equations.
Step-by-step explanation: hope this helps
Hi there!
The derivative of the function is the slope of the function at a specific x-value, or its instantaneous rate of change.
For example, take the equation y = x².
Using the power rule, we get:
y' = 2x
If we plug in any x-value into this equation, we can find the slope of the function at any point.
Ex:
x = 0; 2(0) = slope of 0
x = 2; 2(2) = slope of 4
Answer
y = 1(x +1) - 3
Explanation
A quadratic equation of the form y = ax^2 + bx + c
This written in complete the square form provides you with the vertex (either a maximum or minimum point depending on the equation).
This results in y = a(x + p) + q
Where - p is the x value and q is the y value of turning point.
For graph 22, x = -1 and y = -3
Therefore, the equation is of the form
y = a(x + 1) - 3 (*)
We still need the value a, this can be obtained by using the y-intercept we are given.
We are told x = 0 when y = -2
Substitute this in (*) equation:
-2 = a(0+1) - 3
-2 = a - 3
a = 1
Therefore final equation is
y = 1(x +1) - 3
This should provide you with the train of thought of how the second question should also be tackled.
If unsure about why the equation
y = a(x + p) + q gives the vertex ask in comments I will respond
Answer:
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Answer: D) 101
Step-by-step explanation:
By linearity, we can break it up into 2 integrals. The integral and derivative of f easily cancel out
I used the table for values of f(x) at 10 and -1. Wouldn't be surprised if this was part of a series of questions about f because I really can't see how you could use the hypothesis that f is twice differentiable on R. Same for the other table values. I'm curious about how you found the answer. Was it a different way?
