In this question, you are asked to make a pattern start with 125 with 6 less number each pattern. Then the pattern equation would be: 125-6x where x is determined by the position of the number.
The question doesn't specify how many numbers in the pattern that needs to be written but the pattern should be like this: 125, 119, 113, 107, 101, 95, 89, 83, 77
Answer: The y-value of the vertex is
Step-by-step explanation: we know that
The equation of a vertical parabola into vertex form is equal to
where
(h,k) is the vertex of the parabola
In this problem we have
-----> this a vertical parabola open upward
Convert to vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Factor the leading coefficient
Complete the square. Remember to balance the equation by adding the same constants to each side
Rewrite as perfect squares
The vertex is the point
The y-value of the vertex is
Answer:
1. C(9,4) : n=9, s=4
2. C(10,5) : r=5
3. C(5,5) : n=5
4. C(7,7) : n=6
5. C(18,17) : r=3
Step-by-step explanation:
The rule for differentiation for variable with exponents has the formula:
d/dx (xⁿ) = nxⁿ⁻¹
where n is the exponent
Thus, for the given equation, the solution is as follows:
y = 2x²
dy/dx = 2(2)x²⁻¹ = <em>4x
Thus, the derived equation of the given would now be 4x.</em>
Answer:
Step-by-step explanation:
We do not have enough information for slope intercept form. But we can use the point-slope formula to find the information. The formula is 
where we substitute a point (x,y) for 
.
We have m=3/4 and (4, 1). We input m and 
.
We now simplify the parenthesis and solve for y.
We convert -4 into a fraction with 1 as the denominator.
We add 1 to both sides to isolate y,
This is slope intercept form. The line as slope 3/4 and y-intercept (0,2) or b=2.
