Helena is correct in saying that the point-slope form will generate the equation. The point-slope form is written as:
y-y₁ = m(x-x₁), where,
m = (y₂-y₁)/(x₂-x₁) is the slope of the line
(x₁,y₁) and (x₂,y₂) are the coordinates of the two points
On the other hand, the slope-intercept form is written as:
y = mx + b, where,
m is the slope of the line
b is the y-intercept
In this case, since only two points were given, the y-intercept of the line is not readily known. Thus, it is only through the point-slope form that the equation of the line can be determined. This is because it only requires the substitution of the x and y-coordinates of the points in the equation.
The equation of a line given two points needs to be found. Samuel claims that slope-intercept form will generate the equation and Helena claims that point-slope form will find the equation. Who is correct? Explain your reason by describing both forms.
we are given
airthematic sequence
we can use nth term formula
n is number of terms
an is nth term
d is common difference
a1 is first term
We are given
a7=40
we can use it
a18 = 106
we can subtract both equations
now, we can find a1
we can plug d=6
12th term:
now, we can plug values
so, 12th term is 70...........Answer
Answer:
f(x + 1) = 3x² + 5x + 7
Step-by-step explanation:
To find f(x + 1), substitute x = x + 1 into f(x), that is
f(x + 1) = 3(x + 1)² - (x + 1) + 5 ← expand (x + 1)² using FOIL
= 3(x² + 2x + 1) - x - 1 + 5 ← distribute parenthesis by 3
= 3x² + 6x + 3 - x - 1 + 5 ← collect like terms
= 3x² + 5x + 7
In this case, we will use our Pythagorean Theorem.
a = 84
b = 13
c = x
Thus,
x = 85.
