Answer:
-6
Step-by-step explanation:
3n = n² - 54
n² - 3n - 54 = 0
n² - 9n + 6n - 54 = 0
n(n - 9) + 6(n - 9) = 0
(n - 9)(n + 6) = 0
n = 9 , -6
hope this helps
Answer:
Sorry for my bad handwriting it's hard write in a computer
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
Calculate the distance using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = B(0, 0) and (x₂, y₂ ) = (
,
)
AB =
+ 
=
+ 
= 
= 
= 4
1, a.) The two specific conjectures are in the first image.
1, b.) The two general conjectures are in the second image.
2, a.) Two specific conjectures for this pattern are:
- The common difference between two consecutive terms is 3.
- And the given difference is A.P.
2, b.) From our observation two general conjecture is that the given sequence is an arithmetic sequence and the common difference is 3.
For finding its nth term we can use the formula: a(n) = a + (n-1) x d.
2, c.) A formula for the given pattern is 5 + (n-1)3, where n is the number of the term.
Answer:
y = -3x - 16
Step-by-step explanation:
Point-slope form: y - y1 = m(x - x1)
Given: y - 2 = -3(x + 6)
Slope-intercept form: y = mx + b
To write the equation in slope-intercept form, we need to know the slope(m) and the y-intercept(b). By looking at the given equation, we can see that the slope is -3. We are also given the value of one point: (-6, 2).
To find the y-intercept, input the given values of the slope and the point into the equation format and solve for b:
y = mx + b
2 = -3(-6) + b
2 = 18 + b
Subtract 18 from both sides of the equation to isolate b:
2 - 18 = 18 - 18 + b
-16 = b
The y-intercept is -16.
Now that we know the slope and the y-intercept, we can write the equation:
y = -3x - 16