Answer:
C
Step-by-step explanation:
Select the number of punctuation error. Immediately even before I could stop the water, another leak occurred, and water gushed onto the, kitchen floor. A. 1 B. 2 C. 3 D. 4
3. There doesn't need to be a comma after 'the'.
The is a determiner or an article. We don't typically put commas after articles.
<span>(3.5, 3) is the circumcenter of triangle ABC.
The circumcenter of a triangle is the intersection of the perpendicular bisectors of each side. All three of these perpendicular bisectors will intersect at the same point. So you have a nice self check to make sure your math is correct. Now let's calculate the equation for these bisectors.
Line segment AB:
Slope
(4-2)/(1-1) = 2/0 = infinity.
This line segment is perfectly vertical. So the bisector will be perfectly horizontal, and will pass through ((1+1)/2, (4+2)/2) = (2/2, 6/2) = (1,3).
So the equation for this perpendicular bisector is y = 3.
Line segment BC
(2-2)/(6-1) = 0/5 = 0
This line segment is perfectly horizontal. So the bisector will be perfectly vertical, and will pass through ((1+6)/2,(2+2)/2) = (7/2, 4/2) = (3.5, 2)
So the equation for this perpendicular bisector is x=3.5
So those two bisectors will intersect at point (3.5,3) which is the circumcenter of triangle ABC.
Now let's do a cross check to make sure that's correct.
Line segment AC
Slope = (4-2)/(1-6) = 2/-5 = -2/5
The perpendicular will have slope 5/2 = 2.5. So the equation is of the form
y = 2.5*x + b
And will pass through the point
((1+6)/2, (4+2)/2) = (7/2, 6/2) = (3.5, 3)
Plug in those coordinates and calculate b.
y = 2.5x + b
3 = 2.5*3.5 + b
3 = 8.75 + b
-5.75 = b
So the equation for the 3rd bisector is
y = 2.5x - 5.75
Now let's check if the intersection with this line against the other 2 works.
Determining intersection between bisector of AC and AB
y = 2.5x - 5.75
y = 3
3 = 2.5x - 5.75
8.75 = 2.5x
3.5 = x
And we get the correct value. Now to check AC and BC
y = 2.5x - 5.75
x = 3.5
y = 2.5*3.5 - 5.75
y = 8.75 - 5.75
y = 3
And we still get the correct intersection.</span>
Answer:
Step-by-step explanation:
<u>Given recursive formula:</u>
- a₁ = -1
- aₙ = - 3aₙ₋₁ + 6 for n ≥ 2
<u>The first 4 terms are:</u>
- a₁ = - 1, given
- a₂ = - 3*(-1) + 6 = 3 + 6 = 9
- a₃ = - 3*(9) + 6 = - 27 + 6 = - 21
- a₄ = - 3*(-21) + 6 = 63 + 6 = 69
Answer:
Step-by-step explanation:
1). Equation of a line which has slope 'm' and y-intercept as 'b' is,
y = mx + b
If slope 'm' = 1 and y-intercept 'b' = -3
Equation of the line will be,
y = x - 3
x - y = 3
2). Equation of a line having slope 'm' and passing through a point (x', y') is,
y - y' = m(x - x')
If the slope 'm' = 1 and point is (-1, 2),
The the equation of the line will be,
y - 2 = 1(x + 1)
y = x + 1 + 2
y = x + 3
x - y = -3
3). Equation of a line passing through two points 
and 
will be,
If this line passes through (-2, 3) and (-3, 4),
y - 3 = -1(x + 2)
y = -x - 2 + 3
y = -x + 1
x + y = 1
Answer:
6
Step-by-step explanation:
$68 per day and you want it to be >400
68x>400 -divide by 68 on both sides
is about 5.88 -round up to six because it wants a whole number and it needs to be greater then 400
