If we have 2 coordinates say: (x1,y1) and (x2,y2)
Then the formula for the midpoint is:
((x1+x2)/2,(y1+y2)/2)
And the formula for the distance is:
Sqrt((x2-x1)^2+(y2-y1)^2)
So here we have (-1,-4) and (-7,4)
The midpoint is:
((-1+-7)/2,(-4+4)/2) = (-8/2,0/2) = (-4,0)
The distance is:
Sqrt((-7- -1)^2+(4- -4)^2)
= sqrt((-6^2)+(8^2))
=sqrt(36+64)
=sqrt(100)
=10
Answer:
n = 8
Step-by-step explanation:
Continuing the sequence using
+ 
x₄ = x₂ + x₃ =1 + 2 = 3
x₅ = x₃ + x₄ = 2 + 3 = 5
x₆ = x₄ + x₅ = 3 + 5 = 8
x₇ = x₅ + x₆ = 5 + 8 = 13
x₈ = x₆ + x₇ = 8 + 13 = 21
x₉ = x₇ + x₈ = 13 + 21 = 34
x₁₀ = x₈ + x₉ = 21 + 34 = 55 ← with n = 8
9514 1404 393
Answer:
(a) x = (3 -ln(3))/5 ≈ 0.819722457734
(b) y = 10
Step-by-step explanation:
(a) Taking the natural log of both sides, we have ...
2x +1 = ln(3) +4 -3x
5x = ln(3) +3 . . . . . . . . add 3x-1
x = (ln(3) +3)/5 ≈ 0.820
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(b) Assuming "lg" means "log", the logarithm to base 10, we have ...
log(y -6) +log(y +15) = 2
(y -6)(y +15) = 100 . . . . . . . taking antilogs
y^2 -9x -190 = 0 . . . . . . . . eliminate parentheses, subtract 100
(y -19)(y +10) = 0 . . . . . . . . factor
The values of y that make these factors zero are -19 and 10. We know from the first term that (y-6) > 0, so y > 6. That means y = -19 is an extraneous solution.
The solution is ...
y = 10
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When solving equations using a graphing calculator, it often works well to define a function f(x) such that the solution is f(x) = 0, the x-intercept(s). That form is easily obtained by subtracting the right side of the equation from both sides of the equation. In part (a) here, that is ...
f(x) = e^(2x+1) -3e^(4-3x)
Answer:
1 7/8
Step-by-step explanation:
6 - 4 1/8
2 - 1/8
15/8 = 1 7/8
Answer:
0.
Step-by-step explanation:
The angle whose sine is 5/12 = 22.62 degrees and in Quadrant II it is
180 - 22.62 degrees
The angle whose tan is (5/12) = 22.62.
So we can write α as 180 - α and β as α.
sin (α+β) = sin ( 180 - α = α) = sin 180
= 0.