Answer:
Puppy Liz runs 34.61 ft.
Step-by-step explanation:
From the figure we can extract two triangles: one with angle 34° and adjacent 40ft, the other with angle 34°+23° and adjacent 40ft.
Let us call the distance from the pole to the fire hydrant 
, and the distance from the pole to the bench 
, then the distance 
from the fire hydrant to the bench is
which is the distance the Puppy Liz runs.
Now, from trigonometry we have
and
Therefore, the distance Puppy Liz runs is
Answer:
3x^2 -2x + 1 =3(x^2-2/3x+1/3)=3(x-1/3)^2+2/9*3= 3(x-1/3)^2+2/3
(x-1/3)^2 is greater or equal to zero
3(x-1/3)^2 is greater or equal to zero
and 2/3 is greater than zero
So there sum is greater than zero
Proved
Step-by-step explanation:
3x^2 -2x + 1 =3(x^2-2/3x+1/3)
Consider x^2-2/3x+1/3
Remember that (a-b)^2 =a^2-2ab+b^2
x^2=a^2
a=x
-2/3x= -2*x*b
b=1/3
S0 (x-1/3)^2= x^2-2/3x+1/9
x^2-2/3x+1/3= x^2-2/3x+1/9+1/3-1/9= (x-1/3)^2+2/9
3x^2 -2x + 1 =3(x^2-2/3x+1/3)=3(x-1/3)^2+2/9*3= 3(x-1/3)^2+2/3
(x-1/3)^2 is greater or equal to zero
3(x-1/3)^2 is greater or equal to zero
and 2/3 is greater than zero
So there sum is greater than zero
Proved
Answer:
54. slope: -1/5 y-intercept: -6
55. slope: -3x y-intercept: 12
Step-by-step explanation:
Answer:
(6x - 5)(x+5) (Answer A)
Step-by-step explanation:
Take a look at possible answer A: (6x - 5)(x + 5)
Multiplying out these factors yields 6x² + 30x - 5x - 25. This matches the original polynomial, 6x² - 25x - 25.
Answer:
x=-6
Step-by-step explanation:
48/x=-8
times x on both sides of the equation
48=-8x
divide -8 on both sides of the equation
x=-6
