Answer:
9600
Step-by-step explanation:
y varies inversely with the square of x
y=k/(x^2)
for some non-zero constant k
y=6 when x=4
6=k/(4^2)
k=96
y=96/(x^2)
x=0.1
y=96/(0.1^2)
y=9600
Suppose x-6 is listed as a possible answer. That is zero if x = 6. So put x=6 into the original x^2 + 4x - 60 to get 6^2 + 4*6 - 60 = 36 + 24 -60 = 0. hence x-6 is a factor.
Answer (x-6)
on this hand :x-5 is not a factor, because plugging x=5 into does not work.
Answer:
where is the figure
Step-by-step explanation:
u should upload the figure too
You have to multiply 7 3/4 to 9.
First, turn 7 3/4 to an improper fraction which is 31/4.
Next, you multiply 31/4 to 9/1(same thing as 9) across from each other.
Then, you get the answer 279/4(31 x 9 = 279 ;4 x 1 = 4; 279/4).
Last divide 279 to 4 and get 67.75( .75 = 3/4 ; 69 3/4).
Slope of line = tan(120) = -tan(60) = - √3
Distance from origin = 8
Let equation be Ax+By+C=0
then -A/B=-√3, or
B=A/√3.
Equation becomes
Ax+(A/√3)y+C=0
Knowing that line is 8 units from origin, apply distance formula
8=abs((Ax+(A/√3)y+C)/sqrt(A^2+(A/√3)^2))
Substitute coordinates of origin (x,y)=(0,0) =>
8=abs(C/sqrt(A^2+A^2/3))
Let A=1 (or any other arbitrary finite value)
solve for positive solution of C
8=C/√(4/3) => C=8*2/√3 = (16/3)√3
Therefore one solution is
x+(1/√3)+(16/3)√3=0
or equivalently
√3 x + y + 16 = 0
Check:
slope = -1/√3 .....ok
distance from origin
= (√3 * 0 + 0 + 16)/(sqrt(√3)^2+1^2)
=16/2
=8 ok.
Similarly C=-16 will satisfy the given conditions.
Answer The required equations are
√3 x + y = ± 16
in standard form.
You can conveniently convert to point-slope form if you wish.
