ANSWER
The vertex is (-2,1)
EXPLANATION
We want to find the vertex of
We complete the square to obtain,
The first three terms forms a perfect square trinomial.
The vertex form is
This equation is in the form;
where (h,k)=(-2,1) is the vertex.
Answer:
14.4% decrease
Step-by-step explanation:
Here is the formula for finding the percentage of decrease:
(starting value - final value) / starting value * 100.
So for your question,
/
There was a 14.4% decrease within 50 years.
Answer:
yes
Step-by-step explanation:
4:8 and 3:6 when simplified gives the same result which is 1:2
Get them to have a common denominator so you can add them
(1/3)×2= 2/6 and (1/2)×3= 3/6
Add them together
(2/6)+ (3/6)= 5/6
So 5/6 of the class planted either marigolds or tulips and 1/6 of the class planted neither
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.
