Answer:
y = -2x/3 + 2
Step-by-step explanation:
A(0,1), B(2,4)
slope of AB = (yb-ya)/(xb-xa) = (4-1)/(2-0) = 3/2
Slope of perpendicular to AB
m = -1/(3/2) = -2/3
Point to lie on perpendicular, P(0,2)
Equation of perpendicular, point-slope form
(y-yp) = m(x-xp)
y-2 = -(2/3)(x-0)
y = -2x/3 + 2
Answer:
<h2>C. <em>
20,160</em></h2>
Step-by-step explanation:
This question bothers on permutation since we are to select a some people out of a group of people and then arrange in a straight line. If r object are to be arranged in a straight line when selecting them from n pool of objects. This can be done in nPr number of ways.
nPr = n!/(n-r)!
Selection of 6 people out of 8 people can therefore be done in 8C6 number of ways.
8P6 = 8!/(8-6)!
8P6 = 8!/2!
8P6 = 8*7*6*5*4*3*2!/2!
8P6 = 8*7*6*5*4*3
8P6 = 56*360
8P6 = 20,160
<em>Hence this can be done in 20,160 number of ways</em>
Answer:
-1/8
Step-by-step explanation:
lim x approaches -6 (sqrt( 10-x) -4) / (x+6)
Rationalize
(sqrt( 10-x) -4) (sqrt( 10-x) +4)
------------------- * -------------------
(x+6) (sqrt( 10-x) +4)
We know ( a-b) (a+b) = a^2 -b^2
a= ( sqrt(10-x) b = 4
(10-x) -16
-------------------
(x+6) (sqrt( 10-x) +4)
-6-x
-------------------
(x+6) (sqrt( 10-x) +4)
Factor out -1 from the numerator
-1( x+6)
-------------------
(x+6) (sqrt( 10-x) +4)
Cancel x+6 from the numerator and denominator
-1
-------------------
(sqrt( 10-x) +4)
Now take the limit
lim x approaches -6 -1/ (sqrt( 10-x) +4)
-1/ (sqrt( 10- -6) +4)
-1/ (sqrt(16) +4)
-1 /( 4+4)
-1/8
Annual growth rate is (1+0.15)^12. or 5.35025 or 535.025%
Answer:
x=12, y=30
Step-by-step explanation:
to find x:
in a equilateral triangle, all three sides are congruent, so:
4x-4=3x+8
x-4=8
x=12
to find y:
in an equilateral triangle, all the angles are 60°, so:
2y=60
y=30°
