F(x)=2x^2-x-6
Factoring:
f(x)=2(2x^2-x-6)/2=(2^2x^2-2x-12)/2=[(2x)^2-(2x)-12]/2
f(x)=(2x-4)(2x+3)/2=(2x/2-4/2)(2x+3)→f(x)=(x-2)(2x+3)
g(x)=x^2-4
Factoring
g(x)=[sqrt(x^2)-sqrt(4)][sqrt(x^2)+sqrt(4)]
g(x)=(x-2)(x+2)
f(x)/g(x)=[(x-2)(2x+3)] / [(x-2)(x+2)
Simplifying:
f(x)/g(x)=(2x+3)/(x+2)
Answer: Third Option (2x+3)/(x+2)
The Answer is b: x = 18, y = -20
Proof:
Solve the following system:
{4 x + 3 y = 12 | (equation 1)
{7 x + 5 y = 26 | (equation 2)
Swap equation 1 with equation 2:
{7 x + 5 y = 26 | (equation 1)
{4 x + 3 y = 12 | (equation 2)
Subtract 4/7 × (equation 1) from equation 2:
{7 x + 5 y = 26 | (equation 1)
{0 x+y/7 = (-20)/7 | (equation 2)
Multiply equation 2 by 7:
{7 x + 5 y = 26 | (equation 1)
{0 x+y = -20 | (equation 2)
Subtract 5 × (equation 2) from equation 1:
{7 x+0 y = 126 | (equation 1)
{0 x+y = -20 | (equation 2)
Divide equation 1 by 7:
{x+0 y = 18 | (equation 1)
{0 x+y = -20 | (equation 2)
Collect results:
Answer: {x = 18, y = -20
Let m = slope = -4/5
P(x,y) = P(5,10)
Slope-intercept form for the equation of a line:
y=mx+c
Plug m= -4/5 into the slope-intercept formula
y = -4/5x + c
Plug P(5,10) into point-slope formula
y = -4/5x + c
10 = -4/5(5) + c
10 = -4 + c
substract -4 from both sides,
10 - (-4) = -4 - (-4) + c
14 = c
So, the equation is y = -4/5x + 14
In this scenario Jose jumped the distance Lila jumped plus 2 1/3 ft, so...
Lilia + 2 1/3 = 8 1/3
subtract 2 1/3 from each side to get Lila by herself
Lila = 8 1/3 - 2 1/3
Lila = 6
Lila jumped 6 feet
