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Miscellaneous
chapter 8: Inverse and joint variation
Compostites
Logs
Circle, Ellipse, and Hyperbola's
100
What is the rule when dividing rational expressions and when dividing fractions?
KEEP CHANGE FLIP!
100
What is the equation for... 1. direct variation 2. inverse variation
Direct Variation: y=kx Inverse Variation: y=a/x
100
F(x) = 2x+3 g(x) = x+4 F(x) + g(x)
What is 3x+7
100
Simplify the expression. (e^5x)2
e^10x
100
What is the formula for an ellipse? (x2/a2) + (y2/b2) = 1 or (x2/b2)+ (y2/a2)
(x2/a2) + (y2/b2) = 1 or (x2/b2)+ (y2/a2)
200
What is the formula for a line?
y=mx+b
200
Decide is this equation represents direct variation, inverse variation, or neither... xy=7
inverse variation xy=7 xy/x=7/x y=7/x
200
F(x)= 2x-7 g(x)= x^2+4 F(g(x))
What is 2x^2+1
200
Expand the expression: log2^4x
log2^4 + log2^x
200
Write The Equation of the Hyperbola in Standard Form When Given the Vertex and Focus... Foci: (0,4) Vertex: (0/2)
c2=a2+b2 16=4+b2 12=b2 (y2/4)-(x2/12)=1
300
What does Pe^rt stand for?
given(2.81)rate x time
300
Decide is the equation represents direct variation, inverse variation, or neither... y=x-5
neither
300
f(x) = 2x+1 g(x) = 5x g(f(-2))
What is -15.
300
Condense the expression: log4-logx-2logy
log4/xy^2
300
Write the equation of the circle in standard form when given the center and the radius... Center: (0,0) Point on the Circle: (3,4)
x2+b2=r2 (3)2+(4)2=r2 9+16=r2 25=r2 x2+y2=25
400
Using the points, (6,4) and (3,1), what is the y-intercept form?
-2=b
400
What is is the equation when, z varies directly with y and inversely with x....
z=(ay)/x.
400
F(x)=2x+3 g(x)=8x2+3 h(x) = x2-2 f(g(x))
What is 16x^2+9
400
Solve the equation for x: 4^x=10
(xlog4/log4)=(log10/log4) x-1.66
400
Write the equation in standard form.. x2+y2-14x+4y=11
x2-14x+y2+4y=11 x2-14x+49+y2+4y+4=11+49+4 (x-7)2+(y+2)2=64
500
What is the distance formula?
d=square root (x2-x1)^2+(y2-y1)^2
500
The variable z varies JOINTLY with x and y. Write an equation that relates x,y,z. x=1 y=2 z=7, then find z when x=-2 and y=-5.
z=(a)(x)(y) 7=a(1)(2) 7/2=a(2)/2 3.5=a z=(3.5)xy z=(3.5)(-2)(5) z=-35
500
F(x)=2x+3 g(x)=8x2+3 h(x) = x2-2 f(h(x))
What is 2x^2-1
500
Expand the expression: log (square root)xy
1/2log10^x + 1/2log10^y
500
Solve by substitution to find the point, and say how many solutions there are.. x2+y2=10 y=-3x+10 x^2+(-3x+10)2=10 (-3x+10)(-3x+10)= x^2+(9x)2-30x-30x+100=10 10x2-60x+90=0(divide everything by 10) x2-6x+9=0 (x-3)(x-3)=0 x-3=0 x=3 y=-3(3)+10 y=-9+10 y=1 (3,1) one solution
x^2+(-3x+10)2=10 (-3x+10)(-3x+10)= x^2+(9x)2-30x-30x+100=10 10x2-60x+90=0(divide everything by 10) x2-6x+9=0 (x-3)(x-3)=0 x-3=0 x=3 y=-3(3)+10 y=-9+10 y=1 (3,1) one solution