Trig
Find the Sin(30)
0.5
What does the "P" represent in A=P(1+rt)?
Principal
Find the axis of symmetry of:
y=x² -6x +5
x= -b/2a
=-(-6)/2(1)
x=3
Simplify:
x³x⁴
Add 3 and 4
=x⁷
this form instantly tells you the y intercept
standard form
A ladder is 10m long and leans against a wall. the angle with the ground is 60 degrees. How high up the wall does it reach?
10Sin(60)
= 8.66m
You invest $500 at 4% simple interest for three years.
How much interest is earned?
I=Prt
I=(500)(0.04)(3)
=$60
Factor completely:
x² +7x +12
FIND: 2 #s that multiply to 12, add to 7
3x4=12, 3+4=7
(x+3)(x+4)
Simplify:
75÷ 72
=73
or
343
this form tells you the zeros/X intercepts right away
factored form
A ladder reaches 8m up a wall and is 10m long. What angle does it make with ground?
sin-1 (8/10)
=53.1 Degrees
an investment of $1000 earns 5% simple interest for 4 years .What is the final amount?
A=P(1+rt)
A=1000(1+0.05x4)
A=$1200
Solve:
x² -9x +20=0
FIND: 2 #s that multiply to 20, add to -9
-4(-5)= 20, -4 + (-5) = -9
(x-4)(x-5)=0 Set each factor to 0
x-4=0 x=4 x-5=0 x=5
Simplify:
45×42÷43
= 44
or
256
Rewrite y=x2+6x+8 into factored form
y= (x+4)(x+2)
In a triangle, A= 40 degrees, a= 8, and b= 12. Find angle B.
Use the Sine Law.
(sinB/12) = (sin40/8)
=sin-1 (0.9642)
B= 74.8 Degrees
an investment of $2000 earns 5% interest compounded annually for 4 years.
What is the value of the investment at the end of the 4 years? (round to the nearest dollar)
A=P(1+r)^t
A=2000(1.05)^4
A=2000(1.21551)
A=$2431
Find the vertex of:
y=x² -8x +7
x= -b/2a = -(-8)/2(1) = 4 Substitute into equation.
y= (4)² -8(4) +7
y= -9
Vertex: (4,-9)
Simplify:
(23)4÷25
=27
or
128
For y= -3(x+1)2 +12, what way does this parabola open, and what is its maximum value?
Porabola opens down, and has a max value of 12
A triangle has sides 7cm, 9cm, and 12cm. Find the largest angle.
Use Cosine Law.
cosC= (7^2)+(9^2)-(12^2)/(2x7x9)
C=96.4 degrees
J-Fawce deposits $200 at the end of every month into an account earning 4.8% interest compounded monthly.
How much will J-Fawce have after 5 years?
A=200((1+0.048/12)^(5)(12)-1
Divided by 0.048/12
A=200(1.004)^60-1
Divided by 0.004
A=$13,512
Solve using the quadratic formula:
2x² +3x -2 =0
x+=1/2
x-= -2
Simplify:
28X2-3÷ (22)2
=21
or
2
Complete the square to convert y=x2 -10x+21 to vertex form.
y=(x-5)2 -4