Unit 1
Determine the common difference, d, of this arithmetic sequence: 4,19,34,49
d=15
Evaluate|-2x2-3x-4| when x=2
=|-2(2)2-3(2)-4|
=|-8-10|
=18
Factor 3x2+6x-72
3(x-4)(x+6)
Identify the following of the function y=-2(x+2)2-3
The direction of opening
The vertex
The equation of axis symmetry
The intercepts
Downward
(-2,-3)
X=-2
X-int: no
Y-int: -11
Given an arithmetic sequence with t15=38 and d=-3, find t1
tn=t1+d(n-1)
38=t1+(-3)(15-1)
t1=80
Write √750x as a mixed radical and state the restriction of x.
=√25*30x
=5√30x (x≥0)
Solve 1/2x2+3x-9/2=0
x2+6x-9=0
(x+3)2=18
x=-3±√18
x=-3±3√3
If the function y=x2 is vertical compressed by a factor of 1/2, horizontal translated by 4 units right and vertical translated by 6 units up, what is the final function like after the transformation.
y=1/2(x-4)2+6
Find the sum of the series: 11+15+19+...+107
Sn=n(t1+tn)/2
tn=t1+d(n-1) 107=11+4(n-1) n=25
Sn=25(11+107)/2
Sn=1475
Simplify (5√7+3)/√7
=(35+3√7)/7
Determine the value of () that makes x2+10x+() a perfect square
25
Knowing that the vertex of a function is (2,7) and it has downward opening. Write the function in general form.
y=-(x-2)2+7
y=-x2+4x+3
Write 0.1414141414...as a fraction.
o.14141414...=14/100+14/1000+14/10000
t1=14/100, r=1/100
S∞=t1/1-r
=(14/100)/(1-1/100)
=14/99
Is x=-2 a real root for the equation √(2x-5)=√(x-7), explain why.
No, because when x=-2, the radicand on both side is negative and it is the extraneous root.
Determine when the value of k for which kx2+6x+3=0 has real roots.
b2-4ac≥0
36-12k≥0
k≤3
The graph of a quadratic function passes through C(6,-60), and the zeros of the function are 4 and-2. Write the equation of the graph in general form.
y=a(x-x1)(x-x2)
y=a(x-4)(x+2) substitute c (6,-60)
-60=a(6-4)(6+2)
a=-15/4
y=-15/4(x+2)(x-4)
y=-15/4x2+15/2x+30
Ms.Richards earned $58 on her first at work. Her salary was increased at a rate of 2.15% with each day. Determine the total amount Ms.Richard earned after 23 days.
t1=58 r=1+2.15% n=23
Sn=t1(1-rn)/1-r
Sn=58【1-（1+2.15%）23】/1-(1+2.15%)
=1702.5
Ms.Richard can earn 1702.5$ after 23 days.
A square with an area of 50 units is placed beside a smaller square with unknown area. If the perimeter of the shape formed is 20√2 + 4√6 units, what is the area of the smaller area?
Assume the area x units of the small square
P=3√50+3√x+√50-√x and p=20√2 + 4√6
x=24
The area is 24 units
The square of a number is subtracted from the number. Can the difference be negative?
n-n2=k
0=n2-n+k
b2-4ac=1-4k＜0
k＞1/4
There are 2000 new students enrolled in Maple Leaf School with 1500$ tuition per year. If the tuition increases 100$ per year, the school will have 200 less students enrolled. Let x represent how many 200$ increases, then use a formula to represent the total tuition the school can receive(revenue).
Revenue=(1500+100x)(2000-200x)