Absolute Value of a real number

The absolute value of a real number is it's distance from 0 on the number line. Therefore an absolute value must be on the interval [0, oo). If a number is positive then |a|=a and if it is negative then |a|=-a.

Basic Integral Approximations

How many zeros does the function g(x) = 4(x + 2)^5 (x-3)^3 + 5(x-3)^4 (x+2)^4 have?

the degree of this polynomial, when expanded is 8, so there are 8 complex solutions.

find the zeros fro g(x), g(x) = 4(x + 2)^5 (x-3)^3 + 5(x-3)^4 (x+2)^4

by grouping 
 
becomes 
 

which simplifies to 
 
so there are 3 unique solutions: 
x=-2 (multiplicity 4)
x=3 (multiplicity 3)
x=7/9

I need to know if this problem is identity or contradiction. 4 + 4 (n + 2) = 3n - 2 (n - 5)

4+4(n+2)=3n-2(n-5)
4+4n+8=3n-2n+10
4n+12=n+10
3n=-2
n=-2/3 
neither, it is conditional

Prove:

solve the inequality

Solve for x

Solve for x

Solve for x

Solve for S

Solve for N

Write the equation of the line in general form

Find the slope

Simplify the complex rational expression

Simplify the rational expression

Simplify the rational expression

Simplify -2x-5[x-(8+7x)]

Simplify 3(x-10)+2(x+4)

Solve the equation

Write the quadratic equation in standard form

Slope-Intercept form

Prove that a^n/b^n=(a/b)^n

Find the polynomial under specified conditions

Write the equation of the line in general form

Operations on functions

Operations on fractions

Adding rational expressions

Find the domain

If sin A and cos A are the roots of the equation ax^2 - bx + c = 0, then a, b and c satisfy the equation: (A) b^2 - a^2 = 2ac, (B) a^2 - b^2 = 2ac, (C) a^2 + b^2 = c^2 ,(D) a^2 + b^2 = 2ac

A: 
The algebra is tedious, but manageable. Use the pythagorean trig identity for sine and cosine set equal to the squares of the 2 roots written in quadratic equation form. Expand and simplify.

simplify i^-156

One-half of a number is equal to the number plus ten

0.5*x=x+10
0.5* x - x =10
-0.5x=10
x=-20

find three Consecutive odd Numbers whose sum is 234

Please check your problem statement. The sum of any odd number of odd numbers (in this case three odd numbers) will be odd, so they cannot add to 234 - an even number

Solve: x+y=3, 2y=3x-4

Solving... 

1) x+y=3
2) 2y=3x-4 

1)...
x=3-y 

2)...
2y=3(3-y)-4
2y=9-3y-4
5y=5
y=1 

1)...
x=3-1
x=2

Solve: 4/3 s+4 ≥ 12

 

Solve: 15-5t ≥ 55

after dividing every term by 5 yields
 
 

simplify: cot(arcsin(-2/3))

for convenience, we write 
 
 
so that means... 
, ,  

Use the method of substitution to solve the system of linear equations. 2x-y=5, 5x-2y=13

1) 2x-y=5
2) 5x-2y=13 


5x-2(2x-5)=13
x=3 
y=2(3)-5=1

solution: (3,1)

The length of a rectangle is 4cm more than twice its width. The perimeter is 86cm. Find the width and length.

1) l=4+2w
2) 2(l+w)=86 


2) l+w=43 
replacing l...
(4+2w)+w=43
3w=39
w=13cm 



1) becomes
l=4+2*13
l=30cm

Solve: 4m-5n=8, 2m+3n=10

1) 4m-5n=8
2) 2m+3n=10 <-m2 


and after we swap their positions... 


4m+6n=20
4m-5n=8 


then subtract to get 
11n=12
n=12/11 


from 1)... 


4m-5(12/11)=8
4m=8+60/11
4m=148/11
m=37/11

domain of f(x)=log(2*x-x^2)^1/2

2x-x^2=
x(2-x) 
so the domain is 
(-oo,0)U(2,oo)

Determine which ordered pairs are part of the solution set for each inequality. 2x-3y>6,{(3,2),(-2,-4),(6,2),(5,1)}

Testing points is by substitution:
 
2(3)-3(2)>6
6-6>6 False 

2(-2)-3(-4)>6
-4+12>6 True 

2(6)-3(2)>6
12-6>6 False 

2(5)-3(1)>6
10-3>6 True 

The dimensions of a rectangular swimming pool are 15feet by 30 feet. The dimensions of a rectangular deck that surrounds the pool are 31 feet 40 feet. What is the area of the deck only?

 


 
so 790 square feet

Find the real numbers that satisfy the equation: |x| = -1/5

Absolute values are always greater than or equal to 0, so no real number(s) can make this equation true (no solution).

the sum of two numbers is 42. three times the first number is the same as four times the other number. find the number.

1) x+y=42
2) 3x=4y 
so...
x=42-y
3x=3(42-y)=4y
3*42-3y=4y 
7y=3*42
y=3*42/7
y=18 
x=42-18
x=24

Find x and y intercepts of the graph y=-3

This is a horizontal line so no x-intercept and y-intercept: (0,-3)

Find x and y intercepts of the graph x=-1

This is a vertical line so no y-intercept, x-intercept: (-1,0)

Human body temperatures have a mean of 98.20 degrees Fahrenheit and a standard deviation 0.62 degrees Fahrenheit. You take your temperature and it is 96.98 degrees Fahrenheit. What is your z-score?