Solve: x^2-1 < 0

 
factor to get
 
check intervals... 

x<-1: 
(-)(-) false 

-1<x<1: 
-1 (-)(+) true

x>1:
(+)(+) false


solution interval: (-1, 1)

The number of men in a tour group is 15 times the number of women. If there are 48 people in the group, how many are men?

System:
1) x+y=48
2) x=15y 



Solution...
(15y)+y=48
y=3 


x=15*3=45 
45 men

Find 4 consecutive odd numbers that add up to 200

n+(n+2)+(n+4)+(n+6)=200
4n+12=200
n+3=50
n=47 
so they are...
47, 49, 51, 53

a rectangle has one side equal to (2x+4)cm and a perimeter of (6x+4)cm what is the area of rectangle in terms of x

For convenience let's call the given side the length, so...
 
W are also given the perimeter...6x+4 and we for a rectangle, 
therefore: 

so we have enough information to solve for w: 

 
Now we have enough information to solve for area.

so

For the function: f(x) = 2x + 4 find: f(x+h) + f(x)

We use substitution to evaluate:

f(x+h) + f(x) =
2(x+h)+4 + 2x+4=
4x+ 2h + 8

Find the rate of change between the two points: (8, 1) and (4, 2) where x is in months and y is in inches.

Rate of change is computed using slope: 
m=(y2-y1)/(x2-x1)
so 
m=(2-1)/(4-8)=-1/4 
that means the rate is falling at 0.25 inches every month

How do I solve for, y>4x

When there are two variables the solution is usually expressed as a graph because the solution sets are typically infinite. For example (1,-1), (1,10), (2,1000) are all solutions to y>4x. In fact any ordered pair for which the y coordinate is more than 4 times the x coordinate is a solution. So in general we graph the function (in this case y=4x) and we shade the region(s) where the inequality is true ( in this case above the line withe the line being dashed to show that the boundary is not included)

using the digits 0,1,2,2,3 how many numbers greater than 20000 can be made ?

Assuming digits are to be used only once then as long as the first digit is greater than 1, any number formed will be greater than 20000:
3*4*3*2*1=72

Solve the equation by using the square root property. Express the radical in simplest form: (m+12)^2=-9

 or 
 or 

indicates the sets to which the number belongs -144/4

This number belongs to an infinite number of sets, but if you mean "major" set of numbers, then -144/4 belongs to the negative rational numbers, and thus every set for which the negative rational numbers is a subset.

Give the coordinates of the vertex for the graph of the equation: y=x^2+6x+9

In general...


v(-3,0)

but there is an easier way if we use the fact that it is a perfect square...


so that , 

---

separate 30 into two parts such that the larger is 6 less than twice the smaller. find the working equation of this and the answer.

1) 2x-6=y
2) x+y=30 

then we write... 
x+(2x-6)=30
3x=36
x=12 



and so y=18

|x-1| = 5x+10

absolute value means...
1) x-1=5x+10 
or 
2) x-1=-5x-10 

so for case 1)...
4x=-11
x=-11/4 (extraneous)


and for case 2)...
-6x=9
x=-3/2

how do i do this: 1 /loga(abc) +1 /logb(abc) +1 /logc(abc) ?

use the change of base identity: 
1 /loga(abc) +1 /logb(abc) +1 /logc(abc)=
(log(a)+log(b)+log(c))/log(abc)

solve: 1) 3x+y=17, 2) 4x-y=18

1) 3x+y=17
2) 4x-y=18 

adding the two equations yields:
7x=35


thus
x=5 



now we can find y...
3*5+y=17
y=2

Factor: 15y^2+8y+1

since 3*5=15 and 3+5=8...


15y^2+8y+1=
15y^2+3y+5y+1=
(15y^2+3y)+(5y+1)=
3y(5y+1)+1(5y+1)=
(3y+1)(5y+1)

James is 4 years older than Kabul. In two years, their ages will total 50. How old is James now?

1) j-k=4
2) j+2+k+2=50 

j-k=4
j+k=46 

2j=50


j=25 

what is the truth value of the statement "2+4=6 and 9 is a prime number

Both statements are not true, so the and of them is not true. Thus the statement is false.

find two consecutive odd integers such that three times the smaller one exceeds two times the larger one by 7

1) n-m=2 <-- consecutive odds differ by 2
2) 3m+7=2n 



3(n-2)+7=2n
3n-6+7=2n
n=-1 
so m=-3

For what value of x is this inequality |x – 6|< - 8 true? Why?

for no value of x... 
|x – 6|< - 8 
has no solution because an absolute value of a real valued expression can never (by definition) be negative. Therefore it can never be less than -8

Curtis and Ben have 60 Marbles between them. how many do they each have if Curtis has 4 times as many as Ben

1) b+c=60
2) 4b=c 


so that...
5b=60 

and...
b=12
so we get: 
b=12, c=48

sqrt(x+4)=x+4

 
 
x=-4 
or 

x+4=1
x=-3 
solution set: {-3, -4}

Find a cubic function with integral coefficients having (4 + 3i) and -3 as roots

If coefficients are real and roots are complex, then roots occur in complex conjugate pairs:

 
(x-(4+3i))(x-(4-3i))(x-(-3)) =
x^3-5x^2+x+75

Find the value of x and y (x+5)/i+2y=5+i

1/i=-i
so...

Imaginary part:
-(x+5)=1
x=-6 

real part:
2y=5
y=5/2

does the sum of three consecutive odd integers equal an even integer

No, never. A sum of any three odd numbers will be odd: 
{2n+1) + (2m+1) + (2p+1)= 2(n+m+p)+2 + 1

Lamar is a software salesman. His base salary is 1700$ , and he makes an additional 70$ for every copy of History is Fun he sells. Let p represent his total pay (in dollars), and let n represent the number of copies of History is Fun he sells. Write an equation relating to p to n . Then use this equation to find his total pay if he sells 28 copies of History is Fun.

(n)=70n+1700 
so that 
P(28)=70(28)+1700=3660 
so he earns $3660.00

Solve the inequality. Write the solution set in interval notation. |5 - x| ≥ 3

 
means 
 
or 
 
which lead us to 
 
or
 

ie 
(-oo,2)U(8,oo)