Find the LCM of x^2+6x, x^2-6x

x^2+6x = (x+6)x

x^2-6x = (x-6)x 

LCM: x(x-6)(x+6)

Solve this system: 2x – y = 7, 3x + y = 8

2x – y = 7
3x + y = 8 

5x=15
x=3 

2x - y = 7
6 - y = 7 
y=-1 

Solution: 
(3, -1)

What is the maximum y value for f(x)= -x^2+8x+9

Vertex Formula: 
 

solve y=1/a(x+k) for the variable of x

 

 

 

:)

what is x to the third power divided by x

it is x to the second power if x is not zero. If x is zero the quotient is undefined because division by zero is undefined.

Suppose a and b are positive real numbers for which . If neither a nor b is 1 and a does not equal b, find the value of ab.

 
 
 
 
 

and by our initial conditions... 
 
or... 

 

 

 




:) 

If a cone's radius is tripled and its height is quadrupled, then which of the following statements about its volume will be true?

For a cone  
with a new 
 and  




So the new volume is 36 times greater than the old volume


:) 

How do you factor: 2x^2+ xy- y^2+ 3x+ 1

2x^2+ xy- y^2+ 3x+1= 

(2x-y)(x+y)+3x+1= 

(2x-y)(x+y)+2x+x+1= 

(2x-y)(x+y)+(2x-y)+(x+y+1)= 
(2x-y)(x+y+1)+(x+y+1)= 

(2x-y+1)(x+y+1) 


:)

The length of a rectangle is 10 ft longer than twice the width.If the perimeter is 116 ft find the lenght and width of the rectangle.

l=2w+10 
P=2(l+w)=116 

so 
l+w=58 
2w+10+w=58 

3w=48 
w=16 

l=2(16)+10=42 

length: 42 ft
width: 16 ft

A man is 3 times as old as his daughter, 8 years ago the product of their ages is 112, find their present ages

Notice: 
Factors of 112 are 
1, 112 
2, 56 
4, 28 <--- most likely ages 8 years ago!
7, 16 
8, 14 



Now we verify... 
3(4+8)=36=28+8 

so their ages are 12 and 36

A man is x years old while his son is y years old, the sum of their ages is equal to twice the different of their ages, the product of their ages is 675, find the ages of the man and his son.

Let's try a creative solution not involving algebra directly. 
Factors of 675 are 
1, 675 
3, 225 
5, 135 
9, 75 
15, 45 <--- most likely! 
25, 27 



Now we verify... 
15+45= 2( 45-15) ? 
yes! 

so x=15, y=45

-18+6b<6(2+3b)+6 
-18+6b<12+18b+6 

-18-12-6+6b-6b<12-12+18b-6b+6-6 

-36<12b 
b>-3

Solve: y=x+1, 2x+y=10

y=x+1
2x+y=10 

Substituting...

2x+x+1=10 
3x=9 
x=3 
y=4


Solution: (3,4)



:)

Test the points in the inequality. Are they solutions? (Y/N)

y<3x, 

(3,1) -> 1<3(3)   Y

(-3,2) -> 2<3(-3)   N 

(1,1) -> 1<3(1)    Y

(1,2) -> 2<3(1)   Y

Consider the line 5x+4y=-8 What is the slope of a line perpendicular to this line? What is the slope of a line parallel to this line?

Perform the indicated operation and write your result in standard form. (6+2i)(1 –3i)

(6+2i)(1 –3i)=6(1–3i)+2i(1–3i)

solve this: (x + 1 < 4) ∩ (x - 8 > -7)

x + 1 < 4 AND x - 8 > -7 
x<3 AND x>1 

 


:)

Simplify The Trigonometric Expression

Simplify. (1 + 2/(x + 2))/(1 + 8/(x - 4))

 


or 

Solve each system by substitution method 1) y=x^2+6x+9 2) x+y=3

y=3-x 
y=x^2+6x+9 

leads to

3-x=x^2+6x+9 

x^2+7x+6=0 
(x+6)(x+1)=0 

x=-1 or x=-6


:)

Please help me solve this problem. I am so lost! Thank you. Solve for x: 4^2x-1= 1/2

 


 


 


 



 

:)

Matrix operation

Evaluate: (3-4i)(1+4i)

Using distribution we can write











:) 

If p,q,r are any real numbers,then a)max(p,q) < max(p,q,r) b)min(p,q)=1/2((p+q)-(p-q)) c)min(p,q) < min(p,q,r) d)none of these

d 
none are always true: 

a)max(2,2) < max(2,2,2) false they are equal
b)min(0,1)=1/2((0+1)-(0-1)) False!
c)min(2,2) < min(2,2,2) False they are equal
d)none of these

Solve the system of equations: 8x – 3y = 1, –2x + 3y = 11

Adding the equations yields 
6x=12 
x=2 

then 
8(2)-3y=1 

leads to 
3y=-15 

y=5

solution: (2,5)


:)

A researcher polled 230 freshman at a university and found that 110 of them were enrolled in a history class. Estimate the probability that a randomly selected freshman is enrolled in a history class

p=110/230

compute: 4/(3-i)

simplify: -3/5[2/3-1/2(3/4-1/2)]

-3/5[2/3-1/2(3/4-1/2)]= 
(-3/5)(2/3)-(-3/5)(1/2)(3/4-1/2)= 
-2/5+(3/10)(1/4)= 
-2/5+3/40= 
-16/40+3/40= 
-13/40

Solve: 3x+9y=36, x=8y-10

3x+9y=36 
x=8y-10 

D3: 3x+9y=36 => x+3y=12 

(8y-10)+3y=12 
11y=22 
y=2 


x=8(2)-10=6 

solution: (6,2)

square root of 2/5 all over 2

What is sqrt(12b^7)?

Z^3=-1 find cubic roots ( step by step)

Since it is a cube root... 

 


 
z=-1 
And we use the solver to find the other two: 

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation  (in our case ) has the following solutons: For these solutions to exist, the discriminant  should not be a negative number. First, we need to compute the discriminant : . The discriminant -3 is less than zero. That means that there are no solutions among real numbers. If you are a student of advanced school algebra and are aware about imaginary numbers, read on. In the field of imaginary numbers, the square root of -3 is + or - . The solution is  Here's your graph: