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The definition of a complementary angles is that the sum of the angles is equal to 90. thus we have the ratio 4:5. We then set up the problem as follows 4x + 5x=90. Then you would add (4+5)x=9x 9x=90 divide both sides by 9 and x is equal to 10. Then we go back and multiply to find the value of each angle. ie
4(x)=4(10)=40 5(x)=5(10)=50. The angle values are 40 and 50.

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Side 2=s
side 1=s-5
side 3=s-5+3=s-2
(s)+(s-5)+(s-2)=17
3s-7=17
add 7 to both sides
3s=24
divide both sides by 3
s=6
third side =6-2=4



The first side of a triangle measures 5 in. less than the second side, the third side is 3 in. more than the first side
second side of the triangle =s
first side of the triangle is =s-5
3rd side is =(s-5)+3=s-2

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If you plug in the x and y values for b you will find it incorrect.
x=-9,y=7
2x+3y=41 -18+21=39
2x-3y=-13 -18-21=-39
2x+3y=41
2x-3y=-13
Add each column
4x+0=28
divide both sides by 4
x=7
Plug in the value of 7 for x to get the y value
14+3y=41
Subtract 14 from both sides
3y=27
divide both sides by 3
y=9
Plug in the values of x and y in the second equation
(2*7)-(3*9)=-13
-13=-13

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A rectangle is composed of 4 right angles. With the diagonal you have created two triangles and better yet 2 right triangles. You would then use the pythagorean therom a^2+b^2=c^2
you already have the value for c=61 and a=11 all you have to do is plug in the numbers
121 +b^2=3721
subract 121 from both sides
b^2=3600
b=60
Let us doublecheck
121+3600=3721

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You are trying to get the vertex. In order to do this you need to complete the square f(x)=5x^2-20x+3.Set f(x)=0
0=5x^2-20x+3
Subtract 3 from both sides
-3=5x^2-20x
Factor out the 5 on the right hand side of the equation
-3=5(x^2-4x
divide the 4 by 2 and then square it.
-3=5(x^2-4x+4)
since you added an additonal 20 on the right side -don't forget to multiply the 4 you just added by 5
-3+20=5(x-2)^2
17/5=(x-2)^2
take the square root of each side 17/5sq rt=x-2
sqrt85/5=x-2
add two to both sides
x=2sqrt85/5

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first you solve for 6-3/4 You need to find the common denominator for both numbers in this case it is four. the number 6 becomes 24/4 you haven't changed the number it is still the same quantity but you can now perform the subtraction part with the fraction.64/4-3/4=21/4 divided by 3=7/4
8 divided by 1 is still eight but we need to find a common denominator to solve the problem in this case it is 3. 24/3-1/3=23/3

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x+y=6
x-y=4
Add each colum and you get 2x (+y-y=0)=6+4
2x=10
divide both sides by two and x=5
if x is 5 then y must equal 1
5+1=6
5-1=4

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(3p-5)(p+1)=answer
First figure out what are the factors that give u 5
1,5
What are the factors that give u 3
3,1

Based on this we need to find the two numbers from above that will give u -2
3-5=-2

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Awesome job!

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4y+5x=2y-3x+16
Subtract 2y from both sides
2y+5x=-3x+16
Subtract 5x to both sides
2y=-8x+16
Divide each term by 2

y=-4x+8
This is a equation of a line.

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We know that the difference between the 2 areas is 36. Therefore we are going to set up the equation of subtracting the two areas to get the original dimensions.
x=width of the original rectangle
3x=the length of the original rectangle
x-2=width of the smaller rectangle
3x-2=length of the smaller rectangle

the area of a rectangle is width X length
Area of the original rectangle-Area of smaller rectangle=36
(3x*x)-[(x-2)(3x-2)]=36
Use the foil method
3x^2-2x-6x+4
(3x*x)-[3x^2-2x-6x+4]=36
multply -1 to each term contained within the bracket.
Make sure to pay attention to the sign.
(+)(-)=(-)
(-)(-)=(+)
(3x^2-3x^2+2x+6x-4=36
Combine like terms and simplify
(2+6)x-4=36
8x-4=36
Add 4 to both sides of the equation
8x=40
divide both sides by 8
x=5
The dimensions of the original rectangle was 5,15
Let us double check our answer

the dimensions of the smaller rectangle is 3,13
(3*15)-(3*13)=36 75-39=36

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We know that the matrix has an inverse because the determinant is not equal to zero
[-3 1]
[-5 5]
[a b]
[c d]
To calculate the determinant ad-bc in this case -15+5=-10
Any Matrix inverse =1/ad-bc[d -b]
[-c a]
-1/10[5 -1]
[5 -3]
To double check multiply the matrices together and see if you come up with the identity matrix.
[-3 1]-1/10[5 -1]
[-5 5] [5 -3]
-15+5 3+3 -1/10[-10 0]
-25+25 5-15 -1/10[0 -10]

[1 0]
[0 1] is the identity matrix

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The general equation for a line is y=mx+c
m= slope
Replace m with -2/3 y=-2/3x +c

Plug in the value for the point
5=-2/3(-5) +c
We are trying to find the y intercept c


5=10/3+c
Subract 10/3 to both sides
15/3 -10/3= c
5/3= c
Let's double check that this is the correct linear equation

5=10/3 +5/3
Therefore the eqation is y=-2/3x+5/3

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Equation describes a sloping line. For any equation ax+by+c = 0, slope is . X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 5/2 = 2.5. Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 5/3 = 1.66666666666667. Slope is -2/3 = -0.666666666666667. Equation in slope-intercept form: y=-0.666666666666667*x+1.66666666666667.

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4a^2-2[3b-5b(b+4)]
the first step is to expand this -5b(b+4)=-5b^2-20b

4a^2-2[3b-5b^2-20b]
-2[3b-5b^2-20b]=-6b+10b^2+40b
4a^2-6b+10b^2+40b
Combine like terms and simplify
4a^2+34b+10b^2

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y=2x squared is not a line it is a parabola. Check your equation.

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Break down the #28 into factors 2*2*7 y*y*yThe answer is 2ysqrt 7y
You would subtract the exponents.

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10x-40y

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The negative inverse of the slope m=-1/4

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It is the only conic section that has a - in the equation
x^2/a^2-y^2/b^2=1

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The general equation of a line is y-mx+c
we know the slope of the line
y=-2x+c
Plug in the point
4=(-2)(-2)+c
4=4 +c
subtract 4 from both sides
c=0
the equation of the line is y=-2x

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The unknown number is x
The equation to solve is
2/3x+1/4x=x+8
The lcd is 12
Therefore multiply each term by 12
8x+3x=12x+96
simplfy terms

11x=12x+96

Subtract 12x from both sides
-x=96
divide both sides by -1
x=-96

Let's doublecheck our answer
(2(-96)/3} +(-96/4)=-96+8
-64-24=-88

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log25 1/25= -1
1/25= (25)-1
The log value is the exponent of the base which in this case is 25.

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4x^2 + 4 = 2x + 3
Subtract 3 and 2x from both sides
4x^2+1-2x=0
4x^2-2x+1=0
a=4 b=-2 c=1

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15r^2 = 3r
Subtract 3 r from both sides
15r^2-3r=0
Factor the equation
3r(5r-1)=0
r=0 and r=1/5 these are the solutions to this problem

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x(x-3) = 40
Expand the equation
x^2-3X=40
subtract 40 from both sides
x^2-3X-40=0
Find possible factors for 40
(40,1) (2,20) (8,5)
We see that the 40 has a negative sign which means that one of the factors is negative.
Then we find which two factors when added together can give you -3
I can see from the list that the only possible answer is 5,8

(x-8)(x+5)=0 is the factored form of the above equation

Therefore the answers are x=8 and x=-5

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p2 + 3p - 9 = 0.
Add 9 to both sides of the equation
p2 + 3p=9

Divide the coefficient of the p term(=3) term by 2 and square the resultant value and add to both sides of the equation
p2 +3p +(3/2)^2= 9 +(3/2)^2
This makes the quadratic equation a perfect square
(p+3/2)^2=9 +9/4
Simplify the left side of the equation
(p+3/2)^2=36/4+9/4=45/4
(p+3/2)^2=45/4
Take the square root of both sides
p+3/2= + or -3sqrt5/2
subtract 3/2 from both sides
p=-3/2+3sqrt5/2 or p=-3/2-3sqrt5/2

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Change form to exponent
(x-8)(x+4=2^5=32
Use FOIL to ge x^2-4x=0
factorx(x-4)=0
x=0 or 4
In logs you only use + numbers
Therefore 4 is the correct answer.

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Set the equation to 0. When the ball hits the ground the distance is 0. Then use the quadratic formula.

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 : . Discriminant d=2436 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -0.604870334906633, 2.47987033490663. Here's your graph:

t=2.8

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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 : . Discriminant d=1 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -3, -2. Here's your graph:

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 -12 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 -12 is + or - . The solution is Here's your graph:

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The equation is y=90-x
x=time she spends on her English HW
y= time that she spends on her Math HW

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ln 9.3 = ln e^(.047x)
2.23001=.047x
Divide both sides by 0.047
47.4471=x
Let's doublecheck our answer
9.3=e^2.23