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Ok so we have two consecutive integers
Lets call the first 1 a, and the second one a+1
Now the formula,
So we have the second one squared plus 3 times the first one=177
now we need to solve for a, so we will expand the
giving us
collect like terms, and move the 177 to the left side.

you can factor this or if you are not comfortable with factoring you can use the quadratic formula
Now if we factor we get
which gives us ,
Now I am assuming they wanted the positive intergers, so you have a=11, and then a+1=12. So you integers are 11 and 12

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Ok, So for functions that are a fraction, the denominator cannot equal zero.
So you solve to see what is not allowed, factoring gives you , and that gives you and , so x cannot equal 0 or 3. As for how to express this answer
Domain:(,0)U(0,3)U(3,)

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Let's call x the smaller number and y the larger number.
So we have and
Now rearrange the first equation to say and substitute into the second equation. -> -> ->
Now that we have plug into to get 50+1=3*y}}}-> ->
So your ordered pair is (10,17)

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The sum of a number and four times its reciprocal is 29/5.Find the number
Let's call the number n.
The reciprocal would be
So the formula should look like.

now multiply every term on both sides by n, the in the will cancel to become 1, leaving you with 4*1=4
multiply both sides by 5.
subtract from both sides
now you have a solvable quadratic equation, that factors into.

So or -> divide both sides by 5

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ok so what happened here is that the reciprocal means
One number plus sixteen times its reciprocal is equal to ten.
So the formula should look like.

now multiply every term on both sides by n, the in the will cancel to become 1, leaving you with 16*1=16
subtract 10n from both sides.
now you have a solvable quadratic equation, that factors into.

So or

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Ok so lets call one leg x
The other leg is three times the length 3x and 2 cm less so 3x-2.
The Area of a triangle is
For a right Triangle the base is one leg and the height is the other leg.
We also know that the Area is 48.
So Multiply by 2 to cancel the
Subtract 96 from both sides.
Factor out the 3.
Use the qudratic formula to solve/

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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=129 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 6.17890834580027, -5.17890834580027. Here's your graph:

And since you cannot have a negative length in a triangle, is the length of the leg we called x. To find the length of the other leg multiply by 3 and then subtract 2 to get the length of the other leg.

So the length of the other leg is

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Going back to this step (cos^2x - sin^2x) cosx - (2 sinx cosx) sinx
You need to use identities
So
Simplify.

And everything is now in terms of powers.

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i is defined as the
So we have.
Now we FOIL.

Simplify.
note that
And now put back as i since that is what teachers expect.

So

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Ok so lets rewrite everything in terms of and
So we have
Multiply everything out.
common denominator of on the right.
we know that
So

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means plug in 3 for x so we get
So

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To do this you need to solve both equations for y, once you have done this you will be able to see the slopes and that will tell you if they are perpendicular.
So add 8y to both sides.
subtract 3 from both sides.
And divide through by 8.
So the slope is that comes from the number attached to the x.
For the next equation.
Add 8x to both sides.
And divide through by 8.

So the slope is
The definition for two lines to be perpendicular is that the slope of one must be the negative reciprocal of the slope of the other. The negative reciprocal of is and we only got so they are not perpendicular.

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The first step will be to subtract 3 from all 3 parts.
Now divide by -2. And remember to reverse the <= signs when dividing by a negative.

Expressed in interval notation this is [-3,3]

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The first step in such a problem is to solve the given equation for y.
So subtract x from both sides.
Now divdie everything by -2.
The number attached to the x is the slope of this line, To get a line that is perpendicular you need to take the negative reciprocal which would be or just -2.
We now do m stands for slope so we have.
Now you plug in (4,-7), 4 for x and -7 for y to get the line that passes through that point and solve for b.

add 8 to both sides.

Going back to you will now put in the b you found.
And is your final answer.

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Ok so to buy 40 tickets in packets of 5 means youe need 8 packets.
So 8 packets of 5 tickets costs . So 40 tickets in packets costs $46
Now for single tickets . So buying 40 single tickets costs $60
The differance is the ammount he saves . So he saves $14
Which is answer C

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You need to implicit differentiation for this problem and solve for
So we have.

The derivative is the 2y produces the because y is a function so you have to apply the chain rule to it.
So now.



And x and y are given by (3,4) giving x=3 and y=4. (,)
So
Now for the tangent line you have.

so we have
Giving us Add 4 to both sides. 4 can be rewritten as


And that is your tangent line.

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I am assuming you did not lose any parentheses. So this has to do with order of operations.
parentheses take precedence over everything and then exponents take precedence over multiplication and subtraction.
For the first term you square first and then multiply.
But for you have to cube before multiplying by -1.
So we have

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I am going to replace theta with x since i have no way to make the computer display theta.
So what we have is.

The referance angle that makes sin equal to is 30 degress or
If we want this angle in the 4th qudrant we get or
So we know that our angle is 330 degrees or
We also know that So we need to find out what cos(x) is to find sec(x).
So we need to find cos of 330 degrees. The referance angle was 30 degrees and . Cos is positive in the 4th quadrent so
And is
So
And if you rationalize this.

So choice C is the correct answer.

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Ok so distribute first to remove parentheses.
Now combine like terms.
Add 6v to both sides.
Subtract 2 from both sides.
And divide both sides by 9.

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The area of a triangle is
Now for a right triangle sides A=12 and B=10 are the base and the height.
So your area is
So the area of your triangle is 60.

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Not sure which you wanted so I will solve both.
For
we will multiply both sides by
Giving us
When we distribute the 5
Now add 35 to both sides.

and divide both sides by 15.

Now the other interpretation of your problem.
For this one you would need to get a common denominator first.
So
With the common denominator we have.
Now we will multiply both sides by 3x.
Giving us Add 21x to both sides.
Divide both sides by 36.

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Ok so lets say that Andy has x quarters and y half dollars.
So
And now for the values of the coins.
Each quarter is worth 0.25 and you multiply by x, and each half dollar is worth 0.5 and you multiply by y. When you add them up you get the amount the coins are worth.
So
Putting this into the second equation gives us.
Distributing the 0.25 gives us.
Combine like terms.
Subtract 3.5 from both sides.
Divide both sides by 0.25.
We now know that and we can plug this into to gives us
So and

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The sum of two numbers equals eighteen. The total of three times the smaller and two times the larger is 44.
Ok so we have two unknown numbers. We will call the smaller one x and the larger one y.
So and
Now we have a system of equations.
And we can write
Now when you see x in the second equation replace it with
This gives us.

Subtract 48 from both sides.
Divide both sides by -1.

And x was so
So and

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This problem is done using the Pythagoran theorem. Which says that
This says that the two shorter sides of a right triangle squared equal the long side squared

And the triangles longest side is the diagnol line across the tv set.
So we know the diagnol of the tv is 15, so
And we know the leangth is 12 so
This gives you that



Since b is the height of your triangle the height is 9.

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solve for x:

So first we divide both sides by 42.5

Now we will take ln of both sides. This helps because there is a property of logarithms that says the following In english it basically allows you to take the exponent outside the logarithm.
So applying this to our equation gives us.

Now I will move the x outside.

Now all that is left is to divide both sides by

Using a calculator you can get a decimal value of.

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Ok so first we need the slope. You compute this using Where m is your slope.
So you have (3,4) and (5,8)
Giving us
So
Now to write the the equation you can pick (3,4) or (5,8)
So it will look like or
I will use the first point (3,4).
So now we have
Next multiply out the two on the right hand side.
Now add 4 to both sides.
This gives you your final answer of

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Ok so we have What you can do in algebra is flip both sides of an equation. So will become and which is really will become
So now we have.
Now you divide both sides by two. Dividing a fraction can be confusing so you can multiply by instead of dividing by 2.

Giving us.

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A motel charges 80.00 per day for double occupancy and 70 pr day for single occupancy. If 80 rooms are occupied one night for a total of 5800.00 how many rooms of each type are occupied?
Ok I am goint to define as the number of single occupancy rooms. And what this tells us is that is the number of double occupancy rooms.
So now we set up the equation.
So it is the number of single occupancy rooms times the single rate + the number of double occupancy rooms times the double rate = to the total amount made by the hotel.
Solving the equation.

Subtract 6400 from both sides.
And divide both sides by -10.
this tells us that there were 60 single occupancy rooms since I defined as single occupancy. And double occupancy was , so So there must be 20 double occupancy rooms.

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Two formulas you need are and the other is
Using these we can rewrite the left side to become.

Now we distribute the that is on the outside.
this proves your identity.

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I am assuming you want this solved for 0
So first we need a common denominator
We will start by factoring the current denominators.

Now for the common denominator.
Now your denominator cannot equal to zero since you are not allowed to divide by 0. so x cannot equal to 1, 3, or -3.
Since the bottom cannot equal 0 the only time the fraction will equal 0 is when the numerator equals 0.
Now we multiply out the numerator.

Next we combine like terms.

Now we set the numerator equal to 0 and solve.
Add 7x to both sides.
Divide both sides by 7.

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I need help with COMPLETELY factoring out the polynomial
Ok first step would be to factor out which leaves us with
Now we can use the differance of squares formula which says that
For us and
This gives us we factored the using difference of squares.

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I am assuming this is the original problem, it wasn't completely clear.
the next step is to rewrite the right hand side.
Now we state the restrictions, these happen when you divide by 0. So x cannot equal to 3 or -4
Your next step is to create a common denominator on the left side.

Now we will only pay attention to the numerators since the denominators match.
This gives us.

Now combine like terms.

subtract 9x from both sides.

add 13 to both sides

Divide both sides by 2.

This gives you the solution but since this is among the values that are not allowed your equation has no solution.