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Add 1 to both sides: $x^2-3x=1$

Divide by x: $x-3 = \frac{1}{x}$

Subtract x from both sides: $-3 = \frac{1}{x} - x$

Our answer is $$-3$$

1. If a, b, and c are different whole numbers and if a^2+b^2+c^2=90, find the largest possible value of the sum a+b+c.  

I have more time now, so I came back to see if I could figure out problem #1.  

Since a, b, & c are whole numbers, their squares are likewise whole numbers.   

Since a² + b² + c²  totals 90, no single one of them can be 90 or larger.   

This is a list of the squares less than 90.  What three of them total 90?   

1,  4,  9,  16,  25,  36,  49,  64,  81  

By brute force I find  

  1 + 25 + 64   //   sum of square roots is 1 + 5 + 8 = 14  

16 + 25 + 49   //   sum of square roots is 4 + 5 + 7 = 16  

Those are the only ones, unless I missed one/some.  Check it to see if I overlooked any.  It's very possible. 

_.

the answer is 58207660913467407226562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

S-A-S      yes they are congruent.

Slope,m, of given line is  7/4    perpindicular slope will be  - 1/m  = -4/7

  using thepoint given  (10,5)

(y-5) = - 4/7 ( x-10)

The graph of  y = x² + bx + c  is a parabola that opens upward and intersects the x-axis at  -4  and  8 .

An equation for a parabola that opens upward and intersects the x-axis at  -4  and  8  is  y = (x + 4)(x - 8)

Let's take the second equation and expand the right side by FOILing it:

y  =  (x + 4)(x - 8)

y  =  x² - 4x - 32

Now we can see that  x² - 4x - 32  matches  x² + bx + c  and so we can say...

b = -4

c = -32

b + c = -36

803 is the answer

How can the first book and the last book both be math books if all math books must be at the beginning?

$\mathbf{M} = \boxed{\begin{pmatrix} -7 & -4 & 0 \\ -5 & -3 & 0 \\ 0 & 0 & 1 \end{pmatrix}}.$

603 is the anwser to your question.

2. A seven is written at the right end of a 2-digit number to make it a 3-digit number, thereby increasing the value of the 2-digit number by 700. Find the orginial 2-digit number.   

Just by visualizing this, I see that the original number was 77.  I don't know how to work problem #1.  

_.

Each side of quadrilateral ABCD is tangent to a circle. If AB = 84, BC = 78 and CD = 73, find DA.

DA = 79

link::https://web2.0calc.com/questions/pls-help-due-tmrow_7

One way as follows:

I assume you want to find k and a from  ksin(x-a) = 3 cos x + √3 sin x, in which case:

Hi May,

It is nice to meet you.

What you have done is completely correct.

You should state right from the beginning that      

$2\le x<6$

so you have 

$2x(x-6)(2x-15)=162\\ $

From the way the question is worded, it seems likely that the answer will be an integer

so

You could just plug in x=2,3,4 5  and see if one of them works 

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However, if none of those work, or if you want to do it in a more complicated way then here is an alternative.

Expand it and take it all to the same side. (start by dividing both sides by 2)

You will get

$2x^3-27x^2+90x-81=0$

You need to look for factors and the way the question is worded it seems that there will most likely be an integer value of x

If there is an integer one to find it will be a factor of 81.

choices   

$\pm1,\;\pm3,\; \pm81$

[edit: I forgot  +/-9]

I usually look at the plus and minus at the same time as it saved time, but I am hoping for a pos one so not this time

Normally Id start with  +/-1 but we are looking for one between 2 and 6   so I will try 3

If x=3 then

LHS=2*27-27*9+90*3-81 = 0 = RHS

So x=3 will make this work.

You can continue on to look for other possibilities if you want but you already have your answer.

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If you were going to continue then you would  use algebraic division for this.

$(2x^3-27x^2+90x-81)\div (x-3)$   

The you would use the quadratic formula to find the other 2 solutions.

The car cost $2500 this is a set amount it will not change

Then

the car cost   $0.65 for every mile driven

If the car drives 10km in the year.  

How much will the 65c costs be?

How much will the total cost be?

What will be the total cost?

If the car drives x km in the year.  

How much will the 65c costs be?

How much will the total cost be?

What will be the total cost?

Please answer copy, paste and answer all these questions and then you will understand.

And we will be able to see that you understand.  (or we will be able to see what you do not understand)

So now it is your turn to answer  SmartMathman

Yes, the question as it stands, is confusing but trivial

a,b,c  ARE p1, p2, p3 

am I missing something?

I'm too lazy to do this, but I'll give you a hint:

Since all 3 angles and 1 side are known, you can use the law of sines to calculate side BC.

Important: The "Angle Bisector" Theorem says that an angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

AE / AB = EC / BC

BC = (AB * EC) / AE

7/16

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7/8 * 1/2 = 7/16

 If the area of the circle is 4pi cm², then the radius  r = 2

The distance from O to A is 2r

You can order 432 different shakes.

What is the radius of the circle inscribed in triangle ABC if AB = 10, AC = 17, BC = 22? Express your answer as a decimal to the nearest tenth.

1/   Find the triangle area using Heron's formula.

2/   Calculate the value of inradius using this formula:   r = A / s       ( 's' --semiperimeter)