pre cal help

**Peyton Sawyer** · September 30th 2008, 07:17 PM

1. what is the area of a square whose diagnol is 1 unit longer than the length of a side?

2. if a 3 didget number is chosen at random, from the set of all 3 diget numbers what is the probablility all 3 didgets will be prime?

3. x+y=b
x+2y=b^2

for what value of "b" will the solution of the system consist of pairs of positive numbers?

4. Find the equation of a line perpendicular to 3x-5y=17 that goes throgh the point (4,3)

5.ms sanders has Epogen 2200 units subcutaneous injection 3 times a week ordered for the anemia caused by chronic renal failur. Epogen 3000units/ml is avalible. How many millilieters will the patient recieve for each dose?

**Prove It** · September 30th 2008, 10:16 PM

Originally Posted by Peyton Sawyer

1. what is the area of a square whose diagnol is 1 unit longer than the length of a side?

2. if a 3 didget number is chosen at random, from the set of all 3 diget numbers what is the probablility all 3 didgets will be prime?

3. x+y=b
x+2y=b^2

for what value of "b" will the solution of the system consist of pairs of positive numbers?

4. Find the equation of a line perpendicular to 3x-5y=17 that goes throgh the point (4,3)

5.ms sanders has Epogen 2200 units subcutaneous injection 3 times a week ordered for the anemia caused by chronic renal failur. Epogen 3000units/ml is avalible. How many millilieters will the patient recieve for each dose?

1. If we let $x$ be a side length of the square, it's diagonal is $x+1$ .

Using Pythagoras' Theorem, we can see that

$x^2 + x^2 = (x+1)^2$ (since $a^2 + b^2 = c^2$ ).

Solving for $x$ we get...

$2x^2 = x^2 + 2x + 1$

$x^2 - 2x - 1 = 0$

Use the Quadratic formula to find $x$ (only one answer will be acceptable). Then square $x$ to find the square's area.

**Prove It** · September 30th 2008, 10:33 PM

Originally Posted by Peyton Sawyer

1. what is the area of a square whose diagnol is 1 unit longer than the length of a side?

2. if a 3 didget number is chosen at random, from the set of all 3 diget numbers what is the probablility all 3 didgets will be prime?

3. x+y=b
x+2y=b^2

for what value of "b" will the solution of the system consist of pairs of positive numbers?

4. Find the equation of a line perpendicular to 3x-5y=17 that goes throgh the point (4,3)

5.ms sanders has Epogen 2200 units subcutaneous injection 3 times a week ordered for the anemia caused by chronic renal failur. Epogen 3000units/ml is avalible. How many millilieters will the patient recieve for each dose?

3. Use the elimination method to get $y$ in terms of $b$ . Substitute back into equation 1 to get $x$ in terms of $b$ .

You should get $x=2b - b^2$ and $y=b^2 - b$ .

You want both x and y to be positive.

So $2b - b^2 > 0$ and $b^2 - b >0$ .

Solving the first gives...

$b^2 < 2b$ and so, dividing by b, we get

$b < 2$ if $b>0$ and $b>2$ if $b<0$ .

Solving the second gives...

$b^2 > b$ and so $b > 1$ if $b>0$ and $b<1$ if $b<0$ .

So putting the inequalities together, we find that if $b>0$ , b is both greater than 1 and greater than 2. So $b>2$ . And if $b<0$ we find that b is both less than 1 and less than 2. So $b<1$ .

**Chop Suey** · September 30th 2008, 11:10 PM

Originally Posted by Peyton Sawyer

1. what is the area of a square whose diagnol is 1 unit longer than the length of a side?

Another way to solve number 1:
Knowing that in a 45-45-90 triangle the hypotenuse is \sqrt(2) multiplied by side:

$x + 1 = \sqrt{2}x$

$(\sqrt{2}-1)x = 1$

$x = \ldots$

EDIT:
As for number 4, simply solve for y to get the function in the form of:

$y = mx + b$

Recall that m is the slope, and that the slope of a line that is perpendicular to the line in question is given by:

$m_{perpendicular} \cdot m_{line} = -1$

Once you have the slope and the given point, simply plug in point slope form:

$y - y_1 = m(x-x_1)$

and solve for y.

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