1. ## pre cal help

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?

2. 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 $\displaystyle x$ be a side length of the square, it's diagonal is $\displaystyle x+1$.

Using Pythagoras' Theorem, we can see that

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

Solving for $\displaystyle x$ we get...

$\displaystyle 2x^2 = x^2 + 2x + 1$

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

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

3. 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 $\displaystyle y$ in terms of $\displaystyle b$. Substitute back into equation 1 to get $\displaystyle x$ in terms of $\displaystyle b$.

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

You want both x and y to be positive.

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

Solving the first gives...

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

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

Solving the second gives...

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

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

4. 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:

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

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

$\displaystyle x = \ldots$

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

$\displaystyle y = mx + b$

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

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

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

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

and solve for y.