Solve Algebra 2 Problems 3, 7, 9 & 19

[mustang]

Problem 3. The sum of the two numbers is 3 and the sum of their reciprocas is 12/5. Find the numbers.


Problem 7. What is the linear term of the equation
q = 3x^2 + 2x - 1?

Problem 9. Write the equation of the ellipse with foci at (12,1) and (-12,1) and the endpoints of the major axis at (0,6) and (0,-4) Then graph the ellipse.


Problem 19. If f(x)=3x^2-2 and g(x)=2x^2+3, find[f o g](-4)

 

[arildno]

Problem 35. What have you done so far?

 

[TALewis]

Problem 3.

Let your two unknown numbers be m and n. You're given two statements about the relationship between m and n. Each statement can be written as an equation. You'll have two equations and two unknowns. You can solve this system of equations simultaneously for m and n.

The first equation is absolutely trivial. Hint on the second: The reciprocal of m is 1/m .

Show us a little of what you've done so we can help a little more.

 

[ShawnD]

Problem 3. The sum of the two numbers is 3 and the sum of their reciprocas is 12/5. Find the numbers.

2 equations, 2 variables, 2 easy

$$x + y = 3$$

Isolate one of the variables.

$$x = 3 - y$$

Now write the other equation

$$\frac{1}{x} + \frac{1}{y} = \frac{12}{5}$$

Substitute the isolated variable.

$$\frac{1}{3 - y} + \frac{1}{y} = \frac{12}{5}$$

Now multiply each term by all of the denominators.

$$5y + (15 - 5y) = 36y - 12y^2$$

Just solve for that equation and you'll have Y. Then substitute that answer for Y back into the first equation.

Problem 19. If f(x)=3x^2-2 and g(x)=2x^2+3, find[f o g](-4)

I think you are supposed to fill in -4 for the g equation, then use the g equation as x in the f equation. It's like this:
f(g(-4)) = ??