Math 123c test

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Math 123c Sample Test 4 Show all work.

1. Identify the center and radius of each circle. Draw= it and label the highest, lowest, leftmost and right most point= s.

a. (x – 3)² + (y + 5)² =3D 9 = &nb= sp; = b. x ² + y ² – 4x + 12y =3D 9

2. Find the center line, the vertex of the parabola

y =3D x²– 4x –21

b. y² – x + 2y= =3D 4

3. Graph= the following ellipses. Find the center, label the highest, lowest, leftmo= st and right most points on the ellipse= .

     a. _{=
                  =
            &nb=
sp;      b. x² – 2x + 4y^=
2+
8y =3D 11}

4. Graph the following hyperbolas. Find the center, draw the center box, label the vertice= s.

     a. _{=
            &nb=
sp;            =
            b. 4y²+ 8y – x^=
2 + 2x =3D 13}

5. S= olve the following system of equations using substitution method.

X =3D 2 + Y

Y =3D 4 – X

6. S= olve the following system of equations by the elimination method.

2X + Y =3D 2

3X – 2Y =3D 12

7. S= olve the following system of equations by the elimination method or the substitution method.

A. 2X – 3Y =3D -4 = &nb= sp; = B. 2X + Y + 4Z =3D 12

X – 2Y =3D -3 = &nb= sp; = X + 2Y + 2Z =3D 9

= &nb= sp; = = &nb= sp; 3X – 3Y –2Z =3D1

C. 2X + Y =3D 2

3X + 2Y =3D 12=

8. A= . Solve the system = &nb= sp; = B. Draw the graphs of the system

X2 + Y² =3D 25 = &nb= sp; = X² + Y² =3D 25

      4X^{2 <=
/sup>–
9Y   =3D 0        =
            &nb=
sp;            =
            &nb=
sp;
4X²– 9Y &nbs=
p;
=3D 0}

9. S= olve the following system of equations using matrix notation and row operations:

2X + Y + 4Z =3D 12

X + 2Y + 2Z =3D 9

3X – 3Y –2Z =3D1

10. Solve the equation (using a common base), without using the calculator.

11. Solve the equation using the calculator.

a. 8 =3D 7 ^2x+1 = &nb= sp; = &nb= sp; b. -4 + 3ln(2 – = 3x) =3D 2

12. 2 hamburgers, 2 fries, and 1 soda = cost $11. 1 hamburger, 3fries, and= 2 sodas cost $11.

3 hamburgers, 2 fries and 4 sodas c= ost $17. How much does each item cost? =

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