Algebra Answers

Use Cramer's rule to solve the unknown of the system: x + 2y =2 - z,3x - 6y = 2 - 2x,2x =8 + z

i.x =2, y=1/3, z=-2

ii.x =-3,y =2, z=-1/2

iii.x =4,y =-1/2, z =-3

iv.x =3, y =1/2, z=-2

Roko paid $12.50 for 25 game tickets.Louisa paid $17.50 for 35 game tickets.What is the constant of proportionality?

The concentration of pollutants , in grams per liter, in the river Buriganga is approximated by P(x) = .04e−4x, where x is the number of miles downstream from a tannery industry that the measurement is taken. Find each of the following: • P(0.5), P(1) • The concentration of pollutants 2 mi downstream • the number of miles downstream where the concentration of pollutants is .002g per liter.

Assessment

Solve the following.

1. The perimeter of a rectangle is 24 cm. Express the area of the rectangle in terms of the width x.

2. The area of a rectangle is 85 cm. Express the perimeter of the rectangle as a function of the width x.

3. A piece of wire y cm long is bent into a circle. Express the area of the circle as a function of the circumference y.

4.  Express the length of the radius of a circle as a function of the 

5. Express the length of the diameter of a circle as a function of the circumference.

6.The perimeter of a rectangle is 50 centimeters. Express its area A as a function of the length x.

7. A wire of length x is bent into the shape of a square. Express the area of the square as a function of x. 

If z = 2 ( cos 2¥/3 + isin 2¥/3 ), then z^3=

i. 2 - i8√3

ii. -4 + i4√3

iii.-8-i√2

iv. -8 - i4

Simplify (√5+1)÷(√5-1)

the locus of the complex number z such that Iz+3I = Iz-1I is?

A.     A line

B.     A circle

C.     A quadratic curve

An ellipse 

, In a cartesian plane (OXY) the solution of the equation e^2x – 2e^x + 1 = 0 represent,

A.     A point

B.     A line

C.     A circle

6, Solve the inequalitThe catheti of a triangle has length 4m. If the hypotenuse of the triangle is 9m, that is the projection of this catheti on the hypotenuse.

A.     16/9

B.     4/3

C.     4y tan(x+ ∏/3) ≥ √3 

5, A square of length l, a rhombus is out of this triangle making it have an angle of 60⁰ on a single diagonal. What is the area of this rhombus?