## Math Project

**1.**

**Medium Problem**

**Multiply the matrices:**

[3 -9] [4 6 1] [(3)(4) +(9)(5) (3)(6)+(-9)(7) (3)(1)+(-9)(3)]

[2 1] * [5 7 -3] = [(2)(4)+(1)(5) (2)(6)+(1)(7) (2)(1)+(1)(-3)]

2*2 2*3

Step 1: Multiply row by column

Step 2: Add to get the sum and answer for the each number

Step 3: Simplify

= [(12+-45) (18+-63) (3+-27)] = [-33 -45 -25]

[(8+5) (12+7) (2+-3)] [13 19 -1]

2*3

**2.**

**Hard Problem**

**Find the Determinant of a 2 by 2 Matrix**

A= [a b] det(A) = [a b]= a*b-c*b

[c d] [c d]

A= [4 9]

[3 2]

Step 1: Multiply together A and B

Step 2: Take the product of A and B and subtract the product of C and D from the the product of A and B.

Step 3: Simplify to get the determinant

**3.**

**Ridiculous Problem**

**Find the Determinant of a 3*3 Matrix**

Det(A) = [ a b c] = a(ei-hf)-d(bi-hc)+g(bf-ec)

[d e f]

[g h I ]

3x3

Det(A) = [ -2 4 7]

[5 6 8]

[-1 3 0]

Step 1: Plug in the numbers for each letter

Step 2: Simplify to get the determinant

**4.**

**Medium Problem**

**Solve for x.**

**Problem:**

**x2- 3= 2x**

Step 1: Stet the problem up equal to zero:

**x2– 2x – 3= 0**

Step 2: Factor:

**(x – 3) (x +1)= 0**

Step 3: Find x:

**x – 3= 0 or x +1 =0**,

**x=3 or x= -1**

**5.**

**Easy Problem**

**Graph 4x- 8y= 16**

Step 1: Subtract 4x from both sides of the equation

Step 2: Divide 8 from both sides of the equation, which will give you an equation in y-intercept:

**y= -2 – 2/4x**

Step 3: Graph the equation

**6.**

**Hard Problem**

**Solve x 2+bx+c by factoring**

**Problem: x 2- 10x – 24 = 0**

Step 1: Write original equation:

**x 2-10x- 24=0**

Step 2: Factor

Step 3: Zero product property

Step 4: Solve for x.

**7.**

**Medium Problem**

**Graph a quadratic Function in Vertex Form: y= 1/2 (x+2) squared +4**

Step 1: Identify the constants:

**a= ½, h= -2, k=4**

Step 2: Plot vertex:

**(h, k)= (-2,4)**

Step 3: Find axis of symmetry:

**x= -2**

Step 4: Plug a number in for x to find x and y

Step 5: Plot the vertex, and the point you found

Step 6: Graph

**8.**

**Evaluate an algebraic expression:**

**Evaluate: -8x-3x+2, when x=-10**

Step 1: Substitute -10 into the equation

Step 2: Evaluate and multiply

Step 3: Add together to get sum

**9.**

**Tell whether a relation is a function:**

Directions: To tell whether a relation is a function, an input can go to one output. If an input is mapped onto two outputs, than it is not a function, however an output can have to two inputs.

**10: Simplify the square root of 36 over 2**

Step 1: Separate the fraction with two square root signs, one over 36 and the other over 2.

Step 2: Simplify the square root of 36

Step 3: Multiply the square root of 2 to the top and bottom of the equation to get rid of the square root in the denominator

**11. Linear Programing Problem:**

**Sophie makes wedding rings. She doesn’t want to run out. She can make one regular size ring with one diamond in one hour. She can make a ring with 3 diamonds in two hours. She only has 50 diamonds and only 6 hours of time to work. She wants to make at least 4 rings with 3 diamonds. How many regular rings can she make and how many large rings can she make with 3 diamonds to maximize her profit?**

Step1: Create a key:

**r= regular ring, l= large ring w/ 3 diamonds**

Step 2: Create an equation:

**60r+ 120l is less than or equal to 360, 1x+3y is less than or equal to 50**

Step 3: Write out things you know from the equation, so that you can begin to graph:

**y greater than or equal to 4, x greater than or equal to 2, x greater than or equal to 0, y greater than or equal to 0**

Step 4: Graph lines and shade in on graph

Step 5: Create an equation for her profit:

**P= 400r +700l**

Step 6: Pug in points from graph into equation to get the profit:

**P= 400(2)+700(2)= $2,220**