Algebra 1 quarter 4 project

8-2 Dividing Monomials Simplify each expression. Assume that x and y are not equal to zero. ((-3x^5y)^0/8xy^7)^0

((-3x^5y)^0/8xy^7)^0 = 1 or a^0 = 1

8-2 Dividing Monomials Simplify ((2p^2)/3)^4.

((2p^2)/3)^4 = (2p^2)^4/3^4 = 2^4(p^2) ^4/3^4 = 16p^8/81

11-5 The Distance Formula What is the distance between these two points (0,0), (5,12)

(0,0), (5,12) D= [(5-0)^2+(12-0)^2]^(1/2) D=[5^2+12^2]^(1/2) D=[25+144]^(1/2) D=169^(1/2)

11-5 The Distance Formula Whats the distance between these two points (1,2), (3,4)

(1,2), (3,4) D=[(3-1)^2+(4-2)^2]^(1/2) D=[(2)^2+(2)^2]^(1/2) D=[4+4]^(1/2) D=[8]^(1/2)

12-5 Dividing Polynomials Find the Quotient (3r^2-15r)÷3r

(3r^2-15r)÷3r =3r^2-15r/3r =3r^2/3r-15r/3r =r/1-5/1 =r-5

8-5 Adding ad subtracting Polynomials Find (3x^2-4x+8) + (2x-7x^2-5).

(3x^2-4x+8) + (2x-7x^2-5) = [3x^2+(-7x^2)] + (-4x+2x) + [8+(-5)] = -4x^2-2x+3

8-1 Multiplying Monomials Simplify each expression. (5x^7) (x^6)

(5x^7) (x^6) = (5)(1)(x^7)(x^6) turns into (5)(1)(x^7+x^6) = 5x^13

8-8 Special Products Find each product. (6p-1)^2

(6p-1)^2 = (6p)^2-2(6p)(1)+1^2 = 36p^2-12p+1

8-8 Special Products Find (8c+3d)^2

(8c+3d)^2 = (8c)^2+2(8c)(3d)+3d^2 = 64c^2+48cd+9d^2

12-3 Multiplying Rational Expressions Find the product (n-1)(n+1)/(n+1)x(n-4)/(n-1)(n+4)

(n-1)(n+1)/(n+1)x(n-4)/(n-1)(n+4) =(n-1)(n+1)(n-4)/(n+1)(n-1)(n+4) =(n-4)/(n+4)

12-5 Dividing Polynomials Find the Quotient (n^2+10n+12)÷5n

(n^2+10n+12)÷5n =n^2+10n+12/5n =n^2/5n+10n/5n+12/5n =n/5+2+12/5n

11-3 radical equations Solve for x. (x+2)^(1/2) = x-4

(x+2)^(1/2) = x-4 (x+2)^(1/2)^2 = (x-4)^2 x+2 = x^2-8x+16 0 = x^2-9x+14 0 = (x-7)(x-2) x=7 x=2

8-7 Multiplying Polynomials Find (x+3)(x+2).

(x+3)(x+2) = x(x+2) + 3(x+2) = x^2+5x+6

12-3 Multiplying Rational Expressions Find the product (x-8)/(x+8)(x-3)X(x+4)(x-3)/(x-8)

(x-8)/(x+8)(x-3)X(x+4)(x-3)/(x-8) =(x-8)(x+4)(x-3)/(x+8)(x-3)(x-8) =(x+4)/(x+8)

9-1 Factors and Greatest Common Factors Find the prime factorization of -140. -140=-1x40

-140=-1x40 = -1x2x70 = -1x2x7x10 = -1x2x7x2x5 or -1x2^2x5x7

9-4 Factoring Trinomials: ax^2+bx+c Factor 10x^2-43x+28.

10x^2-43x+28 = 10x^2+mx+nx+28 = 10x^2+(-8)x+(-35)x+28 = (5x-4)(2x-7)

12-9 Solving Rational Equations Solve for x. 12/x+5=4/x+2

12/x+5=4/x+2 12(x+2)=4(x+5) 12x+24=4x+20 12x+24-4x-24=4x+20-4x-24 8x=-4 x=-4/8 x=-1/2

9-2 Factoring Using the Distributive Property Use Distributive property to factor each polynomial. 12a^2+16a

12a^2+16a 12a^2=2x2x3xaxa 16a=2x2x2x2xa GCF=2x2xa or 4a

12-7 Rational Expressions with Unlike Denominators Find the LCD of 15m^2b^3 and 18mb^2

15m^2b^3 and 18mb^2 15m^2b^3=3×5×m×m×b×b×b 18mb^2=2×3×3×m×b×b LCD=2×3×3×5×m×m×b×b×b=90m^2b^3

9-2 Factoring Using the Distributive Property Use Distributive property to factor each polynomial. 18cd^2+12c^2d+9cd

18cd^2+12c^2d+9cd 18cd^2= 2x3x3xcxdxd 12c^2d= 2x2x3xcxcxd 9cd= 3x3xcxd GCF=3xcxd or 3cd

8-3 Scientific Notation Express each number in standard notation. 2.45 x 10^8

2.45 x 10^8 = 245,000,000

8-7 Multiplying Polynomials Multiply 24x36.

24x36 = 144+ 720 = 864

9-6 Perfect Squares and Factoring Factor each polynomial. 25x^2+5x-6

25x^2+5x-6 = 25mx+nx-6 = 25x^2+15x-10x-6 = (5x+3)(5x-2)

12-6 Rational Expressions with Like Denominators Find the sum of 2x/x+1+2/x+1

2x/x+1+2/x+1 =2x+2/x+1 =2x+2/x+1 =2(x+1)/x+1 =2/1 =2

11-2 operations with radical expressions Simplify: 2x20^(1/2)+3x45^(1/2)+180^(1/2)

2x20^(1/2)+3x45^(1/2)+180^(1/2) =2(2x5^(1/2))+3(3x5^(1/2))+6x5^(1/2) =4x5^(1/2)+9x5^(1/2)+6x5^(1/2) 19x5^1/2

8-4 Polynomials Arranging the terms of each polynomial so that the powers of x are in ascending order. 2xy^3+y^2+5x^3-3x^2y

2xy^3+y^2+5x^3-3x^2y = 2x^1y^3+y^2+5x^3-3x^2y = y^2+2xy^3-3x^2y+5x^3

12-8 Mixed Expressions and Complex Fractions Simplify 3+6/x+3

3+6/x+3 =3/1+6/x+3 =3(x+3)/x+3 + 6/x+3 =3(x+3)+6/x+3 =3x+9+6/x+3 =3x+15/x+3

8-3 Scientific Notation Express each number in scientific notation. 30,500,000

30,500,000 = 3.0500000 x 10^n = 3.05 x 10^7

12-6 Rational Expressions with Like Denominators Find the sum of 3n/12+7n/12

3n/12+7n/12 =3n+7n/12 =10n/12 =5n/6

12-9 Solving Rational Equations Solve for x. 3x/x-1+6x-9/x-1=6

3x/x-1+6x-9/x-1=6 (x-1)(3x/x-1+6x-9/x-1)=(x-1)6 3x+6x-9=6x-6 9x-9=6x-6 9x-9-6x+9=6x-6-6x+9 3x=3 3x/3=3/3 x=1

8-6 Multiplying a Polynomial by a Monomial Find 3x^2 - 7x + 10.

3x^2 - 7x + 10 (x) -2x^2 = -6x^4+14x^3-20x^2

8-6 Multiplying a Polynomial by a Monomial Simplify 4(3d^2+5d) - d(d^2-7d+12).

4(3d^2+5d) - d(d^2-7d+12) = 12d^2+20d-d^3+7d^2-12d = -d^3+19d^2+8d

8-5 Adding ad subtracting Polynomials Find the equation that models the number of elementary teachers E for this time period. 44n+2216

44n+2216 (+) -11n - 942 = 33n + 1274

9-5 Factoring Differences of Squares Factor 48a^3-12a.

48a^3-12a 48a^3-12a= 12a(4a^2-1) = 12a [(2a)^2-1^2] = 12a(2a+1)(2a-1)

9-6 Perfect Squares and Factoring Factor each polynomial. 4x^2-36

4x^2-36 4x^2-36= 4(x^2-9) = 4(x^2-3^2) = 4(x+3)(x-3)

11-4 The Pythagorean Theorem Find b when a=5 and c=15.

5, b, 15 5^2+b^2=15^2 25+b^2=225 b^2=200 b=14

12-4 Dividing Rational Expressions Find the Quotient 5x^2/7÷10x^3/21

5x^2/7÷10x^3/21 =5x^2/7×21/10x^3 =5x^2×21/7×10x^3 =1×3/1×2x =3/2x

9-4 Factoring Trinomials: ax^2+bx+c Factor 7x^2+22x+3.

7x^2+22x+3 = 7x^2 + mx + nx = 3 = 7x^2+1x+21x+3 = (7x+1)(x+3)

8-4 Polynomials Arranging the terms of each polynomial so that the powers of x are in ascending order. 7x^2+2x^4-11

7x^2+2x^4-11 = 7x^2+2x^4-11x^0 = -11+7x^2+2x^4

11-2 operations with radical expressions Simplify: 8x5^(1/2) + 3x5^(1/2)

8x5^(1/2) + 3x5^(1/2) 11x5^(1/2)

9-1 Factors and Greatest Common Factors Find the prime factorization of 90. 90=2x45

90=2x45 =2x3x15 = 2x3x3x5

11-6 Similar Triangles Are these the triangles abc and def similar? AB=2 BC=2.5 AC=3 and DE=4 EF=5 DF=6

AB=2 BC=2.5 AC=3 and DE=4 EF=5 DF=6 AB=2≈DE=4, BC=2.5≈EF=5, AC=3≈DF=6 yes they are similar

11-6 Similar Triangles Are these the triangles abc and def similar? AB=4 BC=5 AC=6 and DE=8 EF=10 DF=14

AB=4 BC=5 AC=6 and DE=8 EF=10 DF=14 AB=4≈DE=8,BC=5≈EF=10, AC=6≠DF=14 no not similar

8-1 Multiplying Monomials Simplify each expression. [(3^2)^3)]^2

[(3^2)^3)]^2 = (3^2*^3)^2 = (3^6)^2 = 3^12 or 531,441

12-7 Rational Expressions with Unlike Denominators Find the LCD of a+1/a + a-3/3a

a+1/a + a-3/3a a=a 3a=3×a LCD=3x

11-3 radical equations Solve for a a^(1/2) = 10

a^(1/2) = 10 a^(1/2)^2 = 10^2 a = 100

12-4 Dividing Rational Expressions Find the Quotient b^2-9/4b÷(b-3)

b^2-9/4b÷(b-3) =b^2-9/4bx1/(b-3) =b^2-9x1/4bx(b-3) =b-3x1/4b =b-3/4b

11-7 Trigonometric Ratios What is the cos of 50

cos 50° cos 50°=.6427876097 round to the nearest ten thousandth ≈ .6428

12-2 Rational Expressions State the excluded values of this expression. m+3/m-2

m+3/m-2 m-2≠0 m≠0+2 m≠2

12-2 Rational Expressions State the excluded values of this expression. m-6/m-20

m-6/m-20 m-20≠0 m≠20+0 m≠20

9-5 Factoring Differences of Squares Find each binomial. n^2-25

n^2-25 n^2-25=n^2-5^2 = (n+5)(n-5)

11-4 The Pythagorean Theorem Is this a right triangle? 20, 30, 40

right triangle? 20, 30, 40 a^2+b^2=c^2 20^2+30^2=40^2 400+900=1600 no not a right triangle.

11-7 Trigonometric Ratios What is the sin of 35

sin 35° sin 35°=.5735764364 round to the nearest ten thousandth ≈ 0.5736

12-1 Inverse Variation Find x2 if x1=7 y1=4 and x2=? y2=14

x1=7 y1=4 and x2=? y2=14 7x4=x2x14 28=x2x14 28/14=x2 2=x2

12-1 Inverse Variation Find y2 if x1=9 y1=(-6) and x2=6 y2=?

x1=9 y1=(-6) and x2=6 y2=? 9x(-6)=6y2 -54=6y2 -54/6=y2 -9=y2

9-3 Factoring Trinomials: x^2+bx+c Factor x^2+6x+8.

x^2+6x+8 = (x+m)(x+n) = x^2+6x+8= (x+2)(x+4)

9-3 Factoring Trinomials: x^2+bx+c Factor x^2-10x+16.

x^2-10x+16 = (x+m)(x+n) = x^2-10x+16= (x-2)(x-8)

12-8Mixed Expressions and Complex Fractions Simplify x^2y^2/a÷x^2y/a^3

x^2y^2/a÷x^2y/a^3 =x^2y^2a×a^3/x^2y =a2y

11-1 Graphing Quadratic Functions Solve for y. y+1 = (x+1)^2

y+1 = (x+1)^2 y+1= x^2+2x+1 y= x^2+2x

11-1 Graphing Quadratic Functions Solve for y. y= -3x^2-6x+4

y= -3x^2-6x+4 x= -b/-2a x= - -6/2(-3) or 1