Q4 project

11-1: Simplifying Radical Expressions~Simplify 3/5-√2

Simplify 3/5-√2 3/5-√2=3/5-√2=5+√2/5+√2 =3(5)+3√2/5²-(√2)² =15+3√2/25-2 =15+3√2/25

8-6: Adding and Subtracting Polynomials~ Simplify x²(x+2)+3(x³+4x²)

Simplify x²(x+2)+3(x³+4x²) x²(x+2)+3(x³+4x²) =x²(x)+x²(2)+3(x³)+3(4x²) =x³+2x²+3x³+12x² =4x³+14x²

8-1: Multiplying Monomials~Simplify: (2ab²)(3a²b³)

Simplify: (2ab²)(3a²b³)~ Commutative Property (2ab²)(3a²b³)= (2×3)(a×a²)(b²×b³)= 6a³b⁵ Simplify: (2x²y³)³ (2x²y³)³= 2³(x²)³(y³)³ =8x⁶y

9-3 Factoring trinomials x²+bx+c Solve a²-3a-4=0.

a²-3a-4=0 original equation (a+1)(a-4)=0 Factor 1×(-4) = -4 and 1+(-4)=3 a+1=0 or a-4=0 zero product property a= -1 a=4 The solution is -1,4 simplify

11-4:The Pythagorean Theorem Find the length of the missing side

c²=a²+b², c=25,a=15,b=? =25²=15²+b² =625=225+b² =400=b² =20=b

12-6 Rational Expressions with Like Denominators Find m²/m+4 -16/m+4

m²/m+4-16/m+4=m²-16/m+4 subtract the numerators =(m-4)(m+4)/m+4 cancel like terms and factor =m-4 simplify

12-5 Dividing Polynomials Find(x³-2x²-22x+21) / (x-3)

x ²+ x-19 x-3 x³-2x²-22x+21 (-) x-3x ² Multiply x and x-3 x²-22x Subtract (-)x²- 3x Multiply x and x-3 -19x+21 Subtract (-)-19x+57 Multiply -19 and x-3 -36 Subtract The quotient is x² + x-19-36/x-3

12-2 Rational Expressions Simplify x+4/x²+12x+32 State the excluded values of x

x+4/x²+12x+32=x+4/(x+4)(x+8) Factor and cross out the same like the x+4 = 1/x+8 simplify

9-6 Perfect squares and factoring Solve (x-4)²=121

x-4=±√121 Square root Property x-4=±11 121=11×11 x=4±11 Add 4 to each side x=4+11 or x=4-11 =15 =-7 the solution is (-7,15)

12-7 Rational Expressions with Unlike Denominators Find x/x+3 + 5/x-2

x/x+3 + 5/x-2= x-2/x-2*x/x+3 + x+3/x+3*5/x-2 the LCD is (x+3)(x-2) =x²-2x/(x+3)(x-2) + 5x + 15/(x+3)(x-2) Multiply =x²+3x+15/(x+3)(x-2) Add

12-1 Inverse Variation If y varies inversely as x and y=24 when x=30 find x when y=10

x¹/x²=y¹/y² Proportion for inverse variation 30/x²=10/24 x¹=30 y¹=24 y²=10 720=10x² cross multiply 72=x² thus x=72 when y=10.

12-8 mixed expressions and complex Fractions y-(40/y-3)/y+5

y-(40/y-3)/y+5=(y(y-3)/y-3)-40/y-3)/y+5 The LCD in the numerator is y-3 =(y²-3y-40/y-3)/y+5 Add in the numerator =y²-3y-40/y-3 / (y+5) Rewrite as a division sentence =y²-3y-40/y-3 * 1/y+5 Multiply by the reciprocal of y+5 =(y-8)(y+5)/y-3*1/y+5 cancel out like terms and factor =y-8/y-3 simplify

12-4 Dividing Rational Expressions y²-16/y²-64 / y+4/y-8

y²-16/y²-64 / y+4/y-8=y²-16/y²-64 × y-8/y+4 Multiply the reciprocal of y+4/y-8 (y-4)(y+4)/(y-8)=1(y+8) × y-8=1/y+4 or

11-3:Radical Equations~ Solve √5-4x-6=7

√5-4x-6=7 √5-4x=13 5-4x=169 -4x=164 x=-41

11-2:Operations with Radical Expressions~Simplify √6-√54+3√12+5√3

√6-54+3√12+5√3 =√6-√3³×6+3√2²×3+5√3 =√6-(√3²×√6)+3(√2²×3)+5√3 =√6-3√6+3(2√3)+5√3 =√6-3√6+6√3+5√3 =-2√6+11√3

8-2: Dividing Monomials~Simplify 2x⁶y/8x²y²

Simplify 2x⁶y/8x²y² 2x⁶y/8x²y²= (2/8)(x⁶/x²)(y/y²)= (1/4)(y⁶⁻²)= x⁴/4y

12-3 Multiplying Rational Expressions Find 1/x²+x-12 × x-3/x+5

1/x²+x-12 × x-3/x+5 = 1/(x+4)(x-3)=1/(x+4)(x-3)× x-3/x+5 Factor =1/(x+4)(x+5) Simplify

9-1 Factors and Greatest common factors Find the GCF of 15x² and 45xy²

15x²y=3×5×(x)×(x)×(y) Factor each number 45xy²=3×3×(x)×(y)×(y) Combine common prime factors The GCF is 3×5×(x)×(y) or 15xy simplify

9-5 Factoring Difference of Squares Factor 3x³-75x

3x³-75x=3x(x²-25) The GCF of 3x³ and 75x is 3x =3x(x+5)(x-5) Factor the difference of squares

12-9 Solving Rational Equations Solve 5n/6+1/n-2=n+1/3(n-2)

5n/6 + 1/n-2=n+1/3(n-2) 6(n-2)*(5n/6 + 1/n-2)=6(n-2)*n+1/3(n-2) Multiply each side by the LCD 6(n-2) 1(n-2)(5n)/1 + 6(1)/1 = 2(1)(n+1)/(1)(1) Distributive property (n-2)(5n)+6=2(n+1) simplify 5n²-10n+6=2n+2 Multiply 5n²-12n+4=0 Subtract (5n-2)(n-2)=0 Factor n=2/5 or n=2 simplify

9-2 Factoring Using the distributive property Factor 2x²-3xz²-2xy+3yz

=(2x²-3xz)+(-2xy+3yz) Group common factors =x(2x-3z)-y(2x-3z) Factor out the GCF from each grouping =(x-y)(2x-3z) Factor out the common factor 2x-3z.

Q4 Math project Sections 8,9,11,12

By Anthony Lujano And Martin Flores

8-3: Scientific Notation~Express 5.2×10⁷ in scientific notation

Express 5.2×10⁷ in scientific notation 5.2=52,000,000,n=7

11-6:Similar Traingles~ FInd the measure of side α if the two triangles are similar

FInd the measure of side α if the two triangles are similar 10/5=6/α =10α=30 =α=3

9-4 Factoring Trinomials ax²+bx+c Factor 12x²+22x-14

Factors of -42 are -3×14=-42 -3+14=11 6x²+11x-7=6x²+mx+nx-7 =6x²-3x+14x-7 =(6x²-3x)+(14x-7) =3x(2x-1)+7(2x-1) =(2x-1)(3x+7) Thus the complete factorization of 12x²+22x-14 is 2(2x-1)(3x+7)

8-5: Adding and Subtracting Polynomials~Find (7r²+9r)-(12r²−4)

Find (7r²+9r)-(12r²−4) (7r²+9r)-(12r²-4)=7r²+9r+(-12r²+4) =(7r²-12r²)+9r+4 =-5r²+9r+4=-5r²+9r+4

8-8: Special Products

Find (r-5)² (a-b)²=a²-2a+b² (r-5)²=r²-2(r)(5)+5 =r²-10r+25

11-7:Trigonometric Ratios~Find the SINE,COSINE, and tangent of ∠A. Round to the nearest ten thousand

Find the SINE,COSINE, and tangent of ∠A. Round to the nearest ten thousand SIN A= opposite leg/hypotenuse =20/25 or .8000 cos A=adjacent leg/hypotenuse =15/25 or .6000 Tan A= opposite leg/adjacent leg =20/15 or 1.3333

8-4: Polynomials~Find the degree of 2xy³+x²y

Find the degree of 2xy³+x²y Polynomial: 2xy³+x²y Terms: 2xy³, x²y Degree of Each Term: 4,3 Degree of Polynomial: 4

11-5:The Distance Formula~ Find the distance between the points with the coourdinates (-5,1) and (1,5)

Find the distance between the points with the coourdinates (-5,1) and (1,5) d=√(x2-x1)+y2-y1)² =√1-(-5)²+(5-1)² =√6²+4² =√36+16 =√52 or about 7.1 units

8-7: Multiplying Polynomials~ Find: (2y-5)(4y²+3y-7)

Find: (2y-5)(4y²+3y-7) =2y(4y²+3y-7)-5(4y²+3y-7) =8y³+6y²-14y-20y²-15y+35 =8y³-14y²-29y+35