Math

Write inequalities to represent the situations below. 1. to ride a roller coaster, a visitor must be at least 56 inches tall. Use h to represent the height (inches) of a visitor able to ride) 2. Hans exercises no less than 50 minutes per day. Use t for exercise (minutes) No more than: w less than or equal to 2,300 At most: w less than or equal to 50

1. to ride a roller coaster, a visitor must be at least 56 inches tall. Use h to represent the height (inches) of a visitor able to ride) Answer =h more than or equal to 56 2. Hans exercises no less than 50 minutes per day. Use t for exercise (minutes) Answer = t more than or equal to 50

Solve for w. 2w-16-3=21w-14-4w

2w-16-3=21w-14-4w =2w-19=17w-14 =2w-5=17w =-5=15w =-5/15=w Answer = -1/3 = w

Simplify. 5/3/3

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Rewrite the set Q by listing its elements. Make sure to use the appropriate set notation. q(x/x is an integer and -5(greater than or equal to) x (less than) -4)

q(x/x is an integer and -5(greater than or equal to) x (less than) -4) Answer = q=(-5)

Solve for x. sqrt x = 7 sqrt x = -7 (equal no solution)

sqrt x = 7 =(sqrt x)^2 = 7^2 Answer = x= 49

Solve for v. sqrtx-13 = 6

sqrtx-13 = 6 =(sqrtx-13)^2 = 6^2 =u-13 = 36 Answer = v=49

Find all excluded values for the expression. This is, find all values of v for which the expression is undefined. v-7/v^2-36

v-7/v^2-36 =v^2-36=0 =(v-6)(v+6) = 0 =v-6 = 0 =v+6 = 0 Answer = 6,-6

Solve for v. v^2-8v+15=0

v^2-8v+15=0 =(v-5)(v-3) = 0 = v=5 = v=3 Answer = 5,3

Solve for y. w=1/9(x+y-2)

w=1/9(x+y-2) =9*w=9*1/9(x+y-z) =9w=x+y-z Answer = 9w-x+z=y

Graph. x (more than or equal to) 6 (more than or equal to) is a solid dot (more than) open dot (more than is right, less is left)

x (more than or equal to) 6 Answer = 6->

A total of 332 tickets were sold for the school play. They were either adult tickets or students tickets. The number of student tickets sold was 3 times the number of adult tickets sold. How many tickets were sold? # of adult tickets sold = x # of student tickets sold = 3x Total # of tickets sold = 332 Pamela is 14 years younger than Jiri. The sum of their ages is 46. What is Jiri's age? x-14+x=46 A local hamburger shop sold a combined total of 711 hamburgers and cheeseburgers on Tuesday. There were 61 more cheeseburgers sold than hamburgers. How many hamburgers were sold on Tuesday? 711 total

# of adult tickets sold = x # of student tickets sold = 3x Total # of tickets sold = 332 = 3x+x = 332 = 4x=332 Answer = x=83 x-14+x=46 =2x-14=46 =2x=60 Answer = x=30 711 total =x+61*x=711 =2x+61=711 =2x=650 Answer = x=325

(-4)^-2 rewrite without an exponent.

(-4)^-2 =1/(-4)^2 =1/(-4) * (-4) Answer =1/16

Solve. (v+7)(v-9)=0

(v+7)(v-9)=0 =v+7=0 =v-9=0 = v=-7 = v=9 Answer = -7,9

Solve for v. -1/2+1/7v=-4/5

-1/2+1/7v=-4/5 LCD of 2,7,5 = 70 =70(-1/2+1/7v)=70(-4/5) =-70*1/2+70*1/7v=70*4/5 =-35*1/1+10*1/1v=-14*4/1 =-35+10v+-56 =10v=-21 Answer = -21/10

Solve for inequality for y. -17 less than or equal to -4y+3

-17 less than or equal to -4y+3 =-20 more than or equal to -4y Answer = 5 more than or equal to y

For each equation, choose the statement that describes its solution. If applicable, give the solution. -2(w+2)+7=3(w+6) -no sol. -w=? -all real #'s are solutions -6(u+1)=2(1-3u)-8 -no sol. -w=? -all real #'s are soltuions

-2(w+2)+7=3(w+6) =-2w-4+7=3w+18 =-2w+3=3w+18 =-2w-3w=18-3 =-5w=15 =w=15/-5 Answer = w=-3 (w=?) -6(u+1)=2(1-3u)-8 =-6u-6=2-6u-8 =-6u-6=-6u-6 =-6u+6u=-6+6 Answer = 0=0 (All real #'s are solutions)

Solve for the inequality for w. -3w-7 more than 2w+8

-3w-7 more than 2w+8 =-5w-7 more than 8 =5w more than 15 Answer = w less than -3

Solve for v. -5=6/v-6

-5=6/v-6 =-5*(v-6)=6/v-6*(v-6) =-5(v-6)=6 =-5v+30=6 =-5v=-24 Answer = 24/5

Solve for u. -8 = -4/u

-8 = -4/u =u-8 = -4/u * u =-8u/-8 = -4/-8 =u=4/8 Answer = u=1/2

Solve for v. /2v+3/=11

/2v+3/=11 =2v+3=11 =2v+3=-11 =2v=8 =2v=-14 Answer = 4,-7

Solve for y. /y/=6 and /y/=-4

/y/=6 Answer =y=6,-6 /y/=-4 Answer =No solution. /u/=0 Answer =u=0

Solve for a. 6/A=P

6/A=P =6=AP Answer = 6/P=A

9 sqrt 11 -6 sqrt 11 simplify.

9 sqrt 11 - 6 sqrt 11 =9-6 =3 Answer = 3 sqrt 11

Charmaine purchased a prepaid phone card for $25 long distance calls cost 22 cents a minute using this card. Charmaine used her card only once to make a long distance call. If the remaining credit on her card is $19.72, how many minutes did her call last. Duration = x minutes Initial credit = $25 Cost long distance = $0.22 Remaining credit = $19.72

Duration = x minutes Initial credit = $25 Cost long distance = $0.22 Remaining credit = $19.72 =25-0.22x=19.72 Answer = x=24

Simplify. y^-2/y^9 (a^m/a^n = a^m-n)

y^-2/y^9 =y^-2-9 =y^-11 Answer =1/y^11

(-3x^2y)^4 simplify, write answer without parentheses.

(-3x^2y)^4 =(-3)^4(x^2)^4 y^4 =81(x^2)^4 y^4 Answer = 81x^8 y^4

(-5+5y+w)(-6) use the distributive property to remove the parentheses.

(-5+5y+w)(-6) =(-5)(-6)+(5y)(-6)+(w)(-6) =30+(-30y)+(-6w) Answer = 30-30y-6w

Evaluate the expression. (-5/7)^0 = ? -(3)^0 = ? (any -a^0 or a^0 = -1 or 1)

(-5/7)^0 Answer = 1 -(3)^0 Answer = -1

(3/2)^-2 rewrite without an exponent.

(3/2)^-2 =(2/3)^2 =2^2/3^2 Answer =4/9

(3x-4)(6x+5) multiply

(3x-4)(6x+5) =18x^2+15x-24x-20 Answer = 18x^2-9x-20

(3x^4 z^6 - 8x^3)(-2xz^5) rewrite without parentheses.

(3x^4 z^6 - 8x^3)(-2xz^5) = (3x^4z^6)(-2xz^5)-(8x^3)(2xz^5) =(-6)x^5z^11-(-16)x^4z^5 Answer = -6x^5z^11 + 16x^4z^5

(4v^2-6v-7)+(3v^2-5v+1) simplify.

(4v^2-6v-7)+(3v^2-5v+1) =4v^2-6v-7+3v^2-5v+1 Answer = 7v^2-11v-6

(5a+2b)(5a-6b) multiply.

(5a+2b)(5a-6b) =25a^2-30ab+10ab-12b^2 Answer = 25a^2-20ab-12b^2

(5u+5w+6)(3u-4) multiply.

(5u+5w+6)(3u-4) =5u(3u-4)+5w(3u-4)+6(3u-4) =15u^u-20u+15uw-20w+18u-24 Answer = 15u^2-2u+15uw-20w-24

(5u^u-u-6)(2u+7) multiply.

(5u^u-u-6)(2u+7) =5u^2(2u+7)-u(2u+7)-6(2u+7) =10u^3+35u^2-2u^2-7u-12u-42 Answer = 10u^3+33u^2-19u-42

(5x-2w)^2 rewrite without parentheses.

(5x-2w)^2 =(5x-2w)(5x-2w) =25x^2-10xw-10xw+4w^2 Answer = 25x^2-20xw+4w^2

(7x-4)(-5x+2) multiply.

(7x-4)(-5x+2) =-35x^2+14x+20x-8 Answer = -35x^2+34x-8

(a+6)(a-6) multiply. (A+B) (A-B) = A^2 - B^2

(a+6)(a-6) =a^2-6^2 Answer =a^2-36

Multiply and simplify. (sqrt x + 2 sqrt 3)^2 = ? , (sqrt x - sqrt 3)(sqrt x + sqrt 3) = ?

(sqrt x + 2 sqrt 3)(sqrt x + 2 sqrt 3) Answer =x + 4sqrt3x +12 (sqrt x - sqrt 3)(sqrt x + sqrt 3) Answer =x-3

Multiply and simplify. (sqrt x - sqrt 5)(sqrt x + sqrt 5) =? (sqrt x - 2 sqrt 5)^2

(sqrt x - sqrt 5)(sqrt x + sqrt 5) Answer =x-5 (sqrt x - 2 sqrt 5)^2 Answer =x-4sqrt5x +20

(u^-3)^6 simplify without a negative exponent. (power rule : (a^m)^n = a^mn) (negative rule : a^-m = 1/a^m)

(u^-3)^6 =u^(1-3)*6 =u^-18 Answer = 1/u^18

(u^4/-2w^3)^5 simplify.

(u^4/-2w^3)^5 =(u^4)^5/(-2w^3)^5 =(u^4)^5/(-2)^5(w^3)^5 =(u^4)^5/-32(w^3)^5 Answer =u^20/-32w^15

(v+6)^2 rewrite without parentheses

(v+6)^2 =v^2+6v+6v+36 Answer = v^2+12v+36

(y^4)^2 simplify.

(y^4)^2 =y^4 * y^4 Answer =y^8

-1/12-(-3/8) evaluate.

-1/12-(-3/8) =-1/12*2/2 =2/24 =-3/8*3/3 =-9/24 =-2/24-(-9/24) =-2+9/24 Answer = 7/24

-1/2+1/3 add.

-1/2 +1/3 =-1/2 * 3/3 + 1/3 * 2/2 =-3/6 + 2/6 =-3+2/6 Answer = -1/6

-16/5 / (-12/25) divide, answer as fraction, mixed number in simplest form.

-16/5 / (-12/25) =-16/5*-25/12 =4/5 * -25/3 =4/1*-5/3 Answer = 20/3

-2w^6(-9w^3+5w^2-2w) rewrite without parentheses.

-2w^6(-9x^3+5w^2-2w) =(-2w^6)(-9w^3)+(-2w^6)(5w^2)-(-2w^6)(2w) =18w^9+(-10)w^8-(-4)w^7 Answer = 18w^9-10w^8+4w^7

Factor completely. -2x^2+7x-6

-2x^2+7x-6 =-1(2x^2-7x+6) =-1(x-2)(2x-3) Answer = -(x-2)(2x-3)

-3-3^3/(2-1)^3

-3-3^3/(2-1)^3 (or use calculator) =-3-3^3/1^3 =-3-27/1 =-30/1 Answer = 1

Evaluate. -6^2 = ? and (-7)^2 = ?

-6^2 = -36 and (-7)^2 = 49 (calculator)

-6w-4(-5x+5w)-4x simplify.

-6w-4(-5x+5w)-4x =-6w+20x-20w-4x Answer = -26w+16x

Solve for u. -7/2u=14

-7/2u=14 =u=-2/7*14 Answer =u=-4

Simplify. 1-z/x+4 divided by 4/x+4+x

1-z/x+4 divided by 4/x+4+x =(1-z/x+4)*x+4 divided by (4/x+4+x) * x+4 =1(x+4)-2/4+x(x+4) =x+4-z/4+x^2+4x =x+2/x^2+4x+4 Answer = 1/x+2

1/6^p-5 rewrite without a negative exponent (rule 1 : a^-n = 1/a^n) (rule 2 : 1/a^-n = a^n)

1/6^p-5 Answer =p^5/6

10v^7-26v^6-12v^5

10v^7-26v^6-12v^5 =2v^5(5v^2-13v-6) Answer = 2v^5(v-3)(5v+2)

125^1/3 = ? 81^1/4 = ? (a^1/n = sqrt n^a)

125^1/3 Answer = 5 81^1/4 Answer = 3

12abc/16bc simplify.

12abc/16bc =3abc/4bc (12 and 16 canceled from 4) Answer =3a/4 (bc from both top and bottom cancel out)

12y^3/40y^5 simplify.

12y^3/40y^5 = 3y^3/10y^5 Answer = 3/10y^2

15-20/(-5) evaluate

15-20/(-5) =Division first = -4 =15-(-4) Answer = 19

17^1/3 write the following as a radical expression. (x^m/n = sqrt n^x^m = sqrt (n^ x)^m)

17^1/3 =sqrt 3^17^1 Answer = sqrt 3^ 17

Divide 2x+10/5 divided with 6x+30/7

2x+10/5 divided with 6x+30/7 =2x+10/5 * 7/6x+30 =1/5 * 7/3 (2(x+5) and 6(x+5) cancels out) Answer = 7/15

Rewrite expression by factoring out (y+3) 2y^2(y+3)-7(y+3)

2y^2(y+3)-7(y+3) Answer =(y+3)(2y^2-7)

Factor by grouping. 2y^3+5y^2+12y+30

2y^3+5y^2+12y+30 =(2y^3+5y^2)+(12y+30) =(2y^3+5y^2) GCF = y^2 =(12y+30) GCF = 6 =y^2(2y+5)+6(2y+5) Answer =(2y+5)(y^2+6)

32^-2/5 = ? (1/81)^-3/4 = ? simplify

32^-2/5 = ? (1/81)^-3/4 = ? =1/32^2/5 =1/(32^1/5)^2 =1/(5^sqrt 32)^2 =1/2^2 Answer for 1 = 1/4 = 1/81^-3/4 =81^3/4 =(81^1/4)^3 =(4^sqrt 81)^3 =3^3 Answer for 2 = 27

32^3/5 simplify.

32^3/5 =32^(1/5*3) =(32^1/5)^3 =(sqrt 5^32)^3 =2^3 Answer = 8

3^-3 rewrite without an exponent. 1/9^-2 (rule 1: a^-n = 1/a^n) (rule 2: 1/a^-n = a^n)

3^-3 =1/3^3 Answer =1/27 1/9^-2 =9^2 Answer =81

3x+15x^3-2x^2-3x^4 what are the degree and leading coefficient of the polynomial?

3x+15x^3-2x^2-3x^4 =-3x^4+15x^3-2x^2+3x Answer = leading exponent 4 = leading coefficient -3

40v^4w^2/36v^3w^2

40v^4w^2/36v^3w^2 =10v^4w^2/9v^3w^2 =10vw^2/9w^2 Answer = 10v/9

Factor. 49y^2-9 (A^2-B^2)=(A+B)(A-B)

49y^2-9 =49y^2-9 =(7y)^2-3^2 Answer = (7y+3)(7y-3)

Solve for x. 4= 3x+20/2

4= 3x+20/2 =2(4) = 3x+20 =8=3x+20 =-12=3x Answer =-4=x

4u *2u^4 *y^7 *6y^8 multiply.

4u*2u^4*y^7*6y^8 =(4*2*6) u*u^4*y^7*y^8 =48u^1+4*y^7+8 Answer = 48u^5y^15

Multiply 4x-32/5 * 3/8x-64

4x-32/5 * 3/8x-64 =4(x-8)/5 * 3/8x-64 =1/5 * 3/2 (4(x-8) cancels out with 8(x-8) Answer = 3/10

Add 5/x+1 + 7/x+1

5/x+1 + 7/x+1 =5+7/x+1 Answer = 12/x+1

5c^4(8c+9c^8) use the distributive property.

5c^4(8c+9c^8) =5c^4*8c+5c^4*9c^8 =(5*8)c^4*c+(5*9)c^4*c^8 =(5*8)c^5+(5*9)c^12 Answer = 40c^5+45c^12

5x^2+7x+2

5x^2+7x+2 =5x^2+(2+5)x+2 =5x^2+2x+5x+2 =x(5x+2)+1(5x+2) Answer = (5x+2)(x+1)

6 sqrt 6(sqrt 6 - sqrt 7) multiply.

6 sqrt 6 (sqrt 6 - sqrt 7) =6sqrt 6*6 - 6 sqrt 6*7 =6 sqrt 36 - 6 sqrt 42 =6*6 - 6 sqrt 42 Answer = 36 - 6 sqrt 42

Factor. 64x^2-16x+1

64x^2-16x+1 =(8x)^2-2(8x)(1)+1^2 Answer = (8x-1)^2

factor completely 6w^2+36w-96

6w^2+36w-96 =6(w^2+6w-16) Answer = 61(w-2)(w+8)

7x+21 factor.

7x+21 =7(x)+7(3) Answer = 7(x+3)

Find LCM of 8x^4 and 6x^3

8 and 6 = 24 x^4 and x^3=x^4

Find LCM of 9 and 12

Answer = 36

Find the GFC of this: 18w^2v^8y^7 and 12v^6y^4

Answer = 6v^6y^4

-7x^2+17x-6

GCF is 1 =1(7x^2-17x+6) =-1(x-2)(7x-3) Answer = (-x+2)(7x-3)

Factor 20n^3+15n^2

GCF is 5n^2 =5n^2(4n)+5^2(3) Answer = 5n^2(4n+3)

Factor 18x^2vy^5-30v^6x^8

GCF is 6x^2v =6vx^2(3y^5)-6x^2v(5v^5x^6) Answer = 6vx^2(3y^5-5v^5x^6)

Find the GCF of 10m^4 and 6m^3

GCF of 10 and 6 is 2 Answer = 2m^3

Solve for y. K=4yz

K=4yz =K/4z=4yz/4z Answer = K/4z=y

add. 5/9d + 1/6d

LCD is 18d =5/9d(2/2) =10/18d =1/6d(3/3) =3/18d Answer = 13/18d

Subtract 7/4-3/5c

LCD is 20c =7/4(5c/5c) =35c/20c =3/5c(4/4) =12/20c Answer =35c-12/20c

Subtract. y/5 - 6/7

LCD is 35 =y/5 (7/7) =7y/35 =6/7(5/5) =30/35 Answer = 7y-30/35

Evaluate. a. -3^sqrt 125 = ? b. 4^sqrt-16 = ?

a. -3^sqrt 125 = ? b. 4^sqrt-16 = ? = -3^sqrt 125 = -5 =4^sqrt -16 = not a real number

Solve for y. c=2(y+k)

c=2(y+k) =c/2=y+k Answer =c/2-k=y

simplify. 1-7/5/7/6+2

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simplify. sqrt 63 + 18/21

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sqrt 12* sqrt 6 simplify.

sqrt 12 * sqrt 6 = sqrt 12*6 =sqrt 72 =sqrt 36*2 =sqrt 36 * sqrt 2 Answer = 6 sqrt 2

sqrt 20 simplify. sqrt a*b = sqrt a * sqrt b

sqrt 20 =sqrt 4*5 =sqrt 2 * sqrt 5 =2*sqrt 5 Answer = 2 sqrt 5

sqrt 20 - 6/16 simplify.

sqrt 20 - 6/16 =2 sqrt 6 -6/16 =2(sqrt 6 - 3)/16 Answer = sqrt 6 -3/8

sqrt 30/sqrt 15 simplify.

sqrt 30/ sqrt 15 =sqrt 30/15 Answer = sqrt 2

sqrt 5 (6- sqrt 6) multiply.

sqrt 5 (6- sqrt 6) =sqrt 5 *6 - sqrt 5 * sqrt 6 =sqrt 5 * 6 - sqrt 5*6 =sqrt 5 *6 - sqrt 30 Answer = 6 sqrt 5 - sqrt 30

sqrt 5 * sqrt 3 simplify.

sqrt 5 * sqrt 3 =sqrt 5*3 Answer = sqrt 15

sqrt 64/49 simplify sqrt a/b = sqrt a/sqrt b

sqrt 64/49 =sqrt 64/sqrt 49 Answer = 8/7

sqrt 7x * sqrt 3x simplify.

sqrt 7x * sqrt 3x =sqrt 7x*3x =sqrt 21x ^2 Answer = x sqrt 21

sqrt y^20 assume variable is a positive real number.

sqrt y^20 =(y^10)^2 =y^10 y^10 =y^20 Answer = sqrt of y^20 is y^10

3y(-8y^7) Multiply

steps taken: 3y(-8y^7) = 3*y*(-8)*y^7 =3*(-8)*y*y^7 =3*(-8)*y^1*y^7 =-24y^1+7 Answer =-24y^8

simplify u-6/u^2-12u+36

u-6/u^2-12u+36 =Factor u^2-12u+36 Answer = 1/u-6

simplify. v^2 * v^-4 (a^m*a^n = a^m+n)

v^2 * v^-4 =v^-2 =1/v^2

Solve for w. w+2/9 = 4/5

w+2/9 = 4/5 =5(w+2)=4*9 =5w+10=36 =5w+26 Answer = w=26/5

Simplify. x+4/x^5 divided by x-4/x

x+4/x^5 divided by x-4/x =x+4/x^5 divided by x-4/x =x+4/x^5 * x/x-4 =x+4/x^4 * x-4 Answer = x+4/x^4 (x-4)

Factor x^2+12x+36 1. A^2+2AB+b^2 = (A+B) ^2 2. A^2 -2AB +B^2 = (A-B)^2

x^2+12x+36 =x^2+12+36 =x^2+2(x)(6)+6^2 Answer = (x+6)^2

Solve for y. y+3/4=1/3

y+3/4=1/3 (calculator) =y=1/3-3/4 Answer =-5/12

Write the following as a radical expression. y^1/8

y^1/8 =8^sqrt y^1 Answer = 8^sqrt y

Simplify. y^2+y-6/5y^2-45

y^2+y-6/5y^2-45 =y^2+y-6 =(y-2)(y+3) =5y^2-45 =5(y^2-9) =5(y+3)(y-3) =(y-2)(y+3)/5(y+3)(y-3) Answer =(y-2)/5(y-3)

Simplify. y^2+y-6/5y^2-45

y^2+y-6/5y^2-45 =y^2+y-6 =(y-2)(y+3) =5y^2-45 =5(y^2-9) Answer =5(y+3)(y-3)

Solve for x. z=5x-9y

z=5x-9y =z+9y+5x-9y+9y =z+9y=5x =z+9y/5=5x/5 Answer = z+9y/5+x

z^2 y^6/z^3 y^6 simplify.

z^2 y^6/z^3 y^6 =y^6/zy^6 (z^2/z^3 = z*z/z*z*z....cancel out) Answer =1/z (y^6/y^6...cancel out)

Factor z^2+11z+18

z^2+11z+18 =z^2+11z+18 Answer =(z+2)(z+9) answer 2 and 9 (2+9=11, 2*9=18)

Factor z^2-25 (order matters) (A^2-B^2)=(A+B)(A-B)

z^2-25 =z^2-25 =z^2-5^2 Answer = (2+5)(2-5)

(u+1)(u-5) multiply.

(u+1)(u-5) =u^2-5u+u-5 Answer =u^2-4u-5

sqrt 64x^4 simplify. (sqrt AB = sqrt A sqrt B)

sqrt 64x^4 =sqrt 64 sqrt x^4 =8 sqrt x^4 Answer = 8x^2

Find all excluded values u+5/u-11

u+5/u-11 =u-11 =0 Answer = u=ll