Algebra 3 Exam SG

Solve for y in terms of x: 1/3x = 3/4y

(4/3)1/3x = 3/4y(4/3)

Write the equation of the circle in the form (x - h)^2 + (y - k)^2 = R^2 with radius sqr(3) and center (-4, -1)

(x + 4)^2 + (y + 1)^2 = 3

Simplify to a form that uses only positive-integer exponents: ((a+b)^2(a-b)^2)/a^2-b^2

- ((a^2+b^2)(a^2-b^2))/a^2-b^2 - a^2-b^2

Use completing the square to solve the problem: x^2 - 6ix - 9 = 0

- (-6i)/2 = -3i - (-3i)^2 - x^2 - 6ix - 9 + 9 - 9 = 0 - (x - 3i)^2 = 0 - x = 3i

Solve and check: -(x-2)=9

- (-x)+2=9 - (-x)=7 - x=-7 - (-(-7-2)=9 - 7+2=9

Write in slope intercept form the line that passes through (4, -2) and (-4, 0)

- (0 + 2)/(-4 - 4) = 2/-8 = -1/4 - y + 2 = -1/4(x-4) - y + 2 = 1/4x + 1 - y = -1/4x - 1

Rewrite in simplified form using only positive exponents: (10^12 X 10^-12)^-1

- (10^0)^-1 - 1^-1 - 1

Simplify by rewriting each expression so that the variable occurs only once: (4y^3)(3y)(y^6)

- (12y^4)(y^6) - (12y^10)

A plane with a normal airspeed of 165 miles per hour flies 425 miles against a head wind and then returns with the same wind as a tail wind. If the outbound trip takes 1.2 times as long as the return. What is the wind spped?

- (165 + w)t + 425 = t = 425/(165-w) - (165 - w)1.2t = 425

Factor in integers, if possible, if possible. If the expression is not factorable, say so: 9x^2+8

- (3x)^2+2(2)^2 - not possible

Simplify: [(3x-2)+y]^2

- (3x-2)^2+y^2 - (3x-2)(3x+2)+y^2 - 9x^2+6x-6x-4+y^2 - 9x^2-4+y^2 - [3x-2+y][3x-2+y] - 9x^2-6x+3xy - (-6x-3xy+4-2y+2y^2 - (-2y)

Simplify (6 X 10^3)(2 X 10^4)

- (6X2)(10^3+4) - 12 X 10^7

Factor as far as possible using integer coeffcients: r^4-s^4

- (r^2)^2-(s^2)^2 - (r^2-s^2)^2(r^2+s^2)^2 - (r-s)^2(r+s)^2(r+s)^2(r+s)^2 - (r^2-s^2)(r^2+s^2) - (r-s)(r+s)(r^2+s^2)

Solve: x - 16 = sqr(x + 4)

- (x - 16) (x - 16) = x + 4 - x^2 - 32x + 256 = x + 4 - x^2 - 33x + 252 = 0 - x^2 - 12x -21x + 252 = 0 - x(x - 12) - 21(x - 12) = 0 - (x - 21)(x - 12) = 0 - x = 21, 12 - check work - 12 doesn't work - x = 21

Multiply and express the answer using positive exponents only: (x^1/2 + y^1/2)^2

- (x^1/2 + y^1/2) ^2 - (x^1/2 + y^1/2)(x^1/2 + y^1/2) - x + x^1/2y^1/2 + x^1/2 + y^1/2 + y - x + 2x^(1/2)y^1/2 + y

Multiply, and express the answer using positive exponents only: (x^3/2 - y^3/2)(x^3/2 + y^3/2)

- (x^3/2)^2 - (y^3/2)^2 - x^3 - y^3

Factor as far as possible using integer coefficients: (y-x)^2-y+x

- (y-x)(y+x)-(y-x) - (y-x)(y-x-1)

Find all integers b such that x^2+bx-18 can be factored using integer coefficients.

- 1(18)=pq method - b= +-17, +-7, +-3

Solve the problem by factoring: x^4-18x^2+81=0

- 1(81)= pq method - (x^4-9x^2)-(9x^2+81) - x^2(x^2-9)-9(x^2-9) - (x^2-9)(x^2-9) - x= +-3

Show as rational number: 36^-1/2

- 1/(36^1/2) - 1/sqr36 - 1/+-6

If there is a 0.26 gallon in a 1 liter, how many liters, how many liters in 5 gallons.

- 1/0.26 = x/5 - 5/0.26 = 19.23

Evaluate for x=1/2, y=-2/3, and z=1/6: x(y-z)/y^2

- 1/2(-2/3-1/6)/(-2/3)^2 - (-1/3-1/12) / 4/9 - (-5/12) / 4/9 = -15/16

Solve and check: 1/2x+3=3/4x-5

- 1/2x+8=3/4x - 8=1/4x - x=32 - 1/2(32) + 3/4(32)-5 - 16=3=24-5 - 19=19

Solve: m/4 - m/3 = 1/2

- 12(m/4 - m/3) = 12(1/2) - 3m-4m=6 - (-m)=6 - m=(-6)

An office worker can fold and stuff 14 envelopes per minute. If another office worker can fold and stuff 10 envelopes per minute, how long will it take them working together to fold and stuff 1,560 envelopes.

- 14t = 1560 t = 111.4 - 10t = 1560 t = 156 - 24t = 1560 - t = 65

Factor in the integers if possible. If the expression is not factorable, say so: 16x^2+7x+6

- 16(6)= pq method - b^2-4(16)(6)<0

Solve for x in terms of y: 2-3(x+3y)=x-5(y+6)

- 2-3(x+3y) = x-5(y+6) - 2-3x-9y = x-5y-30 - (-4x) = 32+4y - x = 8-y

Simplify by removing parentheses, if any, and combining like terms: 2(m+3n) + 4(m-2n)

- 2m+6n+4m-8n - 6m-2n

Evaluate for x=3, y=-2, and z=6: x(y-z)/y^2

- 3(-2-6)/(-2)^2 - 3(-8)/(-2)^2 - (-24)/4=(_6)

Factor: 3x^2-12y^2

- 3(x^2-4y^2) - 3(x-2y)(x+2y)

Convert 30degrees 15' 45" to decimal degrees

- 30 + 15/60 + 45/3600 - 30 + .25 + .0125 - = 30.2635

Solve: 1/2x - 3/5= 7/6x

- 30x(1/2 - 3/5) = 30x(7/6x) - 15-18x=35 - (-18x)=20 - x = (-20/18) - x = (-10/9)

Simplify by removing grouping symbols, if any, and combining like terms: 3a-2{a-[a+4(a-3)]-5}

- 3a-2{a-[a+4a-12]-5} - 3a-2{a-[5a-12]-5} - 3a-2{a-5a+12-5} -3a-2{-4a+7} - 3a+8a-14 - 11a-14

Simplifying by removing grouping symbols, if any, and combining like terms: a^2-3ab+b^2+2a^2+3ab-2b^2

- 3a^2-3ab+b^2+3ab-2b^2 - 3a^2+b^2-b^2 - 3a^2-b^2

A rectangle has length equal to 3 times its width. If the width is increased by 20 feet and the length decreased by 20 feet, the rectangle becomes a square. Find the width of the rectangle.

- 3w-20=w+20 - 2w=40 - w=20

Solve: x(3x + 7) = x(5x + 2)

- 3x^2 + 7x = 5x^2 + 2x - 5x = 2x^2 - 5x - 2x^2 = 0 - -x(5 + 2x) = 0 - -x(5 + 2x) = 0 - (-x) = 0 - x = 0 - x = -5/2

Convert 40.65 decimal degrees to degree-minute-second form.

- 40degrees 39' 0" - .65 X 60 = 39.00

If the mass of the earth is 6 X 10^27 grams and each gram is 1.1 X 10^27 grams and each gram is 1.1 X 10^-6 ton, find the mass of the earth in tons.

- 6 X 10^21g X (1.1 X 10^-6)/g - 6.6 X 10^-21

Use the ac test to factor, if possible, using integer coefficients: 6x^2-28x+15

- 6(15)= pq method - b^2-4ac

Two cars leave Chicago at the same time and travel in opposite directions. I one travels at 62 kilometers per hour and the other at 88 kilometers per hour, how long will it take them to be 750 kilometers apart?

- 62t + 88t = 750 - 150t = 750 - t = 5hrs

Solve 5/x - 4/3x = 1/2

- 6x(5/x - 4/3x) = 6x(1/2) - 30 - 8 = 3x - 22 = 3x - x = 22/3

Multiply: (3y+2)(2y^2+5y-3)

- 6y^3+15y^2-9y=4y^2+10y-6 - 6y^3+19y^2+y-6

Simplify, and express the answer using positive exponents only. (8 X 10^-6)1/3

- 8^1/5 X 10^-6 X 1/3 - 2 X 10^-2 - 2/100=1/50

A rectangle with the area 108 square inches has length and width that add to 21. Find the dimension of the rectangle.

- A = 108 = lw - w+l=21 - w=21-l - (21-l)l=108 - 21l-l^2=108 - 0=l^2-21+108 - 0=(l-9)(l+2) - l=9, 12 - l=9

Solve for r: A = P(1 + r)^2

- A/P = (1 + r)^2 - +- square root of A/P = 1 + r - -1 +- (sqr AP)/P = r

Solve: x^2 + x - 1/2 = 0

- [(-1) +- sqr(1 - 4(-1/2)] / 2 - (-1/2) +- (sqr3/2)

Solve for a: a^2 + b^2 = c^2

- a^2 = c^2 - b^2 - a = +- square root of (c^2 - b^2)

Factor by grouping if possible: ab+cd-bd-ac

- ab-bd-ac+cd - (ab-bd)-(ac-cd) - b(a-d)-c(a-d) - (a-d)(b-c)

Identify 123 as a monomial, binomial, or trinomial and give its degree.

- monomial - degree = 0 - x^0 is understood

If in a pay telephone the ratio of quarters to dimes is 5/8 and there are 96 dimes, how many quarters are there?

- q/d = 5/8 = x/96 - (5 X 96)/8 - x=60

Taking a 600-mile trip at an average speed 10 miles per hour faster than she usually drives reduces a woman's travel time by 2 hours. What is her normal driving speed?

- t = 600/v

Remove grouping symbols and combine like terms: w-{x-[z-(w-x)-z]-(x-w)}+x

- w-{x-[z-(w-x)-z]-(x-w)}+x - w{x-[-w+x]-x+w}=x - w-{x+w-x-x+w}+x - w-x-w+x+x-w+x - -w+x+x - (-w+x+x) - (-w+2x)

Solve: sqr(x) = x - 12

- x = x^2 - 24x + 144 - 0 = x^2 - 25x - 144 - 0 = (x - 9)(x - 16) - x = 9, 16 - check work - 9 doesn't work - x = 16

Solve for x: x+a/x+b=c

- x+a=c(x+b) - x+a=cx+cb - a-cb=cx-x - a-cb=x(c-1) - (a-cb)/(c-1)

Write the equation in standard form and solve: x = 3/(x-2)

- x^2 - 2x = 3 - x^2 - 2x - 3 = 0 - (x - 3)(x + 1) = 0 - x = -1, 3

Solve the problem by factoring: (x+1)(x+2)-6x= (2x-1)(x-1)

- x^2+2x+2-6x(2x+1)(x-1) - x^2-3x+2=(2x+1)(x-1) - (x-1)(x-2)=(2x-1)(x-1) - (x-1)(x-2)-(2x-1)(x-1) - (x-1)(x-2)-(2x-1) - (x-1)(x-2-2x+1) - (x-1)(-x-1)=0 - x= +-1

Factor as far as possible using integer coefficients: x^5-x^4+x-1

- x^5-((x^2)^2+x-(1)^2)\ - x^5-(x^2-1)^2 - x^5-(x-1)(x+1)(x+1)(x+1) - (x^5-x^4)(x-1) - x^4(x-1)+(x-1) - (x-1)(x^4+1)

Solve for x in terms of y: (x + y) / (x - y) = x/y

- xy + y^2 = x^2 - yx - 0 = x^2 - 2yx + y^2 - a = 1 b = -2y c = y^2 - x = [(-2y) +- sqr(-2y)^2 - 4(1)(y^2)] / 2 - x = 2y/2 +- sqr(4y^2 - 4y^2) / 2 - x = y - no solution

Solve for x: y = (2x-3)/(3x-5)

- y (3x - 5) = 2x - 3 - 3xy - 5y = 2x - 3 - 3 - 5y = 2x - 3xy - 3 - 5y = x(2 - 3y) - x = (3 - 5y)/(2 - 3y)

Write in slope-intercept form the equation of the line that is parallel to y = -3x + 1/3 and goes through (0, 2). Write in slope-intercept form equation of the line that is perpendicular to y = -3x + 1/3 and goes through (0, 2).

- y - 2 = -3(x - 0) - y - 2 = -3x + 0 - parallel: y = -3x + 2 - y-2 = 1/3( x-0) - y - 2 = 1/3x - 0 - perpendicular: y = 1/3x + 2

Solve for x: y = 3x + 7

- y = 3x + 7 - y - 7 = 3x - (y - 7)/3 - (y-7)/3 = x

Find a number such that 4 less than three-fifths the number is 9 more than one-third the number

-3/5x-4=9+1/3x - (-4) = 9 + 5/15x -9/15x - (-13) = -4/15 - 195/4

Rewrite in simplified form using only positive exponents: (x^-2y^3)^-1

-x^2y^-3 - (x^2)/y^3

Rewrite y = x^2 - 3x + 3 in the form y = a(x - h)^2 + k

-y = x^2 - 3x + 9/4 - 9/4 + 12/4 - y = (x - 3/2)^2 + 3/4

Write the number in standard notation: 1.002003 X 10^-5

.00001002003

Write the number in scientific notation: 1,234,000,567,000

1.23 X 10^12

Rewrite in simplified form using only positive exponents: (a^2 - b^2)^-1

1/(a^2-b^2)

Write in scientific notation: .00072

7.2 X 10^-4

Replace the question mark with the appropriate symbol or expression: x^?x^4m-1= x^5m+3

?=m+4

Simplify to a form that uses only positive integer exponents: (cd)^12

c^12d^12

Simplify, assuming n is restricted so that each exponent represents a positive integer: x^5-nx^n+3

this is an easy one - x^8

Write an equation to find 3 consecutive integers whose sum is 78 and then find the integers

x+x+1+x+2=78