Math 1010 / Algebra 2 / Fall 2020

Solve the inequality and graph. lx+6l>2

(-infinity,-8)U(-4,infinity)

Give the solution set in both graph and interval form: t<7 and t<8

(-infinity,7) and <----) with 7 being the highest in the graph.

4x-9>-13 or 3x+4<_25

(-infinity,infinity)

For the compound inequality, give the solution set in both interval and graph form. 2x-2>-6 or 5x+5<_10

(-infinity,infinity)

Solve lx+2l>-13

(-infinity,infinity)

Solve the inequality lxl>_-7

(-infinity,infinity)

Subtract and write in lowest terms 9/(w^2-4) minus (w+6)/(w^2-5w-14) *type denominator in factored form. Do not factor the numerator.

(-w^2+5w-51)/(w+2)(w-7)(w-2)

Graph the function f(x)=-2x

(0,0),(1,-2),(-1,2)

Multiply and simplify (a^2+2a-63)/(a^2+3a-70) times (a^2-2a-80)/(a^2-17a+72)

(a-10)/(a+10)

For the following pair of functions, find a) (f+g)(x) and b) (f-g)(x) f(x)=4x^2+6x-1 g(x)=-5x^2+3x-12

(f+g)(x)= -x^2+9x-13 , (f-g)(x)= 9x^2+3x+11

For the following functions find A) (f+g)(x) and B) (f-g)(x) f(x)=4x^2+6x-1 g(x)=-5x^2+5x-8

(f+g)(x)=-x^2+11x-9 (f-g)(x)=9x^2+x+7

Find (f+g)(x) and (f-g)(x). f(x)=4x^2+7x-1 g(x)=-5x^2+5x-8

(f+g)=-x^2+12x-9 (f-g)=9x^2+2x+7

let f(x)=x^2-6, g(x)=5x. Find (fg)(3)

(fg)(3)=45

Let f(x)=x^2+6 and g(x)=2x+9. Find the expression (gof)(x)=? and simplify.

(gof)(x)=2x^2+21

Find (hog)(x). g(x)=5x+8 h(x)=x+6

(hog)(x)=5x+14

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

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

(n^2-16)/9n+36 fraction divided by (4-n)/9

-1

Divide, write in lowest terms. (m^2-25)/(6m+30) divided by (5-m)/6

-1

2x+y-z=10 , 6x+3y-3z=30 , -x-1/2y+1/2z=-5

0=0 Dependent solution all have the same graph {x,y,zl2x+y-z=10}

Solve the system of equations. 5x+5y-20z=5 , 5x+y-z=10 , -x-y+4z=5

0=20 the system is inconsistent, empty set.

Person A can paint the neighbors house 6 times as fast as person B. The year A&B worked together, it took them 10 days. How long would it take each to paint the house?

10/x + 10/6x=1 Person A = 35/3 days Person B = 70 days

An experienced employee can enter tax data into a computer two times as fast as a new employee. Working together, it takes the employees 10 hours. How long would it take the experienced employee working alone?

10/x+10/2x=1 Which is 10/x+5/x=1 x=15 so 15 hours.

Over a specified distance, rate varies inversely with time. If a car on a test track goes a certain distance in one-half minute at 162 mph, what rate is needed to go the same distance in two-thirds minute?

121.5 mph (xy=k)

Add. Simplify if possible. (1/z+2)+(9/5z)+(2/z^2+2z)

14/5z

A boat can travel 20 miles against the current in the same time it can travel 180 miles with the current. The rate of the current is 4mph. Find the still water rate.

20/x-4 = 180/x+4 x=5

Simplify. 5/a^2 - 1/2a divided by 3/a + 5/3a

3(10-a)/28a

Add or subtract, write in lowest terms. t/t+4 + 7-t/t - 16/t^2-4t

3/t

Graph the solution of the set of inequalities. 3x+2y<6 x-y<2

3x+2y<6 (2,0)(0,3) x-y<2 (4,2)(6,4)

Find (f/g)(x) and give any x values not in the domain of the quotient function. f(x)=9x^2-6x g(x)=3x

3x-2 and 0 x values were not in the domain of the quotient function

Graph the solution set of the following system of linear inequalities. 4x+5y<10 x-4y>8

4x+5y<10 (0,2)(-5,6) x-4y>8 (8,0)(0,-2) Test point (-6,0) Shade bottom of graph

Write the expression in lowest terms (5p^2-5p)/(4p-4)

5p/4

Connies boat can travel 6 miles upstream in the same time it can travel 22 miles downstream. Still boat rate is 7mph, find current.

6/7-x = 22/7+x x=4mph

Compound inequality x<_2 and x>_5

AND = No overlap no solution (-infinity,2] upside down U [5,infinity)

In triangle ABC, the measure of Angle B is 4 degrees more than 3 times the measure of angle A. Angle C is 41 degrees more than Angle A.

B=3A+4, C=A+41, A=B=C=180 A=27 B=85 C=68

What do you do when the question says use the graph to find f(0)=

Find the spot on the graph where x is equal to zero and type in the y value f(0)=y

Graph the solution of the system of inequalities. 5x+2y<10 x-y<5

Had it all wrong on paper.

The intensity I of light from a light bulb, measured in watts per sq meter (w/m^2), varies inversely as the sq of the distance d from the light bulb. Suppose I is 70 w/m^2 when distance is 5m. Find I when the distance is 4m away.

I=109 3/8 w/m^2 70*5^2=x*4^2 =109.375 .375= 3/8 or 70=k/5^2 = 1750=x*4^2 = x=109.375 .375= 3/8

The intensity I of light from a light bulb, measured in watts per sq meter (w/m^2), varies inversely as the sq of the distance d from the light bulb. Suppose I is 80 w/m^2 when distance is 8m. Find I when the distance is 3m away.

I=568 8/9w/m^2 I=k/m^2 then k=x*m^2

Solve the system of equations. 4x+4y-16z=7, 3x+y-z=5, -x-y+4z=4

Inconsistent, solution is an empty set

Sole each system of equations. 2x-5y+1/2z=4, 8x-20y+2z=16, -16x+40y-4z=-6

Inconsistent, solution set =0

For the compound inequality, give solution set in interval and graph form. x<_3 and x>_5

It's and, no overlap no answer. (-infinity,3] and [5,infinity) have no overlap

Find LCD 25/12m and 5/(12m-20)

LCD = 12m(3m-5)

Find LCD: 9/175m and 3/75m-125

LCD=175m(3m-5)

If the question says "Use the graph to find the indicated value of the function f(-4)= ? " What do you do?

Locate the -4 on the x axis and find the value of y. If the line is passing through (-4,-8) then f(-4)=-8

Find all values for which the expression is undefined. (x-2)/(x^2+8)

There are no values for which the expression is undefined. x^2 will always be greater than or equal to 0 and +8 makes it at least 8

Solve and graph l8x-3l<_6

[-3/8,9/8]

Solve lm+3l+4<_8

[-7,1]

Solve the following inequality & graph the solution set. l-4x+12l<_1

[11/4,infinity)

Let g(z)= -z^2+5z+5 Find g(-5)

g(-5)=-45

Let g(y=-y^2+9y+10 Find g(-5)

g(-5)=-60

Let g(x)=3x+5 & h(x)=x-6. Find (hog)(5)

h(g(x))=14

Solve for m. 1/F=1/2 + 1/m

m=Fz/z-F

Write the expression in lowest terms. (5x^3+8x^2+3x)/(5x^3-17x^2-12x)

x+1/x-4

Find the sum. x/x-3 + -18/x^2-9 Write in lowest terms.

x+6/x+3

In the figure shown, z=x+30,x+y=100. Determine 3rd equation involving x,y,z and find the measures of the angles.

x+y+z=108 x=50 y=50 z=80

In the figure shown, z=x+10 and x+y=110. Determine a 3rd equation involving x,y,and z and then find the measures of the 3 angles.

x+y+z=180 x=60 z=70 y=50

In the triangle shown, z=x+10, x+y=90 determine 3rd equation and find x, y, & z.

x+y+z=180 x=80 y=10 z=90

Multiply, write in lowest terms. (2x^2-9x+7)/(x^2-1) times (x^2+x)/(2x^2-5x-7)

x/x+1

Solve the system: x+2y+z=8, 2x+y-z=1, x-y-z=-2

x=3 y=0 z=5

Find values for which the rational expression is undefined. (3x+3)/(x^2-5x+4)

x=4 and x=1

Solve the system of equations. 3x-2y+8z=14, x+3y+z=14, 3y-z=8

x=4, y=3, z=1

Graph the solution set of the system of linear inequalities. y<_2x-5 x<2y+6

y<_2x-5 (0,-5)(1,-3)(-1,-7)(3,1) x<2y+6 (6,0)(8,1)(4,-1) Color fill in upper right corner of overlap on graph

Graph the Function f(x)=-3

y=-3x (0,0), (1,-3), (-1,3)

Graph, give domain and range. f(x)=4x+3

y=4x+3 (0,3)(1,7)(-1,-1) Domain (-infinity, infinity) Range (-infinity, infinity)

8x-y+z=44 , 2x+2y-3z=19 , x-3y+2z=-7

y=5 z=1 x=6

Solve & check 2z/(z^2-4) = 4/(z+2) - 3/(z-2)

z=-14

Solve and check. 2z/z^2-25 = 8/z+5 - 7/z-5

z=-75

Solve for z 1/A=1/t+1/z

z=At/(t-A)

Solve l4y+4l=8

{-3,1}

Solve. l4-6x/5l=18

{-35/3,55/3}

Solve l2x+12l<_0

{-6}

Solve l4y+8l=24

{-8,4}

Solve the compound inequality x+3>7 or 6-x>7

(-infinity,-1)U(4,infinity)

Solve the compound inequality with or. x+6>11 or 1-x>2

(-infinity,-1)U(5,infinity)

Solve. Graph. l-4x+7l>_8

(-infinity,-1/4]U[15/4.infinity)

Solve the following inequality & graph the solution set. lx+11l>8

(-infinity,-19)U(-3,infinity)

Solve the compound inequality and graph. 2x-4<-6 and -4x+4>20

(-infinity,-4) And, no overlap = no set.