Algebra 1 - Distance, Midpoint, Trinomials, Inequalities, Slope, etc.

Algebra 1

100

What is the distance formula?

d=√(x₂-x₁)²+(y₂-y₁)²

200

What is the distance between (8,11) and (8,4)?

7

300

Suppose y varies jointly with x and z. Find y when x = 7 and z = 4, given that y = 30 when x = 3 and z = 5.

k = 2

y = 56

400

Factor the trinomial:

x⁴+5x³+6x²

x²(x+2)(x+3)

OR

x²(x+3)(x+2)

500

A student spins the spinner below and flips a fair coin. Make a table to show the possible outcomes in this experiment and find the theoretical probability of each outcome.

Spinner (each are 1/5): red, red, green, green, green

             Red  Red  Blue  Blue  Blue

heads     RH   RH   BH    BH    BH    

tails       RT    RT    BT    BT    BT     

P(R,H) = 2/10 = 1/5

P(B,H) = 3/10

P(R,T) = 2/10 = 1/5

P(B,T) = 3/10

IS

100

7√xy - 5√xy

2√xy

200

Given the points A and B where A is at coordinates ( 2,-5 ) and B is at coordinates ( -3,-7 ) on the line segment AB, find the midpoint of AB.

(-.5,-6)

300

Identify the asymptotes for the equation

y =   4   .

      x - 3

vertical asymptote: x = 3

horizontal asymptote: y = 0

400

Solve the inequality and graph on a number line:

-4x - 3 < 21

x > 6            (* = filled in circle)

                 *--------->

<-------------|---------->

   6

500

Factor the trinomial:

4x²+x-5

(4x + 5)(x - 1)

OR

(x - 1)(4x + 5)

THE

100

A piano salesperson earns a 10.5% commission on each piano sold. What price must a piano sell for in order for the salesperson to earn a commission of at least $735?

$7000

200

Write a compound inequality that describes the graph below.  (* = filled in circle)

   o-------------*

<---------------|-------------|------------->

-2                 6

x > -2 AND x < 6     OR     -2 < x < 6

300

Find the probability of rolling a sum of 4 or a sum of 5 on two number cubes, each numbered 1 to 6.

P = 7/36

400

Bob is selling chocolate bars. He sold 2 boxes for $5 and 3 for $7. What will Bob charge for 5 chocolate bars if he keeps selling chocolate bars at the same rate?

$11 for 5 chocolate bars

m = $7 - $5 = $2 per chocolate bar

         3 - 2

2 = y₂ - $5 

        5 - 2

y₂ = $2(5 - 2) + $5 = $6 + $5 = $11

500

Cindy was standing in between (middle of) KFC and McDonalds. If McDonald is located at (4,8) and KFC is located at (-10,-8), where is Cindy located at?

(-3, 0)

BEST!!!

100

Write a compound inequality that represents all real numbers that are greater than 2 and less than 5. Graph the solution.

x > 2 AND x < 5     OR     2 < x < 5

     o-------------o

<-------------|-------------|---------->

     2                5

200

Solve the equation 4 | x | = 16

{-4, 4}

300

Factor the trinomial:

3x²+11x+6

(3x + 2)(x + 3)

400

Factor the trinomial:

x² + 2x - 8

(x + 4)(x - 2)

OR

(x - 2)(x + 4)

500

Use the data in the table to make a scatter plot. Draw a trend line on the scatter plot. Find an equation for the trendline.

x  |   1  |  2  |  3  |   4   |   5   |   6  

y  |   5  |  8  |  9  |  10  |  13  |  16  

y = 2x + 3

Scatter plot on trendline on graph paper.