Bell Ringers

ACT based2014-2015

Verbally expanded

4 x 10-5

0.00004 (decimal, 4 zero’s, 4)

Bell Ringer

Equivalent form of (x)(x)(x)(x3)?

X6

Bell Ringer

How many solutions are there to the equation x2 - 7 = 0?

2

√7 & √-7

Bell Ringer

There are 15 balls in a box: 8 balls are green, 4 are blue and 3 are white. Then 1 green and 1 blue balls are taken from the box and put away. What is the probability that a blue ball is selected at random from the box? Solution If 1 green and 1 blue ball are taken from the box, then there are 7 green, 3 blue and 3 white balls, a total of 13 balls. If one ball is selected at random, the probability that it is blue is given by

3 / 13

Bell Ringer

The length of a rectangle is 3 times its width. If the width of the rectangle is 5 inches, what is the rectangle's area, in square inches?

Solution If the width is 5 in and the length is 3 times the width, then the length is 3 * 5 = 15 in; The area is given by 5 * 15 = 75 in2 .

5 in

3(w) in

Area Formula = L x W

Bell Ringer

For all x >2, (2x2 + 2x - 12) / (x - 2)

simplifies to ?Solution

1st) factor: 2x2 + 2x – 12

2nd) GCF: 2(x2 + x - 6)

3rd) factor: (x2 + x - 6) (don’t forget to carry 2 along)

2(x + 3)(x - 2)

4th) Simplify: [ 2(x + 3)(x - 2) ] / (x - 2) =

2(x + 3)

If the hypotenuse of a right triangle is 10 inches long and one of its legs is 5 inches long, how long is the other leg?

Solution Let x be the length of second leg and apply Pythagoras theorem

as follows:

102 = 52 + x2

Solve for x

x = √(100 - 25) = √75 =

5 √3 in

Bell Ringer

If 8y = 3x - 11, then x =

Solution:Solve for x:

X = 8/3y + 11/3

Bell Ringer

2(x - 8)

equivalent? solution:2x - 16

X ?solution:

set equal to zero: 2x - 16 = 0

2x = +16

X= 8

Bell Ringer

What is the slope of the line 4x = -3y + 8

Solution:Solve for y:

Y = - 4/3 x + 8/3

Bell Ringer

When graphed in the (x,y) coordinate plane, at what point do the lines 2x + 3y = 5 and x = -2 intersect?

Solution

To find the point of intersection of two lines, we need to solve the system of equations made up of the equations of the lines. We need to solve the following

system of equations.

2x + 3y = 5 and x = - 2

Substitute x by -2 in the equation 2x + 3y = 5 and solve for y.

2(-2) + 3y = 5

3y = 9

y = 3

The two lines intersect at (-2 , 3).

Bell Ringer

If you drove at average speed of 66 miles per hour, what distance, in miles, did you drive in 99 minutes?

Solution We first convert the speed into miles per minute.

66 / 60 = 1.2 miles per minute

We now use the speed and the time to find the distance.

1.2 (miles/minute) * 99 minutes = 108.9 miles D=rt

Bell Ringer

What is the smallest value of x that satisfies the equation x(x + 4) = -3

Solution: -3

What if it is an inequality?x(x + 4) > -3

Solution: any # greater than -3; to the right of -3 but NOT including -3

Bell Ringer

Bell Ringer

Describe the procedure used to solve an equation for a variable.

Bell Ringer

What is one important difference, with respect to the answer, between solving equations and solving inequalities?

One answer ; Range of answers

**more on flash but must be checked**

Bell Ringer

Graph: │x │> 3

NOT CHECKEDIf x + 4y = 5 and 5x + 6y = 7, then 3x + 5y = ?

Bell Ringer

OWhat important information about a line can you get from a linear equation ?

y = mx + b

Bell RingerWhat is usually the first step in factoring a quadratic trinomial that is not a perfect square and whose terms have no common

factor greater than 1?

Find two integers that have product ac and sum

b.

ax ± bx ± c = 0 2

Bell Ringer

Factor the following:x - x – 6

x + 2x – 3

2

2

(x – 3) (x + 2)

(x + 3) (x – 1)

Bell RingerFactor completely

x + 2x – 152

(x + 5) (x – 3)

Bell RingerFactor completely

3x + 2x – 52

(3x + 5) (x – 1)

Bell Ringer

Completely factor this polynomial

9m - 12m + 4

2

(3m – 2)(3m – 2)

Bell Ringer

Factor

y + 12y + 362

(y + 6)(y + 6)

Bell Ringer

Factor

9y + 12 y + 42

(3y + 2)(3y + 2)

See a pattern

with perfect

squares?

Bell Ringer

Completely factor this polynomial

m - 12m +36

2

(m – 6)(m – 6)

Bell RingerAn accounting firm must regulate the office temperature to protect its computers. The equation │½T – 40 │ = 3, gives the range of acceptable air temperatures for the office in degrees Fahrenheit. What is the range of temperature?

Equation: │1/2T – 40 │ = 3Solve using rules for Absolute

value

1/2T – 40 = 3 1/2T – 40 = -3

74 86

Bell RingerWhat is the sum of the solutions to the

equation

│5M – 30 │= 10

12

Bell RingerWhat is the solution set of this

equation

│3y – 4│ + 1 = 6

{3,-1/3 }

Bell RingerWhat is the product of the solutions to the

equation

│2x – 1│ = 3

-22X – 1 = 3

2X = 4X = 2

2X – 1 = -32X = -2X = -1

Bell RingerGraph the solution of the absolute value

equation

2│x – 1│+3 = 11

-3 5

0

Bell RingerSolve the inequality

│2c – 10│ > 16

C > 13 C < - 3OR

Bell RingerGraph the solution to this

inequality

│X + 4│ < 12

-16 8

0

Bell RingerFactor…not factorable? Is this polynomial

PRIME ?

m - 18m + 30

b - 4ac2

2

(-18) – 4(1)(30) = 14.3

2

P R I

M E

Bell RingerCompletely factor

x +2x - 4

b - 4ac2

2

(2) - 4(1)(-4)2

Bell RingerFactor

x + 3x + 182

b - 4ac2

P R I

M E

Bell RingerWhat is the possible base and

height for the area of this rectangle?

A = x + x - 62

(x + 3)(x – 2)

Bell RingerThe area of a rectangle id given

by A = 6x y + 4y x and the width of the rectangle is w = 2xy. What is the length, l, of the rectangle

if

l = A W

2 2

L = 3x + 2y

Bell RingerWhat is the area of the

below rectangle ?

4x

3x + 5y

12x + 20xy2

Bell RingerWhat is the area of the triangle

below ?A = bh

22x + 7

3x - 96x + 3x –

632

2

Bell Ringer

A volleyball court is shaped like a rectangle. It has a width of x meters

and a length of 2x meters. What is the area of this court?

What is the perimeter of this court?

2x 2

6x

Bell RingerA rectangle has the length

(x+3) and a width of (x – 1).

What is the perimeter?

What is the area?4x + 4

x +2x - 32

Bell Ringer

Find the greatest common factor:

36x y + 108x + 54xy3 2 2

Bell RingerWhat is the area of the circle below ?

3

Hint: look at the formula sheet for formula

2.25∏

Bell RingerWhen Robert was born, his

grandfather invested $1,000 for his college education. At an

interest rate of 4.5%, compounded annually, how

much would Robert have at age 18 ?

A = P (1 + r)

t2208

Bell RingerEvaluate the following algebraic expression:

(8xy + 6x y + 17y ) – (3x y – 6y + 3y )

2 2 2 2 2

Bell RingerWhich of the following linear equations when graphed on a coordinate grid has the steepest slope? You will need to support your answer.a) Y = 1/3x – 2b) Y = 5/2x – 1c) Y = 3x + 1/4d) Y = 4x + 3/5

Bell RingerConner went to visit his friend in

Houston. He drove at a constant rate of 55 miles per hour, and it took 3 hours to arrive. What was the total

distance Conner drove?