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# Bell Ringers - PowerPoint PPT Presentation

Bell Ringers. ACT based 2014-2015. Bell Ringer. Verbally expanded 4 x 10 -5. 0.00004 (decimal, 4 zero’s, 4). Bell Ringer. Equivalent form of (x)(x)(x)(x 3 )?. 6. X. Bell Ringer. How many solutions are there to the equation x 2 - 7 = 0?. 2 √7 & √-7. Bell Ringer.

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### Bell Ringers

ACT based

2014-2015

Verbally expanded

4 x 10-5

0.00004 (decimal, 4 zero’s, 4)

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

6

X

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

2

√7 & √-7

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?

SolutionIf 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

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?

Area Formula = L x W

3(w) in

5 in

SolutionIf 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 .

(2x2 + 2x - 12) / (x - 2)

simplifies to ?

Solution1st) 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?

SolutionLet x be the length of second leg and apply Pythagoras theorem as follows: 102 = 52 + x2Solve for x x = √(100 - 25) = √75 =

5 √3 in

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

Solution:

Solve for x:

X = 8/3y + 11/3

2(x - 8)equivalent?

solution:

2x - 16

X ?

solution:

set equal to zero: 2x - 16 = 0

2x = +16

X= 8

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

Solution:

Solve for y:

Y = - 4/3 x + 8/3

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

SolutionTo 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).

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

SolutionWe 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

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

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

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

**more on flash but must be checked**

Graph: │x │> 3

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

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

y = mx + b

What 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.

2

ax ± bx ± c = 0

Factor the following:

x - x – 6

x + 2x – 3

2

(x – 3) (x + 2)

2

(x + 3) (x – 1)

Factor completely

x + 2x – 15

2

(x + 5) (x – 3)

Factor completely

3x + 2x – 5

2

(3x + 5) (x – 1)

Completely factor this polynomial

9m - 12m + 4

2

(3m – 2)(3m – 2)

Factor

y + 12y + 36

2

(y + 6)(y + 6)

Factor

9y + 12 y + 4

2

See a pattern with perfect squares?

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

Completely factor this polynomial

m - 12m +36

2

(m – 6)(m – 6)

An 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 │ = 3

Solve using rules for Absolute value

1/2T – 40 = 3

1/2T – 40 = -3

74  86

What is the sum of the solutions to the equation

│5M – 30 │= 10

12

What is the solution set of this equation

│3y – 4│ + 1 = 6

{3,-1/3 }

What is the product of the solutions to the equation

│2x – 1│ = 3

-2

2X – 1 = 3

2X = 4

X = 2

2X – 1 = -3

2X = -2

X = -1

Graph the solution of the absolute value equation

2│x – 1│+3 = 11

-3

5

0

Solve the inequality

│2c – 10│ > 16

C > 13 C < - 3

OR

Graph the solution to this inequality

│X + 4│ < 12

-16

8

0

Factor…not factorable? Is this polynomial PRIME ?

m - 18m + 30

2

P R I M E

2

(-18) – 4(1)(30) = 14.3

b - 4ac

2

2

Completely factor

x +2x - 4

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

2

b - 4ac

2

Factor

x + 3x + 18

P R I M E

2

b - 4ac

2

What is the possible base and height for the area of this rectangle?

(x + 3)(x – 2)

A = x + x - 6

2

2

2

The 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

L = 3x + 2y

What is the area of the below rectangle ?

3x + 5y

4x

12x + 20xy

2

What is the area of the triangle below ?

A = bh

2

2x + 7

3x - 9

2

6x + 3x – 63

2

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

A rectangle has the length (x+3) and a width of (x – 1).

What is the perimeter?

What is the area?

4x + 4

x +2x - 3

2

Find the greatest common factor:

36x y + 108x + 54xy

2

3

2

What is the area of the circle below ?

3

2.25∏

Hint: look at the formula sheet for formula

When 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)

2208

t

2

2

2

2

2

Evaluate the following algebraic expression:

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

Which of the following linear equations when graphed on a coordinate grid has the steepest slope? You will need to support your answer.

• Y = 1/3x – 2

• Y = 5/2x – 1

• Y = 3x + 1/4

• Y = 4x + 3/5

Conner 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?