Bell Work:

Find the surface area of this right triangular prism. Dimensions are in feet.

6

812

10

Answer:

Surface Area = 2(area triangle) + area bottom + area back + area top

= 2[1/2(8 x 6)] + (8 x 12) + (6 x 12) + (10 x 12)

= 2(24) + 96 + 72 + 120

= 48 + 288

= 336 ft 2

Lesson 16:More Complicated

Evaluations

The procedures discussed in Lesson 14 are also used to evaluate more complicated expressions. The use of parentheses, brackets, and braces is often helpful in preventing mistakes. We will use all of these symbols of inclusion in the following examples.

Example:

Evaluate

-a[-a(p - a)]

If p = -2 and a = -4

Answer:

Use parentheses, brackets and braces as required.

-(-4){-(-4)[(-2) – (-4)]}

= 4{4[2]}

=4{8}

= 32

Example:

Evaluate

ax[-a(a – x)]

If a = -2 and x = -6

Answer:

This time we will not use parentheses. We will replace a -2, -a with 2, x with -6 and –x with 6.

12[2(-2 + 6)]

12[2(4)] = 12[8] = 96

Example:

Evaluate

-b[-b(b – c) – (c – b)]

If b = -4 and c = -6

Answer:

We replace b with -4, -b with 4, c with -6 and –c with 6.

4[4(-4 + 6) – (-6 + 4)]

4[4(2) – (-2)] = 4[8 + 2] = 4[10]

=40

Lesson 17:

Factors and Coefficients, Terms, The Distributive Property

Coefficient*: Any factor or any product of factors of a product.

4 is the coefficient of xy 4(xy)

x is the coefficient of 4y x(4y)

y is the coefficient of 4x y(4x)

xy is the coefficient of 4 xy(4)

4y is the coefficient of x 4y(x)

4x is the coefficient of y 4x(y)

If the coefficient is a number, we call it a numerical coefficient. 4(xy)

If the coefficient consists entirely of variables or letters, we call it a literal coefficient. xy(4)

A term is an algebraic expression that

1. Consists of a single variable or constant.

2. Is the indicated product or quotient of variables and/or constants.

3. Is the indicated product or quotient of expressions that contain variables and/or constants.

A term is thought of as a single entity that represents or has the value of one particular number. For instance, the expression

x + 4xym - 6p - 8

y + 2

Is an expression that has four terms.

We have noted that the order of adding two real numbers does not change the answer. Also, the order of multiplying two real numbers does not change the answer. We call these two properties of real numbers the commutative property for addition and commutative property for multiplication.

Distributive Property*: for any real numbers a, b, c,

a(b + c) = ab + ac

Example:

Use the distributive property to find the value of

4(6 – 2 + 5 – 7)

Answer:

4(6 – 2 + 5 – 7)

= 4(6) + 4(-2) + 4(5) + 4(-7)

= 24 – 8 + 20 – 28

= 8

Example:

Use the distributive property to expand

mn( x + y + 2p)

Answer:

mn( x + y + 2p)

= mnx + mny + 2mnp

Example:

Use the distributive property to expand

(x – 3y + xz)mp

Answer:

(x – 3y + xz)mp

= mpx – 3ymp + mpxz

HW: Lesson 16 #2-30 Even

Lesson 17 #2-30 Even