Question 5 of 23

<img src="https://tex.z-dn.net/?f=%28%20%5Cfrac%7B1%7D%7B2%7D%20%20%7Ba%7D%5E%7B2%7D%20%20%2B%20%20%20%5Cfrac%7B1%7D%7B2%7D%20ab

Zigmanuir [339]

Answer:

$\frac{1}{2}$ (a + 2b)(a - b)

Step-by-step explanation:

Assuming you require the expression to be factored

Given

$\frac{1}{2}$ a² + $\frac{1}{2}$ ab - b² ← factor out $\frac{1}{2}$ from each term

= $\frac{1}{2}$ (a² + ab - 2b²) ← factor the quadratic

Consider the factors of the coefficient of the b² term(- 2) which sum to give the coefficient of the ab- term (+ 1)

The factors are + 2 and - 1, since

2 × - 1 = - 2 and 2 - 1 = + 1, thus

a² + ab - 2b² = (a + 2b)(a - b) and

$\frac{1}{2}$ a² + $\frac{1}{2}$ ab - b² = $\frac{1}{2}$ (a + 2b)(a - b)

5 0

3 years ago

Meg pounded a stake into the ground. When she

jeka94

The dog is able to run around in a circle with a radius of9 ft.

The area of a circle is A = pi r^2

A = (3.14) (9)^2
A= (3.14)(81)
A= 254.34 sq ft

3 0

3 years ago

The Butlers bought a $332,000 house. They made a down payment of 42,000 and took out a mortgage for the rest. Over the course of

Zarrin [17]

Answer:

Step-by-step explanation:

(a)Mortgage = 332000 - 42000 = 290000

15 * 12 = 180 months

Total monthly payments = 180 * 2447.19 =440494.2

Total = 440494.2 + 42000 = 482494.2

(b) Interest = 482494.2 -290000

= 192494.2

4 0

3 years ago

Read 2 more answers

to rent a building for a school dance ava paid $120 plus $2.50 for each student who attended. If she paid a total cost of $325 h

deff fn [24]

Answer:

82 students

Step-by-step explanation:

8 0

3 years ago

Estimate the solution to the system of equations 7x−y=7 x+2y=6 i need help

Yanka [14]

Answer:

(4/3, 7/3)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Terms/Coefficients
Coordinates (x, y)
Solving systems of equations of using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

7x - y = 7

x + 2y = 6

Step 2: Rewrite Systems

Equation: x + 2y = 6

[Subtraction Property of Equality] Subtract 2y on both sides: x = 6 - 2y

Step 3: Redefine Systems

7x - y = 7

x = 6 - 2y

Step 4: Solve for y

Substitution

Substitute in x: 7(6 - 2y) - y = 7
Distribute 7: 42 - 14y - y = 7
Combine like terms: 42 - 15y = 7
[Subtraction Property of Equality] Subtract 42 on both sides: -15y = -35
[Division Property of Equality] Divide -15 on both sides: y = 7/3

Step 5: Solve for x

Define original equation: x + 2y = 6
Substitute in y: x + 2(7/3) = 6
Multiply: x + 14/3 = 6
[Subtraction Property of Equality] Subtract 14/3 on both sides: x = 4/3

7 0

3 years ago