1. Which expression is equivalent to (–2)(a + 6)? (1 point)
–2a + 6
2a + 12
–2a – 12
–2a + 12
2. To which subsets of real numbers does the number –22 belong? Choose all subsets that apply. (2 points)
whole numbers
rational numbers
integers
irrational numbers
natural numbers
3. What is an algebraic expression for the following word phrase: "6 times the difference of b and p?" (1 point)
6b – p
6(b – p)
6 – bp
6bp
4. What is the simplified form of the expression?

A fraction with a numerator of 5(14 – 2) squared and a denominator of 2. (1 point)
60
30
72
360
5. Evaluate u + xy, if u = 18, x = 10, and y = 8. (1 point)
188
36
98
224
Essay

6. A square field has an area of 479 ft2. What is the approximate length of a side of the field? Give your answer to the nearest foot. Explain your response. (2 points)

7. Workpad

Note: Remember to show all of the steps that you use to solve the problem.

Simplify the expression (7 + 5) + 4 • 13 – 2. (1 point)

1.
-2(a + 6) = -2 · a - 2 · 6 = -2a - 12

2.
-22:
whole numbers
rational numbers
integers

3.
6 · (b - p) = 6(b - p)

4.
[5(14 - 2)²]/2 = (5 · 12²)/2 = (5 · 144)/2 = 720/2 = 360

5.
u + xy
u = 18; x = 10; y = 8, subtitute

18 + 10 · 8 = 18 + 80 = 98

6.
A = 479 ft²;
a - length of a side
A = a²
therefore
a² = 479 ⇒ a = √479 ⇒ a ≈ 21.886 ⇒ 22 (ft)

7.
(7 + 5) + 4 · 13 - 2 = 12 + 52 - 2 = 64 - 2 = 62

Answer Link

xero099 xero099 · Answer 2 · 2021-08-19T15:49:49+02:00

1) [tex](-2)\cdot (a+6)[/tex] is equivalent to [tex]-2\cdot a -12[/tex].

2) The number [tex]-22[/tex] is both an Integer and a Rational Number.

3) 6 times the difference of b and p is equivalent to [tex]6\cdot (b-p)[/tex].

4) [tex]\frac{5\cdot (14-2)^{2}}{2}[/tex] is equivalent to [tex]360[/tex].

5) [tex]u + x\cdot y[/tex] is equal to 98.

6) The side length of the Square is approximately 22 feet.

7) [tex](7+5) + 4\cdot 13 - 2[/tex] is equivalent to [tex]62[/tex].

1) In this question we proceed to use Algebra methods to find an equivalent Expression:

[tex](-2)\cdot (a+6)[/tex]

[tex]-2\cdot a -12[/tex]

Hence, [tex](-2)\cdot (a+6)[/tex] is equivalent to [tex]-2\cdot a -12[/tex].

2) The number [tex]-22[/tex] is both an Integer and a Rational Number. Integers comprises Whole Numbers with negative Sign and every Integer has its equivalent Rational Number.

3) In this question, we are require to translate a Sentence into an Algebra expression:

"6 times the difference of b and p"

[tex]6\cdot (b-p)[/tex]

6 times the difference of b and p is equivalent to [tex]6\cdot (b-p)[/tex].

4) In this question, we proceed to simplify the following Rational Number into its most simple form, in this case, a Whole Number:

[tex]\frac{5\cdot (14-2)^{2}}{2}[/tex]

[tex]\frac{5\cdot 12^{2}}{2}[/tex]

[tex]\frac{720}{2}[/tex]

[tex]360[/tex]

[tex]\frac{5\cdot (14-2)^{2}}{2}[/tex] is equivalent to [tex]360[/tex].

5) In this question we evaluate a given Function. If we know that [tex]z = u + x\cdot y[/tex], [tex]u = 18[/tex], [tex]x = 10[/tex] and [tex]y = 8[/tex], then the result is:

[tex]z = u + x\cdot y[/tex]

[tex]z = 18 + 10\cdot 8[/tex]

[tex]z = 98[/tex]

In a nutshell, [tex]u + x\cdot y[/tex] is equal to 98.

6) From Geometry we know that the Area of a Square can be determined by this formula:

[tex]A = x^{2}[/tex]

Where:

[tex]A[/tex] - Area, in square feet.

[tex]x[/tex] - Side length, in feet.

If we know that [tex]A = 479\,ft^{2}[/tex], then the side length of the square is:

[tex]x = \sqrt{A}[/tex]

[tex]x = \sqrt{479\,ft^{2}}[/tex]

[tex]x\approx 21.886\,ft^{2}[/tex]

The side length of the Square is approximately 22 feet.

7) In this question, we need to Simplify the given Expression by Algebra means:

[tex](7+5) + 4\cdot 13 - 2[/tex]

[tex]12 +52 - 2[/tex]

[tex]62[/tex]

[tex](7+5) + 4\cdot 13 - 2[/tex] is equivalent to [tex]62[/tex].

Please see this question related to Algebra: https://brainly.com/question/14413003