Question

1. solve the equation $x^2 = 10$. what are the square roots of 625

a. $x = \pm\sqrt{10}$
b. $x=\sqrt{10}$
c. $x=\pm5$
d. $x=5$

1. which equation has no solution?

a) $\sqrt{x} - 8 = -14$
b) $-\sqrt{x} - 8 = -14$
c) $\sqrt{x} - 18 = -14$
d) all of the equations have a solution
e) none of the equations have a solution

1. select all the rational numbers.

$\square$ $\frac{4}{6}$ $\square$ $\sqrt{2}$ $\square$ $7.45454...$
$\square$ $0.34$ $\square$ $0.358746...$ $\square$ $-\frac{2}{5}$

1. which property is the following expression?

$11 + (w + 2) = 11 + (2 + w)$
a) commutative property of addition
b) commutative property of multiplication
c) associative property of addition
d) associative property of multiplication

1. which property is used in the following expression?

$(5 \cdot a) + 3 = 3 + (5a)$
a) distributive property
b) community property of addition
c) associative property of addition
d) associative property of multiplication

1. which property is the following exp

$(x + 5)3 = 3x + 15$
a) distributive property
b) community property of additio
c) associative property of additio
d) associative property of multip
e) community property of multip

Explanation:

Problem 6

Step1: Take square root of both sides

$x = \pm\sqrt{10}$

Problem 7

Step1: Analyze equation a)

$\sqrt{x}-8=-14 \implies \sqrt{x}=-6$ (Square root can't be negative, no solution)

Step2: Analyze equation b)

$-\sqrt{x}-8=-14 \implies -\sqrt{x}=-6 \implies \sqrt{x}=6 \implies x=36$ (Valid solution)

Step3: Analyze equation c)

$\sqrt{x}-18=-14 \implies \sqrt{x}=4 \implies x=16$ (Valid solution)

Problem 8

Step1: Identify rational numbers

Rational numbers can be written as $\frac{p}{q}$ ($q
eq0$, integers $p,q$):

• $\frac{4}{6}$: Fraction of integers
• $0.34=\frac{34}{100}$: Fraction of integers
• $7.4545...$: Repeating decimal (rational)
• $-\frac{2}{5}$: Fraction of integers
• $\sqrt{2}$ and $0.358746...$ (non-repeating/non-terminating) are irrational

Problem 9

Step1: Match to addition property

$11+(w+2)=11+(2+w)$ swaps $w$ and $2$ in addition, which is Commutative Property of Addition.

Problem 10

Step1: Match to addition property

$(5\cdot a)+3=3+(5a)$ swaps $(5a)$ and $3$ in addition, which is Commutative Property of Addition.

Problem 11

Step1: Match to multiplication property

$(x+5)3=3x+15$ distributes 3 to $x$ and 5, which is Distributive Property.

Answer:

1. A. $x = \pm\sqrt{10}$
2. a) $\sqrt{x} - 8 = - 14$
3. $\frac{4}{6}$, $0.34$, $7.4545...$, $-\frac{2}{5}$
4. a) Commutative Property of Addition
5. b) Commutative Property of Addition
6. a) Distributive Property