Question

Help me answer all of them ;-;

Answer 1

Answer:

2) D, 3) A, 4) A, 5) B

Step-by-step explanation:

2) We proceed to demonstrate the statement algebraically:

(i) $3\cdot (m+2)-4\cdot (2\cdot m -9)$ Given.

(ii) $3\cdot m + 6 + (-4)\cdot (2\cdot m) +(-4)\cdot (-9)$ Distributive property.

(iii) $3\cdot m +6 +[(-4)\cdot (2)]\cdot m + (-4)\cdot (-9)$ Associative property.

(iv) $3\cdot m + 6 -8\cdot m + 36$ $(-a)\cdot b = -a\cdot b$/$(-a)\cdot (-b) = a\cdot b$

(v) $-5\cdot m +42$ Distributive property/Definition of addition/Result.

Answer: D

3) We proceed to demonstrate the statement algebraically:

(i) $-2\cdot (4\cdot x -5\cdot y - 5\cdot x )$ Given.

(ii) $-2\cdot [(4-5)\cdot x - 5\cdot y]$ Associative and distributive properties.

(iii) $-2\cdot (-x-5\cdot y)$ Definition of addition.

(iv) $(-2)\cdot (-x) + [(-2)\cdot (-5)]\cdot y$ Distributive and associative properties.

(v) $2\cdot x + 10\cdot y$ $(-a)\cdot (-b) = a\cdot b$/Result

Answer: A

4) We proceed to demonstrate the statement algebraically:

(i) $-\frac{8}{9}\cdot \left(27+\frac{2}{3}\cdot x \right)$ Given.

(ii) $\left(-\frac{8}{9} \right)\cdot (27) + \left[\left(-\frac{8}{9} \right)\cdot \left(\frac{2}{3} \right)\right]\cdot x$ Distributive property.

(iii) $-24-\frac{16}{27}\cdot x$ $\frac{a}{b}\cdot c = \frac{a\cdot c}{b}$/$(-a)\cdot b = -a\cdot b$/Associative property/$\frac{a}{b}\cdot \frac{c}{d} = \frac{a\cdot c}{b\cdot d}$/$\frac{a\cdot c}{b\cdot c} = \frac{a}{b}$/Result

Answer: A

5) We proceed to demonstrate the statement algebraically:

(i) $-\frac{1}{3}\cdot \left(3\cdot x -\frac{1}{2} \right)$ Given.

(ii) $\left[\left(-\frac{1}{3} \right)\cdot 3\right]\cdot x +\left(-\frac{1}{3} \right)\cdot \left(-\frac{1}{2} \right)$ Distributive property.

(iii) $-x +\frac{1}{6}$ $(-a)\cdot b = -a\cdot b$/$(-a)\cdot (-b) = a\cdot b$/$\frac{a}{b}\cdot \frac{c}{d} = \frac{a\cdot c}{b\cdot d}$/$\frac{a\cdot c}{b\cdot c} = \frac{a}{b}$/Result

Answer: B