Answer:
Quadratic Equation | Factoring
Solve each quadratic equation using factoring.
1) v² + 5v + 6 = 0
doing middle term factorisation
v²+(3+2)v+6=0
v²+3v+2v+6=0
v(v+3)+2(v+3)=0
(v+3)(v+2)=0
either
<u>v=-3</u>
<u>or</u>
<u>v=-2</u>
2) g² - 3g = 4
keeping all terms in one side
g²-3g-4=0
doing middle term factorisation
g²-(4-1)g-4=0
g²-4g+g-4=0
g(g-4)+1(g-4)=0
(g-4)(g+1)=0
either
<u>g=4</u>
<u>or</u>
<u>g=-1</u>
3)w² + 4w = 0
w(w+4)=0
either
<u>w=0</u>
<u>or</u>
<u>w=-4</u>
4) s² - 8s + 12 = 0
doing middle term factorisation
s²-(6+2)+12=0
s²-6s-2s+12=0
s(s-6)-2(s-6)=0
(s-6)(s-2)=0
either
<u>s=6</u>
<u>or</u>
<u>s=2</u>
5) x ²+ 2x - 35 = 0
doing middle term factorisation
x²+(7-5)x-35=0
x²+7x-5x-35=0
x(x+7)-5(x+7)=0
(x+7)(x-5)=0
either
<u>x=-7</u>
<u>or</u>
<u>x=5</u>
6) r(r + 2) = 99
opening bracket
r²+2r=99
keeping all terms in one side
r²+2r-99=0
r²+(11-9)r-99=0
r²+11r-9r-99=0
r(r+11)-9(r+11)=0
(r+11)(r-9)=0
either
<u>r=-11</u>
<u>or</u>
<u>r=9</u>
7)k(k-4)=-3
opening bracket
k²-4k=-3
keeping all terms in one side
k²-4k+3=0
k²-(3+1)k+3=0
k²-3k-k+3=0
k(k-3)-1(k-3)=0
(k-3)(k-1)=0
either
k=3
or
k=1
8)t²+ 3t + 2 = 0
doing middle term factorisation
t²+(2+1)t+2=0
t²+2t+t+2=0
t(t+2)+1(t+2)=0
(t+2)(t+1)=0
either
<u>t</u><u>=</u><u>-</u><u>2</u>
<u>or</u>
<u>t</u><u>=</u><u>-</u><u>1</u>
9)m ^ 2 - 81 = 0
m²=81
doing square root in both side

<u>m=±9</u>
<u>either</u>
<u>m</u><u>=</u><u>9</u>
<u>or</u>
<u>m</u><u>=</u><u>-</u><u>9</u>
10) h²- 17h + 70 = 0
doing middle term factorisation
h²-(10+7)h+70=0
h²-10h-7h+70=0
h(h-10)-7(h-10)=0
(h-10)(h-7)=0
either
<u>h</u><u>=</u><u>1</u><u>0</u>
<u>or</u>
<u>h</u><u>=</u><u>7</u>
6m (m+2) = 0 is the factored form
m=0, m=-2 is m
Steps are on paper
If you need more explanation, comment
The inventory of Dollar Dress Shop at cost when the retail method is used is $117, 500.
<h3>How to find the inventory cost?</h3>
When using the Retail method to find the inventory at cost, the Beginning inventory, the purchases, and the net sales are used.
The formula for finding the cost of inventory using the retail method is:
= Beginning inventory + Purchases - Net sales
= $ 87, 500 + $ 325, 000 - $ 295, 000
= $117, 500
The inventory cost of Dollar Dress Shop with the retail method is $ 117, 500.
Find out more on inventory cost at brainly.com/question/20318114
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Answer:
Step-by-step explanation:
7x + 6 < 3(x - 2)
7x + 6 < 3x - 6
7x - 3x < -6 - 6
4x < -12
x < -12/4
x < -3
<span>{x | x < -3}</span>