Mathematics
emmaemp
2

Answer: a) -3+-2   b) 6 - -5   c) -3 x 9  d) 2x (x+6)  e) In a necklace the ratio of yellow beads to blue beads is 3:1. What percentage of the beads are yellow?  f) 3 (2x - 1) = 21   g)  Match these sequences to their algebraic expression: i) 4, 6, 8, 10, ...     ii) 7, 10, 13, 16, ... iii) 2, 5, 8, 11, ... iv) 3n   1  iiv) 2n    2    iiiv) 3n   4

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(1) Answers
DestinyNicolle

[latex](-)+(+)=(-)[/latex] [latex](-)+(-)=(+)[/latex] [latex]a)-3+(-2)= -3-2=-5[/latex]  [latex]b)6-(-5)= 6+5=11[/latex]  [latex]c)-3*9= -18[/latex]  [latex]d)2x(x+6)=2x^{2}+12x[/latex] [latex]2x^{2}+12x=0[/latex] Δ[latex]=b^{2}-4ac[/latex] in this case: [latex]a=2[/latex] [latex]b=12[/latex] [latex]c=0[/latex] so: Δ[latex]=2^{2}-(4*12*0)[/latex] Δ[latex]=4-0[/latex] Δ[latex]=4[/latex] [latex] \sqrt{} [/latex]Δ=2 [latex] x_{1}= \frac{-12-2}{2*2}=\frac{-14}{4}=\frac{-7}{2}=-3\frac{1}{2}[/latex] [latex] x_{2}= \frac{-12+2}{2*2}=\frac{-10}{4}=\frac{-5}{2}=-2\frac{1}{2}[/latex] e) total amount of beads in this neclace is "4" so: [latex]\frac{3}{4}*100[/latex]%[latex]=\frac{3*100}{4}[/latex]%[latex]=75[/latex] [latex]f)3(2x-1)=21[/latex] [latex]6x-3=21[/latex] [latex]6x=21+3[/latex] [latex]6x=24[/latex] [latex]x=4[/latex] 1. [latex]4, 6, 8, 10, ... =2n+2[/latex] for example: [latex]n=1[/latex] [latex]2*1+2=4[/latex] [latex]n=2[/latex] [latex]2*2+2=6[/latex] etc. 2. [latex]7, 10, 13, 16, ...=3n+4[/latex] for example: [latex]n=1[/latex] [latex]3*1+4=7[/latex] [latex]n=2[/latex] [latex]3*2+4=10[/latex] etc. 3. [latex]2, 5, 8, 11, ...=3n-1[/latex] for example: [latex]n=1[/latex] [latex]3*1-1=2[/latex] [latex]n=2[/latex] [latex]3*2-1=5[/latex] etc.

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