Choice C
$$Blue=\frac{1}{4}=\frac{6}{24}$$ $$Purple=\frac{1}{8}=\frac{3}{24}$$ $$Green=\frac{1}{12}=\frac{2}{24}$$ $$Orange=\frac{3}{8}=\frac{9}{24}$$ $$Red=\frac{1}{6}=\frac{4}{24}$$
The chance of stopping in green is the lowest.
Choice D
$$70\ beats \times 60\ minutes\times24\ …
Choice K
$$\frac{(-7)^{2}-1}{(-7)+1}$$ $$=\frac{49-1}{-6}$$ $$=\frac{48}{-6}$$ $$=-8$$
Choice C
$$x+y=50---50\ questions$$ $$x\cdot5+y\times2=130---130\ points$$ $$\Rightarrow 5x+2y=130$$
Choice J
$$50=2\times5\times5$$ $$30=2\times3\times5$$ $$70=2\times5\times7$$ $$[50,30,70]=2\times3\times5\times5\times7=1050$$
Choice C
$$B=7LH$$ $$420=7\times30\times H$$ $$H=2$$
Choice G
$$y=mx+b$$ $$5x+7y=7$$ $$\Rightarrow 7y=-5x+7$$ $$\Rightarrow …
Choice E
$$\triangle A=\frac{1}{2}bh$$ $$h=\overline{AB}$$ $$20=\frac{1}{2}\times5\times \overline{AB}$$ …
Choice J
$$3-4-5\ triangle$$ $$\Rightarrow 300:400:500$$ $$x=500$$
Choice D
$$=\mid (-54)+20\mid$$ $$=\mid -34 \mid$$ …
Choice G
$$6x-y=x+5y$$ $$\Rightarrow 5x=6y$$ $$\Rightarrow y=\frac{5x}{6}$$
2010 June(68C) Math Question 27
Similar Triangles & Types of Triangles
- Simplify Algebraic Expressions
Choice E
$$2:7=10:x$$ $$x=\frac{7\times10}{2}=35$$
Choice G
$$=x^{5+-(3^{2})}$$ $$=x^{5+(-9)}$$ $$=x^{-4}$$
Choice A
$$10.3(1.08)=11.124$$ $$15-11.124=-3.876\approx-3.88$$
Choice K
$$11.124\div(7+4+10+4)$$ $$=11.124\div25$$ $$=0.44496\approx0.44$$
Choice B
Lollipop: L
Candy bar: C …
Choice G
$$2r=36$$ $$\Rightarrow 2\pi r=36\pi$$
Choice D
$$\frac{[3(x-2)]^{2}}{3}$$ $$=\frac{3^{2}(x-2)^{2}}{3}$$ $$=3(x-2)^{2}$$ $$=3(x^{2}-4x+4)$$ $$=3x^{2}-12x+12$$
Choice F
$$6x-6 \lt 7+10x$$ $$\Rightarrow -6-7 …
Choice C
The two sets of opposite …
Choice J
$$Slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$$ $$\Rightarrow m=\frac{4-2}{9-5}=\frac{2}{4}=\frac{1}{2}$$
Choice E
At 1:30, the hour hand …
Choice F
$$\sin 55°\approx 0.82=\frac{20}{Support\ rope}$$ $$\Rightarrow …
Choice C
$$\pi r^{2}\times20$$ $$=3.14\times 6^{2}\times20$$ $$=2260.8$$ …
Choice G
$$20:35=12:x$$ $$x=21$$
Choice C
$$x(2x)=162$$ $$2x^{2}=162$$ $$x^{2}=81$$ $$x=9$$ $$2(x+2x)=6x=54$$
Choice K
$$$10\times0.6\times0.9=5.4$$
Choice C
$$(C)\ y=\frac{4x+3}{x-2}$$
Since I can't …
Choice J
$$3+x=y$$ $$\frac{x}{2}+5=y$$ $$\Rightarrow \frac{x}{2}+5=3+x$$ $$\Rightarrow …
Choice D
$$100+15=115$$
Choice K
$$405°=360°+45°$$ $$360°+30°=390°$$
Choice D
$$(a,b)+(3,-11)=(5,-7)$$ $$\frac{a+3}{2}=5 \Rightarrow a=7$$ $$\frac{b+(-11)}{2}=-7 …
Choice F
$$\sin25°=0.423,\ \cos25°=sin(90-25)°=\sin65°=0.906$$ $$\frac{200}{\sin 90°}=\frac{x}{\sin25°}=\frac{y}{\sin65°}$$ $$\Rightarrow …
Choice B
A graph is said to …
Choice K
$$\Rightarrow 8\times8=64$$ $$64-\pi (4)^{2}=64-3.14(16)=13.76\approx14$$
Choice B
$$(width+length)2=perimeter$$ $$width=w$$ $$length=w+x$$ $$\Rightarrow (w+w+x)2=P$$ …
Choice F
$$13^{2}=5^{2}+x^{2}$$ $$\Rightarrow x=12$$ $$\cos \theta=\frac{-12}{13}$$
Choice A
$$(a+b)^{2}=a^{2}+b^{2}$$ $$\Rightarrow a^{2}+2ab+b^{2}=a^{2}+b^{2}$$ $$\Rightarrow 2ab=0$$ …
Choice J
$$ $1\times3+$3\times0=$3 $$ $$ $1\times4+$3\times1=$7 …
Choice A
Choice H
Choice C
$$f(g(x))$$ $$=\frac{3}{(x+1)^{2}-1}$$ $$=\frac{3}{x^{2}+2x+1-1}$$ $$=\frac{3}{x^{2}+2x}$$ $$=\frac{3}{x(x+2)}$$ …
Choice F
$$\mid x-1 \mid \lt B$$ …
Choice A
$$Area\ of\ a\ circle:\pi r^{2}$$ …
