Choice H
$$18000\times2=36000$$ $$83000-36000=47000$$ $$\frac{47000}{7000}=6.7$$
You will need 7 trucks.
Choice D
$$15=3\times5$$ $$25=5\times5$$ $$30=2\times3\times5$$ $$\Rightarrow 2\times3\times5\times5=150$$
Choice K
$$11.38 + 1.85 = 13.23 gallons$$ $$13.23\times$1.36=$17.99$$ $$$17.99+4=$21.99$$
Choice F
$$3.9\times 10^{-1}=0.39$$ $$3.9\times 10^{-2}=0.039$$ $$3.9\times 10^{-3}=0.0039$$
There will always be one less zero in front of the three and the nine.
Choice D
$$=5c(2d-5c)-3d(2d-5c)$$ $$=10cd-36c^{2}-6d^{2}+15cd$$ $$=25cd-36c^{2}-6d^{2}$$
Choice G
$$\angle ADB=180°-30°-20°=130°$$ $$\angle EDA=180°-130°=50°$$ $$\angle EAD=180°-83°-50°=47°$$
Choice D
$$x + y = 21 $$ $$x – y = 15$$ $$\Rightarrow 2x=21+15=36$$ $$x=18$$ $$y=3$$ $$xy=18\times3=54$$
Choice K
For Green Tree, the equation is 50 + 0.25m = 100, so m = 200.
For Big Rock, the equation is 60 + 0.2m= 100, so m = 200.
Therefore, she can drive the same amount of miles with either company.
Choice E
$$\frac{(x-5)^{2}}{x^{2}-25}$$ $$=\frac{(x-5)(x-5)}{(x-5)(x+5)}$$ $$=\frac{(x-5)}{(x+5)}$$
Choice F
$$\frac{3}{8}=\frac{x}{80}$$ $$x=30$$
Choice B
Just get the decimal equivalents …
Choice H
$$t=0,y=12, $$
The y-intercept is …
Choice C
T is the speed of …
Choice F
$$x=0,y=-3 \Rightarrow (F)、(H)$$ $$x=2,y=0 \Rightarrow …
Choice D
$$25\times 3^{5}=6075$$
Choice K
$$\frac{9}{36}=\frac{16}{x}$$ $$\Rightarrow x=64$$
Choice D
You can spend exactly $14 …
Choice H
$$y=ax^{2}+bx+c$$ $$y=2x^{2}-12x+4$$ $$x=\frac{-b}{2a}=\frac{12}{4}=3$$ $$\Rightarrow x=3,y=-5$$
Choice B
$$\frac{(2,8)+(-2,6)}{2}=(0,7)$$
Choice J
$$c=2\pi r=12\pi$$
Choice C
This is a 3-4-5 right …
Choice F
$$\sin=\frac{opposite}{hypotenuse}$$ $$\angle CDA = \frac{\overline{AC}}{\overline{AD}}$$
Choice A
DCBF is a rectangle, with …
Choice J
$$\triangle FGH=\frac{1}{4}\Box ABGH$$ $$\Box ABGH=\frac{1}{4}\Box …
Choice D
$$2\frac{1}{6},3\frac{1}{3},4\frac{1}{2}$$
The common difference is …
2010 December(69A) Math Question 38
Algebraic & Function Expressions
- Simplify Algebraic Expressions
Choice G
$$B=x+2$$ $$y=A-4 \Rightarrow A=y+4$$ $$B+A=(x+2)+(y+4)=x+y+6$$
Choice C
$$10,10,x,x$$ $$20+2x=64$$ $$x=22$$ $$\Rightarrow 10,22,22$$
Choice H
Choice B
The midpoint of AD to …
Choice G
The area of a rhombus: …
Choice D
$$5\times4\times3\times2\times1=120$$
Choice G
$$3^{2}+h^{2}=6^{2}$$ $$h=3\sqrt{3}\approx 3\times1.73=5.19$$
Choice A
$$x^{2}\lt x$$
Only for x …
Choice G
$$48+66=114$$
Choice A
If the radius of the …
Choice F
$$C^{2}=D \Rightarrow C=\sqrt{D}$$ $$C=\sqrt{B} \Rightarrow …
Choice D
If you double the radius …
Choice J
$$2^{2}+x^{2}=3^{2}$$ $$x=\sqrt{5}$$ $$\cos \angle A=\frac{\sqrt{5}}{3}$$
Choice E
The point where a line …
Choice F
$$-16t^{2}+32t-16=0$$ $$\Rightarrow t^{2}-2t+1=0$$ $$t=1,-2$$
The …
Choice C
$$\angle CBD=180°-132°=48°$$ $$132°=3x$$ $$x=44°$$ $$\angle …
Choice F
$$\csc =\frac{hypotenuse}{opposite}=\frac{1}{\sin}$$ $$=\frac{1}{0.4}=\frac{5}{2}$$
Choice E
If B has a slower …
Choice K
Each of the first five …
Choice E
If x is positive or …
Choice J
It's in the first quadrant, …
Choice A
Picture a vector of the …
Choice K
$$=\frac{\sqrt{r}}{\sqrt{s}}+\frac{\sqrt{s}}{\sqrt{r}}$$ $$=\frac{\sqrt{r}\times\sqrt{r}}{\sqrt{s}\times\sqrt{r}}+\frac{\sqrt{s}\times\sqrt{s}}{\sqrt{r}\times\sqrt{s}}$$ $$=\frac{r+s}{\sqrt{rs}}$$