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Type: Posts; User: miranda

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1. ## Thread: Distance between two points SAT Subject test Math

by miranda
Replies
2
Views
5,466

### The distance between two points A(a_{1}, a_{2},...

The distance between two points A(a_{1}, a_{2}, a_{3}) and B(b_{1}, b_{2}, b_{3}) is given by the following formula:

d=\sqrt{(a_{1}- b_{1})^2+(a_{2}- b_{2})^2+(a_{3}- b_{3})^2}
So, in our case...
2. ## Thread: x-intercepts SAT Subject test Math

by miranda
Replies
2
Views
5,474

### This is a GDC (graphic display calculator)...

This is a GDC (graphic display calculator) question.

For example in CASIO fx-9860 we have to do the following procedure in order to find the real roots (x-intercepts) of this graph....
3. ## Thread: Function SAT Subject test Math

by miranda
Replies
2
Views
2,941

### This is a GDC (graphic display calculator)...

This is a GDC (graphic display calculator) question.

For example in CASIO fx-9860 we have to do the following procedure in order to find the real roots (x-intercepts) of this graph....
4. ## Thread: SAT math factor theorem

by miranda
Replies
2
Views
2,825

### The Factor Theorem states that a polynomial p(x)...

The Factor Theorem states that a polynomial p(x) has a factor x-r if and only if f(r)=0.
From Factor theorem we have that P(4)=0.

So, P(4)=2(4)^4-4(4)^3+(k+1)(4)^2-k(4)+8=0 \Rightarrow

...
5. ## Thread: SAT subject mathematics Complex numbers

by miranda
Replies
2
Views
2,701

### We know that for the imaginary unit i hold the...

We know that for the imaginary unit i hold the following
i^2=-1,
i^3= i^2 \cdot i=(-1) \cdot i=-i
and i^4=(i^2)^2=(-1)^2=1.

Also, 2013 can be written as 4*503+1

So, i^{2013}=(i^4)^{503}...
6. ## Thread: SAT subject math 2 - Complex numbers

by miranda
Replies
2
Views
2,819

### For the imaginary unit i holds that i^2=-1 ...

For the imaginary unit i holds that i^2=-1

So, (x-i)(x+i)=x^2-(i)^2=x^2-(-1)= x^2+1

Therefore the correct answer is (C).

by miranda
Replies
1
Views
2,547

### This is an easy SAT question using GDC and find...

This is an easy SAT question using GDC and find the roots of the given quadratic equation.
Another way is to recognize the identity x^2+4x+4=(x+2)^2 and thus the equation has one double (repeated)...
8. ## Thread: percentage sat math question

by miranda
Replies
2
Views
3,059

### The percentage decrease in TV price is given by...

The percentage decrease in TV price is given by the following formula:

\frac{\$\ 400-\$\ 450}{\\$\ 450} \cdot 100 \%\ = 11\%

Therefore the correct answer is (B).
9. ## Thread: sat math parabola

by miranda
Replies
2
Views
2,286

### The axis of symmetry of the parabola is given by...

The axis of symmetry of the parabola is given by the equation x=-2. So f(-4)=9, since the -4 has equal distance from -2 as 0.

Therefore the correct answer is (C).

Hope these help!
10. ## Thread: geometry perimeter triangle

by miranda
Replies
2
Views
2,860

### The perimeter of triangle RST is P=2x+y=14 ...

The perimeter of triangle RST is P=2x+y=14

and we also know that \frac{x}{y}=\frac{4}{3} \Rightarrow x=\frac{4y}{3}

P=2\frac{4y}{3} +y=14\Rightarrow 8y+3y =42 \Rightarrow 11y =42 \Rightarrow...
11. ## Thread: geometry question area

by miranda
Replies
2
Views
2,648

### The triangle DGF is equilateral since DG=DF as...

The triangle DGF is equilateral since DG=DF as radii and we also know that DG=GF.
Therefore, each angle of the triangle DGF measures 60^o.
We’ ll use two formulas for areas.

The first one gives...
12. ## Thread: geometry triangle's angles

by miranda
Replies
2
Views
2,782

### The sum of angles in a triangle is always 180^o ...

The sum of angles in a triangle is always 180^o

So, x+y+50=180 \Rightarrow x+y=130 (1)

2x-y=110 (2)

Solving the simultaneous equations (1), (2)

x+y=130 \Rightarrow x+2x-110=130 ...
13. ## Thread: sat math word problem

by miranda
Replies
2
Views
2,810

### Let x,y be the Jim’s and John’s age now...

Let x,y be the Jim’s and John’s age now respectively.
So, the proposition “Five years ago, Jim was half as old as John is now” can be written as
x-5=\frac{y}{2} (1)

and the proposition “John is...

by miranda
Replies
2
Views
2,350

### absolute value inequality

This absolute value inequality can be solved as follows

|a+4|>5

a+4>5 \ or\ a+4<-5

a>1 \ or\ a<-9

Therefore the correct answer is (C).
15. ## Thread: sat expression inequality

by miranda
Replies
2
Views
2,172

### From the given inequalities we deduce that a>0,...

From the given inequalities we deduce that a>0, b<0, \ and\ c>0 and the only NOT negative i.e. positive expression is ab^2c^3

Therefore the correct answer is (B).
16. ## Thread: values of x inequality

by miranda
Replies
2
Views
2,125

### First we transform the inequality as x^2

First we transform the inequality as x^2<17 and then plug-in the values of (A)-(D) to find a choice which doesn’t satisfy the inequality.
Therefore the correct answer is (D).
17. ## Thread: expression sat math

by miranda
Replies
2
Views
2,226

We know that
(x+y)^2= x^2+2xy+y^2 =12+2(-\frac{3}{2})=12-3=9?

Therefore the correct answer is (A).
18. ## Thread: ratio of areas

by miranda
Replies
2
Views
3,006

### ratio of circles' areas

The ratio of the areas of two circles is 9:4 \frac{A_{1}}{ A_{2}}=\frac{\pi (r_{1})^2}{\pi (r_{2})^2}=\frac{ (r_{1})^2}{ (r_{2})^2}=\frac{9}{4} \Rightarrow \frac{ r_{1}}{ r_{2}}=\frac{3}{2}...
19. ## Thread: area circumference of a circle

by miranda
Replies
2
Views
2,632

### sat math geometry circle

The circumference is given by the formula C=2\pi r=12\pi \Rightarrow r= 6 /units/
The area is given by the formula A=\pi r^2=\pi (6)^2=36 \pi /units/ ^{2}
Therefore the correct answer is (C).
...
20. ## Thread: sat number question

by miranda
Replies
2
Views
2,765

### sat question with digits

4^{1}=4
4^{2}=16
4^{3}=64
4^{4}=256
……
We observe that when the power is even then the unit digit of the result is 6 and when the power is odd then the unit digit of the result is 4.
Therefore...
21. ## Thread: sat math expression question

by miranda
Replies
2
Views
1,858

### sat math expressions

First we solve for x : z=x^7 \Rightarrow x=z^{\frac{1}{7}} in terms of z

then we solve for y : z=x^7 \Rightarrow x=z^{\frac{1}{4}} in terms of z

So, xy= z^{\frac{1}{7}} z^{\frac{1}{4}}=...
22. ## Thread: sat math probability permutations

by miranda
Replies
2
Views
2,710

### probability permutations

In this case we have permutations since the order matters. Additionally we must divide the number of permutations by 2! , 4!, 3! and 2! Since there are 2 black boxes, 4 white boxes, 3 blue boxes and...
23. ## Thread: sat math permutations

by miranda
Replies
2
Views
2,797

### sat math permutation question

In this case we have permutations since the order matters. Additionally we must divide the number of permutations by 2! Since the digit “1” appears twice.
24. ## Thread: sat math counting question

by miranda
Replies
2
Views
2,469

### sat math counting question

Every digit of the password can be chosen with 10 different ways. Therefore the number of possible passwords are 10*10*10*10*10=10^5.
25. ## Thread: sat math counting

by miranda
Replies
2
Views
2,644

### sat math counting question

The visitor can choose for his entry to the museum between 4 different ways and for his exit also between 4 different ways. Therefore the visitor can enter and leave the museum in 4*4=16 ways.
The...
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