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Lana K.

Tutor for 4 years

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SAT II Mathematics Level 2

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Question:

If f(x)=4x^2 - 1 and g(x)=8x + 7, g ॰ f(2) =

Lana K.

Answer:

This reads "g of f of 2" so you would start with f(2)=4(2^2)-1=15. Then you would do g(15)=8(15)+7=127 so the final answer would be 127.

French

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Question:

Formulez les deux sortes d'hypotheses avec si: a) eventuellement demain si... b) hier soir si... 1. Si je couds 2. Si mes parents me punissent 3. Si le père se bat ses enfants

Lana K.

Answer:

1. a) Si je cousais b) Si j'avais cousu 2. a) Si mes parents me punissaient b) Si mes parents m'avaient puni(e) 3. a) Si le père battait ses enfants b) Si le père avait battu ses enfants

Basic Math

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Question:

Write the equation for a line that passes through the following two points, (5,3) and (3,2), in a) slope-intercept form, b) point-slope form, and c) general form.

Lana K.

Answer:

a) The equation of a line in slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept. To find the slope of the line, you would use the following equation: (Y2-Y1)/(X2-X1) where Y1 and X1 come from the first point given, (5,3), and Y2 and X2 come from the second point given, (3,2). When you plug these two points in, you would get: (2-3)/(3-5) which is equal to 1/2, so the slope of the line is 1/2. To find the y-intercept of the line you would plug 1/2 into y=mx+b and chose one point. Let's use (3,2): 2=(1/2)(3)+b Then you get: 2=(3/2)+b Subtract (3/2) from both sides to get: 1/2=b The final equation in slope-intercept form would be: y=(1/2)x+(1/2). b) A line in point-slope form looks like (Y-Y1)=m(X-X1) Since we already have m (the slope) from part a to be 1/2 and we already have a point given (let's use (5,3)), we can write the equation as: (Y-3)=(1/2)(X-5) c) General form looks like Ax+Bx+C=0 where A, B, and C are constants. We can take the slope-intercept form from part a and use that to create our formula in general form. Since y=(1/2)x+1/2, we can say that the general equation is: y-(1/2)x-(1/2)=0

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