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Algebra

MathThe domain asymptote and xintercept of y = 4  log(x+5) has to be determined. The graph of the given function is: The domain of the function is all values of x for which y is real and defined....

MathThe area of the circle with equation x^2 + y^2  8x + 4y = 0 has to be determined. The equation of a circle with center (h, k) and radius r is (x  h)^2 + (y  k)^2 = r^2. Expressing the equation...

Math`y+4=4(x2)` The slope of this line is 4, therefore the slope of the line perpendicular to this is `1/4` . 1) We cannot find the xintercept of the perpendicular line unless we are told a point...

MathYou accidentally left out the number of toppings from the second pizza but I assume it is 4 since it appears to be one higher by the price given. We are to find the price of a plain pizza and the...

MathTo satisfy the first constraint, namely A+B+C+D=6 we need four natural numbers (0 and integers) that sum to 6. The possibilities are (where the string of four numbers is in no particular order):...

MathInterpolation is the process of estimating or predicting the value `y = f(x_3)` of an unknown but observable function`f` at a point `x_3` between two points `x_1` and `x_2` (`x_2>x_1`) where the...

HistoryThe correct answer to this question is D. It was AlKhwarizmi who is typically credited with developing algebra, or at least with writing the first known book on the subject. He did this in the...

MathWe wish to evaluate the expression `10^(((x+y)/2)  3z)` First, simplify the power into seperate terms involving each of `x`, `y` and `z` only: `10^(((x+y)/2)  3z) = 10^(x/2 + y/2  3z)` Then...

MathFirst evaluate the expression under the square root sign: `x^2 + 2x + (y1)^2  2xy = x^2 + 2x + y^2  2y + 1  2xy` `= x^2 + y^2 2xy + 2(xy) + 1` Now `(xy)^2 = x^2 + y^2  2xy` So that...

MathWe have 1) x + y + z = 2013 2) xyz = 2013 It is clear that one of the values, x for example, needs to be very close to 2013. Using the golden ratio is a natural avenue to try here. The golden ratio...

MathA factor is a term that divides an expression exactly. The gcf is the greatest common factor. Let's start with the additive expression `16x^3 + 16x^2 + 10x` This factorises to `2x(8x^2 + 8x + 5)`...

Math`E_6` is an elementary matrix. That is it is a matrix that can be reached from the identity matrix of the same dimension by an elementary operation. We have that `E_6 ((1,3,4),(2,2,3),(5,4,4)) =...

Math`E_4` is an elementary matrix. That is, one that can be reached from the identity matrix of the same dimension by an elementary operation. In this case the operation is multiplying row 2 by 4....

MathThe matrix `U` is the product of some particular set of elementary matrices. An elementary matrix can be reached from the identity matrix of the same dimension by an elementary row or column...

MathI can usually do these, but this one has confused me and I need help. Four times a number is four...We use a letter to designate our mystery number, it doesn't matter what letter we use, but most use `x` Then we need to use the relationships in the story problem to set up an equation. Four times...

Math`f(x)=3x+1` `g(x) = x+2` `(f+g)(x)= f(x)+g(x)=(3x+1)+(x+2)=4x+3`` `That's how you find the sum of two functions of x.