Can Someone Help Me Solve These Algebra 2 Questions

How can I solve this Algebra question?

I was thinking of writing a solution for an analogous problem, since I am not much into solving homework problems for others. But I see that someone did it for you already, so… given that you described this as an algebra problem, let me show you how to find a general solution, for any width of paper, any number of columns, any margins, etc.Let the width of the paper be denoted by the letter [math]w[/math], and the margins by the letter [math]m[/math]. Since there are two margins, we need to subtract the width of the margin twice to get the usable width: it will be [math]w - 2m[/math].Let the number of columns be denoted by the letter [math]n[/math], and the width of each column by the letter [math]c[/math]. Then the total width occupied by [math]n[/math] columns (without gutters) would be [math]nc[/math].But in between the [math]n[/math] columns, there are also [math]n-1[/math] gutters. Let the ratio of the width of a gutter to the width of a column be denoted by the letter [math]g[/math]. Then the width of one gutter will be [math]gc[/math], and the width of all the [math]n-1[/math] gutters together will be [math](n-1)gc[/math].Together, the widths of the columns and the widths of the gutters must be the same as the total width minus the two margins. This gives us a nice equation:[math]nc + (n-1)gc = w - 2m.[/math]This equation can be solved for any of the symbols it contains, but it so happens that in your exercise, all the symbols have assigned values except for one: [math]c[/math], the width of a column. So we need to solve this equation for [math]c[/math], which is very easy to do, since c is a common factor on the left-hand side. First, I rewrite the equation to show this:[math][n + (n-1)g]c = w-2m,[/math]next, I divide by the factor that multiples c on the left-hand side:[math]c = \dfrac{w-2m}{n + (n-1)g}.[/math]Go ahead, try it: plug in the values for [math]w = 8.5''[/math], [math]m = 1''[/math], [math]n = 3[/math], [math]g = 1/8[/math]. See what you get.The beauty of doing things this way is that you can now use the formula for other combinations of numbers. A good example is [math]w = 8.5''[/math], [math]m = 0.5''[/math], [math]n = 4[/math], [math]g = 1/3[/math]. That was the analogous problem that I wanted to use in my answer before I realized that someone already offered a solution of the original question.

Can someone help me on algebra?

The superhero’s height is given by:[math]f(x) = -16x^2 + 200x[/math]From this, we note that he is starting on the ground. Also, we will ignore the superhero’s own height.Suppose we want to know whether his height can ever be 612 ft high.We set his height function equal to 612 and then see if we can solve it. We will use a discriminant to check what kind of solutions it has.[math]612 = -16x^2 + 200x[/math][math]-16x^2 + 200x - 612 = 0[/math][math]-4x^2 + 50x - 153 = 0[/math]The discriminant of this polynomial is [math]50^2 - 4*(-4)(153) = 4948[/math]. Because this discriminant is positive, this polynomial has two real solutions. This means the expression, at some time [math]x[/math], [math]f(x) = 612 ft[/math].Note:The question does not ask for the specific time when [math]f(x) = 612[/math].It asks a yes-no question, and asks you to explain.Using a discriminant, you can say—for certain—whether his height reaches 612 ft. without knowing when it happens.However, some teachers may expect a graph or even a solution.Going a step further:If one were using calculus, you can find when the superhero reaches his maximum height.For a function [math]f(x)[/math], the maximum or minimum value is obtained when [math]f’(x) = 0[/math].Where [math]f(x) = -16x^2 + 200x[/math], then[math]f' = -32x + 200[/math][math]0 = -32x + 200[/math][math]x = 200/32 = 6.25[/math]So, the maximum height is attained after 6.25 seconds.That height is [math]f(6.25) = -16(6.25)^2 + 200(6.25) = 625 ft.[/math]Because the maximum value is 625 ft., the superhero can clear a building that is 612 ft.I only include this last part to stoke your curiosity.

Can someone help me answer this question?

We know that 1/2 of the unknown number plus one is equal to one hundred. We can find out that “99+1” is a hundred by subtracting one from a hundred. “99” is half of all the birds. Multiply by two. The one bird is talking to 198 birds.There is also a second answer that can be found from question. Let's say that the single bird is talking to 66 birds. The massive group of birds tell the 1, half of us (33birds) plus the one bird makes the total amount of birds 100... 66+33+1=100.The ACTUAL answer would be determined by how you interpret the question. I guess it could kind of show a person’a subconscious view of the world if you looked into it… but that’a different story. Is the glass full or empty?

Can someone help me with this algebra exercise ?

If we interpret your question as finding a set of vectors that are a basis of the plane: [math] 2x + y - 3z = 0[/math] let’s note that the plane is a two dimensional space in three-space. Accordingly, spanning the space requires only two independent vectors in the plane.(1, 1, 1) lies in the plane as does (0, 3, 1). So those two vectors form a basis.vectors of the form (2, 0, 0) do not satisfy the equation for the plane and hence cannot be part of the basis.