Help me with these mathematics problems -- please!?

Question

A. If T varies directly as S, and S=15 when T=12, find S when T=4.
B. For what value of X is the expression 7/(X + 8) undefined? (The expression is written as a fraction.
C. How do I write an equation to represent a line witha slope of -3 adn a Y-intercept of 1. (Please explain why -- I know the equation is Y=3X+1)
D. What is an irrational number?
EWhatis a trinomial, and how can I find an equivalent to (3x-1)(x+4)?
F. The factor of 2n(squared)-6 are? (How do I find the factors of a equation like this?)

Answer 1

First are the answers, and their individual in-depth explanations are below. Hope this helps!
A. S=5
B. X=-8
C. Y=-3X+1
D. It is a number that cannot be expressed as the ratio of two integers.
E. A trinomial is a polynomial expression with three terms (after simplification). The trinomial you are looking for is 3x^2+11x-4.
F. 2 and (N^2 - 3). Factor out all common factors.



A. Let K be the constant of variation. T=KS. 12 =15K. K=4/5. Now T=(4/5)S. Substitue the values you've been given. 4=(4/5)S. S=5

B. X = -8. An undefined expression includes division by zero, since this is impossible. To make the denominator zero, X+8=0.

C. Actually, it's Y=-3x+1. This is just slope-intercept form, y=mx+b, where m=slope and b=y-intercept. But think about it. Y-intercept is where the graph crosses the y intercept, so the x-coordinate has to be zero. If you substitute 0 for x in the equation, you get Y=1, so this is correct.

D. It is a number that cannot be expressed as the ratio of two integers. It is still a real number, though (so no square roots of negative numbers!) There are two types of irrational numbers: Radicals (the square root of five, the fifth root of 11) and Transcendental numbers (pi, e)

E. A trinomial is a polynomial expression with three terms (after simplification). For example, x^2 +x+1 or y^21+13y^3+231. Each term has a different exponent of the variable (Including zero. That is, y^0 =1)
To get the trinomial you are looking for, use the FOIL technique for multiplying binomials. Multiply the First terms 3x*x (=3x^2). Outside terms are 3x*4 (=12x) and Inside terms are (-1)*x (=-x). Finally, the Last terms together are (-1)*4 (=-4). Now add all of these products together. 3x^2+12x+-x-4 = 3x^2+11x-4.

F. Factor out all common factors. Your original equation is 2n^2-6. 2n^2 = 2*n*n.
6= 2*3.
The only factor these have in common is two. Take that out:
2*(n^2-3)


[edit] I just successfully finished an honors Algebra 2 course and I consulted my textbook to answer this question, so I know what I'm talking about!

Answer 2

A. S = 5 Set it up like a proportion.
B. X = -8 -8 + 8 = 0 Any number divided by 0 is undefined.
C. If the slope is -3, the equation should be: y = -3x + 1
The best way to find the line is to plug in numbers. For example, if y = 0, what is x? 0 = -3x + 1 ( x = 1/3). If x = 1, what is y? y = -3(1) + 1; y = -2. Now that you have some numbers, you can plot them on a graph to find the line. Your three plots: (1/3, 0), (1, -2), and (0, 1). When you plot them, the line they create slopes down from left to right - math people call this a "negative slope". If you plotted them and had a positive slope, the line would slope up, from left to right.
D. An irrational number is any number that goes on and on forever without repeating in its decimal form. "Pi" is a good example.
E. I usually deal with polynomials, and to find an equivalent, use the FOIL method (First, Outside, Inside, Last), meaning, First, multiply 3x and x = 3x squared (2 as an exponent), Second, multiply 3x and 4 = 12x, Third, multiply -1 and x = -1x, Lastly, multiply -1 and 4 = -4. You now have 3x(squared) + 12x - 1x - 4, or 3x(squared) + 11x - 4.
F. Do you mean "prime factorization"? In that case, factor it out like this: 2 x n x n - 2 x 3.

Answer 3

3

Answer 4

A. T(S) = T(S)
12(15)=4(S)
180 = 4S
S = 45

B.
X = -8

C. y = -3x + 1 because in the y=mx+b form, the y-int is b and the slope is m

D. A decimal number that has no end, ex pi (3.14156254...)

E. A trinomial has three different... variables?
(3x-1)(x+4) = 3x^2 + 6x - 4
The solutions to this trinomial is X = {1/3, -4} because you solve for the quantities (3x-1) and (x+4)

F. the factor is 2 because it is common in both values. It turns out to be 2(n[squared] +3)

Answer 5

for letter c in the slope intercept form y= mx+b
m=slope b= y intercept
so if you know the slope and y intercept substitute them for m and b

for example: if the slope is 8 and the y intercept is 3 the equation is y=8x+3

a trinomial is an expression with 3 terms
find the equivalent by using the FOIL method
the answer is 3x(squared)+11x-4 Do u know FoIL

Answer 6

B. 7/(x+8) is undefined when (x+8)=0 since you can't divide by zero. x+8=0 when x=-8. The answer is when x=-8

c. The answer you 'know' is wrong.

e. a trinominal is a polynomial with three parts. Multiply the two factors together:
3x - 1
x + 4
------------
3x(squared) -x +12x -4 = 3x(squared) +11x -4

f. First divide out the two that leaves n(squared) - 3
So n(squared) = 3
n = sqrt of 3 or about 1.7

Answer 7

1.S=T+3
so,S=4+3
S=7

2.can't define, because the questions is not completed with the comparing answers

3. y-intercept is a
slope is b
and the regression format is y=a+bx
so, y=1-3x

4. irrational number is non-round number, e.g : 1.23, 1.356,34.3
and rational number is round number e.g : 1,2,34,56,43

5. trinomial means x^3 and the equivalent to the questions is 3x^2+11x-4 and this called binomial because x^2

6. 2n^2-6 is came from this format something 1/2n^2+..... (i don't remember) or you refer to your text book

Answer 8

I'm in a hurry and the rest need thought.
But I answered the easy ones. I hope they'll still be useful:

A. S=5
E. 3x(squared) + 11x - 4

Sorry. :)