Simplify x + 7 / x^2 + 4x - 21 (This is a fraction)
Answer choices - 1/x-3; where x does not equal 3.-7
x - 3; where x does not equal 3
1/x-7; where x does not eaul 7
x-7
Do the data in the table represent a direct varation or an inverse varition? writie an equation to model the data in the table
1|3|4|7|
5|15|20|35
Direct; y = 1/5x
inverse; xy = 5
direct; y = 5x
inverse; xy = 1/5
What are the excluded values of the funcation? y = 5/6x-72 (this is a fraction
answer choice - x = 0
x= 12
x=72
x=11
As for number one, is the answer 1/x-3 where x does not equal 3,7
#1
(x + 7)/(x^2 + 4x - 21)
= (x+7)/((x+7)(x-3))
= 1/(x-3) , x ≠ -7, 3
you had 7, but that would make the denominator 14 , which is perfectly ok to divide by
Hint:
take the denomiator and solve it for zero.
Whatever the solution, that x becomes the restricted value
And for #2 you are absolutely correct, the equation is indeed
y = 5x
#3, the 6x - 72 ≠ 0
6x ≠ 72
x ≠ 12
So x = 12 is the "excluded" value
You should try the first one yourself
These are usually done by factoring, as you can see in my other replies to your previous questions.
For this one, look at the numerator of x+7
It has disappeared in all the choices of answers.
That should give you a hint that it probably canceled.
So factor the bottom, knowing that one of the factors more than likely was x+7
Let me know what you got
#2. As a general rule, if y increased as x increases or if y decreases as x decreases you might be looking at a direct variation
If y increases as x decreases, or vice versa, you might be looking at an inverse variation.
If you first row are the x's : 1 3 4 7
and the 2nd row are the y's : 5 15 20 35
notice that the corresponding y is 1/5 of the x
do we have a direct variation of y = (1/5)x
#3, we cannot divide by zero.
So which value or values make our denominator zero?
that becomes your restriction.
btw, looking at your answers the question should have said:
y = 5/(6x-72)
for number 2, i thought it was y = 5x because if you multiply 5 by any of the numbers in the x colum, it equal y
Also for number 3, could you further explan, are you saying the answer is zero?
just give a simple answer ur wasting ur time by putting all this unnecessary wording
To simplify the fraction x + 7 / (x^2 + 4x - 21), we can factor the denominator and then cancel out any common factors between the numerator and denominator.
Let's factor the denominator (x^2 + 4x - 21):
1. Find two numbers that multiply to -21 and add up to +4. The numbers are +7 and -3.
2. Rewrite the middle term (4x) using the two numbers found in step 1. So, x^2 + 7x - 3x - 21.
3. Group the terms and factor by grouping, we have (x^2 + 7x) - (3x + 21).
4. Factor out a common factor from each group, resulting in x(x + 7) - 3(x + 7).
5. Finally, factor out the common factor (x + 7), and we get (x - 3)(x + 7).
Now, we can rewrite the fraction: (x + 7) / [(x - 3)(x + 7)].
Notice that we have a common factor of (x + 7) in both the numerator and denominator. We can cancel out (x + 7), leaving us with 1 / (x - 3).
Therefore, the simplified fraction is 1 / (x - 3), where x does not equal 3.
For the second question:
Based on the given table data, we need to determine if it represents a direct variation or an inverse variation.
In a direct variation, the ratio of y to x is constant. So, we can check if the ratios y/x are constant for each pair of values in the table.
Calculating the ratios:
3/1 = 15/5 = 20/4 = 35/7 = 3.
Since the ratios are constant (equal to 3), we can conclude that the data represents a direct variation.
The equation to model the data in the table is y = kx, where k is the constant ratio (in this case, k = 3). Thus, the equation is y = 3x.
For the third question:
To find the excluded values of the function y = 5/6x - 72, we need to identify the values of x for which the function is undefined (division by zero is undefined).
The function involves division, so we need to find the values of x that make the denominator (6x) equal to zero.
Setting the denominator equal to zero:
6x = 0
Solving for x, we find that x = 0.
Therefore, the excluded value of the function is x = 0.