<h2>Answer</h2>
<h2>Explanation</h2>
Remember that the square root function is not defined, in the set of real numbers, for negatives values, so its radicand (the thing inside the square root) must be zero or bigger than zero. In other words, to find the domain of a square root function, you should set the thing inside the radical bigger or equal to zero and solve for x. Let's find the domain of each one of our functions:
For
The thing inside the square root is 
, so we are setting that bigger or equal than zero and solve for x to find the domain of the function:
domain
For 
domain
For 
and 
domain
As you can see, the only one that has the domain is the first choice.
Answer:
the number of times in a month the train must be used, so that the total monthly cost without the pass is the same as the total monthly cost with the pass, is b. 24 times
Step-by-step explanation:
in normal purchase, train ticket (A) = $2.00
using frequent pass,
frequent pass (P) = $18
train ticket using frequent pass (B) = $1.25
Now, let assume the number of times in a month the train must be used = M
so,
A x M = P + (B x M)
$2.00 x M = $18 + ($1.25 x M)
($2.00 x M) - ($1.25 x M) = $18
M x ($2.00 - $1.25) = $18
M = $18 : $0.75
M = 24
Thus, the number of times in a month the train must be used is 24 times
These are 2 questions and 2 answers:
<span>1.
Question 1: The area of a rectangular carpet is given by the trinomial 5x^2 - 3x -
14. What are the possible dimensions of the carpet? Use factoring.
Answer: 5x^2 -3x -14
Explanation:
You might probe the different pairs of factors given in the answer choices to check wich product is equal to the oirginal polynomial or you can factor from zero.
I will show you how to factor that polynomial from zero:
1) given: 5x^2 - 3x - 14
2) multiply and divide by the leading coefficient =>
5 [5x^2 - 3x -14 ]
----------------------
5
3) Enter the the factor 5 inside the parenthesis:
5.5x^2 - 5.3x - 5.14
--------------------------
5
4) rearrange conviniently to show (5x) as a common factir of the first two terms
(5x)^2 - 3(5x) - 70
--------------------------
5
5) factor the numerator using 5x as common term of the two binomials:
(5x ) ( 5x ) <----> open the parenthesis
(5x - ) (5x + ) <-----> include the signs
(5x - 10) (5x + 7) <---> two numbers that add up - 3 and their product is - 70
=>
(5x - 10)(5x + 7)
---------------------
5
6) divide (5x - 10) by 5 => x - 2
7) factored expression
(x - 2) (5x + 7)
8) Conclusion: the answer is the option B. (5x + 7) and (x - 2)
2. Question 2. The area of a rectangular barnyard is given by the trinomial 6x^2 +
7x – 20. What are the possible dimensions of the barnyard? Use factoring
Answer: </span><span><span>option C. (2x + 5)(3x - 4)</span>
Explanation:
The procedure is the same of the question 1.
1) given: 6x^2 + 7x - 20
2) multiply numerator and denominator by 6 and rearrange to show (6x) as common factor ot the first two terms =>
(6x)^2 + 7(6x) - 120
--------------------------
6
3) factor the numerador using 6x as common factor ot two binomials, and simplify:
(6x + )(6x - )
(6x + )(6x - )
(6x + 15) (6x - 8)
=>
(6x + 15)(6x -8)
---------------------
6
(6x + 15)(6x - 8)
---------------------- =
3.2
(6x + 15) (6x - 8)
------------- . ------------ =
3 2
(2x + 5)(3x - 4)
4) answer: option C. (2x + 5)(3x - 4)</span>
I believe it would be all of the above let me know if it is right
