Which of the following is a rational number but not an integer -9 0 -4.3 3

<img src="https://tex.z-dn.net/?f=5x-%20%5Cdfrac%7B%20%5Csqrt%7B%209%20%7B%20x%20%7D%5E%7B%202%20%7D%20-6x%2B1%20%5Cphantom%7B%5

Morgarella [4.7K]

Answer:

$=5x+1$ or $=5x-1$

Step-by-step explanation:

One is given the following equation:

$5x-\frac{\sqrt{9x^2-6x+1}}{1-3x}$

The problem asks one to simplify the expression, the first step in solving this equation is to factor the equation. Rewrite the numerator and denominator of the fraction as the product of two expressions. Remember the factoring patterns:

$(a-b)^2=a^2-2ab+b^2$

$=5x-\frac{\sqrt{9x^2-6x+1}}{1-3x}$

$=5x-\frac{\sqrt{(3x-1)^2}}{-(3x-1)}$

Now simplify the numerator. Remember, taking the square root of a squared value is the same as taking the absolute value of the expression,

$=5x-\frac{\sqrt{(3x-1)^2}}{1-3x}$

$=5x-\frac{|3x-1|}{-(3x-1)}$

Rewrite the expression without the absolute value sign in the numerator. Remember the general rule for removing the absolute value sign:

$|a-b|\\=a -b$ or $(-a-b) = b-a$

$=5x-\frac{|3x-1|}{-(3x-1)}$

$=5x-\frac{3x-1}{-(3x-1)}$ or $=5x-\frac{-(3x-1)}{-(3x-1)}$

Simplify both expressions, reduce by canceling out common terms in both the numerator and the denominator,

$=5x-\frac{3x-1}{-(3x-1)}$ or $=5x-\frac{-(3x-1)}{-(3x-1)}$

$=5x-(-1)$ or $=5x-(1)$

Simplify further by rewriting the expression without the parenthesis, remember to distribute the sign outside the parenthesis by the terms inside of the parenthesis; note that negative times negative equals positive.

$=5x-(-1)$ or $=5x-(1)$

$=5x+1$ or $=5x-1$

6 0

2 years ago

Solve. i really need help z =

BlackZzzverrR [31]

$\dfrac{7z-1}{2}=3z-2\\
7z-1=6z-4\\
7z-6z=-4+1\\
z=-3$

5 0

3 years ago

One number is 6 more than a second number, the sum of the two numbers is 330. what are the numbers?

maksim [4K]

Let's have the first number, the larger number, be x. We'll have the second, smaller number be y.

We know that x = y + 6, since x is 6 greater than y.

We also know that 330 = x + y.

Because x = y + 6, 330 = y + 6 + y, which simplifies to 330 = 2y + 6.

Now all we need to do is simplify the equation. First, we subtract 6 from both sides:

330 - 6 = 324

2y + 6 - 6 = 2y.

So we have 324 = 2y. Then we divide both sides by 2 to get:

162 = y

Plug in y = 162 into the equation x = y + 6 to get:

x = 162 + 6

x = 168

Let's check to make sure our answer is right. 168 is 6 more than 162. 162 + 168 equals 330. So our two numbers are 168 and 162.

7 0

3 years ago

Ben works for software company in Cleveland. To train new employees, Ben travels to their two other locations, Buffalo and Phila

Andru [333]

Answer:

Explanation:we will solve this question with help of linear programming.

Now, let Ben goes x times in buffalo trip and goes y times in Philadelphia trip. Thus, according to the question, Min Z= 180x+300y

And s.t.r. 2x+3y≤105, where x≥5, y≥15.

since at (0,0) 0≤105(true), so area of 2x+3y≤105 will cover the origin.

But, 0≥5 and 0≥15 are false, so their area will not cover the origin.

Thus, after drawing the graph of these three lines we will get a feasible reason of triangle ABC, where point A≡(5,31.667), B≡(5,15), and C≡(30,15)

Z at A- 180×5+300×31.667=10,400.1

at B-180×5+300×15=1350( which is minimum.)

at C- 180×30+300×15=5,850

Thus, Ben should go 5 times to buffalo trip and 15 times to Philadelphia to minimize his cost which is $1350.

3 0

3 years ago

Pls help I don't understand !! !!

NemiM [27]

100cm is equivalent to 1m so 500cm is equivalent to 5m. What you need to do is divide 500cm (5metres) by 25cm (one quarter of a metre). So the number sentence using 'division' should look like 500cm divided by 25cm which equals 20. Don't forget to use proper symbols for division though. Let me know if this helps:)

5 0

3 years ago

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