Simplify the rational expression. State any excluded values.
Answers
You get (x - 6)(x + 6) on the top.
On the bottom, you can undistribute (pull out) -7x.
This gives you -7x(x-6) on the bottom.
Now you can cancel like terms in the numerator and denominator.
You can cancel the (x-6).
You can also move the negative sign from the 7x to the (x + 6)
This leaves you with -(x + 6) over 7x, or (6 - x) over 7x.
To find excluded values, all you need to know is that you can't divide by zero under any circumstances, and you can't have a zero on the top in a rational expression.
The only values for x that would make either of these statements true are if x = 0 (7 × 0 = 0 on the bottom), or if x = 6 (6 - 6 +0 on the top)
So the answer is (6 - x) over 7x, x ≠ 0, 6
Related Questions
Normal line to the curve y=ln(2x+a) at x=1 is perpendicular to x-4y+2 = 4ln3. Find the value of a.
To the lovers of math: challenge : please helpA company manufactures high-powered fountains that can be used to create elaborate water shows set to light and music.The company makes three models offountains, each of which can launch a vertical stream of water to a different height, as indicated in the table below. Model A Model B Model Cheight 77 100 240 time to fall (s) 2.194, ----, ---- initial velocity 70.2 , ----, 123.9 complete the following tasks, filling in the missing values in the table as you find them:(1)Find the time water would take to fall from each height in the table back to its starting level.(2)Find the initial upward velocity required for fountain B to launch the water to its maximum height(3)Create a function that will give you the minimum initial upward velocity ,v ,required to launch water to any given height , h. thank you
Which shows 60^2 − 40^2 being evaluated using the difference of squares method?(A)60^2-40^2=(3600+1600)(3600-1600)=10,400,000 (B)6^2-40^2=3600-1600=2,000 (C)60^2-40^2=(60-40)^2=20^2=400 (D)60^2-40^2=(60+40)(60-40)=(100)(20)=2,000
8u+3-u+2u=9 please help me I really need help in this
Answers
Area = bh/2
where b is the base and h is the height.
We calculate as follows:
270 = b (15) / 2
b = 36
hypotenuse = sqrt ( 15^2 + 36^2 ) = 39
Answer:
hypotenuse = 39m
Step-by-step explanation:
Area of a triangle= 1/2 * base * height
where base = ?
height = 15
Plugin values into the formula:
270 = 1/2 base (15)
base = 270 (2)
15
base = 36
hypotenuse = √(base² + height²)
= √( 36² + 15² )
= 39
Answers
Consider julie's scores on three final exams (x), along with the class means and standard deviations: subject x mean standard deviation history 75 70 5 english 92 90 10 math 80 70 3 science 84 70 7 compared to the other students who took the test, in what class is was julie's highest score?
Answer: In order to find in what class Julie's has scored highest, we need to find the z score corresponding to Julie's score. The subject who has the highest z score will indicate that Julie has scored highest in that subject.
Z score for History:
z score for english:
z score for math:
z score for science:
Since the z score for Math is highest, therefore, in Math class Julie's score is highest.
Parallel
Perpendicular
They intersect at an angle other than 90 degrees
Answers
Answer:
Perpendicular
Step-by-step explanation:
Here, we want to know the relationship between the two lines .
The easiest way to go about this is to get their slopes;
Mathematically, the equation of a straight line can be expressed in the form;
y = mx + c
where m is the slope;
Hence;
2x -5y = 10
Isolating the y part
5y = 2x -10
divide through by 5
y = 2/5x - 2
So the slope here is 2/5
for the second line
10x + 4y = 20
Divide by 2 all through
5x + 2y = 10
Isolate y
2y = 10-5x
Divide by 2 again
y = 5 -5/2x
The slope here is -5/2
What do we notice? we can see that if we multiply the two slopes by each other, we get -1
That is;
2/5 * -5/2 = -1
What this means is that both lines are perpendicular.
This is because the slopes of perpendicular lines, when multiplied by each other = -1
Final answer:
The two given lines, 2x - 5y = 10 and 10x + 4y = 20, intersect at an angle other than 90 degrees. We determined this by finding the slope of each line and seeing that they are neither equal (for parallel lines) nor negative reciprocals (for perpendicular lines).
Explanation:
To determine the relationship between the lines 2x - 5y = 10 and 10x + 4y = 20, we need to analyze their slopes. Both equations can be rewritten in slope-intercept form (y = mx + b) to determine their slopes. The first equation becomes y = (2/5)x - 2, and the second equation becomes y = (-10/4)x + 5.
The slopes of the two lines are m1 = 2/5 and m2 = -10/4. Since the slopes are different, the lines are not parallel. To determine if they are perpendicular, we need to check if their slopes are negative reciprocals.
The product of the slopes is (2/5)(-10/4) = -4/5. Since the product is not -1, the lines are not perpendicular. Therefore, the correct relationship is that the lines intersect at an angle other than 90 degrees.
Learn more about Relationship between two lines here:
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B) yes, by SAS criterion
C) yes, by SSA criterion
D) no, not possible to tell.
Answers
Triangle ABE have these angles:
∠ABE = 45° ; ∠EAB = 63° ; missing ∠ is 72°
Triangle MNP have these angles:
∠MNP = 72° ; ∠NMP = 63°; missing ∠ is 45°
AA criterion is "angle,angle" criterion. It means that the two triangles have at least two of their angles equal. Since a triangle have a total of 180°, when two of their angles are equal, the 3rd angle is also equal.
As you can see, both triangles have 45°, 63°, and 72° measurement of angles. Thus, they are similar.
Answers
-------
Answers
m - 9 - 7 = ?
? = 0
Now, let's add the number 16 to the sides that you're working with
Here's what I am talking about in case you don't know what I am talking
m - 16 = 0
+ 16
-------
16
So, the value of m is 16 ;
This is basic mathematics.Just practice your addition and subtraction facts in the problem like this
16-9=7
hope this helped:)