simplify the sum state any restrictions on the variables (x+6)/x^2-36 + 1/x-6
PLEASE SHOW YOUR WORK
Answers
Answer:
x ≠ 6
Step-by-step explanation:
Simplify The Equation,
[tex] \frac{(x + 6)}{x {}^{2} - 36} + \frac{1}{x - 6} \\ = \frac{(x + 6)}{ ({x})^{2} -(6)^{2} } + \frac{1}{x - 6} \\ = \frac{(x + 6)}{(x + 6)(x - 6)} + \frac{1}{x - 6} \\ = \frac{(x + 6) + 1(x + 6)}{(x + 6)(x - 6)} \\ = \frac{x + 6 + 1x + 6}{(x +6)(x - 6)} \\ = \frac{2x + 12}{(x + 6)(x - 6)} [/tex]
Factorize The Equation,
[tex] \frac{2x + 12}{(x + 6)(x - 6)} \\ = \frac{2(x + 6)}{(x + 6)(x - 6)} \\ = \frac{2}{x - 6} [/tex]
From the Given function,
x-6 ≠ 0
x ≠ 6
Thus x ≠ 6 is a restriction.
The solution is : x ≠ 6, is a restriction on the variables
(x+6)/x^2-36 + 1/x-6.
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
Simplify The Equation,
(x+6)/x^2-36 + 1/x-6
=(x+6)/(x-6) (x+6) + 1/x-6
= (x+6)+(x+6) /(x-6) (x+6)
=(2x+12)/(x-6) (x+6)
Factorize The Equation,
(2x+12)/(x-6) (x+6)
= 2(x+6) /(x-6) (x+6)
=2/ (x-6)
From the Given function,
x-6 ≠ 0
x ≠ 6
Thus x ≠ 6 is a restriction.
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Related Questions
The perimetre of a rectangle is 38cm length is 12.5, What is the Area?..
Answers
Answer:
[tex]\boxed{\mathtt{Area = 81.25cm^{2}}}[/tex]
Step-by-step explanation:
[tex]\textsf{For this problem, we are asked to solve for the \underline{Area} of a Rectangle.}[/tex]
[tex]\textsf{We are given the \underline{Perimeter}, and the \underline{Length}.}[/tex]
[tex]\textsf{We should begin by identifying the formulas for Perimeter and Area.}[/tex]
[tex]\mathtt{Perimeter = Length + Length + WIdth + Width}[/tex]
[tex]\mathtt{Area = Length \times Width}[/tex]
[tex]\textsf{Because we're given the Perimeter and the Length, we can identify the Width.}[/tex]
[tex]\large\underline{\textsf{Substitute:}}[/tex]
[tex]\mathtt{38 cm = 12.5 + 12.5 + Width + Width}[/tex]
[tex]\large\underline{\textsf{Combine Like Terms:}}[/tex]
[tex]\mathtt{38 cm = 25 cm+ 2(Width)}[/tex]
[tex]\large\underline{\textsf{Subtract 25 from both sides:}}[/tex]
[tex]\mathtt{13 cm = 2(Width)}[/tex]
[tex]\large\underline{\textsf{Divide By 2:}}[/tex]
[tex]\mathtt{6.5 cm = Width}[/tex]
[tex]\textsf{Now that we know the Width, we can identify the Area.}[/tex]
[tex]\large\underline{\textsf{Substitute:}}[/tex]
[tex]\mathtt{Area = 12.5 cm \times 6.5cm}[/tex]
[tex]\boxed{\mathtt{Area = 81.25cm^{2}}}[/tex]
If anyone can do this you will get lots of points please help
Answers
The angles which are formed inside the two parallel lines, when intersected by a transversal, are equal to its alternate pairs.
q and t are alternate interior
r and k are alternate interior
W is 79
The mistake he made is equating an alternate interior angle to an alternate exterior angle
1 .When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles. These angles are always equal.
Alternate exterior angles are those angles that have different vertices, lie on the alternate sides of the transversal, and are exterior to the lines. When a transversal intersects two parallel lines, the alternate exterior angles formed are always equal.
2. check the picture for translation of the angles
3. 8 angles are created, 4 alternate interior and 4 alternate exterior
Angles 6,4 and 2 are congruent to 8
In question 8, the equation above must be equal to the written degree below. Your image isnt so clear
HELP ASAP DUE IN 5 MINUTES!!!!!!!!!!!!!!!!!!!
The singh family orderd a large pizza with a diameter of 20 inches for dinner. If one of the members ate one-eighth of the pizza, how many square inches of pizza are remaining? (use 3.14 for pi)
Answers
Answer:
275.5 square inches of pizza remaining
Step-by-step explanation:
The area of a circle can be calculated using the formula A = πr^2, where r is the radius of the circle.
The diameter of the pizza is 20 inches, so the radius is half of that, or 10 inches.
The area of the entire pizza is:
A = πr^2 = 3.14 x 10^2 = 314 square inches.
If one member of the family ate one eighth of the pizza, then the amount of pizza remaining is 7/8 of the original amount.
The remaining area of the pizza is:
(7/8) x 314 = 275.5 square inches.
Therefore, there are 275.5 square inches of pizza remaining.
Add the algebraic expressions.
a. -6p²+8q² - 2pq- 5 and 2p² -3q² -2pq+3
b. 5x+6y and -8x -3y
Grade8
Answers
Answer:
a: -4p² + 5q² - 4pq - 2
b: -3x + 3y
Step-by-step explanation:
When we combine like terms, we get:
(-6p²+8q² - 2pq- 5) + ( 2p² -3q² -2pq+3) = -4p² + 5q² - 4pq - 2
Therefore, the simplified expression is -4p² + 5q² - 4pq - 2.
Next:
(5x+6y)+ (-8x -3y) = 5x - 8x + 6y - 3y
Combining like terms gives us:
5x - 8x + 6y - 3y = -3x + 3y
Therefore, the simplified expression is -3x + 3y.
Simplify by adding the like terms. 8b+9b+6a+3a.
Grade#8
Answers
Answer:
Step-by-step explanation:
the like terms are the terms with same algebraic terms and same power (indices) .
so,
8b+9b+6a+3a
you have to add 'b' terms and 'a' terms
∴ 17b+9a
Evaluate the following expression for the given value of X.
4.5x + 5.2 - x
x = 6.5
PLEASE HELP A.S.A.P (as soon as possible)
Answers
34.45 - 6.5
27.95
answer is 27.95
A student is buying thank you cards. Each than you card cost $2. The equation t = 2c represents the total cost, t, this student will spend to buy c cards. Which variable is the independent variable in the equation? Which is the dependent variable? Explain how you know.
Answers
Answer:
t is dependent and c is independent because if c increases so will t
The dependent variable, on the other hand, is the variable that is being measured or observed, and it is typically plotted on the y-axis of a graph. In this equation, "t" represents the total cost of the thank you cards, which is something that depends on the number of cards being purchased. The cost is not something that the student can control directly, but rather it is determined by the number of cards being purchased.
Therefore, in the equation t = 2c, "c" is the independent variable because it is being manipulated by the student, and "t" is the dependent variable because it depends on the value of "c".
Mateo’s old bedroom was a square with integer dimensions. His new bedroom is 3 feet wider and 2 feet longer. The increase in area is 46 ft^2. What were the dimensions of Mateo’s old bedroom?
Answers
Answer: 8
Step-by-step explanation:
8*8=64
8+3=11
8+2=10
11*10=110
110-64=46
A dinner plate has a circumference of 125.6 cm. What is the area of the dinner plate? (Use 3.14 for π)
A. 251.2 cm2
B. 1,256 cm2
C. 62.8 cm2
D. 2,512 cm2
Answers
area = 3.14 r^2
circumference = d * 3.14
To solve:
First we need to work backwards from the circumference to find the diameter- we start with 125.6 = 3.14 * d. We then divide by 3.14 to get 40 = d. Divide by 2 to get the radius and we get 20 cm. Then, we plug the radius into the area formula, getting us 3.14 * 20^2. 20^2 = 400, so we get 3.14 * 400. 3.14 * 400 = 1256, so the area is 1256 cm2.
Hope this helped
Gianna and her family went for a drive. They traveled 175 miles in 3 hours. What was their average speed?
Would you write an inequality or an equation?
Answers
To find the average speed, we divide the total distance traveled by the time taken:
Average speed = Total distance ÷ Time taken
Therefore, Gianna and her family's average speed is:
Average speed = 175 miles ÷ 3 hours = 58.33 miles per hour (rounded to two decimal places)
We use an equation to solve this problem.
Equation: Average speed = Total distance ÷ Time taken
Where:
Total distance = 175 miles
Time taken = 3 hours
Substituting these values into the equation, we get:
Average speed = 175 miles ÷ 3 hours
Therefore, the answer is an equation:
Average speed = 175 miles ÷ 3 hours
(I-Ready) How many square feet of outdoor carpet will we need for this hole? 11 ft 7 ft 6 ft 3 ft 2 ft
Answers
Write three paragraphs discussing how the universal idea of human kindness relates to the texts in the unit.
In paragraph 1, discuss and give examples of how the author shows human kindness is demonstrated in the story Thank You Ma'am.
In paragraph 2, discuss and give examples of how the author shows human kindness is demonstrated in the story The Strangers That Came to Town.
In paragraph 3, state a theme shared by both texts. Use evidence from the text to support the theme. Will mark brainlist and 100 points
Answers
In " The Convict and The Bishop," the bishop helped and defended Jean Valjean whom he didn't even know. While everybody else drove him out, the bishop tended to him. He gave Jean a bed to sleep in, a bed and he gave him comfort when nobody else would. This shows that people can be nice to others in need.
In " The Strangers That Came to Town," when Andy and Tom made mischief, they really hurt the Duviches. Thier father made them repay the family by catching 60 fish. When they gave the fish to the Duviches they were overjoyed and invited Andy and Tom's family to eat the fish. The Duviches were shown kindness by the father and returned the kindness by inviting Andy and Tom's family for a meal
How much alcohol must a pharmacist add to 10 cm^3 of an 8% alcohol solution to strengthen it to an 80% solution? PLS ANSWER URGENT THANKS
Answers
The pharmacist must add [tex]36 cm^3[/tex] of pure alcohol to the [tex]10 cm^3[/tex] of 8% alcohol solution to obtain an 80% alcohol solution.
What is alcohol ?Alcohol, also known as ethanol is a clear, colorless liquid that is produced by the fermentation of sugars and carbohydrates by yeasts.
Let's start by writing down the equation that relates the amount of alcohol in the original 8% solution to the amount of alcohol in the final 80% solution:
[tex]0.08 x 10 cm^3[/tex] [tex]+ x = 0.80 x (10 cm^3 + x)[/tex]
Here, x represents the amount of pure alcohol that we need to add to the [tex]10 cm^3[/tex] of 8% solution to obtain the desired 80% solution.
The left-hand side of the equation represents the amount of alcohol in the original solution (which is 8% alcohol), while the right-hand side represents the amount of alcohol in the final solution (which is 80% alcohol).
Now we can solve for x:
[tex]0.08 x 10 cm^3 + x = 0.80 x (10 cm^3 + x)[/tex]
[tex]0.8 cm^3 + x = 8 cm^3 + 0.8x[/tex]
[tex]0.2x = 7.2 cm^3[/tex]
[tex]x = 36 cm^3[/tex]
Therefore, the pharmacist must add [tex]36 cm^3[/tex] of pure alcohol to the [tex]10 cm^3[/tex] of 8% alcohol solution to obtain an 80% alcohol solution.
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Answer: The pharmacist must need 36 cubic centimeters of pure alcohol to 10 cm^3 of a 8% alcohol solution
PLEASE HELP ITS EASY! --According to the diagram, what is the value of x? -x=gray cups -1=gray balls x=white cups 1=white balls
Answers
My guess is 3 because there 5 on the other side and to make it equal you need to add 3
ONLY IF THERE THE SAME SIZE
2A. Find the area of a parallelogram with the following measurements.
a. base = 8cm, height=14cm b. base=18cm, height=6cm
Grade#7
Answers
Answer:
A) 112 [tex]cm^{2}[/tex]
B) 108 [tex]cm^{2}[/tex]
Step-by-step explanation:
Area = length times width
A)
a = lw
a = 8 x 14 = 112
B)
a = lw
a = 18 x 6 = 108
Helping in the name of Jesus.
Answer:
here you go.
Step-by-step explanation:
area of parallelogram= BASE ×HEIGHT
Area=18×6
therefore the answer will be 108The graph shows point L. What is the location of a point 5 units down and 2 units to the left of point L?
Plot the point on the coordinate grid. Need help please will give 20 points
Answers
Answer: the answer is 1,-3
Step-by-step explanation:
Factor the expression completely.
6x+7x
Answers
Answer:
Step-by-step explanation:
6x+7x= ?
- factor x
x(6+7)
x(13)
= 13x
therefore, 13x is your answer.
Rosa spent $11.52 on 8 candy necklaces for each of her two friends. How much did each necklace cost?
Answers
Answer:
Step-by-step explanation:
a
$1.44
Explanation:
Divide 11.52 by the number of candy necklaces (8) to get the price of each necklace.
please help I beg yoi and if its right ill mark you as branliest and ill give 20 points please hurry im timed
Answers
Answer:
Step-by-step explanation:
x 1 or y1
Answer:
1. y = 0
2. y = 1
3. y = 2
4. y = 3
Step-by-step explanation:
It's pretty easy just substitute.
HELP ME IT'S DEALING WITH CONVERTING MEASUREMENTS OF CAPICTY
Answers
Answer:
16 pints
32 cups
2 gallons
Step-by-step explanation:
Total: 8 quarts.
Pints:
There are 2 pints in 1 quart.
It is given that there are 8 quarts. Multiply 2 pints with 8 quarts:
(8 quarts) * (2 pints/1 quart) = 16 pints/8quarts
16 pints
Cups:
There are 4 cups in 1 quart.
It is given that there are 8 quarts. Multiply 4 cups with 8 quarts:
(8 quarts) * (4 cups/1 quart) = 32 cups/8 quarts
32 cups.
Gallons:
There are 4 quarts in 1 gallon.
It is given that there are 8 quarts. Divide 4 quarts with 8 quarts:
(8 quarts)/(4 quarts per gallon) = 2 gallons
2 gallons.
~
Learn more about converting measurements, here:
https://brainly.com/question/17118357
Answer:
16 pints, 32 cups, 2 gallons
Step-by-step explanation:
There are 8 quarts, and I just converted each one.
Answer the questions below. Use the video to
help you! Follow directions and submit your
work.
Arrange the decimals from least to greatest.
(1) 0.045, 4.57, 0.457, 0.42
(2) 1.5, 1.7, 0.17, 0.9
(3) 9.0, 0.09, 0.00009, 0.009, 0.9
Answers
Answer:
The answer is the following
Step-by-step explanation:
1) 0.045, 0.42, 0.457, 4.57
2)0.17, 0.9, 1.5, 1.7
3)0.00009, 0.009, 0.09, 0.9, 9.0
2) 0.17, 0.9, 1.5, 1.7
3) 0.00009, 0.009, 0.09, 0.9, 9.0
All in order of Ascending.
The prism below is made of cubes which measure 1/2 of a centimeter on one side. What is the volume?
Answers
Answer: A
Step-by-step explanation:
You multiply 5*3*3
A box of chocolates contains milk (M), white (W) and dark (D) chocolates. Each chocolate can have one of three centres: caramel (C), mint (M) or nut (N).
a) How many different combinations of chocolate and centre are possible?
b) One possible combination is milk and caramel. Write down all the other possible combinations, write your answers like this: (M, C) You must write all of your answers on one line.
Answers
Answer:
(M,M)(M,N)(W,C)(W,M)(W,N)(D,C)(D,M)(D,N)
Step-by-step explanation:
I’m so confused, I liked Chapter 10 until this.
Answers
B) 75%
C) 50%
D)25%
Please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
#2
Step-by-step explanation:
A'(-7,3) C'(-4,6) D'(-7,6)
What is the value of x?
Enter your answer in the box.
x =
Answers
Answer:
12
Step-by-step explanation:
10x-20+6x+8=180
16x-12=180
16x=180+12
16x=192
x=192/16
x=12
Answer: 12
Step-by-step explanation:
Please help me out I am bad at doing surface area of pyramids image below
Answers
Answer: A= [tex]\sqrt{3} (side^{2} )[/tex]=[tex]\sqrt{3} (2^{2} )[/tex] ≈6.9282 [tex]yd^{2}[/tex]
Step-by-step explanation: In order to find the surface area of the tetrahedron in this case you need to know the side length which is already provided. The equation [tex]\sqrt{3} (side^{2} )[/tex] is the square root of 3 multiplied by the square of the side (2) which gets you roughly ≈6.9282 square yards. And this equation is really easy to do with any tetrahedron. (: have a good rest of your day
Chai has a tea shop.
Chai has 10 workers at her shop. She pays them $49 a hour. In two weeks,how much money will she have gave to her workers?
Answers
Answer:
The answer to your problem is, $16464
Step-by-step explanation:
First we want to figure out how much ours are in two weeks which is:
336 Hours.
So we can do easy math 49 x 336 =
16464.
Convert it to money $16464
Thus the answer to your problem is, $16464
Add the algebraic expressions.
a. -6p²+8q² - 2pq- 5 and 2p² -3q² -2pq+3
b. 5x+6y and -8x -3y
Grade8
Answers
Answer:
a=-4p^2-4pq+5q^2-2
b=-3x+3y
Step-by-step explanation:
PLEASE HURRY! Which pairs of variables would most likely have a positive association?
Gasoline in a car and how long you drive for
Temperature and the sales of ice cream
the height of students and their scores on a test
Answers
Gas in a car and how long you drive and temperature and ice cream