Answers
[tex] \tt : \implies \dfrac{x+2}{x-2} + \dfrac{x-2}{x+2} = \dfrac{5}{6}[/tex]
[tex] \tt : \implies \dfrac{(x+2)(x+2) + (x-2)(x-2)}{(x-2)(x+2)} = \dfrac{5}{6}[/tex]
[tex] \tt : \implies \dfrac{(x+2)^{2} + (x-2)^{2}}{(x-2)(x+2)} = \dfrac{5}{6}[/tex]
Now, we know that :
[tex] \large \underline{\boxed{\bf{(a+b)^{2} = a^{2} + b^{2}+ 2ab}}}[/tex][tex] \large \underline{\boxed{\bf{(a-b)^{2} = a^{2} + b^{2} - 2ab}}}[/tex][tex] \large \underline{\boxed{\bf{(a+b)(a-b) = a^{2} - b^{2}}}}[/tex][tex] \tt : \implies \dfrac{x^{2}+2^{2}+ 2 \times x \times 2 + x^{2}+2^{2} - 2 \times x \times 2 }{x^{2}-2^{2}} = \dfrac{5}{6}[/tex]
[tex] \tt : \implies \dfrac{x^{2}+ 4 + \cancel{4x} + x^{2}+ 4 - \cancel{4x}}{x^{2}-4} = \dfrac{5}{6}[/tex]
[tex] \tt : \implies \dfrac{x^{2} + x^{2} + 4 + 4}{x^{2}-4} = \dfrac{5}{6}[/tex]
[tex] \tt : \implies \dfrac{2x^{2} + 8}{x^{2}-4} = \dfrac{5}{6}[/tex]
By cross multiply :
[tex] \tt : \implies (2x^{2} + 8)6= 5(x^{2}-4)[/tex]
[tex] \tt : \implies 12x^{2} + 48 = 5x^{2}-20[/tex]
[tex] \tt : \implies 12x^{2} + 48 - 5x^{2} + 20 = 0[/tex]
[tex] \tt : \implies 7x^{2} + 68 = 0[/tex]
[tex] \tt : \implies 7x^{2} + 0x + 68 = 0[/tex]
Now, by comparing with ax² + bx + c = 0, we have :
a = 7b = 0c = 68By using quadratic formula :
[tex] \large \underline{\boxed{\bf{x = \dfrac{-b \pm \sqrt{b^{2} - 4ac}}{2a}}}}[/tex]
[tex] \tt : \implies x = \dfrac{-(0) \pm \sqrt{(0)^{2} - 4(7)(68)}}{2(7)}[/tex]
[tex] \tt : \implies x = \dfrac{0 \pm \sqrt{0 - 1904}}{14}[/tex]
[tex] \tt : \implies x = \dfrac{\pm \sqrt{- 1904}}{14}[/tex]
[tex] \tt : \implies x = \dfrac{\pm \sqrt{2\times 2\times 2\times 2\times 7\times 17}}{14}[/tex]
[tex] \tt : \implies x = \dfrac{\pm \cancel{2} \times 2\sqrt{7\times 17}}{\cancel{14}}[/tex]
[tex] \tt : \implies x = \dfrac{\pm2\sqrt{119}}{7}[/tex]
[tex] \large \underline{\boxed{\bf{x = \dfrac{\pm 2\sqrt{119}}{7}}}}[/tex]
Hence value of [tex] \bf x =\dfrac{\pm 2\sqrt{119}}{7}[/tex]
Answer:
I think this answer is right if no tell me please :)
Related Questions
Solve the proportion for e
Please helpp meee
Show work if can thank you
Answers
Answer:
17
Step-by-step explanation:
Cross multiply: 51 × 6 = 306Divide: 306 ÷ 18 = 17So, e = 17I hope this helps!
Make a function table for y=-3x+3
Answers
-2 | 9
-1 | 6
0 | 3
1 | 0
2 | -3
For which of the following conditions is it not appropriate to assume that the sampling distribution of the sample mean is approximately normal?
A random sample of 8 taken from a normally distributed population
A random sample of 8 taken from a normally distributed population
A
A random sample of 50 taken from a normally distributed population
A random sample of 50 taken from a normally distributed population
B
A random sample of 10 taken from a population distribution that is skewed to the right
A random sample of 10 taken from a population distribution that is skewed to the right
C
A random sample of 75 taken from a population distribution that is skewed to the left
A random sample of 75 taken from a population distribution that is skewed to the left
D
A random sample of 100 taken from a population that is uniform
Answers
Answer:
C
Step-by-step explanation:
Using the Central Limit Theorem, it is found that the option in which is it not appropriate to assume that the sampling distribution of the sample mean is approximately normal is:
C) A random sample of 10 taken from a population distribution that is skewed to the right
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.In option C, there is an skewed variable and a sample size less than 30, hence, the Central Limit Theorem is not applicable.
A similar problem is given at https://brainly.com/question/4086221
Name the polynomial below.
x2 + 3x – 11
Answers
Answer:
a second power trinomial
Step-by-step explanation:
The angle of elevation from a park bench 724 feet from the base of the Gateway Arch in St. Louis, Missouri is 22°. How tall is the Gateway Arch, rounded to the nearest whole number?
Answers
Answer:
Gateway Arch is [tex]292.46[/tex] feet tall
Step-by-step explanation:
As we know,
the horizontal distance from the gate of the Arch to the bench [tex]= 724[/tex] feet
The angle of elevation is [tex]22[/tex] degree
Let H be the height of the gate be "H"
Tanθ= Perpendicular/Base
Substituting the given values in above equation, we get -
[tex]tan 22 = \frac{H}{724} \\H = 724 * tan 22\\H = 724 * 0.404\\H = 292.46[/tex]feet
what is 1289 x 845 equal to
Answers
Answer: 1089205
Step-by-step explanation: I multiplied in different steps
state the domain and range of each relation.then state if the relation is a function
Answers
Step-by-step explanation:
I wish i can help but i dont know the answer. sosorry
Callie posted a cute cat video on a popular website. On the first day after she posted the video, the video had 5 views. On the second day, it had 15 views. On the third day, it had 45 views, and on the fourth day, it had 135 views.
A. How many views would you expect the video to have after 5 days? Explain how you found your answer.
B. Which type of reasoning did you use to solve this problem, deductive or inductive? (2 points)
Answers
Answer:
(A) 5th day: 405 views
(B) inductive
Step-by-step explanation:
Each day the views get multiplied by 3.
Answer:
A. I would expect the video to have 405 views after day 5. There is a pattern of the number being multiplied by 3.
B. Deductive reasoning
Step-by-step explanation:
(This is really going to explain BOTH questions at the same time)
Looking that the problem, the number of views keep going up. There is a multiplier behind this, we just don't know WHAT multiplier it would be. To find that out, divide 1 value by the one before it. I'll do 135 divided by 45 as an example. That would equal three. Now we know the multiplier is 3. So, now we need to multiply 135 by 3 to get 405 views after five days.
(This is really summarizing B, whilst answering A.)
Orchid wants to retile her bathroom floor, which has an area of 40 square feet. She is deciding between two types of custom tiles. The square tile is One-half foot by One-half foot and costs $0.45 per tile. The rectangular tile is 2 feet by One-fourth foot and costs $0.80 per tile.
Answers
Answer:
b. She should choose the rectangular tiles because the total cost will be $8 less.
Step-by-step explanation:
Which tile should Orchid choose to minimize costs? Explain.
a. She should choose the square tiles because the total cost will be $8 less.
b. She should choose the rectangular tiles because the total cost will be $8 less.
c. She should choose the square tiles because the total cost will be $14 less.
d. She should choose the rectangular tiles because the total cost will be $14 less.
Area of a square tile = 1/2 × 1/2
= 1/4
= 0.25 square feet
Area of rectangular tile = 2 × 1/4
= 2/4
= 0.5 square feet
Number of square tile needed = Area of the bathroom floor / Area of the square tile
= 40 square feet / 0.25 square feet
= 160
Number of square tile needed = 160
Cost of square tile needed = number of tiles × cost per tile
= 160 × $0.45
= $72
Cost of square tile needed = $72
Number of rectangular tile needed = Area of the bathroom floor / Area of the rectangular tile
= 40 square feet / 0.5 square feet
= 80
Number of rectangular tile needed = 80
Cost of rectangular tile needed = number of tiles × cost per tile
= 80 × $0.80
= $64
Cost of rectangular tile needed = $64
Cost of square tile needed = $72
Cost of rectangular tile needed = $64
Answer:
B
Step-by-step explanation:
Just took the quiz
HELP ILL GIVE BRAINLEY
Answers
Answer: 1/30
Step-by-step explanation:
The term quotient simply refers to the answer to a division equation. Because 1/a/b = 1/ab, 1/6/5 = 1/30.
Hope it helps <3 :D
Answer:1/30
Step-by-step explanation:
i did my math on paper
can you help me please
Answers
wrong one -----/////
. In the box below, type a division sentence for this repeated subtraction sentence. 24-y-y-y-y-y-y-y-y=024−y−y−y−y−y−y−y−y=0
Answers
Answer:
in espanish please
Step-by-step explanation:
.please
Answer:It’s important to know WHY. Great explanations are what makes Brainly awesomeExplain everything. Imagine that the person who was asking, knows nothing at all so you need to start from the very beginningAlways include the steps and/or background required to get to the final answer. Let’s help other people understand and solve future problems on their ownShow all the calculation if it is a numerical questionAlways include the steps and/or background required to get to the final answer. Let’s help other people understand and solve future problems on their own
Step-by-step explanation:
She measures it and finds out it is 24 feet long by 121 2 feet wide. She wants to know how many square feet of sod she will need to completely cover the yard. How much sod will Heather need to cover the yard?
Answers
24ft x 1212ft = 29,088 ft^2 of sod
For 15 points.Explain, in your own words, the steps necessary to solve a system of equations
using the substitution method.
Answers
First, what is an equation?
➳ A mathematical statement which shows that two algebraic expressions are equal is called and equation.
Or, LHS = RHS
Example:- 3x - 5 = x + 8
An equation is said to be a linear equation if it contains only one variable (literal) with highest power 1.
_______________________
Solving an equation:-
To solve the equation x + 5 = 7 means to find the value of an unknown algebraic quantity used in the equation.
Example:-
To solve the equation x + 5 = 7 means to find the value of x.To solve the equation 3y + 2 = 9 means to find the value of y.To solve the equation [tex]\sf \dfrac{2a}{3} + 4 = 10[/tex] means to find the value of a ⠀⠀⠀⠀⠀⠀and so on!⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
★ Rules for solving an equation by the substitution method:-
Rule ❶
If x = 2, the value of the expression 3x + 2 = 3 × 2 + 2 = 6 + 2 = 8
Rule ❷
If x = 0, the value of the expression 3x + 2 = 3 × 0 + 2 = 0 + 2 = 2
Rule ❸
If x = -2, the value of the expression 3x + 2 = 3 × -2 + 2 = -6 + 2 = -4
Now consider the algebraic expression 5x - 2y
This expression consists of variables x and y.
Now if :-
x = 3 and y = 2, 5x - 2y = 5 × 3 2 × 2 = 15 - 4 = 11x = 8 and y = 5, 5x - 2y = 5 × 8 - 2 × 5 = 40 - 10 = 30⠀⠀⠀⠀⠀⠀⠀⠀
The process of finding the value of an algebraic expression by substituting the given value of its variable is called substitution.⠀⠀
Which point below is NOT part of the
solution set?
Answers
Answer:
(-10,-10)
Step-by-step explanation:
Please help and can you sow work.
Answers
The area of a square is 81 cm 2 . Find the perimeter of the square.
PLEASE ANSWER!!!
Answers
Answer:
36
Step-by-step explanation:
9 times 4 buddy
area = 81 so side length ^2 = 81
square root each side
side length = 9
perimeter of square = 4 x side length
= 4 x 9 = 36cm
(20 POINTS!! HELP ASAP) Use the image above to identify and explain the relationship between the segments and circles A and B. In your explanation, be sure to include specific vocabulary and definitions for the relationships.
CD
Answers
Answer:
Step-by-step explanation:
ER is tangent to circle A and B , CD is tangent to circle B PQ is a arc in circle A
rCRS is an arc in circle B. And lastly Ps is also tangent to both circles.
Graph the inequality p < -8
Answers
Answer:
Step-by-step explanation:
Answer:
he showed it
Step-by-step explanation:
you mow 3 lawns in 5 hours. How long will it take to mow 9 lawns? Explain your thinking
Answers
PLEASE HELP THIS IS DUE IN 5 MINUTES!!!!
Answers
Answer:
Its D :) always do parenthesis first!
Step-by-step explanation:
the inequality 7-2/3x
Answers
Answer:
I love algebra anyways
The ans is in the picture with the steps how i got it
(hope this helps can i plz have brainlist :D hehe)
Step-by-step explanation:
2. How can Diego package all the 64 cookies so that each bag has the same number of them? How many bags can he make, and how many cookies will be in each bag? Find all the possible ways to package the cookies.
:
Divide 64 by multiple numbers, and if they divide evenly that’s how many will be in each bag for the number of bags (number you divided by). For example, dividing 64 by 8 (bags) would be 8 cookies in each bag. You can do this with multiple numbers as long as it goes in evenly
Answers
Answer:
Step-by-step explanation:
All the factors of 64 work for this:
1, 2, 3, 4, 8, 16, 32, 64
They all fit in evenly.
Wesley has a baseball sticker with a radius of 2.3 centimeters. Determine the circumference of his baseball sticker to the nearest tenth of a centimeter.
Answers
Answer:
14.4 centimeters
Step-by-step explanation:
The formula for circumference is: [tex]2\pi r[/tex]. In this case, the r (radius) is 2.3. Multiply it by 2 to get the diameter or 4.6. Then multiply 4.6 x [tex]\pi[/tex] (pi) to get 14.444. This rounded to the nearest tenth of a centimeter is 14.4.
Note:
I used 3.14 for [tex]\pi[/tex] (pi).
Hope it helps!
shine sold two tables at 9900 rupees each.he got 10% profit in one sale and 10% loss in the other.did the total sale result in a profit or loss? what percentage?
Answers
the total sale was neither a profit nor loss , 0%
Step-by-step explanation:
1st table :
100%-> 9900
110%-> 10890
10890-9900=990(earned)
------------------------------------------
2nd table :
100%->9900
90%-> 8910
9900-8910=990(lost)
990-990=0
hence the total sale was neither a profit nor loss , 0%
Solve the simultaneous equations by substitution
5x+6y=−11
5x=2y−3
Answers
Answer:
y= -1, x= -1
5x+6y=-11
-(5x-2y=-3)
8y=-8
y=-8/8
y= -1
5x+6(-1)=-11
5x-6 = -11
5x=-11+6
5x=-5
x=-5/5
x=-1
The required solution of the simultaneous equation is x = -1 and y = -1.
Given that,
To solve the given simultaneous equation,
5x+6y= −11
5x = 2y −3
Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
here,
5x = 2y −3 - - - - - (1)
5x+6y= −11
By substitution, from equation 1
2y - 3 + 6y = -11
8y = -8
y = -1
Now,
5x = -2 - 3
x = -1
Thus, The required solution of the simultaneous equation is x = -1 and y = -1.
Learn more about simultaneous equations here:
https://brainly.com/question/16763389
#SPJ2
Need help on this please help
Answers
a number increased by 25% becomes 30 the number is
Answers
Answer:
24
Step-by-step explanation:
Let 'x' be the number
x +25% of x = 30
x + 0.25x = 30
1.25x = 30
x = 30/1.25
x = 24
(WILL GIVE BRAINLIEST)
An oblique cylinder has a radius of 16 meters and a volume of 5,120(pi) cubic meters. Use Cavalieri’s Principle to solve for the height of the solid.
20 meters
25 meters
50 meters
250 meters
Answers
Answer: 20 meters
Step-by-step explanation:
We are told that an oblique cylinder has a radius of 16 meters and a volume of 5,120 pi cubic meters. We will use volume of oblique cylinder to find the height of our given cylinder. volume of a oblique cylinder= πr²hUpon substituting our given values in above formula we will get,5,120π m³ = π ( 16 m² × h )
5,120π m³ = π × 256 m² × h
Let us divide both sides of our equation by 100 pi.Therefore, height of our given oblique cylinder is 20 meters.
sorry if its wrong!!!
The price of a bicycle Rocco wants to pay is $282. If the sales cost is 4% of the total price how much sales tax will Rocco pay?
Answers
Answer:
$11.28
Step-by-step explanation:
Given data
Cost of bicycle= $282
tax= 4%
let us find the sales tax
=4/100*282
=0.04*282
=$11.28
Hence the sales tax is $11.28