simplify;a/2(a+b)+b/2(a-b)​

Answers

Answer 1

Answer:

[tex]\huge\boxed{\sf \frac{a^2+b^2}{2(a^2-b^2)}}[/tex]

Step-by-step explanation:

=> [tex]\sf \frac{a}{2(a+b)} + \frac{b}{2(a-b)}[/tex]

LCM = 2(a+b)(a-b)

=> [tex]\sf \frac{a(a-b)+b(a+b)}{2(a+b)(a-b)}[/tex]

Simplifying further

=> [tex]\sf \frac{a^2-ab+ab+b^2}{2(a^2-b^2)}[/tex]

=> [tex]\sf \frac{a^2+b^2}{2(a^2-b^2)}[/tex]

Answer 2

[tex]\dfrac{a}{2(a+b)}+\dfrac{b}{2(a-b)}=\\\\\dfrac{a(a-b)}{2(a+b)(a-b)}+\dfrac{b(a+b)}{2(a+b)(a-b)}=\\\\\dfrac{a^2-ab}{2(a^2-b^2)}+\dfrac{ab+b^2}{2(a^2-b^2)}=\\\\\dfrac{a^2+b^2}{2(a^2-b^2)}[/tex]


Related Questions

what is the change in each term of the sequence? 0.8, 1, 1.2, 1.4, 1.6​

Answers

Begin by studying the pattern.

Notice that the difference between 0.8 and 1 is 0.2.

In other words, 0.8 + 0.2 is 1.

In the same way, 1 + 0.2 is 1.2.

1.2 + 0.2 is 1.4 and 1.4 + 0.2 is 1.6.

So we can see that the difference

between each of the terms is 0.2.

Answer:

+.2

Step-by-step explanation:

To find the common difference, take the second term and subtract the first term

1 - .8 = .2

Check by subtracting the second term from the third term

1.2 - 1 = .2

The common difference is .2

In March, Mateo ran 19 miles. In April, he ran twice as many miles as he ran in March. In May, he ran four times as many miles as he did in April. How many total miles did Mateo run in the three months? Enter your answer in the box.

Answers

Answer:

209

Step-by-step explanation:

march = 19 miles

april = 19 times 2 = 38

may = 38 times 4 = 152

so that'd be 19 + 38 + 152 = 209 miles in total.

209 miles Mateo ran in the three months.

What is Simplification?

Simplification in mathematical terms is a process to convert a long mathematical expression in simple and easy form.

Given that,

Mateo ran in March = 19 miles,

Also,

Mateo ran in April = 2 times of ran in March = 2 x 19 = 38 miles

Mateo ran in May = 4 times of ran in April = 4 x 38 = 152 miles.

Total distance ran by Mateo in all three months

= ran in March + ran in April + ran in May

= 19 + 38 + 152

= 209 miles.

Mateo ran 209 miles in all three months.

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HELP! URGENT!
Alice wrote three consecutive even numbers. The sum of these numbers was 252.

Pat wrote three consecutive odd numbers. Pat's numbers were larger than Alice's numbers.

The difference between the largest of Pat's numbers and the largest of Alice's numbers was 25.

What was the sum of Pat's numbers?

Answers

Answer:

333

Step-by-step explanation:

Let a represent Alice's numbers and p represent Pat's numbers.

Alice wrote three consecutive even numbers. The sum of the three is 252. This means:

[tex]a+(a+2)+(a+4)=252[/tex]

The first term is even. Each consecutive even term is two more than the previous term. Simplify:

[tex]3a+6=252\\3a=246\\a=84[/tex]

In other words, Alice's first number was 84.

Pat wrote three consecutive odd numbers. His numbers were larger than Alice's numbers. Similar to Alice, we can write:

[tex](p+1)+(p+3)+(p+5)=x[/tex]

The first term is odd. Each consecutive odd term will be 1 more, then 3 more, then 5, etc. We want to find Pat's sum, or x.

We are told that the difference between the largest of Pat's and Alice's  numbers is 25. Therefore:

[tex](p+5)-(a+4)=25[/tex]

Simplify. Substitute a. Solve for p:

[tex]p-a+1=25\\p-84=24\\p=108[/tex]

Therefore, Pat's sum is:

[tex](108+1)+(108+3)+(108+5)=333[/tex]

What is the volume of this rectangular prism?
2 cm
7/3 cm
2 cm

Answers

Answer
9.3
Explanation
I got it right

Answer:

28\3

Step-by-step explanation:

Please answer this question now

Answers

Answer:

1109.12

Step-by-step explanation:

Megan leaves her house at 4:15 to go soccer practice. It takes her 35 minutes to get there. Her practice is two hours long. Then, she drives home, which takes 40 minutes. What time does she get back home?

Answers

Answer:

7:35

Step-by-step explanation:

we take the 35 and 45 and add it together, then take out the 60 minutes and put that in as an hour. the practice is two hours long plus the hour we took out. then the remaining minutes are 20. we add 20 minutes and three hours

Maria cut four equivalent lengths of ribbon. Each was 5 eighths of a yard long. How many yards of fabric did she cut?

Answers

Answer:

2.5 Yards

Step-by-step explanation:

Multiply 5/8 by 4

ASAP!!!!!!!!! PLEASE help me with this question! This is really urgent! No nonsense answers please.

Answers

Answer:

[tex]\huge\boxed{x = 36\°}[/tex]

Step-by-step explanation:

According to secant angle theorem:

[tex]x = \frac{1}{2} (mCDF-mBJH)[/tex]

Where mCDF = 140 , mBJH = 68

[tex]x = \frac{1}{2} (140-68)[/tex]

[tex]x = \frac{1}{2} (72)[/tex]

x = 36°

Kelli swam upstream for some distance in one hour. She then swam downstream the same river for the same distance in only 6 minutes. If the river flows at 5 km/hr, how fast can Kelli swim in still water?

Answers

Answer:

6.11km/hr

Step-by-step explanation:

Let the speed that Kelli swims be represented by Y

Speed of the river = 5km/hr

Distance = Speed × Time

Kelli swam upstream for some distance in one hour

Swimming upstream takes a negative sign, hence:

1 hour ×( Y - 5) = Distance

Distance = Y - 5

She then swam downstream the same river for the same distance in only 6 minutes

Downstream takes a positive sign

Converting 6 minutes to hour =

60 minutes = 1 hour

6 minutes =

Cross Multiply

6/60 = 1/10 hour

Hence, Distance =

1/10 × (Y + 5)

= Y/10 + 1/2

Equating both equations we have:

Y - 5 = Y/10 + 1/2

Collect like terms

Y - Y/10 = 5 + 1/2

9Y/10 = 5 1/2

9Y/ 10 = 11/2

Cross Multiply

9Y × 2 = 10 × 11

18Y = 110

Y = 110/18

Y = 6.1111111111 km/hr

Therefore, Kelli's can swim as fast as 6.11km/hr still in the water.

PT.1     Kelli swam upstream for some distance in one hour. She then swam downstream the same river for the same distance in only 6 minutes. If the river flows at 5 km/hr, how fast can Kelli swim in still water?

Choose the most logical value for the variable to represent.

Let x = Kelli's swimming speed in still water

PT.2    Which expression represents the distance Kelli traveled upstream?

1(x – 5)

PT.3     Which expression represents the distance Kelli traveled downstream?

0.1(x + 5)

PT.4     Solve the equation x – 5 = 0.1(x + 5) for x. Round your answer to the nearest hundredth.  Kelli can swim about 6.11  km/hour.

FWML is a parallelogram. Find the values of x and y. Solve for the value of z, if z=x−y.

Answers

Answer:

x = 5, y = 8, z = -3

Step-by-step explanation:

Opposite sides of a parallelogram are congruent so to find x:

x + 7 = 3x - 3

-2x = -10

x = 5

To find y:

y + 2 = 2y - 6

-y = -8

y = 8

Therefore, z = x - y = 5 - 8 = -3.

10 points to the person who answers this whole thing and I will mark you as brainliest.

Answers

Answer:

Step-by-step explanation:

Perimeter is found by adding together all the lengths of the sides. For us, that is x + (2x + 5) + (6x - 17) + (3x + 2). Now we will just combine like terms. We can also drop the parenthesis because they do nothing for us and mean nothing to the problem.

x + 2x + 5 + 6x - 17 + 3x + 2 becomes

12x - 10

The product of 2 rational numbers is -16/9 . If one of the numbers is -4/3 find the other plz fast

Answers

Answer:

4/3

Step-by-step explanation:

let the other number be x.

-4/3 x=-16/9

x=-16/9×-3/4=4/3

I need help factoring this question, Factor 4(20) + 84.

Answers

Answer:

164

Step-by-step explanation:

B for brackets

O for of

D for division

M for multiplication

A for addition

S for subtraction

You first start with the brackets (20) and multiply with 4 which is equal to 80 and then add it to 84 which makes 164

I hope this helps

In a study of a weight loss program, 40 subjects lost a mean of 3.0 lb after 12 months. Does the weight loss program have statistical significance?

Answers

Answer: Yes, because the results are unlikely to occur by chance.

Step-by-step explanation: apparently, the weight loss program has a statistical significance, because the results are likely to also occur by chance. because it occurrs by chance, this applits to a happening which has occurred without an intent, volition, or plan. an event or encounter that occurs by chance usually implies an occurrence of some importance.

Subtract the matrices

Answers

Answer:

pleas learn subtraction

Step-by-step explanation:

so it can make you better in math

Answer:

[tex]\large \boxed{\mathrm{Option \ A}}[/tex]

Step-by-step explanation:

[tex]{\mathrm{view \ attachment}}[/tex]

What is the best first step to begin simplifying the expression - } (x + 4) = 6?
A.
Distribute -1/2
B.
Distribute -2
c. Multiply both sides of the equation by-2.
D.
Subtract 4 from both sides of the equation.
E.
Subtract 6 from both sides of the equation.

Answers

Answer: D
X+4=6
X=6-4
X=2

if the first step of the equation -8 - 7x = -5x - 10 is " add 10" then what should be done next?

Answers

Answer:

Add 7x to each side

Step-by-step explanation:

-8 - 7x = -5x - 10

Add 10 to each side

-8 - 7x+10 = -5x - 10+10

2 -7x = -5x

Add 7x to each side

2-7x+7x = -5x+7x

2 = 2x

Answer: See below

Step-by-step explanation:

[tex]-8 - 7x = -5x - 10[/tex]

I believe it is adding 8 on both sides

The next step after adding 8 on both sides is adding 5x on both sides

[tex]-7x=-5x-2[/tex]

[tex]-7x+5x=-5x-2+5x[/tex]

[tex]-2x=-2[/tex]

x=1

area of a parrollelogram with a base length of 2.9ft and a height of 5.5ft​

Answers

Answer:

[tex] \boxed{15.95 \: {ft}^{2} }[/tex]

Step-by-step explanation:

base length ( b ) = 2.9 ft

Height ( h ) = 5.5 ft

Let's find the area of parallelogram:

Area of parallelogram : [tex] \mathsf{ = b \times h}[/tex]

plug the values

⇒[tex] \mathsf{2.9 \times 5.5}[/tex]

Multiply

⇒[tex] \mathsf{15.95}[/tex] ft²

--------------------------------------------------------------------

Extra information:

Parallelogram

The quadrilateral in which opposites sides are parallel is called a parallelogram.

The opposite sides of a parallelogram are equal.The opposite angles of a parallelogram are equal.The diagonals of a parallelogram bisect each other.The area of a parallelogram = base × height

Hope I helped!

Best regards!

Area of Parallelogram formula = LxW or LxH. L(2.9) x H(5.5) = 15.95 ft. Hope this helps!

Someone please help me fast !!

Answers

The second answer is correct.
Second answer is the right one

Rafael is at an elevation of 30.5 feet relative to sea level and Jordan is at an elevation of -41.3 feet relative to sea level. Who is at a higher elevation? Who is further from sea level?

Answers

Answer:

a. Rafael

b. Jordan

Step-by-step explanation:

Firstly, we should understand that a negative value of elevation indicates that the position is below sea level.

So the person at a higher elevation is the person above the sea level which is Rafael in the case.

Now to the second question, we want to know who is farther from the sea level.

The correct answer is Jordan.

Let’s see the sea level as an origin (0,0) on a cartesian plane and coordinate. We should understand that although sign maybe different, the numbers which are higher in magnitude in either direction shows the farthest from the origin.

So therefore, Jordan is deeper below the sea level than Rafael who is above the sea level.

What value(s) of x make the equation x2 - 18x + 81 = 0 true?

Answers

Answer:

By factoring we get:

(x -9) * (x -9) = 0

The answers are

x = 9 and x = 9

Step-by-step explanation:

Answer:it’s A

Step-by-step explanation:

3 friends Mary, Peter, John have 10 flowers. Mary has the most flowers, Peter has the least. Know that the number of John's flowers is double Peter's . How many flowers that Peter, John and Mary got? (Detail Solution pls) Thanks

Answers

Answer:

Mary has 7 flowers

Peter has 1 flower

John has 2 flowers

Step-by-step explanation:

M + P + J = 10

J = 2P

M + P + 2P = 10

M + 3P = 10

P = 1

M + 3 = 10

M = 7

How do I even start this? And how to i order the equation to solve

Answers

[tex]f(g(h(x)))=f(g(\sqrt x))=f(\sqrt x-1)=\boxed{(\sqrt x-1)^4+4}[/tex]

This is because

[tex]h(x)=\sqrt x[/tex]

[tex]g(x)=x-1[/tex]

[tex]\implies g(h(x))=\sqrt x-1[/tex]

(that is, replace any instance of x in the definition of g with √x )

and

[tex]f(x)=x^4+4[/tex]

[tex]\implies f(\sqrt x-1)=(\sqrt x-1)^4+4[/tex]

(replace any x in f with √x - 1)

Also acceptable:

[tex](\sqrt x-1)^4+4=((\sqrt x)^4-4(\sqrt x)^3+6(\sqrt x)^2-4\sqrt x+1)+4[/tex]

[tex]=\boxed{x^2-4x\sqrt x+6x-4\sqrt x+5}[/tex]

(assuming x is not negative)

What is negative sqrt 64?

Answers

Answer:

8i. In real numbers only, this isnt possible, but if immagenary numbers are allowed then 8i is your answer          

Determine what type of model best fits the given situation: The height of a tree increases by 2.5 feet each growing season.

Answers

Answer: Linear model

The fact the height increases the same amount each time indicates we have a linear model. The slope is the rate of growth, so it is 2.5 feet per season.

Keep in mind that the linear model only works for a specific interval and doesn't work forever (the tree can't grow forever and at the same rate). A more realistic scenario is that the tree's height grows quickly at first and then slows down over time. For this type of scenario we would use a logarithmic model.

The linear model best fits the given situation option (B) linear is correct.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

The height of a tree increases by 2.5 feet each growing season.

Let h is the height and s be the number of seasons.

The relation between h and s:

h = 2.5s

Thus, the linear model best fits the given situation option (B) linear is correct.

Learn more about the linear equation here:

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Find the rectangular coordinates of the point with the polar coordinates. ordered pair negative 7 comma 2 pi divided by 3

Answers

Answer:

The rectangular coordinates of the point with polar coordinates (7, 2·π/3) is (-3.5,  3.5·√3)

Step-by-step explanation:

The given polar coordinates is (7, 2·π/3)

Where, the 7 represent the distance, r, from the point of reference and 2·π/3, the angle, θ, from the reference point.

Polar coordinates are represented in rectangular form by the equivalence transformation equation given as follows;

The x-coordinate = Radius, r × cos(θ), which gives

We note that 2·π/3 radians = 2 × 180/3 = 120°

x = 7 × cos(2·π/3) = 7 × cos(120°) = 7 × (-0.5) = -3.5

x = -3.5

The y-coordinate = Radius, r × sin(θ), which gives

x = 7 × sin(2·π/3) = 7 × sin(120°) = 7 × (√3)/2 = 3.5·√3

y = 3.5·√3

Therefore, the rectangular coordinates of the point with polar coordinates (7, 2·π/3) is (-3.5, 3.5·√3).

n urn contains 3 red balls, 9 green, 2 yellow, 2 orange, and 4 purple balls. Two balls aredrawn, one at a time with replacement. Find the probability of drawing a green ball and an orangeball.

Answers

Answer:

[tex]\frac{9}{100}[/tex]

Step-by-step explanation:

Given:

Number of red balls, n(R) = 3

Number of green balls, n(G) = 9

Number of yellow balls, n(Y) = 2

Number of orange balls, n(O) = 2

Number of purple balls, n(P) = 4

Two balls are drawn one at a time with replacement.

To find:

Probability of drawing a green ball and an orange ball ?

Solution:

Total number of balls, n(Total) = 3 + 9 + 2 + 2 + 4 = 20

Formula for probability of an event E is given as:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

Probability that a green ball is drawn at first:

[tex]P(Green) = \dfrac{\text{Number of Green balls}}{\text {Total number of Balls}}[/tex]

[tex]P(Green) = \dfrac{9}{20}[/tex]

Now, the ball is replaced , so total number of balls remain the same i.e. 20.[tex]P(Orange) = \dfrac{\text{Number of Orange balls}}{\text {Total number of Balls}}[/tex]

[tex]P(Orange) = \dfrac{2}{20} = \dfrac{1}{10}[/tex]

[tex]P(Green\ then\ orange) = P(Green) \times P(Orange)\\\Rightarrow P(Green\ then\ orange) = \dfrac{9}{10} \times \dfrac{1}{10}\\\Rightarrow P(Green\ then\ orange) = \bold{ \dfrac{9}{100} }[/tex]

Last year, there were 245 pies baked for the bake sale. This year, there were k pies baked . Using k, write an expression for the total number of pies baked in the two years.

Answers

Answer:

245 + k

Step-by-step explanation:

Since we know that,

245 = amt. of pies baked for the bake sale last year.

--> and k = (unknown) amt. of pies baked for the bake sale this year.

Using k, we need to write the total amt. of pies baked for bake sales in the 2 years.

last year + this year =>

respectively, 245 and k

Thus, we get 245 + k

70 POINTS! PLEASE HELP! Explain the difference between the following equation formats: Slope-Intercept, Point-Slope and Standard

Answers

Answer and Step-by-step explanation:

1.  slope intercept

2.  point-slope form

3.  standard

Explanation:

1.   A slope intercept form equation is when it's set up as y = m x + b

m = slope  

b = y-intercept

2.   A point-slope form is when a line passes through a point

and the equation is set up as  y −b = m ( x−a)

m = slope

(a, b) A point that the line passes through

3. standard lope form is when the equation is set up as

Ax + By = C

Combine the radicals. 2√24+5√54 A) 53√6 B) 5√6 C) 19√6 D) 93√6

Answers

Answer:

The answer is option C

Step-by-step explanation:

2√24 + 5√54

To combine the radicals first make sure the radicals have the same square root

That's

For 2√24

[tex]2 \sqrt{24} = 2 \sqrt{4 \times 6} = 2 \times 2 \sqrt{6} [/tex][tex] = 4 \sqrt{6} [/tex]For 9√54

[tex]5 \sqrt{54} = 5 \sqrt{9 \times 6} = 5 \times \sqrt{9} \times \sqrt{6} [/tex][tex] = 5 \times 3 \times \sqrt{6} [/tex][tex] = 15 \sqrt{6} [/tex]

Since they have the same square root we can combine them

That's

[tex]4 \sqrt{6} + 15 \sqrt{6} = (4 + 15) \sqrt{6} [/tex]

We have the final answer as

[tex]19 \sqrt{6} [/tex]

Hope this helps you

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