if (a+b)^2=54, and (a-b)^=46, then a^2+b^2=?

Answers

Answer 1

[tex](a+b)^2 =a^2 +b^2 + 2ab = 54~~~.....(i)\\\\(a-b)^2 = a^2 +b^2 -2ab = 46~~~.....(i)\\\\\\(i)+(ii):\\\\(a+b)^2 +(a-b)^2 = 54+46\\\\\implies a^2 +b^2 + 2ab + a^2 +b^2 - 2ab =100\\\\\implies 2a^2 +2b^2 =100\\\\ \\\implies 2(a^2 +b^2) =100\\\\\implies a^2 +b^2 = \dfrac{100}2 = 50[/tex]


Related Questions

i have 45 points...

Charlie has a box with the following letters inside of it. What is the probability that he will draw a "D," put it back, and then draw an "A?" Write your answer as a simplified fraction.

Answers

Answer:

3/7 and 2/7.

Step-by-step explanation:

P(e) = No of favourable outcomes/ Total no of possible outcomes.

total outcomes=3+1+1+2=7.

(1) p(D) = 3/7.

(2)p(A)=2/7

The probability of drawing a D does not affect the probability of drawing A so the events are independent so you just have to multiply the probabilities

There are 3 D out of 7
There are 2 A out of 7(because we put the card back)

3/7 * 2/7 =6/ 49

Sam needs a bowl to mix her punch. She has 2-cup bowl, and a 6-cup. What is the smallest bowl sam can use to make her punch?

Answers

Answer:

the 2 cup bowl

Step-by-step explanation:

it is literally the smallest bowl she can use at her disposal

For art class, you need to make a scale drawing of the Parthenon using the scale 1 in. = 5 ft. The Parthenon is 228 ft long.

How long should you make the building in your scale drawing?

The building should be (________) inches long. Round to the nearest tenth if necessary.

Answers

Answer:

228/5= 45.6 inches, rounded is 46 inches

Describe the location from the origin of each point in problem 5

Answers

Elaborate, where’s the picture of the problem?

PLS ANSWER 30 POINTSSS

Answers

Answer:

letter B po

Step-by-step explanation:

basta letter B may ganyan din kame eh

3. Segment GE is an angle bisector of both
angle HEF and angle FGH. Prove triangle HGE is
congruent to triangle FGE.
F
H
G

Answers

ΔHGE and ΔFGE are congruent by the Angle-Side-Angle Congruence Theorem (ASA).

Recall:

A segment that divides an angle into equal parts is known as an angle bisector.Two triangles are congruent by the ASA Congruence Theorem if they share a common side and have two pairs of congruent angles.

In the diagram given, Angle bisector, GE, divides ∠HEF into congruent angles,  ∠HEG ≅ ∠GEF.

Also divides ∠FGH into congruent angles, ∠HGE ≅ ∠FGE.

Both triangles also share a common side, GE

This implies that: ΔHGE and ΔFGE have:

two pairs of congruent angles - ∠HEG ≅ ∠GEF and ∠HGE ≅ ∠FGE

a shared side - GE

Therefore, ΔHGE and ΔFGE are congruent by the Angle-Side-Angle Congruence Theorem (ASA).

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x² – 2xy + y², x² + 2xy + y², 4x² – xy + y², x² – y²​

Answers

Answer:

[tex]\left(4x^2-xy+y^2\right)\cdot \left(x+y\right)^2\cdot \left(x-y\right)^2\\[/tex]

Step-by-step explanation:

write the linear equation in slope intercept form (-2,-4) and (-3,-3)

Answers

Answer:

y=7x+18

Step-by-step explanation:

the y intercept is 18 and the slope is 7.

I need help with this.

Answers

Answer:

check online for more information

Name a pair of overlapping congruent triangles. (PST and QTU, STR and UTR, or RPU and RQS)

Then state whether they are congruent by SSS, SAS, ASA, AAS, or HL.

Answers

Answer:

  ΔRUP ≅ ΔRSQ by ASA

Step-by-step explanation:

Angle SRQ is congruent to angle URP by the reflexive property of congruence. The angles at U and S are already marked congruent, as are sides UR and SR. That means we have two angles and the side between them congruent for the two triangles:

  ΔRUP ≅ ΔRSQ by ASA

Pre college need help thiss

Answers

Answer:

25

-35

5

Step-by-step explanation:

yeah-ya.............. right?

Figure A is a scale image of Figure B. What is the value of x?​

Answers

Answer:

good day of school and➕➕ I have a great day of school and I have a great day☀☀☀ of school and➕➕ I

Two pieces of equipment were purchased for a total of $5000. If one piece cost $410 more than the other, find the price of the less expensive piece of equipment

Answers

Answer:

correct answer explained above

Suppose the regression line for the number of runs scored in a season, y , is given by ˆy=−790+5400x , where x is the team's batting average. For a team with a batting average of 0.235, find the expected number of runs scored in a season. Round your answer to the nearest whole number. If we can expect the number of runs scored in a season is 400, then what is the assumed team's batting average? Round your answer to three decimal places.

Answers

Answer:

479 = expected runs

0.220 = assumed batting average

Step-by-step explanation:

ˆy=−790+5400x

For an x value of 0.235, we have to calculate ˆy, or the predicted value. Plugging 0.235 in for x, we get

-790 + 5400 * 0.235 = 479

If ˆy = 400, we have to calculate x.  Plug 400 in for y in our equation to get

400 = -790 + 5400x

add 790 to both sides to isolate the x and its coefficient

1190 = 5400x

divide both sides by 5400 to solve for x

x= 0.220

What is the least common denominator of this equation

Answers

Answer:

LCD = 30

Step-by-step explanation:

[tex]\frac{5}{6}[/tex] x - [tex]\frac{1}{10}[/tex] x = [tex]\frac{2}{15}[/tex]

Multiply through by 30 ( the LCM of 6, 10, 15 ) to clear the fractions

25x - 3x = 4

22x = 4 ( divide both sides by 22 )

x = [tex]\frac{4}{22}[/tex] = [tex]\frac{2}{11}[/tex]

Answer:

5

Step-by-step explanation:

[tex] \frac{5}{6} x - \frac{1}{10} x = \frac{2}{15} \\ \frac{50x - 6x}{60} = \frac{2}{15} (criss \: cross) \\ \frac{44x}{60} = \frac{2}{15 } \\ \frac{11x}{15} = \frac{2}{15} (simplify) \\ 165x = 30(criss \: cross) \\ x = \frac{30}{165} = \frac{6}{33} = \frac{2}{11} \\ x = \frac{2}{11} [/tex]

Pls help I’ll brainlest I need a good grade

Answers

The one in the middle

Rewrite each of the following terms as an extended product. Consider carefully your order of operations and remember that exponents come before multiplication. You do not need to simplify the products.

Answers

#a

[tex]\\ \sf{:}\dashrightarrow 4^3=(2\times 2)^3=2^6[/tex]

#b

[tex]\\ \sf{:}\dashrightarrow 3^2.3^3=3^5[/tex]

#c

[tex]\\ \sf{:}\dashrightarrow (2^3)^4=2^{12}[/tex]

#d

[tex]\\ \sf{:}\dashrightarrow x^3y^4\checkmark[/tex]

#e

[tex]\\ \sf{:}\dashrightarrow 8x^2y^5=2^3x^2y^5[/tex]

#f

[tex]\\ \sf{:}\dashrightarrow( 9x^2)^2=(3^2x^2)^2=3^4x^4[/tex]

Ray had $50. he bought two shirts that cost $19 each. how much money did Ray have after buying the shirts? Alex's answer to the word problem is $29. Is Alex's answer reasonable? explain.​

Answers

Answer: No, it's not

Step-by-step explanation:

19*2=38

50-38 = 12

Alex awnsered 29 which is $17.00 off.

What is the slope of this graph?


a.4

b.−4

c.14

d.−14

Answers

Answer:

B

Step-by-step explanation:

just look at where the line crosses the coordinate plane

Layla borrowed some money from her friend in order to help buy a new video game
system. Layla agreed to pay the friend back some amount every week until her loan
was paid off. Let L represent the amount Layla owes her friend after t weeks. A graph
of L is shown below. Write an equation for I then state the y-intercept of the graph
and determine its interpretation in the context of the problem.

Answers

The linear equation for this scenario is L = -20t + 140. Layla owes her friend $140 and pays the friend $20 per week.

What is an equation?

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

A linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

Let L represent the amount Layla owes her friend after t weeks.

Using the point from the graph (0, 140) and (7, 0):

L - 140 = [(0 - 140)/(7 - 0)](t - 0)

L - 140 = -20t

L = -20t + 140

The y intercept is 140

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Ms.Gómez ran 3/5 of a mile in 5 minutes. Mr. Hernández ran 3/5 of a mile in 3 minutes. How far did Ms gomez and mr Hernandez each run in 1 minute?

Show work or explain

Answers

Answer:

Ms G ran 3/25 mile per minute

Mr H ran 1/5 mile per minute

Step-by-step explanation:

Ms G:

create a proportion from mile/minutes = mile/minutes

let 'm' = amount of miles

3/5÷5 = m÷1

cross-multiply to get:

3/5 = 5m

m = 3/5 × 1/5 = 3/25

Mr H:

3/5÷3 = m÷1

cross-multiply to get:

3/5 = 3m

15m = 3

m = 3/15 or 1/5

help help help help meeee

Answers

Answer: 36!

Step-by-step explanation:

Answer:

B . 34

Step-by-step explanation:

simply subtract the lowest value from the greatest value, ignoring the others.

3. The lacrosse team is raising money by selling cheesecakes. The players plan to sell an entire cheesecake for $24.00 each and slices of cheesecake for $3.50 each. If they want to raise at least $700, how many of each could they sell?

Part A: List three possible combinations of entire cheesecakes and slices of cheesecake the players could sell to reach their goal of raising at least $700.

Part B: Write an inequality to represent the situation.

Part C: Graph the inequality and shade where the solutions are. y X

Part D: What is the difference in the amount of money raised for ordered pairs falling on the line and the ones that fall in the shaded area?

Part E: What do the x- and y-intercepts represent?​

Answers

To reach a raise of $ 700, you can sell 20 entire cheesecakes and 63 slices, or 10 entire cheesecakes and 132 slices, or 15 entire cheesecakes and 98 slices.

To determine, if they want to raise at least $ 700, how many of each could they sell, listing three possible combinations of entire cheesecakes and slices of cheesecake the players could sell to reach their goal, the following calculation must be performed:

C + S = 700 24 x 20 = 480 700 - 480 = 220 / 3.5 = 62.85 24 x 10 = 240 700 - 240 = 460 / 3.5 = 131.42 24 x 15 = 360 700 - 360 = 340 / 3.5 = 97.14

Therefore, to reach a raise of $ 700, you can sell 20 entire cheesecakes and 63 slices, or 10 entire cheesecakes and 132 slices, or 15 entire cheesecakes and 98 slices.

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From a horintal lengh of 101" and a rise of 13 inches over that lengh what is the angle of rise

Answers

Answer: Approximately 7.33 degrees

Work Shown:

tan(angle) = opposite/adjacent

tan(x) = 13/101

x = arctan(13/101)

x = 7.334379 approximately

x = 7.33

JoAnn bought 18 apples for $12.42. What was the price for 1 apple?

Answers

0.69 cents just divide them :)

Answer: $1.45

Step-by-step explanation:

18/12.42 = $1.45

Explain how to find the distance between two integers using the difference.

Answers

Answer:

read explanation for answer

Step-by-step explanation:    Finding the distance between any two integers is obtained by;

Taking the absolute value of the difference between the two integer values.

For instance :

Point A = - 10

Point B = 5

The distance between the two integer points is :

Difference = Point A - Point B = - 10 - 5 = - 15

Absolute value = |-15| = 15

Therefore, This procedure works for any pair of integer distances.

Answer:Find the difference between two integers by adding the additive inverse. The distance is the absolute value of the difference. Check the distance by plotting the original two integers on a number line and counting the units between them.

Step-by-step explanation:

An item is regularly priced at $29. It is on sale for 80% off the regular price.

Answers

And the question is????

Solve the following equation for d:cd – 8 = f

Answers

Answer: Well my friend, there is not enough info to sole the equation..

Step-by-step explanation:

Help someone I don’t know the answer and I need help!

Answers

the correct answer is (-4,4) i hope this helped :)

Answer: I believe the answer is (A)  (-4,4) because the only corner that's going up towards the (f) is stopped over the 4's.

the difference of 16 and 2 divide by 7
make the equation ​

Answers

Answer:

(16-2)/7

Step-by-step explanation:

16-2=14

14/7=2

Equation: (16-2)/7

The difference of 16 and 2 divide by 7 gives result 2 and required equation is x = (16 - 2) / 7.

What is an equation?

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given numbers are 16, 2 and 7.

Let the difference of 16 and 2 divide by 7 gives result x,

The equation for the  difference of 16 and 2 which is 14, divide by 7.

x = (16 - 2) / 7

The equation x = (16 - 2) / 7 can be simplified as,

The difference between 16 and 2 = 16 - 2 = 14

x = 14 / 7 = 2.

The required equation is x = (16 - 2) / 7 and simplified answer is 2.

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