If ab = 9 and a² + b² = 81, then (a+b)² = ?​

Answers

Answer 1

Answer:

99

Step-by-step explanation:

Through some clever algebra, we can combine our first two equations using the fact that

[tex](a+b)^2=a^2+2ab+b^2[/tex]

We have the a² and the b² in the equation [tex]a^2+b^2=81[/tex], and we almost have a 2ab in the equation [tex]ab=9[/tex]. To get that 2ab, we can simply double both sides of the first equation to get [tex]2ab=18[/tex]. From there, we'll add the first two equations together, giving us the summed equation

[tex]a^2+b^2+2ab=81+18\\a^2+2ab+b^2=99[/tex]

And since [tex](a+b)^2=a^2+2ab+b^2[/tex], we can equivalently say that

[tex](a+b)^2=99[/tex]


Related Questions

HI PLEASE HELP IM KINDA CONFUSED WITH KINETIC ENERGY AND POTENTIAL ENERGY ANYONE CAN HELP?

Answers

Answer:

P

K

P

K

P

K

Step-by-step explanation:

If it's not moving, it's potential energy

If it's moving, it's kinetic energy

What is the Rotational speed of someone standing in Helsinki, Finland located at 60°11' N and 24°56' E.? (radius of the earth is 3960 miles)

Answers

Answer:

515.5 mph

Step-by-step explanation:

I am fairly confident we are taking the same test/quiz thing right now and I figured this one out so here ya go:

60 degrees + 11 sec = 60.183 degrees

3960 * cos(60.183) = 1969       some number in relation to the distance to the poles

2 * pi * 1969 = 12371.8

12371.8 / 24 = 515.5mph

look up "How to Calculate Rotational Speed Around Earths Axis" on YT, video is by " VAM! Physics & Engineering" that is where I found the formula stuffs

shoutout Woodinville

Write each polynomial in standard form.
Then, give the leading coefficient.
I
7. 12 + 3x2 - X

Answers

2
-
25x(89+100x) if that’s what you mean

3x+30=180 degrees, what is the value of the letter x in this problem?

Answers

Answer:

50

Step-by-step explanation:

180-30=150/3=50

3x + 30 = 180

     -30     -30     subtract 30 on both sides, solve for 180 - 30 which is 150.

___________

3x = 150

__    ___       divide 3 on both sides, solve for 150 ÷ 3 which is 50.

3       3

x = 50, final answer

hope this helps! :)

find the volume of the cylinder​

Answers

Answer:

hope help you stay happy and safe

Apply the distributive property to factor out the greatest common factor. 35+14=35+14=35, plus, 14, equals

Answers

Answer:

The greatest common factor is 7

[tex]35 + 14 = 49[/tex]

Step-by-step explanation:

Given

[tex]35 + 14 =[/tex]

Required

Apply distributive property

Express 35 as 7 * 5 and 14 as 7 * 2

[tex]35 + 14 = 7 * 5 + 7 * 2[/tex]

Apply distributive property

[tex]35 + 14 = 7 ( 5 + 2)[/tex]

The greatest common factor is 7

Solving further to get the solution

[tex]35 + 14 = 7 * 7[/tex]

[tex]35 + 14 = 49[/tex]

Answer:

7(5+2)

hope this helps <3

you don't have to do all of them

Answers

Answer: lol your using canvas

1. 63

2. D

3. B

4. A

Sorry for the bland explinations havin a bad day.

Step-by-step explanation:

1. The way we solve this is by adding the degrees 72 and 45. then we subtract it by 180. this is because in all triangles the angles always add up to 180 degrees.

2. Like question one what set of angles measures to 180 degrees.

3. The sides of a triangle should define the angle measurements. you can also see if its a triangle if the numbers are continues like 3,4,5 or in this case 4,5,6

4. like in questions 1 and 2 the angles of a triangle has to equal 180 degrees so 60 times 3 is 180 so each angle would have to be 60 degrees.

if the diameter of the semicircle is 6 in fid the area in terms of pi?

Answers

Answer:

i think the is 14.13.

Step-by-step explanation:

You start at (5, 4). You move right 5 units. Where do you end?

Answers

Answer:

(10,4)

Step-by-step explanation:

5 would change to 10 and 4 would stay

Which expression is equivalent to 9.7d+4.1+5.1d-9.2
A) 13.8d−4.1
B) 14.8d+13.3
C) 4.6d−5.1
D −5.1+14.8d

Answers

Answer:

9.7d+4.1+5.1d-9.2

9.7d +5.1d+4.1-9.2 (take same element near)

d(9.7d +5.1) + 4.1-9.2

d(14.8) - 5.1

answer :

D −5.1+14.8d

Step-by-step explanation:

Given the function f(x)= -3(x)^2 , find the value of f(4).

Answers

the value of f(4) would be -48

Step-by-step explanation:

f(x) = -3x²

f(4) = -3(4²)

= -48

1.02 sinusoidal graphs

Answers

Answer:

The answer is 20

Step-by-step explanation:

The wave starts at the origin and doesn't complete the cycle until unit 20.

Answer:

[tex]\displaystyle 20[/tex]

Step-by-step explanation:

[tex]\displaystyle \boxed{y = cos\:(\frac{\pi}{10}x - \frac{\pi}{2})} \\ \\ y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{5} \hookrightarrow \frac{\frac{\pi}{2}}{\frac{\pi}{10}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{20} \hookrightarrow \frac{2}{\frac{\pi}{10}}\pi \\ Amplitude \hookrightarrow 1[/tex]

OR

[tex]\displaystyle \boxed{y = sin\:\frac{\pi}{10}x} \\ \\ y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{20} \hookrightarrow \frac{2}{\frac{\pi}{10}}\pi \\ Amplitude \hookrightarrow 1[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the sine graph, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = cos\:\frac{\pi}{10}x,[/tex] in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [photograph on the right] is shifted [tex]\displaystyle 5\:units[/tex]to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle 5\:units,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{5} = \frac{\frac{\pi}{2}}{\frac{\pi}{10}}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = cos\:(\frac{\pi}{10}x - \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [-15, 1],[/tex]from there to [tex]\displaystyle [5, 1],[/tex]they are obviously [tex]\displaystyle 20\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle 20.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended one unit beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

2. True or false: In an exponential expression, you multiply the base by the exponent.

True
False

Answers

Answer:

true

Step-by-step explanation:

False would be the correct answer to this question

Help bestiess
7x=5x÷67​

Answers

Answer:

7x=5x/67

Step-by-step explanation:

Which Superhero has the greater miles to second ratio
------------------------------------------------------------------------------------------
Choices are:
------------------------------------------------------------------------------------------
A) Super-Man
B) Iron-man
C)Neither they are both equivalent
------------------------------------------------------------------------------------------

Answers

Answer:

Super Man

Have a great day!

The neighbors have $18.57 to spend on strawberry plants. A 6-pack of plants costs $2. How many packs can they buy?

Answers

Answer:

9

Step-by-step explanation:

the answer is 9 because 18 $÷2 = 9

Answer:

9 packs

Step-by-step explanation:

18.57/2=9.285

Can't buy 1.285 one so we go back to 9 which is buyable with the money there is.

5x^+20x +15=0
Pls help

Answers

Is the 5 squared?ejskjsjwbsnnsmsnsnsnmsnsnsnsnsjsjjs

In triangle ABC, the measure of angle CAB is 80° and the measure of angle ABC is 45.5°. What is the measure of angle BCA in degrees? A 125.5°125.5 degrees B 54.5°54.5 degrees C 55.5°55.5 degrees D 64.5°

Answers

Answer:

B 54.5°

Step-by-step explanation:

Since we have a triangle,

CAB + ABC + BCA = 180 (sum of angles in a triangle)

Since CAB = 80° and ABC = 45.5°, substituting these into the equation, we have

80° + 45.5° + BCA = 180°

simplifying, we have

125.5° + BCA = 180°

collecting like terms, we have

BCA = 180° - 125.5°

BCA = 54.5°

So, the answer is B

A rock is dropped down from the top of a​ 500-foot cliff. After 1​ second, the rock is traveling 32 feet per second. After 5 ​seconds, the rock is traveling 160 feet per second.
a. Assume that the relationship between​ time, t, and​ speed, s, is linear, and write an equation describing this relationship. Use ordered pairs of the form​ (time, speed).
b. Use this equation to determine the speed of the rock 7 seconds after it is dropped.

Answers

Answer:

A) s=32t

B) 224 ft/s

Step-by-step explanation:

A)

In the form (time, speed), the question gives us the following data: (1,32) and (5,160). Since we are told that the relationship between​ time, t, and​ speed, s, is linear, we know the equation will fit the formula y=mx+c, where m is slope c is the y-intercept and y and x are the co-ordinate values. Plug in (1,32) and (5,160) to find the formula:

y=mx+c

s=mt+c

32=1m+c

c=32-m

160=5m+C

160=5m+32-m

128=4m

m=32

c=32-m

=32-32=0

So our equation is s=32t

B)

s=32t

s=32(7)=224 ft/s

Neptune is 4.5 billion kilometers from the
sun. Represent this number in scientific
notation

Answers

Answer:

4.5 x 10 ^9

Step-by-step explanation:

Answer:

4.5*10^9

Step-by-step explanation:

The function y = -16t+^2 40 represents the height y (in feet) of a water droplet t seconds after falling from an icicle. After how many seconds does the water droplet hit the ground? Round your answer to two decimal places. ​

Answers

Answer:

The water droplet will hit the ground 1.58 seconds after it started falling.

Step-by-step explanation:

The function:

y = -16*t^2 + 40

represents the height of a water droplet t seconds after falling from an icicle.

We want to find the value of t such that the water droplet hits the ground, and this will happen when y = 0.

Then we only need to solve the equation:

0 = y =  -16*t^2 + 40

0 =  -16*t^2 + 40

16*t^2 = 40

t^2 = 40/16

t = √(40/16) = 1.58

The water droplet will hit the ground 1.58 seconds after it started falling.

Please help meeeeeee!!!!! ill give BRAINLIEST

Answers

Answer:

Step-by-step explanation:

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined. y=6 is a straight line perpendicular to the y-axis at point (0,6) , which means that the range is a set of one value {6} .

Find the value of X.

Answers

In the question you will do

35 is the biggest side it’s named by hypotenuse

So you will do 35=21 to the power x +x

So after you do it it will be

X=441 -35 it will be 406 and after you finish you will do it in the calculator so

The Answer is : 20.15
Theres an easier way. Pythagorean theorem-
A^2+B^2=C^2
A and B are legs while C is the hypotenuse or slanted one.
So rearrange formula.
C^2 - A^2=B^2
1225 - 441 = B^2
784= B^2
Square root it now
28=B

In 2 mins., a conveyor belt moves 300 lbs. Of recycle aluminum from delivery truck to a storage area. A smaller belt moves the same quantity of cans the same distance in 18 mins. If both belts are used, find how long it takes to move the cans to the storage area

Answers

Answer:

1.8 minutes or 108 seconds

Step-by-step explanation:

The question tells us that the larger belt moves 300 lbs in 2 mins. And this is equal to 150 lb per minute

The question also tells us that a smaller belt moves the same quantity of 300 lbs in 18 mins. And this is equal to an average of 16.667 lb per min.

Both belts will move at a rate of 166.667 lb per min.

So it will take them 300 / 166.667 = 1.8 min or 108 s.

Therefore, the answer is 1.8 min

What is the slope of y=250-5x

Answers

Answer:

Step-by-step explanation:

The slope of the line is -5, and the y-intercept is 250

What the person above me said

A girl is on the beach and the angle of elevation from her feet to the top of a lighthouse is 62' If the lighthouse is 30ft tall, how far away is the girl from the lighthouse? Please show

your work!

I need help plssss

Answers

Answer:

15.95 feets

Step-by-step explanation:

Given that:

Angle of elevation = 62°

Using trigonometric relation :

Tanθ = opposite / Adjacent

From the drawing attached :

Opposite = 30 feets

Distance between girl and lighthouse = d

Tan 62 = 30 / d

1.8807264 * d = 30

d = 30 / 1.8807264

d = 15.951283

d = 15.95 feets

Mathhhhhhhhh pls help

Answers

Answer:

vertically opposite angles

Step-by-step explanation:

Write these numbers in order of size.
Start with the smallest number.
9
-3
2.
-2
Smallest

Answers

Answer:

smallest -3,-2,2,9 biggest

Answer:

-3, -2, 2, 9

Step-by-step explanation:

-3 is the smallest (it is below 0), -2 is second because it is closer to 0 than -3 but still below it, 2 follows, and then 9

A can in the shape of a cylinder has a diameter of 6 centimeters and a height of
10 centimeters. Which measurement is closest to the total surface area of the can in
square centimeters?
F 603.19 cm?
G 245.04 cm?
H 376.99 cm?
188.50 cm?

Answers

Answer:

I don't know the answer please

Maya is 14 years old. Her brother Jorge is 3 years more than half her age. Which of the following is the correct expression for Jorge's age?

(7 x 2) + 3
7 − (2 + 3)
(14 ÷ 2) + 3
14 ÷ (7 − 3)

Answers

The answer is C to get half of mayas age we first divide the 14 by 2 then we add the 3 and get our answer which is 10

Answer:

7 x 2 + 3 = 17

7 - 2 + 3= 8

14 ÷ 2 + 3 = 10

14 ÷ 7 - 3  - 1

Step-by-step explanation:

Other Questions
How is REM sleep identified? what is 30% of $240? 203/4108 as a percent a. 4.94%b. 20.24% c. 0.049%d. 49.42% If your house was burning what are the 3 things you would most want to save and why? Calculate the mass of 5.22 mol of He. Maria decides to increase her homework time of 8 hours per week by 15% Calculate her new homework time. Give your answer in hours and minutes Calculate the length of the unknown side of each triangle.a)3 cm5 cmGive your answers to the nearest mm. Pls help Match these Benito Mussolini 1Franklin Roosevelt 2Ganaral Dwight D. Eisenhower 3Battle of the bulge 4D-Day 5German attack in the Ardennes region of Belgium AElected to four terms as president BKilled by his own people in April 1945 CCommander of joint United States and British armies DAlliance invasion of German-occupied France E pls help on my homework. due tonight i need help asapMatch the given graphs with the corresponding functions in the table below. Use the letter in thebottom left corner of the graph.b) Given the function ff(xx) = llllll3(xx + 2) 1, state the following characteristics:Asymptote:__________________ End Behavior: ______________________________________________________________________________c) Describe what an asymptote is, and write the end behavior in your words. 2. You want to see which substances dissolve in water. You test sugar, salt, and pepper. Explain which of these substances will dissolve in water and which will not. Read the information in the box below. Think about the ways young people use cell phones and other wireless devices.Write an essay explaining the positive and negative effects of wireless-device use on teenagers.Be sure toclearly state your thesisorganize and develop your ideas effectivelychoose your words carefullyedit your writing for grammar, mechanics, and spelling i want hindi ginathi 1to30 Why were roads in Ancient Rome originally built? find the value of given expression[tex] \sqrt{29 - 4} [/tex] 1. When observing the specimen, in whichpart of the microscope will you place it?A. baseB. stageC. eyepiece D. inclination joint What is Seth Godins overall message to companies? At steady state, the power input of a refrigeration cycle is 500 kW. The cycle operates between hot and cold reservoirs which are at 550 K and 300 K, respectively. a) If cycle's coefficient of performance is 1.6, determine the rate of energy removed from the cold reservoir, in kW. b) Determine the minimum theoretical power required, in kW, for any such cycle operating between 550 K and 300 K What word means "agreeable"?belligerentcausticdespairingcongruent Solve:V5x+1+6=4V=square root 9. A. 7 B. 15 C. 12D