Example 3.7.4: The sum of two positive numbers is 16. What is the smallest possible value of the sum of their squares

Answers

Answer 1

Answer:

The smallest possible value of the sum of their squares is 128.

Step-by-step explanation:

Let the first number = x

let the the second number = y

x +  y = 16

y = 16 -x

minimum value, f = x² + y²

f(x) = x² + (16-x)²

f(x) = x² + 256 - 32x + x²

f(x) = 2x² - 32x + 256

f(x)' = 4x - 32

4x - 32 = 0

4x = 32

x = 32 / 4

x = 8

The absolute minimum value of x = 8

y = 16 - x

y = 8

The smallest possible value of the sum of their squares is given by x² + y²;

=  (8)² + (8)²

= 128

Therefore, the smallest possible value of the sum of their squares is 128.


Related Questions

Solve 3x + 8 = x + 16

Answers

Answer:

x = 4

Step-by-step explanation:

Move all "x"s to one side of the equation:

(3x + 8) - x = (x + 16) - x

2x + 8 = 16

Subtract 8 from both sides so that all the numbers are on one side of the equation:

(2x + 8) - 8 = (16) - 8

2x = 8

Divide both sides of the equation by 2:

x = 4

What is the unit rate of 36 flowers in 3 bouquets

Answers

Answer:

12 flowers per bouquet

Step-by-step explanation:

Answer:

12 / 1

Step-by-step explanation:

12 times 3 is 36 so 12 flowers in each bouquets.

A triangular playground has sides that are lengths 2x feet, x-1 feet and x feet. If the perimeter of this playground is 27 feet, what are the
lengths of each side of the playground?

Answers

Answer:

The lengths of the sides of the playground are 14 feet, 6 feet, 7 feet

Step-by-step explanation:

At first, let us find the perimeter of the playground

∵ Perimeter of a triangle is P = S1 + S2 + S3

∵ The sides of the triangular playground are (2x) ft, (x - 1) ft, and x ft

S1 = 2x, S2 = x - 1, S3 = x

→ Substitute them in the rule of the perimeter above

∵ P = 2x + x - 1 + x

→ Add the like terms

∴ P = (2x + x + x) - 1

P = 4x - 1

∵ The perimeter of this playground is 27 feet

P = 27

→ Equate the two values of P

4x - 1 = 27

→ Add 1 to both sides

∴ 4x - 1 + 1 = 27 + 1

∴ 4x = 28

→ Divide both sides by 4

∵ [tex]\frac{4x}{4}[/tex] = [tex]\frac{28}{4}[/tex]

x = 7

→ Substitute the value of x in each side to find their lengths

∵ S1 = 2(7)

S1 = 14 feet

∵ S2 = 7 - 1

S2 = 6 feet

S3 = 7 feet

The lengths of the sides of the playground are 14 feet, 6 feet, 7 feet

How many inches combined 1/2 1/3 1/6 1/2 1/8 1:4

Answers

Answer:

Imperial Units

155/8 Inches (fraction) 

15.625 Inches 

1.302083 Feet

 

Metric Units

396.875 Millimeters 

39.6875 Centimeters 

0.396875 Meters

Five hundred consumers were surveyed about a new brand of snack food, Crunchicles. Their age groups and preferences are given in the table.

18–24 25–34 35–55 55 and over Total
Liked Crunchicles 39 66 10 86 201
Disliked Crunchicles 27 19 38 95 179
No Preference 24 37 35 24 120
Total 90 122 83 205 500


One consumer from the survey is selected at random. Use reduced fractions for your responses to each of the following questions.

What is the probability that the consumer is 18–24 years of age, given that they dislike Crunchicles?

Answers

Answer:

The probability that the consumer is 18 - 24 years of age, given that they dislike Crunchicles is 0.151.

Step-by-step explanation:

The age groups and preferences are given as follows:

                                     18 - 24     25 - 34       35 - 55     55 and over      Total

Liked Crunchicles           39             66              10                  86                201

Disliked Crunchicles       27              19             38                  95                179

No Preference                 24             37             35                  24                120

Total                                 90           122             83                205               500

One consumer from the survey is selected at random.

Compute the probability that the consumer is 18 - 24 years of age, given that they dislike Crunchicles as follows:

[tex]P(18-24|DC)=\frac{P(18-24\cap DC)}{P(DC)}[/tex]

                        [tex]=\frac{n(18-24\cap DC)}{n(DC)}\\\\=\frac{27}{179}\\\\=0.15084\\\\\approx 0.151[/tex]

Thus, the probability that the consumer is 18 - 24 years of age, given that they dislike Crunchicles is 0.151.

on (43 - 4) + 12 = 3

Answers

Answer:

No im afraid it equals Fish

Step-by-step explanation:

If you subtract 43-4 equals 39 which how many nemo fish r in the ocean

and if u add 12 to it it equals 51 which how many fish r in the ocean

so the answer is Fish

The general form of an parabola is 3x2+24x−2y+52=0.

What is the standard form of the parabola?

Answers

Answer:

y = 3/2x∧2+12x+26

Step-by-step explanation:

ill gives brainiest The average height of an ostrich is 255 cm.
Suppose that you want to make a scale
drawing of an ostrich. The scale is 30 :1.
What height will you make the ostrich in
your drawing? Explain your thinking.

Answers

Step-by-step explanation:

8.5

_____

30) 255.0

240

0150

150

000

Write the equation in point-slope form that goes through the point (10,5) and has
slope of - 3

Answers

So the answer would be a -5

Pls help with this problem

Answers

Answer:

A.

Step-by-step explanation:

set a proportion

75       x

---   =  ----

1.5       2.25

2.25 times 75

168.75

divide it by 1.5

337.5

337 one half

(Giving brainliest on this one to who ever helps!!)



The steps in an investigation between two negatively charged objects are listed below.

Step 1: Rub a cloth on two uncharged balloons to make them negatively charged.
Step 2: Bring the two negatively charged balloons together.
Step 3: Observe the repulsion between the two objects.

Which statement is true?

A) An object changes its charge when placed near another charged object.
B) Bringing two positively charged objects close together would result in attraction.
C) The two balloons do not have to touch for repulsion to be observed.
D) Two negatively charged objects will attract each other when they touch.

Answers

Let’s use basic knowledge of magnets to help us solve this problem. For them to stick together, one side has to be positive and one side has to be negative.
The two balloons both have a negative charge which means they won’t stick together, they will try and move away from each other.

Let’s use process of elimination.
We can eliminate B because the balloons are negatively charged, not positively charged. We can also eliminate D because when they both have the same charge, their will be no attraction.
We can also eliminate A because if we put the balloons close together, one of them won’t magically change to positive to make it attract to the negative charged balloon.

The only answer we have left is C. It is C because the balloons don’t need to touch each other for repulsion to be observed. Since both of them are negative they will want to stay away from each other.

Final Answer: C- The two balloons do not have to touch for repulsion to be observed.

I hope this helped you :)

Answer:

C) The two balloons do not have to touch for repulsion to be observed.

Step-by-step explanation:

$7.80(1 + 0.055)=
Your answer

Answers

Answer:

$8.229

Step-by-step explanation:

do whats in the paranthese first: 1 + 0.055 = 1.055

when a number is next to another number you multiply: 7.80(1.055) which is 7.80 x 1.055 = 8.229

Please help me! The question is in the screenshot below.

Answers

Answer:

There are two solutions:

= 0.34 , = 11.66

Both solutions are rounded to the nearest hundredth.

82pts

_
Express 0.41(repetitive decimal) as a fraction in its simplest form

Answers

Answer:

Step-by-step explanation:

ty for points

37/90 is the fraction

need some help please ​

Answers

Answer:

Ariel ate the most .

Step-by-step explanation:

hope this helps you.

Answer:

dan

Step-by-step explanation:

find the common denomanator= 28

dan 6/7 to the common denomanator is 24/28

ariel 3/4 is 21/28

Find the slope
How can I find the slope ​

Answers

Answer:

You should use the y2 - y1 /x2 - x1

To find the answer you should be able to plug in the x and the y in the equation with the coordinates that you have but I'm not sure if you don't have what you'll do

2/5 is the answer

(3,1) and (-2,-1) are the two point.
You could do the y2-y1/x2-x1. Which is (-1) - 1 = -2 and (-2) - 3 = -5. Two negatives make a positive so the answer would be 2/5.

If you are god of math you can try this

Answers

Answer:

BRO, u dont need to be a god :D, This is simple math and you just need to use your brains

Step-by-step explanation:

Given is a polynomial, and the values of the variables in it are given by showing what set are they an element of, right? It just gets easier from here

They tell us that 'z' is an element of set C, which stands for Complex Numbers.

And they also tell us that 'a' is an element of set Z, which stands for Integers, which are just numbers with a sign :).

They have also given us a root (solution) to the polynomial, which is also a complex number.

The two statements given are just there for us to verify that we are on the right track to the solution.

We can see that (z = 3 + i) which of course is a complex number, due to the presence of 'i', and 'a' is an integer for when we find its value.

Put it all together and we will get the answer.

Like this,

take the given value of 'z' and place it into the polynomial given, now keep your eyes open here. They said the value of z is as such when the polynomial is an equation which equals 0, so hence we get this:

P(z) = a(3+i)³ - 37(3+i)² + 66(3+i) - 10 = 0,

now just go on simplifying,

=> a(3³+i³+3×3²i+3×3i²) - 37(3²+2×3×i+i²) + 66×3 + 66×i - 10 = 0

=> a(27-i+27i-9i) - 37(9+6i-1) + 198 + 66i - 10 = 0

=> a(27+17i) - 37(8+6i) + 188 + 66i = 0

=>  a(27+17i) = 296 + 222i - 188 - 66i

=> a(27+17i) = 108 + 156i

=> a = (108+156i) / (27+17i)

=> a = (108+156i)(27-17i) / (27)² - (17i)²

=> a = (5568 + 2376i) / (699 + 289)

=> a = 5568 + 2376i / 1488

DONNEEE....yayyyy....lol

12.6 + 4m = 9.6 + 8m

Answers

Answer:

3 = 4m or  0.75 = m

Step-by-step explanation:

12.6 + 4m = 9.6 + 8m

Subtract 4m from both sides of the equation

12.6 = 9.6 + 4m

Subtract 9.6 from both sides of the equation

3 = 4m

Divide by four on both sides of the equation

0.75 = m

I Hope That This Helps! :)

Just answering so the other guy can have brainiest! Hope this helps!

Use long division to change 11/30 to a decimal

Answers

hope this helps! answer= 0.366 to 3 decimal places

Answer: 0.3666667

Step-by-step explanation:

Pls help I don’t understand what the problem is asking

Answers

It A 4 inches I think.

What is the measure of line segment BE in the diagram below?

Answers

Answer:

15

Step-by-step explanation:

∆ABC ~ ∆AED, therefore,

[tex] \frac{AB}{AE} = \frac{BC}{ED} [/tex]

Let BE = x

AB = x + 9

AE = 9

BC = 16

ED = 6

Plug in the values into the equation

[tex] \frac{x + 9}{9} = \frac{16}{6} [/tex]

[tex] \frac{x + 9}{9} = \frac{8}{3} [/tex]

Cross multiply

[tex] (x + 9)(3) = (8)(9) [/tex]

[tex] 3x + 27 = 72 [/tex]

Subtract 27 from each side

[tex] 3x = 72 - 27 [/tex]

[tex] 3x = 45 [/tex]

Divide both sides by 3

[tex] x = \frac{45}{3} [/tex]

[tex] x = 15 [/tex]

Segment BE = x = 15

Use the value of x to find the measure of angle 1 x=25

Answers

Answer:

I’ll just do them both since it’s easier to check.

So to make this easier both of the angles will add up to 180 degrees so let’s make an equation.

5x-5+2x+10=180
First we collect like terms
5x+2x-5+10=180
Add them up
7x+5=180
Move the constant to the right
7x=180-5
7x=175
7x/7=175/7
x=25

So yes it’s true x=25.

Now we find the respective angles,

5x-5
5(25)-5
125-5
120

So angle one is 120 degrees.

2x+10
2(25)+10
50+10
60

So angle two is 60 degrees.

Now to check,

120+60=180





Jessica counted 26 heartbeats in 20 seconds. How many times will her heart beat in 1 minute? WILL GIVE BRAINLIEST!!!!!!!

Answers

Answer:

78

Step-by-step explanation:

multiply 26 by 3 because 60÷20=3

Answer: 78

Step-by-step explanation: 20x3=60 and there is 60 secs in a minute

and 26x3=78

So the answer is 78 heartbeats in a min

Where does warm water accumulate in the Pacific Ocean during El Niño?

the east
the south
the north
the west

Answers

answer:

a. east coast! :)

hope this helps.

Answer:

I put A and got it right on edge Step-by-step explanation:

A ball rolling down the hill is an example of what type of energy

Answers

Answer:

When a ball rolls downhill, the gravitational potential energy of the ball is transformed into motion energy. A ball is rolling up and over a hill. The ball slows down as it moves from Position 1 to Position 3, and it speeds up as it moves from Position 3 to Position 5.

Step-by-step explanation:

Happiness is it qualitative or quantitative?

Please answer

Answers

Qualitative... I think sorry if I’m wrong

Answer:

i think its quantiative  becuase theirs only 2 options but i could be wrong btw srry for bad spelling

Step-by-step explanation:


A rope 160m in length is cut into 5 equal lengths. How long is each length of rope?

Answers

Answer:32m

Step-by-step explanation:

So you would have to divide 160 and 5 and it would equal 32

What is the y-intercept in the equation 2y = x -8

Answers

Answer:

(0,-4)

Step-by-step explanation:

whats the place value of number 4 in the number 1 345.87?​

Answers

Answer:

Tens

Step-by-step explanation:

Decimal Place Values:

millions

hundred thousands

ten thousands

thousands

hundreds

tens

ones

. decimal point

tenths

hundreths

thousandths

ten thousandths

Find the value of angle G, C and F

Answers

Answer:

G is 37

C is 143

F is 37

Step-by-step explanation:

G is 37 because of a rule called complementary angles. They are two angles that equal to 90 degrees! As shown in the angle right next to it, there is a small square that represents 90 degrees, so that means 53 + g would = 90 degrees as well, making g 37.

C is 143 because of a rule called supplementary angles. Supplementary angles are angles on a line that equal to 180 degrees. No matter how many angles are on a straight line, they will all equal to 180. So since I found out g is 37, I just used one of the lines and did 180-37 = 143.

F is 37, and you could find it in two ways. You can use supplementary angles with the angle of c you just found, or you can just use a rule called vertical angles. It is a rule that says any opposite angles from each other are equal. The opposite angle of F would be G. Since G is 37, F would be 37 as well. Definitely look up these terms if I am confusing them for you!! I hope I helped!!

Other Questions
The difference between seize and capture is that _____ is to catch as if by hunting.seizecapture Describe the transformation that takes f(x) = x+1 to g(x) = -x+4. Carby Hardware has an outstanding issue of perpetual preferred stock with an annual dividend of $9.20 per share. If the required return on this preferred stock is 6.5%, at what price should the preferred stock sell what is the primary purpose of the interaction between all of the components of the climate system -7/2 x 1/6Please help! Why do authors use historical background in nonfiction pieces? Select all that apply.[] to create a setting for the story they have created[] to help the reader connect the work with events from the past[] to make the text more interesting[] to make the text more realistic Explain why the contribution of renewable energy to world production is likely to remain less than fossil fuel production (6 marks) Determine one positive and one negative example from the Mexican Constitution and describe why. Which of the following is a good rule of thumb for longdrives?A. Finish the drive as fast as possible without rest, and rest when you aredone.B. Find a safe place to pull over and take a 15-minute rest every four hours.C. Find a safe place to pull over and take a 15-minute rest every two hours.D. Have food and drink readily available, so you don't tire yourself out. Why did the colonists at Plymouth believe that representative government would be the best way to protect their religious freedom?: PLS HELP ITS ALREADY MISSING Example of paradox in the speech of convention Benjamin Franklin escribe esta oracion en el imperfecto: tu haces la tarea todas las noches HELP ME Please and thank you? Adrian is going to the store and needs milk he needs 4 bottles of milk he has 14$ and each cost 4$ does he have enough money A grocery store sells tangerines in 4/5 kg bags. A customer bought 4 kg of tangerines for a school party. How many bags did he buy? Select all the equations that represent the situation.A.4 4/5 = ?B.? 4/5 =4C.4/5 4 =?D.4 4/5 =?E.? 4/5 = 4 WILL GIVE BRAINLIEST! A negative growth rate in a population may be a result of what factor?A) An increase in the fertility rate of the populationB) An increase in the birth rate of a competition speciesC) An increase in the birth rate of a prey speciesD) A decrease in the birth rate of a predator species Help I need help ON THISSSS What statement is true regarding the influence of the church as itapplied to the creation of art during the Middle Ages (5thto the 15thCentury), also known as the Medieval Period that merged intothe Italian Renaissance. Witch trials and burnings were taking placeand the rise of the Spanish Inquisition (1478-1834) brought fear of the"Church" and birthed the seeds of Democracy and Revolutionculminating in the birth of the United States of America.Science and the Church were often at odds with each other resulting in artists andscientists being very secretive regarding their works and inventionsThe Church was a powerful force resulting in most art having a religious natureWealthy politicians often commissioned artists to paint their portraits as propagandaAll of the aboveNone of the Above Which of the following paintings is considered the epitome of French Rococo painting?a.b.c.d.Please select the best answer from the choices providedABCD What is the present value of the following payment stream, discounted at 8% annually: $1,000 at the end of year 1, $2,000 at the end of year 2, and $3,000 at the end of year 3?a. $5,022.10b. $5,144.03c. $5,423.87d. $5,520.00