Find two positive integers such that their sum is 10, and minimize and maximize the sum of their squares.

Answers

Answer 1

Two numbers whose sum is 10 is required.

The answer is

Minimum: 5, 5

Maximum: 9, 1

Let [tex]x[/tex] and [tex]y[/tex] be two numbers

[tex]x+y=10\\\Rightarrow y=10-x[/tex]

The sum of the squares would be

[tex]x^2+y^2=x^2+(10-x)^2\\ =2x^2-20x+100[/tex]

[tex]f(x)=2x^2-20x+100[/tex]

Differentiating with respect with x

[tex]f'(x)=4x-20[/tex]

Equating with zero

[tex]4x-20=0\\\Rightarrow x=\dfrac{20}{4}\\\Rightarrow x=5[/tex]

Double derivative of f(x)

[tex]f''(x)=4[/tex]

[tex]f''(x)>0[/tex]

So, at [tex]x = 5[/tex] the value of the function is minimum.

Therefore, at [tex]x=5[/tex] and [tex]y=10-5=5[/tex] the function has minimum value of [tex]5^2+5^2=50[/tex]

For the finding the maximum values of [tex]x[/tex] and [tex]y[/tex] we have to use trial and error method

[tex]9^2+1^2=82[/tex]

[tex]8^2+2^2=68[/tex]

[tex]7^2+3^2=58[/tex]

[tex]6^2+4^2=52[/tex]

0 and 10 will not be considered as 0 is neither positive nor negative.

So, the maximum value of the numbers is 9 and 1 and the maximum value of the function is 82.

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Related Questions

The two triangles are similar, What is the length of DE?

Answers

Answer:

If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, the triangles are similar. The corresponding sides of similar triangles are in proportion.

I hope this might help you

Mark it as brainliest answer and follow me

Write an equation of a line perpendicular to line CD in slope-intercept form that passes through the point (−1, 6).

Line CD is shown. C is at 1, 1. D is at 3, 5.

y = −0.5x − 5.5
y = −0.5x + 5.5
y = 2x + 13
y = 2x − 13

Answers

Answer:

its b

Step-by-step explanation:

i took the test

y = - 0.5x + 5.5 is the equation of a line perpendicular to line CD in slope-intercept form that passes through the point (−1, 6).

What is the slope-intercept form of a straight line?

The slope-intercept form of a straight line is y = mx + c.

Here, x and y are coordinates, m is the slope and c is the y-intercept of the line.

Given, two points are C(1, 1) and (3, 5).

Therefore, equation of the line CD is:

[tex]\frac{x - x_{1} }{y-y_{1} }[/tex] = [tex]\frac{x_{1}-x_{2}}{y_{1}-y_{2}}[/tex]

⇒ [tex]\frac{x - 1}{y-1}[/tex] = [tex]\frac{1-3}{1-5}}[/tex]

⇒  [tex]\frac{x - 1}{y-1}[/tex] = [tex]\frac{-2}{-4}}[/tex]

⇒2(x - 1) = (y - 1)

⇒ y = 2x - 1

Let, line AB is perpendicular to the line CD and passes through the point (-1, 6).

Therefore, slope of the line CD is = 2.

We know, slope of CD × slope of AB = -1

Therefore, slope of AB = -1 / slope of CD = [tex]-\frac{1}{2}[/tex].

Now, line AB has a slope of [tex]-\frac{1}{2}[/tex] and passes through the point (-1, 6).

Therefore, equation of the line AB is:

(y - y₁) = m(x - x₁)

⇒ [y - (6)] = [tex]-\frac{1}{2}[/tex][x - (- 1)]

⇒ 2(y - 6) = (-x - 1)

⇒ 2y - 12 + x + 1 = 0

⇒ x + 2y = 11

⇒ y = - 0.5x + 5.5

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Simplify the expression using the properties of operations.
The simplified form of the expression (5.23x + 3.76) − (3.67x − 6.39) is

Answers

Answer:

Step-by-step explanation:

5.23x+3.76-3.67x+6.39

x(5.23-3.67) +(3.76+6.39)

1.56x + 10.15

Answer:

1.56x + 10.15

Step-by-step explanation:

(5.23x + 3.76) – (3.67x – 6.39)

(a + b) – (c – d) = a + b – c + d

Remove the parentheses and change the signs as needed:

5.23x + 3.76 – 3.67x + 6.39.

Group the like terms and simplify:

5.23x – 3.67x + 3.76 + 6.39

1.56x +10.15.

For every 2 hours, approximately $1,689 worth of product is sold to consumers. How much money will the company for an entire month (30 days)?

Answers

1,01340 cuase 1,689 times 2 equal 3,378 and times 30 equal 101340

The answer is approximately 608040

Reason: for ever 2 hours its 1689 so times that by 12 to make 24 hours for a day and times that by 30

I WILL MARK BRAINIEST

Answers

Answer:

x=20

4=140

1=40

Step-by-step explanation:

7x=2×+100

5×=100

×=20

4=7(20)=140

1=180-140=40

Answer:

x=20

m<4=140

m<1=40

Step-by-step explanation:

to figure out angle 1 just subtract 140 from 180

PLEASE HELP ASAP I WILL GIVE BRAILY AND 25 POINTS... write an expression equivalent to 4x + 12 using the distributive property

Answers

Answer:4x + 12 = 2 ( 2x + 6)

 Step-by-step explanation:

aye i have a code karen someone help please

go to this question on my page and then go to the first answer and there's a Karen in the comments
"1. what do you do to check weather a number is rational or irrational? in your explanation, use an example of irrational and a rational number. 2. how does finding the square root of a number compare to finding the cube root of a number? use the number 64 in your explanation. REALLY HIGH BRAINIRLY"

Answers

Answer:

1. If you're taking square roots, the number must be a perfect square to give a rational root.

64 = 8^2, so √64 = 8 is rational

Similarly, since

64 = 4^3, ∛64 = 4 is rational.

For small numbers, it's easy to check for possible roots, as there aren't that many candidates. In general, it's much more difficult.

2.

Step-by-step explanation:

What is the constant proportionality in the table below?

Answers

Answer:

1/2

Step-by-step explanation:

Y is half as large as x. I cant see the options but I know that 10/2=5, 6/2=3 and so on so i would go with 1/2

At the end of a snow storm, Riley saw there was a lot of snow on her front lawn. The temperature increased and the snow began to melt at a steady rate. The depth of snow on Riley's lawn, in inches, can be modeled by the equation S = 13 – t, where t is the time, in hours, after the snow stopped falling. What is the x-intercept of the equation and what is its interpretation in the context of the problem?​

Answers

Answer:

The x-intercept of the function is 13 which represents the number of hours until all the snow has melted.

Step-by-step explanation:

Since there were 0 inches of snow on the lawn after 13 hours, the x-intercept of 13 represents the number of hours after the storm stopped when all of the snow had melted away.

Have a good day :)

The x-intercept of the function is 13 which represents the number of hours until all the snow has melted.

What is coordinate geometry?

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Since there were 0 inches of snow on the lawn after 13 hours, the x-intercept of 13 represents the number of hours after the storm stopped when all of the snow had melted away.

Hence, the x-intercept is 13.

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PLEASE HELP ILL GIVE BRAINLIEST

Answers

Answer:

[tex](\frac{x1 + x2}{2}, \frac{y1+y2}{2}[/tex])

Step-by-step explanation:

What transformation happened to the parent linear function when the m is changed to 3? Parent equation: y=x. New equation y=3x​

Answers

Answer:

Step-by-step explanation:

the funtion was dilated by a factor of 3 since insted or x we have 3x

Who can access your credit report?
a friends
b. employers
c. neighbors
d. teachers
Please select the best answer from the choices provided.
Ο Α
С В
ОС
D

Answers

This answer would be B

Answer:

B) employers

Step-by-step explanation:

EDGE 2021

PLEASE ANSWER THESE I'M NOT SURE HOW TO DO IT TYSMMMMM

Answers

Answer:

your answer is 234

Step-by-step explanation:

The total degree inside the triangle is 360.

Add 104 and 22 to gt 126, and subtract from 360 to get the angle value of x, which is 234 degrees.

Just answer number 1
M<7=30 ,m<2 ?

Answers

Answer:

Step-by-step explanation:

1). ∠7 ≅ ∠ 2 (alternate exterior)

m∠7 = m∠2 = 30°

2). ∠4 and ∠1 are supplementary angles

m∠1 = 180° - 72° = 108°

Determine if the following argument always applies, sometimes applies, or never applies. Provide at least 2 examples in your explanation.

"The sum of a number and its opposite is always 1."

Answers

Answer:

Never applies

Step-by-step explanation:

Given

Argument: The sum of a number and its opposite is always 1

Assume a positive number x

The opposite of the number is negative x (i.e. -x)

The sum of both numbers is:

[tex]Sum = x + (-x)[/tex]

Open Bracket

[tex]Sum = x -x[/tex]

[tex]Sum = 0[/tex]

Now, take for instance.

[tex]Number = 5[/tex]

Opposite would be

[tex]Opposite = -5[/tex]

Their sum is:

[tex]Sum = 5 + (-5)[/tex]

[tex]Sum = 5 -5[/tex]

[tex]Sum = 0[/tex]

Another instance is:

[tex]Number = -8[/tex]

Opposite would be

[tex]Opposite = 8[/tex]

Their sum is;

[tex]Sum = -8 + 8[/tex]

[tex]Sum = -0[/tex]

Hence, the argument never applies because the sum is never 1

Solve for n: n/3 > 66 2/3

Answers

Answer: The 2 answers are inequality form and interval notation: n>200, and (200, ∞).

Step-by-step explanation: To solve for n, you’ll need to simplify the both sides of the inequality, and then isolating the variable.

What is the fractional equivalent of repeating decimal 0.5

Answers

if it is repeating then it is 5/9 but if it is just 0.5 then 1/2

The fractional equivalent of the repeating decimal 0.5 is 5/9.

To convert the repeating decimal into a fraction, we can assign a variable, let's say x, to the repeating decimal. In this case, x = 0.5555...

Next, we multiply both sides of the equation by a power of 10 that will eliminate the repeating part.

10x = 5.5555...

Now,we subtract the original equation from the new equation to eliminate the repeating part:

10x - x = 5.5555... - 0.5555...

9x = 5

Simplifying the equation, we get:

x = 5/9

Therefore, the correct answer is A. 5/9.

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The complete question is

What is the fractional equivalent of the repeating decimal 0.5?A.5/9B.1/2C.5/99D.5/100

Triangle abc is isosceles. Measure of angle a=3x+40, Measure angle c=x+50. Measure of angle a = degrees​

Answers

Answer: the answer is 55°

Step-by-step explanation:

You equal the equations out and the number you get from doing that is the fill in for x and the you solve one of the equations replacing x with the number gotten

Simplify (6x ^ 2 + 11x - 3) + (2x ^ 2 - 17x - 4) . (1 point)
1 ) 8x ^ 2 + 6x - 1
2) 8x ^ 2 - 6x - 7
3 ) 8x ^ 2 + 6x + 1
4 ) 8x ^ 2 - 6x + 7

Answers

Answer:

2) 8x^2 -6x-7 hope this helps

round 0.918 to the nearest whole number ​

Answers

0.918 to the nearest whole number would be 1.

This is because 9 is more than 5 so you make it 0 and add 1 to the next number. After that everything else turns to 0’s.

Hope this helps and have a nice day/night!!!

A bakery baked 16 pies in preparation for Thanksgiving. 3/4 of the pies were already sold. How many pies have been sold?

Answers

Answer:

12

Step-by-step explanation:

We have to find 3/4 th of 16

So it's 3/4 * 16 = 12


What is the x-intercept of
3x – 4y = 242

Answers

Answer:

x=242/3

alternative form= 80 2/3, x=80.6

Step-by-step explanation:

3x-4y=242

substitute y = 0

3x-4x0=242

calculate the product

3x-0=242

remove 0

3x=242

divide both sides (by 3 in order to leave x by itself)

done

Find the value of r.

Answers

Answer:

r=0

Step-by-step explanation:

the line passes through the origin which means there is no y-intercept

Please help me I don’t get this Write the equation of the line that is parallel to y=3x-2 and goes through the points (-4,2)

Answers

Alright so answer is y=3x+14

Since you need to find a PARALLEL line to y=3x-2, you already know that the incline is 3x because otherwise the two lines would intersect somewhere.

So for your new equation you now have y=3x+b, so you only need to find b. To do so you’ll need to replace all other variables by numbers with the point that is given and then isolate b.

You can do so with the point that is given to you (-4, 2). You replace y by 2 since the point is (x,y) and replace x by -4.

You now have
2=3(-4)+b
2=-12+b
2+12=b
14=b

You now have your equation: y=3x+14

Hi! I just need somebody to explain how this is done.
I don’t understand the process of this well and I cant find many videos that explain it. thanks!

Answers

Answer:

Exact form: x = [tex]\frac{10.8}{sin(57)}[/tex]

Rounded to the Nearest Tenth: x = 12.9

Step-by-step explanation:

In the right-angled triangle, we can use the trigonometry functions to find the length of a side or a measure of an angle

In the given figure

∵ ∠C is the right angle

ΔACB is a right triangle

m∠B = 57°

AC = 10.8

∵ AC is the opposite side of ∠B

∵ AB is opposite to the right angle

∴ AB is the hypotenuse

AB = x

→ We can use the function sine to find x

∵ sin∠B = [tex]\frac{opposite}{hypotenuse}[/tex]

∴ sin∠B = [tex]\frac{AC}{AB}[/tex]

→ Substitute the values of ∠B, AC, and AB in the rule of sine above

∴ sin(57°) = [tex]\frac{10.8}{x}[/tex]

→ By using cross multiplication

∵ x × sin(57°) = 10.8

→ Divide both sides by sin(57°)

x = [tex]\frac{10.8}{sin(57)}[/tex]

x = 12.87752356

→ Round your answer to the nearest tenth

x = 12.9

Exact form: x = [tex]\frac{10.8}{sin(57)}[/tex]

Rounded to the Nearest Tenth: x = 12.9

What is the scale factor for the dilation of triangle ABC to produce triangle A’B’C’?
0.25, 0.5, 2, 3

What is the scale factor for the dilation of triangle ABC to produce triangle A’’B’’C’’?
0.25, 0.5, 2, 3

Answers

Answer:

.5 for the first blank

2 for the second blank

Seven more than a number, x, is at most 20

Answers

Answer:

x+7 ≤ 20

Just take it step by step:

seven more than a number is a number plus 7 (x+7)- keep in mind we dont know what the number is so we use x to represent the number.

it then says it's equal to at most 20.

This means that it cant equal anything above 20 since 20 is the max. Therefore, it must be 20 and below that x+7 equals

x+7≤ 20

≤ -this symbol means less than or equal to

Step-by-step explanation:

John wants to make a triangular garden. Which of the following are possible dimensions?

Answers

Answer: What are the choices? sorry I had to take up an answer, it wont let me exit out

The length of a rectangle is four times its width.
If the perimeter of the rectangle is 90 yd, find its length and width.

Answers

Answer:

Length of rectangle = 36 yd and width of rectangle = 9 yd

Step-by-step explanation:

Let width of rectangle = w

Length of rectangle = 4w (four times the width)

Perimeter of rectangle = 90 yd

We need to find length and width of rectangle.

The formula used will be: [tex]Perimeter \ of \ rectangle=2(l+w)[/tex]

Where l is length and w is width

Putting values and finding length and width of rectangle

[tex]Perimeter \ of \ rectangle=2(l+w)\\90=2(4w+w)\\90=2(5w)\\90=10w\\w=\frac{90}{10}\\w=9[/tex]

So,width (w) of rectangle is w= 9 yd

Finding length of rectangle = 4w = 4*9 = 36 yd

So, length of rectangle = 36 yd and width of rectangle = 9 yd

Last month you had 8 wins while playing fortnight. This month you had 5. What was your percent of change?
I need work shown.

Answers

Answer:

%62.5

Step-by-step explanation:

Im pretty sure you jsut divide 5/8 and then multiply by 100 to get a percent

5/8=.625

.625*100=62.5

%62.5

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