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Without using any calculus:

If x + y² = 5, then y² = 5 - x, so that

b = x y² = x (5 - x) = 5 x - x²

Complete the square to get

b = 25/4 - (x - 5/2)²

Then b gets a maximum value of 25/4 when x = 5/2.

Simple calculus method:

With b = 5 x - x², differentiate b with respect to x and set the derivative equal to 0 to solve for critical points:

db/dx = 5 - 2 x = 0   ==>   x = 5/2

Take the second derivative to determine whether b is concave or convex:

d²b/dx² = -2

The second derivative is negative, which means b is concave with respect to x, and this indicates x = 5/2 is the site of a local maximum, which is b (5/2) = 25/4.

More complicated calculus method:

Lagrange multipliers. The Lagrangian is

L (x, y, λ) = x y² - λ (x + y² - 5)

where we assume λ ≠ 0.

Take its derivatives:

dL/dx = y² - λ

dL/dy = 2 x y - 2 λ y

dL/dλ = x + y² - 5

Set each derivative equal to 0 to find the critical points. The first equation tells us y² = λ, and the second equation tells us x = λ, so

x + y² - 5 = 2 λ - 5 = 0

Solving this gives λ = x = y² = 5/2, so that b has an extreme value of

b = (5/2) (5/2) = 25/4

Deciding whether this is a maximum or minimum comes down to computing the Hessian determinant at the critical value. The Hessian is

[tex]H(x,y)=\begin{bmatrix}\dfrac{\partial^2b}{\partial x^2}&\dfrac{\partial^2b}{\partial x\partial y}\\\\\dfrac{\partial^2b}{\partial y\partial x}&\dfrac{\partial^2b}{\partial y^2}\end{bmatrix}=\begin{bmatrix}0&2y\\2y&2x\end{bmatrix}[/tex]

with determinant |H (x, y)| = -4 y². At the critical point, the determinant is -10 < 0, which indicates a maximum value of 25/4.

Answer:

  1260 inches

Step-by-step explanation:

1 yard = 36 inches

35 * 36 = 1260 inches

Answer:-7

Step-by-step explanation:Let's solve your equation step-by-step.

3(3x+1)−(4x+1)=6x−3(x+4)

Step 1: Simplify both sides of the equation.

3(3x+1)−(4x+1)=6x−3(x+4)

3(3x+1)+−1(4x+1)=6x−3(x+4)(Distribute the Negative Sign)

3(3x+1)+−1(4x)+(−1)(1)=6x−3(x+4)

3(3x+1)+−4x+−1=6x−3(x+4)

(3)(3x)+(3)(1)+−4x+−1=6x+(−3)(x)+(−3)(4)(Distribute)

9x+3+−4x+−1=6x+−3x+−12

(9x+−4x)+(3+−1)=(6x+−3x)+(−12)(Combine Like Terms)

5x+2=3x+−12

5x+2=3x−12

Step 2: Subtract 3x from both sides.

5x+2−3x=3x−12−3x

2x+2=−12

Step 3: Subtract 2 from both sides.

2x+2−2=−12−2

2x=−14

Step 4: Divide both sides by 2.

2x /2

=

−14 /2

x=−7

Answer: no solution

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

∡BEN=122

x=17

Step-by-step explanation:

Since you know that when two sides are congruent like this then the to angles are congruent then you know that angle BNE equals 29.

Once you know that since we know that 180 is the sum of all three angles set an equation like this:

180=29+29+(11x-65)

Take off parentheses since you can't simplify in them.

180=29+29+11x-65

Combine like terms.

180=11x-7

Solve for x.

187=11x

x=17

Plug that in to (11x-65) to find angle BEN

angle BEN = 11(17)-65

angle BEN=122

Answer:

76%

Step-by-step explanation:

38 multiplied by 100 = 3,800

3,800 divided by 50 = 76

Therefore the answer is 76%

B

Step-by-step explanation:

Answer:

(35-2- is the correct answer you can believe me

Answer:

j

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

x = 3

according to the condition,

y = 7× x + 4

y = 7× 3 +4

y = 21 + 4

y = 25

The question is incomplete:

Netlfix charges $30 a month plus $5 per movie. Hulu charges $26 a month plus $7 per movie. How many movies will you need to watch for the Netflix membership to pay off and cost you less?

Answer:

3 movies

Step-by-step explanation:

From the information given, you can write an inequality that indicates that Netflix membership costs less than Hulu membership:

30+5x<26+7x

Now, you can solve for x:

30-26<7x-5x

4<2x

4/2<x

x>2

According to this, the answer is that you will need to watch 3 movies for the Netflix membership to pay off and cost you less.

Answer:

B

Step-by-step explanation:

35+64+97=196       97+64=161          161/196=B

The probability that a randomly-selected club member holds a brown belt or a purple belt is 0.821 which is nearest to 0.762.

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

Total number of person = 35+64+97 = 196

P(brown belt) = 64/196  

P(purple belt) = 97/196    

Probability that a randomly-selected club member holds a brown belt or a purple belt:

= 64/196 + 97/196

= (64+97)/196

= 161/196 = 0.821

Thus, the probability that a randomly-selected club member holds a brown belt or a purple belt is 0.821 which is nearest to 0.762.

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Answer:

b

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

Answer:

I'm pretty sure it's a.....

The answer is A

Step-by-step explanation:

common sense

Answer:

Yes

Step-by-step explanation

6:3 multiply by 3 is equal to 18:3

Answer:

Yes

Step-by-step explanation:

This is because 6x3 is 18 for the 18:3 and 1x3 is 3 in the 18:3. You can also think it this way, 18/3 and 6/1 if you divide both you get an answer of 6 so they both are the same meaning making them equivalent

Answer:

1.66666666667

Step-by-step explanation:

Answer:

700,000

Step-by-step explanation:

Well, [tex]10^{4}[/tex] as we know is 10(10)(10)(10), or 10 multiplied by itself 4 times.

The easiest way to solve this, is knowing that because 10 is being multiplied by itself 4 times, it'll have the outcome of 10000, which has 4 zeroes. This is very good to remember, so I recommend remembering it :) Just like if the question was about [tex]10^{5}[/tex], it would be 100000, which has 5 zeroes.

So now we add on all of those zeroes to 70.

700000 would be your answer because we added on 4 more zeroes.

Answer:

b. 1/x^4

c. w^7/x^2

e. 1/a^2+b^2

f. 1/b^5

Step-by-step explanation:

Simpilest form means that the exponents must be a postive number. That's what the Edge guy said. I entered these answers in and I got it right on Edge 2021. Today is Janurary 3rd.

The expressions in the simplest forms would be as follows:

b). [tex]1/x^4[/tex]

c). [tex]w^7/x^2[/tex]

e). [tex]1/a^2+b^2[/tex]

f). [tex]1/b^5[/tex]

The simplest form is described as the most compact form of an expression that cannot be broken anymore and does not have any other factor in common than 1.

All the above-mentioned expressions exemplify the simplest forms as they do not have any other factor in common except for 1.

Thus, options b, c, e, and f are the correct answers.

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Answer:

Given that m∠DEF = 142, m∠GEF = (9x - 8)°, and m∠DEG = (3x + 6),

GEF + DEG = DEF

[tex]9x - 8 + 3x + 6 = 142\\\\12x - 2 = 142\\\\12x = 144\\\\x = 12[/tex]

Answer:

Step-by-step explanation:

10^6

Answer:

10^6

Step-by-step explanation:

Answer:

Well, we need a definition or length/width of the figure of it first, let me see what I can find, I'll leave it in my replies.

Step-by-step explanation:

so basically the writing says to draw the lines indicated by arrows and include the markings on the last one because they indicate that all the sides are equal in length  

;P hope this helps!

Answer:

12

Step-by-step explanation:

Plug in for x first:

Y = -2(x+4) +6

Y = -2((-2)+4) +6

Y = -4 + 6

Y = 2

Then use Y to find W;

W = -3 -2y

W = -3 - 2(2)

W = -3(-4)

W= 12

Answer:

y=8 and w=13

Step-by-step explanation:

y=-2(x+4)

-2x-2=4 sooo...

y=4+4

y=8

then plug 8 into the equation for w

w=-3-2y

then you would get

w=-3-16

-3-16

w=13

Answer:

44 bro

Step-by-step explanation:

The percentage of representatives staying at least two nights rented a car is 44%.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

So the percentage actually means a part per 100.

Percentage is usually denoted by the symbol '%'.

Given is a two way table.

From the table, the number of representatives staying at least 2 nights rented a car is 11.

Total number of representatives staying at least two nights = 14 + 11 = 25

Percentage = (11 / 25) × 100

                    = 0.44 × 100

                    = 44%

Hence the percentage for the required number is 44%.

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Answer:

A. All atoms of the same elements are identical

Step-by-step explanation:

Two atoms of the same chemical element are typically not identical. They can be different if their electrons are in different states,

Answer:

88.8%

Step-by-step explanation:

Answer:

89% correct

Step-by-step explanation:

32 out of 36

32/36

8/9

0.89

89 percent correct

Answer:

An easy way to solve this problem is divide $25.00 by 3 or $43.75 by 7. This number represents the amount of money he makes for 1 hour. So with that in mind, the correct equation is:

$8.33 = y

Hope this helped :)!

Answer: 45

Step-by-step explanation: The 3rd partner has 45% of the store. Which is also $315,000.

Answer: the third partner owns 45% or $315,000 of the business.

Step-by-step explanation:

30 percent of 700,000=210,00

25 percent of 700,000=175,000

175,000+210,000=385,000

700,000-385,000= 315,000

the third partner owns 315,000 and 315,000=45%