Here's what Gabriel and Kayla actually wrote.


Gabriel: 3x+6

Kayla: 3(x+2)


These expressions are equivalent.


What do you think that means?

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.

B

Step-by-step explanation:

Answer:

Constant of proportionality [tex] = \frac{1}{400} [/tex]

Step-by-step explanation:

A. The constant of proportionality can be calculated as the ratio of y to x. In this case, y = amount of paint, while x = the area of the wall

The area of the wall determines the amount of paint needed to cover the wall.

Constant of proportionality, k = y/x.

Any given pair cam be used as y and x to find k.

Thus, using (100, ¼),

[tex] k = \frac{\frac{1}{4}}{100} = \frac{1}{4}*\frac{1}{100} [/tex]

Constant of proportionality [tex] = \frac{1}{400} [/tex]

This means that as area of the wall increases, amount of paint increases and the ratio between them would always be [tex] \frac{1}{400} [/tex].

Answer:

76%

Step-by-step explanation:

38 multiplied by 100 = 3,800

3,800 divided by 50 = 76

Therefore the answer is 76%

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:

j

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:

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:

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:

b

Step-by-step explanation:

Answer:

(1,7)

Step-by-step explanation:

SImply replace x by (1) in the expression to find the value of h:

h(1) = 4 (1) + 3 = 4 + 3 = 7

so for x = 1, h is 7 , which is written as: (1, 7)

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:

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.

Learn more about the probability here:

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Answer:

  1260 inches

Step-by-step explanation:

1 yard = 36 inches

35 * 36 = 1260 inches

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:

b

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

Answer:

473 tickets

Step-by-step explanation:

8,500/18=472.2222222 but, since you can’t sell only part of a ticket, you’ll round up to get 473 tickets.

Answer:

13,000 ft.

Step-by-step explanation:

X -------10960----------C---------------D---------------Y

The entire race (from X to Y) is 7 miles.  There are 5,280 ft. in one mile, so 7 miles is 36960 ft.

If we subtract 10,960 from 36,960, then we get the distance from C to Y.

36960-10960 = 26000

They tell you D is at the midpoint between C and Y

So if we divide 26,000 by 2, then we know the distance from C to D and from D to Y.

26000/2 = 13000

The checkpoints are C and D, so the distance between them is 13,000 ft.

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%.

To learn more about Percentage, click :

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Answer:

the top empty box is 5 the second down box is 4 the box under 6 is 8

Step-by-step explanation:

Answer:

y=[tex]\frac{1}{4}[/tex]x+3

Explanation:

you have to use the formula y₂-y₁/x₁-x₂ in order to find your slope and what ever you get from that is your slope

Answer: no solution

Step-by-step explanation:

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:

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:

2.10 is greater than 2.09

Step-by-step explanation:

because 2.10 has more equation than 2.09

Answer:

2.10 is GREATER than 2.09 so **TRUE**

Step-by-step explanation:

hope this helps </3

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%

Answer:

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

Answer:

1.66666666667

Step-by-step explanation: