A= (4,-1)
B= (0,-5)
which one is right ,two answer choices.

The dimension of the container of this size that has the minimum cost is [tex]x = \sqrt[3]{360}[/tex], [tex]y = \sqrt[3]{360}[/tex] and [tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]

The given parameters are:

Assume the dimensions of the container are: x, y and z.

The volume (V) would be:

[tex]V = xyz[/tex]

Substitute 480 for V

[tex]xyz =480[/tex]

And the objective cost function would be:

[tex]C =8xy + 6xz + 6yz[/tex]

Differentiate the cost function using Lagrange multipliers

[tex]8x + 6z = \lambda xz[/tex]

[tex]8y + 6z = \lambda yz[/tex]

[tex]6x + 6y = \lambda xy[/tex]

Divide equation (1) by (2)

[tex]\frac{8x + 6z}{8y + 6z} = \frac{\lambda xz}{\lambda yz}[/tex]

[tex]\frac{8x + 6z}{8y + 6z} = \frac{x}{y}[/tex]

Factor out 2

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

Cross multiply

[tex]4xy + 3yz = 4xy + 3xz[/tex]

Evaluate the like terms

[tex]3yz = 3xz[/tex]

Divide both sides by 3z

[tex]y = x[/tex]

Divide the first equation by the third

[tex]\frac{8y + 6z}{6x + 6y} = \frac{\lambda yz}{\lambda xy}[/tex]

[tex]\frac{8y + 6z}{6x + 6y} = \frac{z}{x}[/tex]

Factor out 2

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

Cross multiply

[tex]4xy+3xz = 3xz + 3yz[/tex]

Cancel out the common terms

[tex]4xy = 3yz[/tex]

Divide both sides by y

[tex]4x = 3z[/tex]

Make z the subject

[tex]z =\frac{4}{3}x\\[/tex]

So, we have:

[tex]y = x[/tex] and [tex]z =\frac{4}{3}x\\[/tex]

Recall that:

[tex]xyz =480[/tex]

Substitute [tex]y = x[/tex] and [tex]z =\frac{4}{3}x\\[/tex]

[tex]x \times x \times \frac 43x = 480[/tex]

So, we have:

[tex]\frac 43x^3 = 480[/tex]

Multiply both sides by 3/4

[tex]x^3 = 360[/tex]

Take the cube roots of both sides

[tex]x = \sqrt[3]{360}[/tex]

Recall that:

[tex]y = x[/tex]

So, we have:

[tex]y = \sqrt[3]{360}[/tex]

Also, we have:

[tex]z =\frac{4}{3}x\\[/tex]

So, we have:

[tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]

Hence, the dimension of the container of this size that has the minimum cost is [tex]x = \sqrt[3]{360}[/tex], [tex]y = \sqrt[3]{360}[/tex] and [tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]

Read more about Lagrange multipliers at:

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Answer:

79.5

Step-by-step explanation:

20+35=55

38*16=608

12.5*55=687.5

687.5-608=79.5

Hope this helps! Plz give brainliest! Also, pls sub to kgirl633 on yt.

Answer: 79.5

Step-by-step explanation:

If any doubt leave a comment

Answer:

wot

Step-by-step explanation:

[tex]\left(\dfrac{3^8}{3^5} \right)^3\\\\\\=\left(3^{8-5}\right)^3\\\\=(3^3)^3\\\\=(3)^{3\cdot 3}\\\\=3^9[/tex]

Based on the right application of the reflexive property and subtraction property of equality, the table that correctly lists the reasons to prove that m∠1 ≅ m∠3 is: the table in option B (See attachment below).

The reflexive property of equality states that:

a + b = a + b.

Since m∠1 + m∠2 = 180°, and m∠2 + m∠3 = 180°, therefore, based on the reflexive property, we would have:

m∠1 + m∠2 = m∠2 + m∠3.

Thus, subtracting m∠2 from both sides of the equation will leave us with: m∠1 = m∠3 (subtraction property of equality).

Learn more about the reflexive property on:

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Answer:

i think area of the rug is 1 square yards

Step-by-step explanation:

area = 3/4×8/6

area = 2/2

area = 1 square yards

Answer:

24

Step-by-step explanation:

12*4/2

Answer:

The answer is 55 6/9, but when simplified, it is 55 1/3

Answer:

the answer is 12m

Step-by-step explanation:

u know the side c and side B.

C=15m but u have to square it which is 225

B=9m but u have to square it which is 81. then subtract 82 from 225.which will give u 144 which is a perfect square route of 12

Answer:

48 feet foot I took the testttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt oh yeah yeah yeah

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

6x + 20 = 10x

I hope this helps!

Answer:

Rate of sales tax = 6% of $60

Sales tax = [tex]\frac{6}{100}[/tex] × 60

               = $3.60

Using Venn probabilities, it is found that:

In this problem, the events are:

In this problem:

The probability of either is:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

Hence:

[tex]P(A \cup B) = 0.62 + 0.73 - 0.48 = 0.87[/tex]

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Answer:

87%.

Step-by-step explanation:

The probability that a resident chosen at random shops at either Comet Mall or at Star Mall is 87%.

Answer:

The steps for solving 7x + 3 = 52 are shown. Explain how each step helps solve the

Step-by-step explanation:

Simplifying

7x + 3 = 52

Reorder the terms:

3 + 7x = 52

Solving

3 + 7x = 52

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.

3 + -3 + 7x = 52 + -3

Combine like terms: 3 + -3 = 0

0 + 7x = 52 + -3

7x = 52 + -3

Combine like terms: 52 + -3 = 49

7x = 49

Divide each side by '7'.

x = 7

Simplifying

x = 7

Answer:

7 3/8 hours

Step-by-step explanation:

5 + 2 = 7

2/8 + 1/8 = 3/8

Therefore, 7 + 3/8 =

7 3/8 hours

Answer:

1 golf ball : $2.50

Step-by-step explanation:

Answer:

t=23

Step-by-step explanation:

Therefore, the area of the triangle is 4/9 cm².

Hoped this helped.

[tex]BrainiacUser1357[/tex]

Price of 6pencils=2.10

Price of one pencil

[tex]\\ \sf\longmapsto 2.10/6=0.35[/tex]

Price of 10pencils

[tex]\\ \sf\longmapsto 0.35(10)=\$3.5[/tex]

The cost of ten pencils is $3.50.

Given

Samir bought 6 equally priced pencils for $2.10.

A rate is a ratio that is used for comparing two different kinds of quantities which have different units.

The cost of 1 pencil is;

[tex]\rm =\dfrac{2.10}{6}\\\\=0.35[/tex]

Therefore,

The cost of 10 pencils is;

[tex]= 10 \times 0.35\\\\=3.50[/tex]

Hence, the cost of ten pencils is $3.50.

To know more about unit rate click the link given below.

https://brainly.com/question/11258929

Answer:

The area is 27

Step-by-step explanation:

Area =1/2 [x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)]

Area =1/2 [2(-6 - 8) + 3(8 - 4) + 7(4 + 6)]

=1/2 [2(-14) + 3(4) + 7(10)]

=1/2 (-28 + 12 + 70)

=1/2 (54)

Area = 27

Answer:

x = 20

Step-by-step explanation:

(2x+10) = 180 - 130

2x + 10 = 50

2x= 40

x = 20

hope this helps! :)

Step-by-step explanation:

y = 2x + 9

y = -x - 3

there are multiple ways to solve this.

let's follow the approach that both x-expressions must be equal :

2x +9 = -x - 3

3x = -12

x = -4

y = -x - 3 = 4 - 3 = 1

Answer:

21 = 10 + 5.5h

Step-by-step explanation:

Total cost = initial cost + hourly cost

21 = 10 + hourly cost

hourly cost = 5.5 per hour, or 5.5 * h as we add 5.5 for each hour

21 = 10 + 5.5h

Answer:

Step-by-step explanation:

$10 + $5.50h ≤ $21

Let h stand for the hours the canoe is rented.

Fixed cost = $10, regardless of h.

$5.50h for the cost of n hours of rental.

Total cost = $10 + $5.50h

The total cannot exceed $21, legally.  

So we should write:

$10 + $5.50h ≤ $21  

If $10 + $5.50h ≥ $21  then ║║║║║║║

Answer: Alice

Step-by-step explanation: Alice won because she started furthest From the starting line.

1) Commutative Property of addition and multiplication: (Commutative, x; Commutative, +) ... 24) -6 + 10 = 4 25) - 8 - 12 = 20 26) -8 +6= -2 27) -7 - 5= -12.

The given information of the base length and the height of the

rectangle are sufficient to find the area of the triangle.

Correct response:

Given that the parameters are;

The base of the triangle = [tex]\sqrt{245}[/tex] cm

The height of the triangle = [tex]\mathbf{\sqrt{20}}[/tex] cm

Required:

To find the area of the triangle

Solution:

Therefore, the area, A, of the given triangle is given as follows;

[tex]A = \dfrac{1}{2} \times \sqrt{245} \ cm \times \sqrt{20} \ cm= \dfrac{1}{2} \times \sqrt{4,900} \ cm^2= \dfrac{1}{2} \times 70 \ cm^2 = 35 \ cm^2[/tex]

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