Solve the following system of equations graphically.
y=3x+4
y=-2x-5

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:

  a) g(0) = -4

  b) x = -2 or +2 for g(x) = 0

  c) domain: all real numbers; range: y ≥ -4

Step-by-step explanation:

g(0) is the value of the function when x=0. That is where the function crosses the y-axis. g(0) = -4.

__

g(x) = 0 where the graph crosses the x-axis. The x-values there are ...

  x = -2 and x = 2

__

The domain is the horizontal extent of the graph. Here, we assume the graph extends to infinity both in the upward direction and to the left and right. Thus the horizontal extent (domain) is from -∞ to +∞, or "all real numbers."

The point where the graph crosses the y-axis is a minimum. There are no y-values below that point. So, the vertical extent (range) of the graph is from y=-4 to +∞.

  y ≥ -4 . . . . range

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

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.

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Hope you could get an idea from here.

Doubt clarification - use comment section.

The correct option is E. 0.579

Given, sin M = 0.759.

We have to find the value of cos N.

Since [tex]\Delta LMN[/tex] is right triangle.

We know that,

[tex]sin(90-\Theta)= Cos \Theta[/tex]

Assuming L is the right angle, So the other two angles are complementary.

Thus, [tex]cos(N) = sin(90-N) = sin(M)[/tex]

Hence,[tex]Cos(N)=Sin(M)[/tex]

Therefore the value of Cos N will be 0.759.

For more details on trigonometric ratio follow the link:

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Using the slope formula, it is found that the slope is of 0.09375 < 0.1, hence, it meets the requirements.

The slope of a ramp is given by it's height divided by it's length, that is:

[tex]m = \frac{h}{l}[/tex]

In this problem:

Then, the slope is given by:

[tex]m = \frac{h}{l} = \frac{75}{800} = 0.09375[/tex]

The slope is of 0.09375 < 0.1, hence, it meets the requirements.

A similar problem about the use of slopes in ramps is given at https://brainly.com/question/18090623

Answer:

x = 3.96

Step-by-step explanation:

apply the pitagoras theorem

x =

[tex] \sqrt{ {2.8}^{2} + {2.8 }^{2} } [/tex]

Answer:

$1.20 per chicken

Step-by-step explanation:

[tex]\frac{money} {chickens}[/tex]

[tex]\frac{18}{15}[/tex]

1.2

__________________________________________________________

Hope this helps!!

If I am wrong, please tell me, I enjoy learning from my mistakes:)

Answer:

y=-7x+19

Step-by-step explanation:

y-y1=m(x-x1)

y-5=-7(x-2)

y=-7x+14+5

y=-7x+19

The equation of the line with slope - 7 which goes through the point (2, 5) is

y = - 7x - 19.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, A line passes through points (2, 5) with a slope of - 7.

∴ 5 = -7(2) + b in slope-intercept form.

5 = - 14 + b.

b = - 19.

y = - 7x - 19.

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Answer: Alice

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

Answer:

1 golf ball : $2.50

Step-by-step explanation:

Answer:

wot

Step-by-step explanation:

Answer:

19.0% (1dp)

Step-by-step explanation:

$625-$525=$100

$100/$525=4/21×100=19.0% (1dp)

Answer:

P = 12 pi units + 24 units.

Step-by-step explanation:

All sides of an equilateral triangle are of the same length.  Here that length is 12 units.  We take a circle of diameter 12 units and cut it in half through its center.  Finally, we join the triangle (remembering that all of the side lengths are 12 units) to the half circle of diameter 12 units.

The half circle portion of the resulting shape has circumference 2(pi)(12 units) divided by 2, or 12 pi units.  This is half the formula C = 2(pi)(r).  The two non-attached sides of the triangle have a total length of 24 units.

Thus, the perimeter of the resulting figure is P = 12 pi units + 24 units.

Answer:

6mph

Step-by-step explanation:

180/4.5=40

180 × (1+15%)=207

207/4.5=46

46-40=6

Answer:

  cos(52°) = 18/x

  x = 18·sec(52°)

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that ...

  Cos = Adjacent/Hypotenuse

In this geometry, that means ...

  cos(52°) = 18/x

You can use the relation sec(x) = 1/cos(x) to rewrite this as ...

  x = 18·sec(52°)

_____

You can also use the complementary angle and the complementary trig function.

  sin(90° -52°) = 18/x

If any doubt leave a comment

Answer:

x = - 9/10

workings

2/3 x = - 3/5

multiply by 3/2 on both sides

x = - 9/10

Answer:

2/3x=-3/5

x=-3/5*3/2

x=-8/10

Answer:

C (is greater than it equal to) 31

Step-by-step explanation:

Isolate the c by adding 11 to both sides (cancels out the 11 and turns 20 into 31). Keep the sign the same!! Hope this helped! <33

Answer:

so first you

Step-by-step explanation:

find the center point of dilation and measure the distance from this center point to a point on the preimage and also the distance from the center point to a point on the image.

Answer:

2

Step-by-step explanation:

sin 90 is 1;

cos 360 is cos 0, or 1; and

tan 0 is 0.

Thus, sin 90° + cos 360° + tan 0° = 1 + 1 + 0 = 2

Step-by-step explanation:

We first calculate the lenght of the diameter, that is also the lenght of the hypotenuse of the right triangle shown in the figure:

d = [tex]\sqrt{3^2 + 4^2} = \sqrt{25} = 5[/tex] cm

The radius of the circle will be half of the diameter: r = d/2 = 2.5 cm

The area of the circle will be: Acircle = pi * r^2 = pi * 6.25 cm^2 = 19.6 cm^2 (circa).

Now from the area of the circle we subtract the area of the square:

Asquare = 4cm * 3cm = 12cm^2

A shaded = Acircle - Asquare = 19.6 cm^2 - 12cm^2 = 7.6 cm^2

Answer:

x = 5

Step-by-step explanation:

6x + 20 = 10x

I hope this helps!

Answer:

He can walk 0.25 blocks in 1 minute

Step-by-step explanation:

If Zack can walk 7.5 blocks in 30 minutes and we are looking for how many blocks he can walk in 1 minute, we will divide 7.5 by 30 as that will be the number of blocks per minute.

7.5/30 = 0.25

31

hope this is helpful!

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]

You can learn more about Venn probabilities at https://brainly.com/question/25698611

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:

35x does not equal 5 times 7Step-by-step explanation:

The second step ''(5 × 7) - (5 × 3)'' has an error.

Given that;

Luis made an error when he used the distributive property to write an equivalent expression.

Here the expression is,

35x - 15

It can be written as;

(5 × 7)x - (5 × 3)

Take 5 as common,

5 (7x - 3)

Therefore, the second step ''(5 × 7) - (5 × 3)'' has an error.

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