2r(2.59 + 10) - 3(r + 4) + s(r - 1)?<br> equivalent?

Inessa [10]

<span>This tells us two things. Our slope is 3 and our y intercept is -4.
This tells us that we need to start at (0,-4).
Plot that point.
Since our slope is 3 (3/1), move up 3 and right 1.

This you will end up at point (1,-1).
Connect these two points in a straight line, and you have graphed your line.
It will look like this</span>

6 0

3 years ago

Read 2 more answers

A container manufacturer plans to make rectangular boxes whose bottom and top measure x by 4x. The container must contain 12ft^3

zheka24 [161]

The height of the container should be equal to 2.57 cm, so as to minimize cost.

<h3>How to calculate the height?</h3>

First of all, we would determine the volume of the rectangular container by using this formula:

Volume = l × w × h

Where:

l represents the length.

w represents the width.

h represents the height.

Substituting the given parameters into the formula, we have;

Volume = x × 4x × h

Volume = 4x²h

At a volume of 12 ft³, we have:

12 = 4x²h

h = 12/4x²

h = 3/x²

For the total area of top and bottom, we have:

Area = (x × 4x) + (x × 4x)

Area = 4x² + 4x²

Area = 8x² sq. units.

Thus, the cost of top and bottom is given by:

Cost = 8x² × 1.50

Cost = $12x²

For the total area of all four sides, we have:

Area = (x × h) + (x × h) + (4x × h) + (4x × h)

Area = xh + xh + 4xh + 4xh

Area = 10xh sq. units.

Thus, the cost of all four sides is given by:

Cost = 10xh × 4.50

Cost = $45xh.

Also, the cost function would be given by:

C(x) = 12x² + 10xh

C(x) = 12x² + 10x(3/x²)

C(x) = 12x² + 30/x

Taking the first derivative, we have:

dC/dx = 24x - 30/x²

24x = 30/x²

24x³ = 30

x³ = 30/24

x = 1.08

Therefore, the height will be:

h = 3/x²

h = 3/1.08²

h = 3/1.1664

Height, h = 2.57 cm.

Read more on minimum height here: brainly.com/question/27308167

#SPJ1

5 0

2 years ago

Which is the last operation performed when evaluating (8 minus 2 x) squared + 4 for x = 3?

kompoz [17]

Answer:

addition

Step-by-step explanation:

The given expression is $(8-2x)^2+4$

We want to determine the last operation performed when evaluating this expression for x=3.

We substitute to get:

$(8-2*3)^2+4$

Multiply within the parenthesis to get:

$(8-6)^2+4$

Subtract to get:

$2^2+4$

Evaluate the exponent to get:

4+4

Add to obtain:

8

Hence the final operation is addition

4 0

3 years ago

Read 2 more answers

PLEASE HELPP!!

Rasek [7]

Answer:

Given:

Two trail maps:

Trail on the first map = 8 cm

Trail on the second map = 6 cm

Scale on first map = 1 cm : 2 km

A) What is the scale factor from the map to the actual trail?

For the first map, the scale factor is 1 cm: 2km. Therefore the actual trail is 8 centimeters * 2 kilometers = 16 km.

The scale factor of the second map is 16 km / 6 cm = 2.67 km : 1 cm

B) The length of the actual trail is 16 kilometers.

Step-by-step explanation:

3 0

3 years ago

Samuel used 1/5 of an ounce of butter to make 1/25 of pound of jelly how many ounces of butter is there per pound of jelly

Svetach [21]

1 ounce --> ?
1/5 --> 1/25
i chaged the freactions to decimal this is what i got,
1ounce --> ?
0.2 ounce--> 0.04 ounces
divide 0.2 ounces by 0.04 ounces and you'll get the answer
0.2 is the answer per pound of jelly you will use o.2 ounces

4 0

3 years ago

2r(2.59 + 10) - 3(r + 4) + s(r - 1)? equivalent?