A container manufacturer plans to make rectangular boxes whose bottom and top measure 4x by 3x. The container must contain 48in.3 The top and the bottom will cost $1.80 per square inch, while the four sides will cost $3.70 per square inch.

What should the height of the container be so as to minimize cost? Round your answer to the nearest hundredth.

Answer:

D

Step-by-step explanation:

use the sine or cosine ratio in the right triangle.

using the sine ratio and the exact value

sin45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{4}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )

2x = 4[tex]\sqrt{2}[/tex] ( divide both sides by 2 )

x = 2[tex]\sqrt{2}[/tex]

The value of x is 2√2.

Hence the correct option is D.

Given that a right triangle with acute angles 45° each, and hypotenuse is 4 units,

we need to find the length of the perpendicular,

In a right triangle, the length of the perpendicular (also known as the altitude) can be found using trigonometric ratios.

In this case, since we have an angle of 45°, we can use the sine or cosine function.

Let's use the sine function to find the length of the perpendicular:

sin(45°) = opposite / hypotenuse

sin(45°) = perpendicular / 4

1/√2 = perpendicular / 4

perpendicular = 4/√2

perpendicular = 2√2

Hence the value of x is 2√2.

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ANSWER: C. 25x^2 + 70x + 49

Hope for help po

rombus Rectangle sqare

Step-by-step explanation:

all have 4 Sides

Answer:

  276 ft²

Step-by-step explanation:

The total surface area of a prism is the sum of its lateral area and the area of its bases. Here, the bases are two triangles, and the area of the sides is that of three rectangles.

The area of a triangle is given by the formula ...

  A = 1/2bh . . . . where b is the base of the triangle, h is its height

We have two identical triangles, so their total area will be ...

  A = 2(1/2bh) = bh = (8 ft)(3 ft) = 24 ft²

The sides of the prism are rectangles, all with the same length: 14 ft. Their total area will be that length multiplied by the total of the rectangle widths. That total is the same as the perimeter of the triangular base:

  P = 5 ft + 5 ft + 8 ft = 18 ft

Then the lateral area is ...

  lateral area = Ph = (18 ft)(14 ft) = 252 ft²

The sum of the base area and lateral area is ...

  (24 ft²) +(252 ft²) = 276 ft² . . . . area of the triangular prism

Answer:

5 and 1/4 is the answer to your problem

Step-by-step explanation:

Answer:

[tex]\frac{21}{4}[/tex] or  [tex]5 \frac{1}{4}[/tex]

Step-by-step explanation:

[tex]1 \frac{2}{4} + 3 \frac{3}{4}\\[/tex]

First, I would convert them into improper fractions. To convert [tex]1 \frac{2}{4}[/tex], I would do 1 x 4 = 4, then + 2 = 6

To convert [tex]3 \frac{3}{4}\\[/tex] , I would do the same: 3 x 4 = 12 + 3 = 15

That leaves us with [tex]\frac{6}{4}[/tex] + [tex]\frac{15}{4}[/tex]

All we have to do is add the numerators (top numbers) so

6 + 15 = 21

Answer = [tex]\frac{21}{4}[/tex]

or, as a mixed number, [tex]5 \frac{1}{4}[/tex]

Hope this makes sense. If you require any further explanation, feel free to ask..

- profparis

If I helped you, I would appreciate a brainliest :D

Answer:

100mph

Step-by-step explanation:

Answer:

this is broken english

Step-by-step explanation:

ok ok

Answer:

inverse variation

Step-by-step explanation:

Answer:

Step-by-step explanation:

44/8

= 5 whole 4 by 8

= 5 4/8

Answer:

5/2 = 2.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

We can see that 9 is being added to each term.

Thus, we obtain the following rule:

To make this easier, let's simplify the rule.

Substitute 41 as "x" to obtain the 41st term:

The value of 41st term of sequence 8, 17, 26 is,

⇒ 368

An arithmetic sequence is the sequence of numbers where each consecutive numbers have same difference.

Given that;

The sequence is,

⇒ 8, 17, 26.

Now, The common difference is,

⇒ d = 17 - 8 = 9

⇒ d = 26 - 17 = 9

Thus, The sequence is in arithmetic.

Hence, The value of 41st term of sequence 8, 17, 26 is,

⇒ a + (n - 1)d

⇒ 8 + (41 - 1) 9

⇒ 8 + 369 - 9

⇒ 8 + 360

⇒ 368

Thus, The value of 41st term of sequence 8, 17, 26 is,

⇒ 368

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Answer:

20720

Step-by-step explanation:

-3x^2y +4x

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

= 12^4 -16

20736 - 16

= 20720

I hope this helped!

Answer:

When x = -4 and y = 2, -3x^(2y) + 4x is -784.

Step-by-step explanation:

-3x^(2y) + 4x

Substitute given variables.

-3(-4)^(2(2)) + 4(-4)

Multiply 2 and 2.

-3(-4)^4 + 4(-4)

Multiply -3 and -4.

Raise -4 to the 4th power.

-3(256) + 4(-4)
Multiply -3 and 256.

-768 + 4(-4)

Multiply 4 and -4

-768 + (-16)

Add -768 and -16.

-784

Answer:

18.37500

Step-by-step explanation:

Here You Go! Hope It Helps Bud

Answer:

D

Step-by-step explanation:

Well, the right edge is 1 line away from 6 so it is 5 15/16 inches.

There are 16 lines for each 1 line. so it is 5 inches and 15 lines out of 16

Using it's concept, it is found that the period of the function is of 20 seconds.

The period of a function is given by the distance between it's repetitions.

In this problem, the function starts at 0s, with 4.8 ft, then in intervals of 2s, the heights are of 6.6 ft, 7.6 ft, 7.8 ft and so on. The same pattern starts again after 20 seconds.

Hence, the period of the function is of 20 seconds.

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Answer:

x=20

Step-by-step explanation:

These vertically opposite angles are equal

3x+50=6x-10

50+10=6x-3x

3x=60

x=20

Step-by-step explanation:

3x+50=6x-10(vertically opp angles)

3x-6x=-10-50

-3x=-60

Divide both side by - 3

X=20

Answer:

54.45 in²

Let the base and height be 9.9 inches and 5.5 inches respectively.

Formula;

Area of parallelogram = Base × Height

Substitute the base and the height in the formula:

Evaluate the area of the parallelogram:

Answer:

54.45 in²

Step-by-step explanation:

Formula

Area of a parallelogram = base × height

If you turn the parallelogram so that the sides that measure 9.9in are the base, you will see that 5.5in is the height (refer to the attached diagram).  Therefore, we can use the formula with these values to calculate the area.

Given:

⇒ area = 9.9 × 5.5 = 54.45 in²

Answer:

(5,5)

(-3,-15)

(6,-12)

(-2,8)

Step-by-step explanation:

Multiply the value of "a" with the coordinates.

#1

y=ax²

Coordinates (1,5)

#2

So

Coordinates (5,-15)

#3

So

Coordinates (-2,-12)

#4

So

Coordinates (-4,8)

Answer:

4.9% increase

Step-by-step explanation:

Starts at 61 inches

Ends at 64 inches

64 - 61 = 3 inches increase

percent of 3 to 61

3 / 61

≈ 0.49

= 4.9%

Answer:

x=16, y=26, z=13

Step-by-step explanation:

opposite angles are congruent so (3x+30)=(4x+14)

Solve for x

x=16

adjacent sides are supplementary so insert x in both equations just to make sure it is correct and you get 78

so 3y=78 and 6z=78

solve for y and z

y=26, z=13

Answer:

D

Step-by-step explanation:

y=5x-2 since the formula is. y=mx+c

Answer:

b=330.90 and c=314.97

Step-by-step explanation:

b=245×sin71.2/sin44.5. c=245×sin64.3/sin44.5. you get the 64.3 by subtracting 180_(71.2+44.5)

Answer:

D is the correct answer

Step-by-step explanation:

2n-1<5= n<3

2n-1>-5= n>-2

Answer:

the answer is 5100 im pretty sure.

Step-by-step explanation:

yes

Answer:

For this question, we use the formula for the volume of a cylinder.

(formula for vol. of cylinder)

V = π[tex]r^{2}[/tex]h

Where 'π' represents pi(22/7 or 3.14), 'r' represents the radius which is being squared, and 'h' stands for the height.

We utilize the information that we know:

Which we then plug into our equation(volume of cylinder formula):

V = π[tex]r^{2}[/tex]h

904.78 = 3.14(6^2) · h

Next solve for the h(height).

904.78 = 3.14(36) · h

904.78 = 113.04 · h

904.78 = 113.04h

/113.04     /113.04

8.00406935598 = h, which we round to 8.

8 centimetres is the height of this cylinder.

we subtracted 4 from the x value

we subtracted 7 from the y value

Answer:

(x,y) => (x-4,y-7)

false if the prices increase tomorrow or true if the prices decrease.

so basically it's always uphill so false

hope it helps...!!!

ANSWER:

false

EXPLANATION:

Answer:

There should be 16, 20 cent coins in the box

Step-by-step explanation:

First we have to do 1.60 x 2 which equals 3.2

Then we divided by 0.20 because the equals the 20 cent coins

We get 16

We can check our work by 0.20 x 16 and that gives us 3.2

I hope this helps!

Answer:

The hundred thousands place

Step-by-step explanation:

Answer:

The hundred thoudsands place; (700,000)

Step-by-step explanation:

The places of the number are listed below:

Hundred Thousands - 700,000
Ten Thousands - 10000
Thousands - 4000
Hundreds - 500
Tens - 80
Ones - 3

The digit 7 is in the hundred thoudsands place.

hope this helps!