WILL MARK BRAINLIEST IF YOU ANSWER BOTH QUESTIONS WITH SOLUTION

Answer:

180

Step-by-step explanation:

Answer:

this is the correct answer happy

The volume of the box is the amount of space in it.

The dimension of the postcard is:

[tex]\mathbf{Length = 10}[/tex]

[tex]\mathbf{Width = 18}[/tex]

Let x represents the length of the cut.

So, the dimension of the box is:

[tex]\mathbf{Length = 10 -2x}[/tex]

[tex]\mathbf{Width = 18 -2x}[/tex]

[tex]\mathbf{Height = x}[/tex]

(a) The function that represents the volume of the box

This is calculated as:

[tex]\mathbf{V(x) = Length \times Width \times Height}[/tex]

So, we have:

[tex]\mathbf{V(x) = (10 - 2x) \times (18 - 2x) \times x}[/tex]

Expand

[tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]

Hence, the volume function is: [tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]

(b) The dimension that maximizes the volume

We have:

[tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]

Differentiate

[tex]\mathbf{V'(x) = 180- 112x + 12x^2}[/tex]

Set to 0

[tex]\mathbf{180- 112x + 12x^2 = 0}[/tex]

Using a calculator, we have:

[tex]\mathbf{x = 7.3,2.1}[/tex]

The value x = 7.3 is greater than the dimension of the box.

So, we have:

[tex]\mathbf{x = 2.1}[/tex]

Recall that:

[tex]\mathbf{Length = 10 -2x}[/tex]

[tex]\mathbf{Width = 18 -2x}[/tex]

[tex]\mathbf{Height = x}[/tex]

So, we have:

[tex]\mathbf{Length = 10 -2 \times 2.1 = 5.8}[/tex]

[tex]\mathbf{Width = 18 -2 \times 2.1 = 13.8}[/tex]

[tex]\mathbf{Height = 2.1}[/tex]

Hence, the dimension that maximizes the volume is 5.8 by 13.8 by 2.1

(c) The maximum volume

This is calculated as the product of the dimension of the box

So, we have:

[tex]\mathbf{Volume = 5.8 \times 13.8 \times 2.1}[/tex]

[tex]\mathbf{Volume = 168.1}[/tex]

Hence, the maximum volume of the box is 168.1 cubic inches

Read more about volumes at:

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Answer:

B

Step-by-step explanation:

-16x - 32

We can factor out -16 from the -16 and -32 which leads us to this equation:

-16 (x + 2)

Meaning B would be the correct answer

Answer: B. -16(x + 2)

Step-by-step explanation:

The GCF, or greatest common factor, of -16 and -32, is -16.

Thus, distribute out -16 to get -16(x + 2)

Hope it helps :) and let me know if you want me to elaborate.

[1] Complementary means the angles will add up to 90 degrees

 () Blank one is BOC

 () Blank two is 90

 () Reason blank I am unsure as I do not know the wording that is being looked for, but it is either "given," "complementary angles" or something similar

[2] Since AOC is equal too BOC + 30, we can decide the following is true

 () First blank is BOC

 () Second blank is 30

[3] 30°

 () BOC + BOC + 30 = 90 [Given]

    2(BOC) = 60 [Subtract 30 from both sides & combine like terms]

    BOC = 30 [Divide by 2]

[4] 60°

 () 90 - 30 = 60

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

I and IV

Step-by-step explanation:

based on the unity circle 0 and 360 is on the same plane..hope it's answerd

Answer:

4200

hope helpful <3 !!!!!!!!!!!!!

Answer: Tax(240), Total cost(6240)

Step-by-step explanation:

6000 x .04 =240

240 +6000 = 6240

Answer:

i think you need to add all that up

Step-by-step explanation:

Answer:

Simplify:

[tex]\frac{( {x}^{2} + 6x + 9) }{x - 3} [/tex]

Factoring:

[tex] {x}^{2} + 6x + 9[/tex]

The first term is, x2 its coefficient is 1 .

The middle term is, +6x its coefficient is 6 .

The last term, "the constant", is +9

Step-1 : Multiply the coefficient of the first term by the constant 1 • 9 = 9

Step-2 : Find two factors of 9 whose sum equals the coefficient of the middle term, which is 6 .

-9 + -1 = -10

-3 + -3 = -6

-1 + -9 = -10

1 + 9 = 10

3 + 3 = 6 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 3 and 3

[tex] {x}^{2} + 3x + 3x + 9[/tex]

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x+3)

Add up the last 2 terms, pulling out common factors :

3 • (x+3)

Step-5 : Add up the four terms of step 4 :

(x+3) • (x+3)

Which is the desired factorization.

Multiply (x+3) by (x+3)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (x+3) and the exponents are :

1 , as (x+3) is the same number as [tex](x+3) {}^{1}[/tex]

and 1 , as (x+3) is the same number as[tex](x + 3) {}^{1} [/tex]

The product is therefore, [tex](x + 3) {}^{(1 + 1)} = (x + 3) {}^{2} [/tex]

$200

Simple interest is the same value of interest each year. It is based on the original value. The original value here is $5000.

You must find 2% of the $5000 dollars. This is 0.02 * 5000, or $100.

The question asks for the value after two years, so you must double this to $200.

The question asks how much interest he is paid, which does not include the original $5000. The answer is therefore $200.

Answer:

6 time

Step-by-step explanation:

97÷14=6•928

=6 or round it up to 7

Answer:

6

Step-by-step explanation:

97÷14=6.928

6 or round it up to 7

[tex]n = - 1[/tex]

Answer:

Step-by-step explanation:

[tex]\frac{6}{4.5}=\frac{4}{x}[/tex]

6x = 4 × 4.5

6x = 18

x = 3

Step-by-step explanation:

9x2 -3x -2 factors to (3x-2)(3x +1)

solve 3x-2 =0 and 3x+1=0

making the roots -1/3 and 2/3

Answer:

55 degrees

Step-by-step explanation:

if u and v are parallel and cut by the transversal in the middle the two angles would be congruent or equal to each other , therefore the angle in question is also 55

Answer:

the left side is the answer

Answer:

-60m/s²

Step-by-step explanation:

The first thing to do is know the equation:

(Final velocity - initial (original) velocity) / time (seconds)

Next you check the units:

10 minutes = 600 seconds

Then you use the equation to solve the problem:

(4000 - 40000) = -36000

-36000 / 600 = -60

Units for acceleration = m/s²

Answer = -60m/s²

The value is negative because the satellite's velocity has decreased

Hope this helps.

Answer:

Yeah sure, but I cant guarantee i will answer all the questions. What grade level?

You may begin by calculating the slope's angle, then marking the slope's midway point, or 0, then the left end, -1, and finally the right end, 1.

Answer:

Step-by-step explanation:

what is the question

Step-by-step explanation:

check the attached file

Answer:

  $21.83

Step-by-step explanation:

The amount spent will be the difference between the starting balance and the ending balance:

  18.53 -(-3.30) = 18.53 +3.30 = 21.83

You spent $21.83 on lunch this week.

Answer:

Fast Freddy can go 15 miles per hour which is 4 minutes per mile

Speedy Sam can go 7.5 miles per hour which is 8 minutes per mile

Fast Freddy ran faster because he went 15 mph which is double the speed of Speedy Sam.

Step-by-step explanation:

Speedy Sam: So, we can find how fast per mile, by multiplying 4 by 2 because, it takes 4 minutes to go 1/2 of a mile, so double it to make a full mile. So the rate is 8 minutes per mile for Speedy Sam. If you wanted to calculate miles per hour, it would be 7.5 miles per hour because, you would simply take 60 minutes, an hour, and divide it by 8 minutes per mile, to get 7.5 miles per hour.

Fast Freddy: We can right away notice that after one mile, it hits 4 minutes. Making the rate 4 minutes per mile. To find the miles per hour, we would do, 60 minutes divided by 4 minutes per mile to get 15. Meaning fast freddy goes 15 miles per hour

Answer:

First truck = x

Second truck = y

x + 35 = y

x = 2/3y

So

2/3y +35=y

1/3y = 35

y = 35*3

y = 105

And ,

x = 2/3y = 70

The first truck carry 70 tons while the second carry 105 tons

If the first truck carries 35 tons less rice than the second truck, then;

x = y - 35

If the number of paddy in the first truck is 2/3 of the amount in the second truck

x = 2/3 y

Equate both to have:

2/3 y = y - 35

2/3y - y = -35

-y/3 = -35

y = 105

Since x = 2/3 y

x = 2/3 * 105

x = 70

Hence the first truck carry 70 tons while the second carry 105 tons

Laern more on equations here: https://brainly.com/question/16863577

Answer:

whats the question

Step-by-step explanation:

Answer:

710

Step-by-step explanation:

81+74+72+66+67+72+66+66+72+65+71= 701

701 rounded to the nearest tenth is 710

Answer:

15 Dimes and 75 Nickles

Step-by-step explanation:

N = Nickles

D = Dimes

5D + D = 90

6D= 90

D= 15

90 - 15 = 75

N = 75

There are 75 nickels and 15 dimes does she​ have.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Susan has a collection of 90 nickels and dimes.

And, The number of nickels is five times the number of​ dimes.

Now,

Since, The number of nickels is five times the number of​ dimes.

Let number of dimes = x

Then, Number of nickels = 5x

Since, Susan has a collection of 90 nickels and dimes.

Hence, We can formulate;

⇒ 5x + x = 90

⇒ 6x = 90

⇒ x = 15

Thus, The number of dimes = 15

And, Number of nickels = 5 × 15  = 75

Therefore, There are 75 nickels and 15 dimes does she​ have.

Learn more about the mathematical expression visit:

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The answer is -7 (option A)

Steps are in the attachment.

_________

Hope it helps ✌