The volume of a crate with length of x feet, width of 8 - x feet, and a height of x - 3 feet is given by V(x)=x(8−x)(x−3) find the maximum volume of the crate and the dimensions for this volume

Answer:

9 minutes

Step-by-step explanation:

We can write a proportion to solve

5 gallons     15 gallons

-------------- = ---------------

3 minutes         x minutes

Using cross products

5x = 3*15

5x = 45

Divide by 5

5x/5 = 45/5

x = 9

Answer:

0

Step-by-step explanation:

You can't divide anything by zero

0÷0=

=0

Answer:

c no is correct pls mark me branilest

Answer:

(x, y) = (y, x). Exercise 1.3.4. Let X,Y,Z and W be nonempty sets. Then, prove the following statements

Answer:

It is integer and rational .....

Step-by-step explanation:

Hope it helps

Answer:

[tex]38[/tex] and [tex]68[/tex].

Step-by-step explanation:

Let [tex]x[/tex] be the smaller one of the two number.

[tex]x[/tex] must be a positive integer. The other number would be [tex](x + 30)[/tex].

The question states that the product of the two numbers is [tex]2584[/tex]. In other words:

[tex]x\, (x + 30) = 2584[/tex].

Rearrange this equation and solve for [tex]x[/tex]:

[tex]x^{2} + 30\, x - 2584 = 0[/tex].

The first root of this quadratic equation would be:

[tex]\begin{aligned}x_{1} &= \frac{(-30) + \sqrt{30^{2} - 4 \times (-2584)}}{2} \\ &= \frac{(-30) + \sqrt{900 + 10336}}{2} \\ &= \frac{(-30) + \sqrt{11236}}{2} \\ &= \frac{(-30)}{2} + \sqrt{\frac{11236}{2^{2}}} \\ &= (-15) + \sqrt{2809} \\ &= (-15) + 53 \\ &= 38 \end{aligned}[/tex].

Similarly, the second root of this quadratic equation would be:

[tex]\begin{aligned}x_{1} &= \frac{(-30) - \sqrt{30^{2} - 4 \times (-2584)}}{2} \\ &= (-15) - 53 \\ &= -68\end{aligned}[/tex].

Since the question requires that both numbers should be positive, [tex]x > 0[/tex]. Therefore, only [tex]x = 38[/tex] is valid.

Hence, the two numbers would be [tex]38[/tex] and [tex](38 + 30)[/tex], which is [tex]68[/tex].

9514 1404 393

Answer:

  38 and 68

Step-by-step explanation:

Let x represent the average of the two numbers. Then their product is ...

  (x -15)(x +15) = 2584

  x^2 = 2584 +225 = 2809 . . . . . . use relation (x -a)(x +a) = x^2 -a^2; add a^2

  x = √2809 = 53

Then the two numbers are ...

  53 +15 = 68

and

  68 -30 = 38

The two numbers are 38 and 68.

_____

Additional comment

Solving the problem in this way is equivalent to writing the quadratic equation for the smallest (or largest) number and solving that by completing the square. The "solution" x = -53 is not relevant in this problem.

Answer:

6) F

7) B

Step-by-step explanation:

6)

[tex]\boxed{perimeter \: of \: rectangle = 2(length + breadth)}[/tex]

60= 2[½(n -6) +2n +5]

Expand:

60= 2(½)(n -6) +2(2n) +2(5)

60= n -6 +4n +10

Simplify:

60= 5n +4

Minus 4 on both sides:

5n= 60 -4

5n= 56

Divide both sides by 5:

n= 56 ÷5

n= 11.2

Thus, option F is correct.

7)

[tex]\boxed{area \: of \: rectangle = length \: \times breadth}[/tex]

13q +2= 9(q +6)

Expand:

13q +2= 9q +54

Bring q terms to one side, constant to the other:

13q -9q= 54 -2

Simplify:

4q= 52

Divide both sides by 4:

q= 52 ÷4

q= 13

Thus, option B is correct.

Answer:

Step-by-step explanation:

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Answer:

Step-by-step explanation:

Consider the function and its inverse shown in the second attachment. The function is ...

  f = {(a, 3), (b, 1), (c, 2)}

The inverse function is ...

  f^-1 = {(3, a), (1, b), (2, c)}

You will notice that the "x" and "y" of each pair are swapped between the function and its inverse. That is the point of an inverse function. It gives you the input that caused the function to create the output. For example, the pair (3, a) in the above inverse function tells you that the output 3 was the result of an input of 'a' to the original function.

__

On a graph, the swapping of input and output is essentially equivalent to relabeling the axes. If we keep the same x- and y-axis labels, it is equivalent to reflecting the function graph across the line y=x. That reflection is represented by the transformation (x, y) ⇒ (y, x).

__

The point of the exercise here is for you to identify some ordered pairs of one of the functions and realize that the inverse function reverses their order. You are to see that the graph of the function and its inverse are reflections of each other across the diagonal line y=x.

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Answer:

  7/8 in  (you are correct)

Step-by-step explanation:

The amount of nail that goes into the framing member is ...

  1 3/4 -3/8 -1/2

  = 1 6/8 -3/8 -4/8

  = 1 -1/8 = 7/8 . . . . inches

Answer:

1st box: 1

2nd box: 1

Step-by-step explanation:

1: 3 * 7 = 21, so only put the 1 and carry the 2.

2: 5 * 6 = 30, but we have a 1 from the previous answer given so 31, but only put the 1.

I hope this helps :)

Answer:

rational

Step-by-step explanation:

Answer:

1523797

Step-by-step explanation:

Have a good day, hope I helped

Answer:

1,523,797

Step-by-step explanation:

734,839 + 788,958

= 1,523,797

Answer:

Step-by-step explanation:

Please see the picture below

Answer:

Step-by-step explanation:

it apperes to me that all are rational numbers

Hope this helps

Answer:

because P(x) has factors of (x-2) and (x+1) => x = 2 and x = -1 are the solutions of P(x)

so we have:

[tex]\left \{ {{2^{4}+2^{3}a-2^{2}+2b-12 =0} \atop {1-a-1-b-12=0}} \right.\\=>\left \{ {{8a+2b=0} \atop {a+b=-12}} \right.\\<=>\left \{ {{4a+b=0} \atop {a+b=-12}} \right.\\<=>\left \{ {{a=4} \atop {b=-16}} \right.[/tex]

=> [tex]P(x)=x^{4} + 4x^{3}-x^{2} -16x-12[/tex]

With P(x) = 0

=> [tex]x^{4}+4x^{3}-x^{2} -16x-12 = 0[/tex]

=> ........

Step-by-step explanation:

Answer:

[tex]y = - 9x \\ theny = 2x + 33 \\ - 9x = 2x + 33 \\ - 9x - 2x = 33 \\ - 11x = 33 \\ x = \frac{ - 33}{11} = - 3 \\ x = - 3 \\

then\\ y=-9×-3=21\\ thank \: you[/tex]

Answer:

2W + 56 = 78 , W = 10

Step-by-step explanation:

perimeter of rectangle = 2*the Length + 2*the Width

Answer:

Sara has enough money to buy all three items because after the sale and tax, the total of all three items is less than $100 at only $93.01.

Step-by-step explanation:

Solve for the sale:

43.98 × 0.25

10.995

38.59 × 0.25

9.6475

31.99 × 0.25

7.9975

Add these all together:

10.995 + 9.6475 + 7.9975

28.64

Subtract this amount from the original cost of all the items:

(43.98 + 38.59 + 31.99) - 28.64

114.56 - 28.64

85.92

Solve for the sales tax:

85.92 × 0.0825

7.0884

Add the sales tax to the total:

85.92 + 7.0884

93.0084

Round up to the nearest cent:

93.01

93.01 < 100

Answer:

55

Step-by-step explanation:

20 * 3 = 60

60 marks - 5 Incorrect answer (5 marks deducted)

55 Marks

Answer:

3/5

Step-by-step explanation:

1.) Find the Greatest Common Factor of 6/10.

2

2.) Divide both the numerator and the denominator by the greatest common factor.

6÷2

10÷2

3.) Simplify 6÷2/10÷2

3/5

Answer:

6

Step-by-step explanation:

2+4=6

(1+1)+(1+1+1+1)=6

Ans: 6

Answer:

15400

Step-by-step explanation:

since we know that 200 is in one day.

All we have to do is multiply 200 by 77.

Which is 15400.

Answer:

78

Step-by-step explanation:show your work

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Answer:

0.14

Answer:

Step-by-step explanation:

i dont know  but work hard

Answer:

It is -80

Step-by-step explanation:

u just subtract