Solve the following equation. Then place the correct number in the box provided. 8 + x = 13 + 2x

Answer:

  (a)  1568 in³

  (b)  1728 in³

Step-by-step explanation:

You want to know the volume of the box that can be formed from the pattern shown, and the maximum volume that can be had by changing the 4-inch dimension.

The volume of the box is the product of its length, width, and height. The height of the box is shown as 4 inches.

The length is shown as the difference between 36 inches and twice the 4-inch dimension:

  length = 36 -2(4) = 28 . . . . inches

The width is shown as half the difference between 36 inches and twice the 4-inch dimension. That will make it be half the length.

  width = (1/2)(36 -2(4)) = 14 . . . . inches

Then the volume of the box from the pattern shown is ...

  V = LWH = (28 in)(14 in)(4 in) = 1568 in³

Using the above observations regarding dimensions, we can write the volume in terms of the height of the box (x) as ...

  height = x

  length = 36 -2x

  width = 18 -x

  volume = (x)(36 -2x)(18 -x) = 2x³ -72x² +648x

The maximum volume will be found at the value of x that makes the derivative of volume be zero:

  V' = 6x² -144x +648 = 0

  x² -24x +108 = 0 . . . . . . . . divide by 6

  (x -6)(x -18) = 0 . . . . . . . . factor

Values of x that make the derivative zero are x=6 and x=18. The original equation is a cubic with a positive leading coefficient, so we know these values correspond to a local maximum and a local minimum, respectively.

The largest volume possible is obtained with a corner cut of 6 inches. That volume is ....

  V = (6)(36 -2·6)(18 -6) = 6(24)(12) = 1728 . . . . cubic inches

The largest volume possible is 1728 in³.

Answer:

[tex]2(35)+4=74[/tex]

∠SQR = 74

Step-by-step explanation:

[tex](2m+4)+(3m+1)=180\\5m+5=180\\ -5\\5m=175\\/5\\175/5=35[/tex]

Answer:

SQR = 74

Step-by-step explanation:

2m + 4 + 3m + 1 = 180

5m + 5 = 180

5m = 175

m = 35

35 * 2 + 4

70 + 4 = 74

Angle SQR = 74

Answer:

The number of books in the owner's office are 4.

Step-by-step explanation:

It is given that the book store had a new bookshelf that could hold 62 books the owner put 5 books on each of the shelves and the rest back in his office.

Now, let us assume the there are 'n' number of total books that the owner have with him;

=> total books = n

and the total books the shelf could hold is;

=> total books the shelf could hold = 62

Further, it is provided that the owner put 5 books on each of the shelves and the rest back in his office;

=> n = 62/5

=> n = 12.4

Therefore, the number of books in the owner's office are 4.

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Answer:

a. 2x + 11

b. (5/x) - 2

c. (x + 8) * 4

Step-by-step explanation:

I may be wrong on b and c because the wording is a bit weird. Here is a list of common wording and their respective things. Have a great day!

Answer: 495

Step-by-step explanation: If the car traveled for 90 miles on 2 gallons of gas and we now have 11 gallons Divide 2÷11 = 5.5 or



90×5.5 = 495

The number of miles Aubrey's car can travel is 495 miles

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the distance traveled by Aubrey's car for 11 gallons be = A

Now , the equation will be

The distance traveled by Aubrey's car for 2 gallons = 90 miles

So ,

The distance traveled by Aubrey's car for 1 gallon = distance traveled by Aubrey's car for 2 gallons / 2

The distance traveled by Aubrey's car for 1 gallon = 90 / 2

The distance traveled by Aubrey's car for 1 gallon = 45 miles

So , the equation will be

The distance traveled by Aubrey's car for 11 gallons A = The distance traveled by Aubrey's car for 1 gallon x 11

The distance traveled by Aubrey's car for 11 gallons A = 45 x 11

The distance traveled by Aubrey's car for 11 gallons A = 495 miles

Therefore , the value of A is 495 miles

Hence , The number of miles Aubrey's car can travel is 495 miles

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The debt per capita of Illinois is $11933, Indiana is $ 7601, Ohio is $ 7291 and Kentucky is $ 8687

Given to find the debt-per capita ratio

Let us convert them into dollars

1 billion dollars= 10^9 dollars

1 million= 10^6

State            Debt          Population                     Debt per capita

Illinois 151.67*10^9   12.71*10^6        (151.67*10^9) /(12.71*10^6)

                                                                    = $11933.12                          

Indiana    50.85*10^9     6.69*10^6       (50.85*10^9) /(6.69*10^6)    

                                                                      =$7600.90

Ohio 85.23*10^9  11.69*10^6        (85.23*10^9) /(11.69*10^6)

                                                                      =$7290.85

Kentucky  38.83*10^9  4.47*10^6        (38.83*10^9) /(4.47*10^6)

                                                                           =$ 8686.80

So, The debt per capita of Illinois is $11933, Indiana is $ 7601, Ohio is $ 7291 and Kentucky is $ 8687

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Answer: 1.083333

Step-by-step explanation:

The function g (x) is called an inner function and the function f (x) is called an outer function. Hence, we can also read f [g (x)] as “the function g is the inner function of the outer function f”.

Given that,

f(x) = 2x²+2  and

g(x)=x2-1

So find the (f- g)(x).

(f- g)(x) means,

Multiply x into f and g functions

Then, (f- g)(x) = f(x)-g(x)

Replace with f(x) and g(x) values in this equation

So,

(f- g)(x)= f(x)-g(x)

          = (2x²+2) - (x2-1)

Distribute the subtraction to all three of the last terms.          

          = 2x²+2-2x+1

          = 2x²-2x+2+1

Combine like terms

  (f- g)(x) = 2x²-2x+3

Therefore,

f(x) = 2x²+2 and

g(x)=x2-1,    

So,

       (f- g)(x) = 2x²-2x+3.

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the chances are always 50 50

If the school earns $264 for 8 senior tickets and 12 child tickets and $237 for 11 senior tickets and 6 child tickets then the price of 1 senior ticket be $15 and the price of child ticket be $12.

Given that on the first day of ticket sales, the school sold 8 senior citizen tickets and 12 child tickets for a total of $264 and the school earns $237 on IInd day by selling 11 senior citizen tickets and 6 child tickets.

We are required to define the variables and solve the system of the equations.

Suppose the price of 1 ticket of senior citizen be x.

Suppose the price of 1 ticket of child be y.

The equations will be:

8x+12y=264--------1

11x+6y=237--------2

Multiply equation 1 by 11 and multiply equation 2 by 8 and then subtract equation 2 from equation 1.

88x+132y-88x-48y=2904-1896

84y=1008

y=1008/84

y=12

Use the value of y in equation 1 to get the value of x.

8x+12y=264

8x+12*12=264

8x+144=264

8x=264-144

8x=120

x=120/8

x=15

Hence if the school earns $264 for 8 senior tickets and 12 child tickets and $237 for 11 senior tickets and 6 child tickets then the price of 1 senior ticket be $15 and the price of child ticket be $12.

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The cost of a Senior citizen ticket is $15, while a children's ticket cost $12.

On the first day:

The school sold 12 child tickets and 8 senior citizen tickets for a total amount of $264.

On the second day:

The school sold 11 senior citizen tickets and 6 child tickets for a total of $237.

Let A be the price of a senior citizen ticket and B be the price of a child ticket.

So, the equation for the first day:

8A + 12B = 264

The equation for the second day,

11A + 6B = 237

Multiplying the equation for the second day by 2 and subtracting the equation for the first day.

We get,

22A + 12B - 8A - 12B = 474 - 264

14A = 210

A = 15

Substituting the value of A in the equation 8A + 12B = 264,

8A + 12B = 264

8(15) + 12B = 264

120 + 12B = 264

12B = 144

B = 12

Therefore, the price of a senior citizen ticket is $15 and the price of a child ticket is $12.

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The number of cars in the parking lot is 105.

The first step is to determine the total number of cars that the parking lot can accommodate. This can be determined by multiplying the number of rows by the total number of cars in each row.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers.

Total number of cars that can be in the parking lot  = number of rows x number of cars in each row

6 x 20 = 120

The next step is to subtract the number of empty spaces from the capacity of the parking lot . Subtraction is the operation that is used to determine the difference between two or more numbers.

Number of cars = capacity of the parking lot - empty spaces

120 - 15 = 105

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Answer:

6.25 minutes

Step-by-step explanation:

96 choice = 2 minutes

300 choice = x

solve for x,

x = 6.25 minutes

Answer:

6 minutes 15 seconds

Step-by-step explanation:

➟ 2/96 = 0.02083

Now we have find the value of minutes per question let's crosscheck it using 96 to make sure it's correct before using it for 300

➟ 0.02083 × 96

➟ 1.9 = 2

Time to calculate for 300 multiple choice test

➟ 0.02083 × 300

➟ 6.249

➟ 6.25

➟ 6 minutes 15 seconds

Answer:

a)

[tex]2.35 \times {10}^{ - 3} [/tex]

b)

[tex]2.5 \times {10}^{1} [/tex]

c)

[tex]4 \times {10}^{3} [/tex]

Step-by-step explanation:

above I think

The value of the expression 3m^3n^2(8mn^3) is 24m^4n^5

The expression is given as:

3m^3n^2(8mn^3)

Rewrite properly as

3m^3n^2(8mn^3) = 3m^3n^2 * (8mn^3)

Remove the bracket

So, we have

3m^3n^2(8mn^3) = 3m^3n^2 * 8mn^3

Apply the law of indices in evaluating the product

So, we have

3m^3n^2(8mn^3) = 24m^4n^5

Hence, the value of the expression 3m^3n^2(8mn^3) is 24m^4n^5

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Answer:

[tex]\textsf{Rewrite the original equation as $x^2+\dfrac{1}{3}x=\boxed{\dfrac{2}{9}}$}[/tex]

[tex]\textsf{Add appropriate number to make the left side a perfect square trinomial}[/tex]

[tex]x^2+\dfrac{1}{3}x+\boxed{\dfrac{1}{36}}=\dfrac{2}{9}+\boxed{\dfrac{1}{36}}[/tex]

[tex]\textsf{Factor the left side as a perfect square and combine the right hand side into one number}[/tex][tex]\left(x+\boxed{\dfrac{1}{6}}\:\right)^2=\boxed{\dfrac{1}{4}}[/tex]

[tex]\textsf{Final answers $x=\boxed{\dfrac{1}{3}, - \dfrac{2}{3}}$}[/tex]

Step-by-step explanation:

Given equation:

[tex]18x^2+6x-4=0[/tex]

Add 4 to both sides:

[tex]\implies 18x^2+6x-4+4=0+4[/tex]

[tex]\implies 18x^2+6x=4[/tex]

Divide both sides by 18:

[tex]\implies \dfrac{18x^2}{18}+\dfrac{6x}{18}=\dfrac{4}{18}[/tex]

[tex]\implies x^2+\dfrac{1}{3}x=\dfrac{2}{9}[/tex]

Add the square of half the coefficient of x to both sides:

[tex]\implies x^2+\dfrac{1}{3}x+\left(\dfrac{\frac{1}{3}}{2}\right)^2=\dfrac{2}{9}+\left(\dfrac{\frac{1}{3}}{2}\right)^2[/tex]

[tex]\implies x^2+\dfrac{1}{3}x+\left(\dfrac{1}{6}}\right)^2=\dfrac{2}{9}+\left(\dfrac{1}{6}\right)^2[/tex]

[tex]\implies x^2+\dfrac{1}{3}x+\dfrac{1}{36}=\dfrac{2}{9}+\dfrac{1}{36}[/tex]

Factor the perfect square trinomial on the left side and combine the numbers on the right side:

[tex]\implies \left(x+\dfrac{1}{6}\right)^2=\dfrac{1}{4}[/tex]

Square root both sides:

[tex]\implies \sqrt{\left(x+\dfrac{1}{6}\right)^2}=\sqrt{\dfrac{1}{4}}[/tex]

[tex]\implies x+\dfrac{1}{6}=\pm \dfrac{\sqrt{1}}{\sqrt{4}}[/tex]

[tex]\implies x+\dfrac{1}{6}=\pm \dfrac{1}{2}[/tex]

Subtract 1/6 from both sides:

[tex]\implies x+\dfrac{1}{6}-\dfrac{1}{6}=\pm\dfrac{1}{2}-\dfrac{1}{6}[/tex]

[tex]\implies x=-\dfrac{1}{6}\pm\dfrac{1}{2}[/tex]

Therefore:

[tex]\implies x=-\dfrac{1}{6}+\dfrac{1}{2}=\dfrac{1}{3}[/tex]

[tex]\implies x=-\dfrac{1}{6}-\dfrac{1}{2}=-\dfrac{2}{3}[/tex]

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The most appropriate form of equation of a line in 3D will be given by-

[tex]\frac{x + 1}{1} = \frac{y-3}{-5} = \frac{z-5}{0}[/tex]

is the required equation of the line.

What is equation of line in 3D?

Suppose a line passes through two points ([tex]x_1, y_1, z_1[/tex]) and ([tex]x_2, y_2, z_2[/tex]).

Equation of line is given by

[tex]\frac{x-x_1}{l} = \frac{y - y_1}{m} = \frac{z - z_1}{n}[/tex]

where [tex]l, m, n[/tex] are the Direction ratios

[tex]l = x_2 - x_1,\\ m = y_2 - y_1, \\n = z_2 - z_1[/tex]

Here,

[tex]x_{1} =-1, y_{1} = 3, z_{1} = 5, x_2 = 0, y_2 = -2, z_2 = 5[/tex]

l = 0-(-1)=1

m = -2-3 = -5

n= 5-5=0

Equation of line =

[tex]\frac{x -(- 1)}{1} = \frac{y-3}{-5} = \frac{z-5}{0}[/tex]

[tex]\frac{x + 1}{1} = \frac{y-3}{-5} = \frac{z-5}{0}[/tex]

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Answer:

between 4 and 5

Step-by-step explanation:

The direction cosines of the line are:

x = 8 / √116

y = 6 / √116

z = -4 / √116

Direction ratio helps in knowing the components of a line or a vector with reference to the three-axis, the x-axis, y-axis, and z-axis respectively.

We have,

Let the direction ratio of the line be (x, y, z)

The line is perpendicular to the lines whose direction cosines are proportional to 3,-2,3 and 1,-2,-1.

Now we have,

3x - 2y + 3z = 0 _____(1)

x - 2y - z = 0 _____(2)

We will find the value of x, y, and z using cross product.

x / 2 + 6 = y / 3 + 3 = z / -6 + 2

x / 8 = y / 6 = z / -4

We get,

x = 8

y = 6

z = -4

The direction cosines of the line are:

x = 8 / √8² + 6² + (-4)²

x = 8 / √64 + 36 + 16

x = 8 / √116

y = 6 / √116

z = -4 / √116

Thus the direction cosines of the line are:

x = 8 / √116

y = 6 / √116

z = -4 / √116

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Equation (A) 3¹ can be correctly placed in Jeremy's work.

So, in the situation, Jeremy concludes: [tex]\sqrt{9}=9^{\frac{1}{2}}[/tex]

Therefore, (A) 3¹ is the equation that should be correctly placed in Jeremy's work.

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The complete question is given below:

Jeremy determines that √9= 9^1/2. Part of his work is shown

√9=3=3^1=3^1/2 + ^1/2=____=9^1/2

Which expression or equation should be placed in the blank to correctly complete Jeremy's work?

A: 3¹

B: (3^2)^1

C: 3^1/2 + 3^1/2

D: 3^1/2 x 3^1/2= (3x3)^1/2

E: 3^1/2 x 3^1/2= (3x3)^1/2+^1/2

Answer:

108

Step-by-step explanation:

3²(2³+4) calculate to the power of 2 and get 9.

9 (2³+4) calculate 2 to the power of 3 and get 8.

9 (8+4) add 8 and 4 to get 12.

9 · 12 = 108 multiply 9 and 12 to get 108.

A total 44 pieces can be cut out through the material of stock.

The dimensions of the piece required,

length = 9''

breadth = 4''

thickness = 3/16''

The dimension the the available material pieces in the stock of first piece,

length = 48''

breadth = 12''

thickness = 3/16''

The dimension the the available material pieces in the stock of second piece,

length = 36''

breadth = 28''

thickness = 3/16''

Let say that N pieces can be obtained from these two pieces, So, by calculating area method,

Area of n small pieces = Area of the two stock pieces

N x (9'' x 4'') = (48'' x 12'') + (36'' x 28'')

N x 36''² = 576''² + 1008''²

N x 36''² = 1584''²

N = 1584''²/36''²

N = 44.

So, a total of 44 pieces can be cut out through the material of stock.

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Answer:

f'(x) = 5

Step-by-step explanation:

differentiate using the power rule

[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex] and [tex]\frac{d}{dx}[/tex] (constant) = 0

given

f(x) = 5x + 5 , then

f'(x) = 5[tex]x^{(1-1)}[/tex] + 0

     = 5[tex]x^{0}[/tex] + 0

    = 5

Check the picture below.

Answer:

3 < x < 5

Step-by-step explanation:

Expression is |2x − 8| < 2

The absolute rule says that if |u| < a then -a < u < a

Here u = 2x-8

So we get -2 < 2x - 8 < 2

This means

2x - 8 > -2            

==> 2x > -2 + 8       (add 8 to both sides)

==> 2x > 6               (simplify)

==> x > 3                  (divide by 2 both sides)

and,

2x - 8 < 2 gives

==> 2x < 2 + 8          (add 8 to both sides)

==> 2x < 10              (simplify)

==> x < 5                  (divide by 2 both sides)

So the solution to |2x − 8| < 2

is 3 < x < 5

There are 40 rows with 53 seats in each row.

This auditorium is divided into rows of seats, and because it is rectangular, each row has the same number of seats.

So,

Therefore, there are 40 rows with 53 seats in each row because we can't have a negative number of rows.

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If  we want to choose 6 objects, without replacement, from 8 distinct objects then total number of ways are 20160 (8x7x6x5x4x3).We can use the concept of permutation to find number of ways.

The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply put, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.

Combination and permutation are part of the accounting discipline's mathematical branch. Combinations are used in business decision-making to choose from among the available objects. In contrast, the arrangement of such objects that are chosen through combinations uses permutations.

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Answer:

[tex]fg x5 \\ 5fg[/tex]

9.9 and 9.95 are the result of rounding off 9.949 to the nearest tenth and hundredth.

So, rounding off:

Therefore, rounding off of 9.949 to the nearest tenth and hundredth is 9.9 and 9.95.

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