You are a store clerk assigned to stack notebooks in a box for shipment. Each notebook is 29 centimeters long, 21.5 centimeters wide, and 1.5 centimeters thick. The box can hold a maximum of 12 notebooks.

To the nearest whole number of cubic centimeters, what is the minimum volume of the box?
A. 64
B. 624
C. 935
D. 7,500
E. 11,223

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

-2x + 8 = -2x + 8

-2 makes the equation equal.

Option A is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 6 is an equation.

We have,

-2x + 8 = __x + 8

The equation has infinitely many solutions when both sides of the equation are equal.

Now,

-2x + 8 = -2x + 8 is equal on both sides.

Thus,

-2x + 8 = -2x + 8

-2 makes the equation equal.

Option A is the correct answer.

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Answer:its c

Step-by-step explanation:

Answer:

1.  c < -4

2.  -4 < c < 0

3.  c = 0

4.  c > 0

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.8 cm}\underline{Discriminant}\\\\$b^2-4ac$ \quad when $ax^2+bx+c=0$\\\\when $b^2-4ac > 0 \implies$ two real roots.\\when $b^2-4ac=0 \implies$ one real root.\\when $b^2-4ac < 0 \implies$ no real roots.\\\end{minipage}}[/tex]

Given quadratic equation:

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

If the quadratic equation has no real roots, then the discriminant is less than zero:

[tex]\implies b^2-4ac < 0[/tex]

[tex]\implies (4)^2-4(-1)(c) < 0[/tex]

[tex]\implies 16+4c < 0[/tex]

[tex]\implies 4c < -16[/tex]

[tex]\implies c < -4[/tex]

If the quadratic equation has two real roots, then the discriminant is greater than zero:

[tex]\implies b^2-4ac > 0[/tex]

[tex]\implies (4)^2-4(-1)(c) > 0[/tex]

[tex]\implies 16+4c > 0[/tex]

[tex]\implies 4c > -16[/tex]

[tex]\implies c > -4[/tex]

Using Descartes' Rule of Signs, if c > 0 there would be one sign change and so a maximum of one positive root.  If c < 0 there would be 2 sign changes and therefore a maximum of 2 negative roots.

Therefore, for the two roots to have the same sign, -4 < c < 0.

If c = 0 then:

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

[tex]\implies -x(x+4)=0[/tex]

[tex]\implies x(x+4)=0[/tex]

Therefore, the roots would be 0 and -4 so there would be one negative root and one root equal to zero.

Using Descartes' Rule of Signs, if c > 0 there would be one sign change and so a maximum of one positive root.

Therefore, for the equation to have two roots with opposite signs, c > 0.

Answer:

67.38°

Step-by-step explanation:

AD = DB = 24/2 = 12

<bcd = 12/5

< bcd = 67.38°

The expression 3(n + 1) is equivalent to the given expression 7n-(4n-3).

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

The expression is given in the question following:

7n - (4n-3)

We have to determine the equivalent expression

As per the question, we have

⇒ 7n - (4n-3)

Open the parentheses and distribute the negative sign,

⇒ 7n - 4n + 3

⇒ 3n + 3

⇒ 3(n + 1)

Thus, the expression 3(n + 1) is equivalent to the given expression.

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Answer:

[tex]y=-\dfrac{1}{3}x+5[/tex]

Step-by-step explanation:

A line's slope is defined as rise over run.

The rise and run between the coordinates (0, 5) and (3, 4) is:

rise: -1

run: 3

Therefore, the slope of the line is -1/3. This is what x is multiplied by.

Next, to find what is added to x, find where the line crosses the y-axis. IN this case, that point is when y = 5, so in the second blank put 5.

Answer: 10) 18x+21     11) 20 + 30a     12)  8x + 10y

Step-by-step explanation:

Distributive property means to multiply each number within the parenthesis by the number outside of the parenthesis.

10) 3(6x + 7)

     3*6x + 3*7

     18x + 21.

With that, you should be able to see how the other questions were answered.

The linear function that models the problem of movie theater sells popcorn is

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

The equation as described in the problem is represented using linear function as as follows

c = cost of the bucket = $3.50

m = cost of refills = $2.50

y = 2.50x + 3.50

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Answer:

500 rounded to the nearest tenth equal 500

TQ/VQ=TV/VR is true for the given triangle. Option B is correct

A triangle is a three-sided polygon that consists of three edges and three vertices.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Two pairs of corresponding angles are equal

Three pairs of corresponding sides are proportional

Two pairs of corresponding sides are proportional and the corresponding angles between them are equal.

From these we can say that the sides TV is proportional to Rs and TQ is proportional to VQ

Hence, TQ/VQ=TV/VR is true for the given triangle. Option B is correct

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Answer:

hamburgers cost $0.80 each

Step-by-step explanation:

Answer:

[tex]x=\frac{1}{2}[/tex]

Step-by-step explanation:

Even roots can NEVER have a negative result, therefore the value of x can ONLY be positive values.

Answer:

5.12

Step-by-step explanation:

If u times 1.6 and 3.2 you get 5.12 also i got it correct on my test

The linear function that represents the situation is of:

C(y) = 13y + 145.

The intercept is of:

C(0) = 145, meaning that the flat fee to pay the game is of $145.

The slope-intercept representation of a linear function is given by the rule presented as follows:

y = mx + b

The coefficients of the function and their meaning are listed as follows:

Two points of the function, from the table, are given as follows:

(8, 249) and (13,314).

The slope is given by the change in y of the two points divided by the change in x, hence:

m = (314 - 249)/(13 - 8) = 13.

Hence:

C(y) = 13y + b

When y = 8, C(y) = 249, hence the intercept b of the function is obtained as follows:

249 = 13(8) + b

b = 249 - 13 x 8

b = 145.

Meaning that the flat fee to pay the game is of $145.

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Ingrid must deposit $402.74 at the end of each quarter for 8 years in order to have enough money to pay for her car.

Answer: 6u^3

Step-by-step explanation:

You have to add the exponents when you multiply them.

But before that, you can multiply the coefficients of 2 and 3 so you get 6.

Now you have u and u^2 left.

u = u^1

u^2 = u^2

1+2 =3

Answer: A 50 miles

Step-by-step explanation:

Its A becuase 60%=0.6 and 0.6 times 50 is 30 which means 60 percent of 50 is 30.

Answer:

y - 4 = 32/3 x

Step-by-step explanation:

A (-3/8; 0)

B (0; 4)

slope = (4-0)/(0-(-3/8)

4/3/8

4 * 8/3

32/3

y-4 = 32/3 (x-0)

y -4 = 32/3 x

[tex]i=\sqrt{-1}[/tex]

[tex](9\sqrt{-81})(-10\sqrt{64})[/tex]

⇒ Take out i from the first square root:

[tex]= (9i\sqrt{81})(-10\sqrt{64})[/tex]

⇒ Evaluate the square roots:

[tex]= (9i\times9)(-10\sqrt{64})\\= (9i\times9)(-10\times 8)[/tex]

⇒ Multiply:

[tex]= (81i)(-10\times 8)\\= (81i)(-80)\\= -6480i[/tex]

-6480i

Answer:

[tex]y=-x-\frac{7}{12}[/tex]

Hope this helps!

Answer:

I believe the answer is 15.

Step-by-step explanation:

let me know if I am correct.

Answer:

40% off of 75 is 45$

Step-by-step explanation:

Answer:990

990

990

990

990

990

Step-by-step explanation:

Answer:

Variable y exponente.

Step-by-step explanation:

En una expresión algebraica la reducción de términos semejantes se da entre los términos de igual variable o incógnita y exponente.

Por ejemplo:

3x² + 5x²

se pueden reducir pues tienen la misma variable x y el mismo exponente 2, su resultado se genera solo sumando, restando, los coeficientes, en este caso 3 y 5

3x² + 5x² = 8x²

En el caso:

3y² + 5x²

No se puede reducir pues la variable o incógnita no son iguales:

x≠y

En el caso:

3x² + 5x³

No se pueden reducir pues su exponente no es igual.

x/5 - 4 represents 4 less than the quotient of x and 5.

Answer:

c = -1.75a + 15

Answer:

54

Step-by-step explanation:

9x6

The measurements of [x] and [y] are 37 and 61 respectively.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given are two triangles as shown in the figure.

Triangles ΔMPN and ΔSTU are congruent. We can write -

2x - y = 13

2x - 50 = 24

Now -

2x - 50 = 24

2x = 74

x = 37

then -

2 x 37 - y = 13

74 - 13 = y

y = 61

Therefore, the measurements of [x] and [y] are 37 and 61 respectively.

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Answer:

count backwards

Step-by-step explanation:

1, 0, -1, -2, -3

Answer:two ways

Step-by-step explanation: you can either count the spaces or you could just add until you get one of the answers -3 +4 =1 1- 4=-3

Answer:

x- intercept = - [tex]\frac{1}{14}[/tex]

Step-by-step explanation:

to find the x- intercept, that is where the line crosses the x- axis, let y = 0 in the equation and solve for x

14x - 11(0) = - 1

14x = - 1 ( divide both sides by 14 )

x = - [tex]\frac{1}{14}[/tex] is the x- intercept

The cost to replace all the windows on all the building in the United States is $7,200,000.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Given that the cost to replace a window is $3 per window. IT should be noted that when there are 2,400,000 windows, the cost to replace all the windows on all the building in the United States will be:

= Cost of replacement × Total window

= $3 × 2,400,000

= $7,200,000

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The cost to replace a window is $3 per window. If there are 2,400,000 windows, how much would it cost to replace all the windows on all the building in the United States?