Let f(x) = 2x - 6 Solve f-1(x) when x = 2.

The total costs t of the eggs is the dependent variable.

Even though everything can be almost always related to its reason, when we talk about two related things, there might happen that one of those things is dependent on other.

Thus if variable is taking its values independently of any visible direct cause, then that variable is called independent variable.

The variables that take their values based on some other variables' values are called dependent variables.

Given that the number of eggs e in the carton and the total costs t of the eggs.

Here, we know the number of eggs, e, to know how much it costs.

Hence, it is the dependent variable.

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Answer:

  12 inches

Step-by-step explanation:

15 - 3 = 12

The board is 12 inches long.

_____

A measuring tape is like a number line. To find the distance between two numbers on the number line, you subtract the smaller one from the larger one. The tape measure works the same way. Subtract the number at one end of the board from the number at the other end of the board to find the length of the board.

Answer:

P=2(l+w)

Step-by-step explanation:

It is given that perimeter, P, of a rectangle is the sum of twice the length and twice the width.

Let length of rectangle is l and width of the rectangle is w.

Perimeter = 2 × Length + 2 × Width

[tex]P=2\times l+2\times w[/tex]

[tex]P=2l+2w[/tex]

Taking out common factors.

[tex]P=2(l+w)[/tex]

[Note: (l+l)+(w+w) units is also true but according to the statement only option 1 is true]

Therefore, the correct option is 1.

Answer:   C.  ΔSQR

Step-by-step explanation:

In [tex]\triangle{STR}[/tex] and [tex]\triangle{SQR}[/tex], we have

[tex]\angle{TSR}\cong\angle{OSR}\\\\\angle{STR}\cong\angle{QRS}=90^{\circ}[/tex]

By AA- similarity postulate , we get

[tex]\triangle{STR}\sim\triangle{SQR}[/tex]

To calculate the rate at which the water level drops, use the formula dh/dt = dV/dt / (25Ï) and the given drainage rate of 250 liters per minute. The resulting rate is -0.01/Ï meters per minute, which represents the speed of the water level decreasing.

To determine the rate at which the water level inside the cylindrical tank drops, we use the given volume formula of the cylinder, V = 25Ï h, where V is volume in cubic meters, h is height in meters, and Ï is the constant pi (approximately 3.14159).

Draining the tank at a rate of 250 liters per minute corresponds to a volume rate of 0.25 cubic meters per minute (since 1 cubic meter equals 1000 liters). Using the formula dV/dt = 25Ï dh/dt, we want to find the rate dh/dt at which the height of the water decreases.

Rearranging for dh/dt gives us dh/dt = dV/dt / (25Ï). Substituting the known rate of volume change, dV/dt = -0.25 m³/min (negative because the volume is decreasing), we get dh/dt = -0.25 / (25Ï), which simplifies to dh/dt = -0.01 / Ï meters per minute. Therefore, the rate at which the water level drops is -0.01/Ï meters per minute.

Answer:the answer would be c which is 146

Step-by-step explanation:

The value of x is 75.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

6 consecutive integers are x − 2, x − 1, x, x + 1, x + 2, x + 3

Now, the integers add up to 447.

So, x-2 + x-1 + x+ x +1 + x+2 + x+3= 447

6x -3 + 6 = 447

6x = 450

x= 75

Hence, the value of x is 75.

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There are 700 students were enrolled at Valley View Middle School before the increase.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

The number of students at Valley View Middle School increased by 10%, to 770 total students.

Now,

Since, The number of students at Valley View Middle School increased by 10%,

And, The number student after the increase = 770

So, We can formulate;

The number of students before the increased is calculated as;

= 770 / (1 + 10%)

= 770 / 1.1

= 700

Thus, There are 700 students were enrolled at Valley View Middle School before the increase.

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Answer:

103 mg.

Step-by-step explanation:

We have been given that the decay of 230 mg of an isotope is described by the function [tex]A(t)=230e^{-0.031t}[/tex], where t is time in years.

To find the amount left after 26 years, we will substitute [tex]t=26[/tex] in our given function as:

[tex]A(26)=230e^{-0.031\cdot 26}[/tex]

[tex]A(26)=230e^{-0.806}[/tex]

Using exponent property [tex]a^{-n}=\frac{1}{a^n}[/tex], we will get:

[tex]A(26)=230\times \frac{1}{e^{0.806}}[/tex]

[tex]A(26)=\frac{230}{e^{0.806}}[/tex]

[tex]A(26)=\frac{230}{2.2389343}[/tex]

[tex]A(26)=102.72744\approx 103[/tex]

Therefore, 103 mg of isotope will be left after 26 years.

Answer:

Y-axis and y = -x

Step-by-step explanation:

The student's question is about the sequence of rigid transformations that resulted in polygon A'B'C'D' from polygon ABCD. While the reflections lines are unspecified, typically two reflections across intersecting lines equal a rotation around the point of intersection by twice the angle between the lines.

The student's question involves identifying the type of rigid transformations that polygon ABCD underwent to form polygon A'B'C'D'. Unfortunately, there seem to be missing elements in the provided description of the transformations. Normally, a rigid transformation would include details such as the lines across which the reflections occur. That said, a sequence of two reflections across two intersecting lines is equivalent to a rotation around the point of intersection of the lines, with the angle of rotation being twice the angle between the two lines.

If we could infer that the lines of reflection are perpendicular to each other, the overall transformation would be a rotation of 180 degrees. This would mean that polygon A'B'C'D' is the result of this 180-degree rotation of polygon ABCD about the point of intersection of the two reflection lines.

It is difficult to estimate the mass of an average flat screen computer monitor without specific data.

In order to estimate the mass of an average flat screen computer monitor, you could use the rule-of-thumb approach by mass. This approach involves finding the average mass of similar monitors. However, since we do not have specific data on the mass of an average flat screen computer monitor, it is difficult to provide an accurate estimate.

The mass estimate can also be influenced by factors such as the size, type, and materials used in the construction of the monitor. Therefore, it is recommended to refer to the product specifications provided by the manufacturer for the most accurate information regarding the mass of a specific model of flat screen computer monitor.

We want to find what separates terms in an algebraic expression.

The answer is: The sum and subtraction symbols.

By definition, a "term" can be a signed number, a variable, a constant multiplying a variable, or more complex things, like expressions inside parentheses.

The terms in an algebraic expression are the things we are adding or subtracting.

Thus, what we use to separate them are the sum symbol (+) or the subtraction symbol (+).

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The solutions of the equation [tex]-x^2+4x=x-4[/tex] is:

               x= -1 and x=4

The solution of the graphs of the equation is equal to the x-value of the point of intersection of the graph of two functions i.e. the function on the left side of the equality on the right side of the equality.

Here, the expression is:

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

Hence, we will see at which point the graph  of:

[tex]y=-x^2+4x[/tex]

and [tex]y=x-4[/tex] meet.

The point of intersection of the graph is: (-1,-5) and (4,0).

Hence, the solution of the graph is: x= -1 and x=4

Answer: Hello mate!

"four times a certain number increased by 6 is equal to 94"

is equivalent to: 4*x + 6 = 94

where x represents the number.

Now we would want to find the value of x.

4*x + 6 = 94

4*x = 94 - 6 = 88

x = 88/4 = 22

then the value of the number x that makes the statment true is x = 22.