Using the function f(x) = 2x + 7 find the following: (show your work)

1. f(x) = 13
2. f(x)=21


To use function notation we either replace the x in the equation or the f(x) in the equation.
To find f(2) we replace the ________ in the equation with _________ and then solve for f(x).
To find f(x)=2 we replace the _________ in the equation with __________ and then solve for x.

The function that gives the area (A) of the garden in terms of the width (x) is A(x) = x × (35 - x)

The domain of the function would be: 0 ≤ x ≤ 35

To find the function that gives the area of the garden, let's start by understanding the problem. Patricia wants to enclose a rectangular garden with a total of 70 feet of fencing material. This means that the sum of all sides of the rectangular garden (perimeter) should be equal to 70 feet.

For a rectangular garden, the perimeter is given by the formula:

Perimeter = 2 × (length + width)

In this case, since one of the sides is the width (x) and the other side is the length, the formula becomes:

70 = 2 × (x + length)

Solving for the length:

x + length = 70 / 2

length = 35 - x

Now, the area of a rectangle is given by the formula:

Area = length × width

Substitute the expression for the length:

Area = (35 - x) × x

Now, you have a function that gives the area (A) of the garden in terms of the width (x):

A(x) = x × (35 - x)

The domain of this function is the range of valid values for x. Since x represents the width of the garden, it should be a positive value. Also, the width cannot exceed 35 (since the length is 35 - x). So, the domain of the function is:

0 ≤ x ≤ 35

This means that the width (x) can take any value between 0 and 35 feet, inclusive, within the context of the problem.

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Final answer:

To find the area of the garden, we need to relate the width and length of the garden to the amount of fencing material. The function that gives the area of the rectangular garden is A = x(35 - x). The domain of the function is 0 ≤ x ≤ 35.

Explanation:

To find the function that gives the area of the rectangular garden, we need to relate the width and length of the garden to the amount of fencing material. Since the garden has four sides, two sides of length x and two sides of length y, we have the equation 2x + 2y = 70. Solving for y, we get y = 35 - x. The area of a rectangle is given by the formula A = x * y. Substituting y = 35 - x, we get A = x(35 - x) = 35x - x^2.

The domain of the function f(x) = 35x - x^2 is determined by the values of x that make sense in the context of the problem. In this case, the width cannot be negative and it cannot be greater than 35 (since the length cannot be negative or greater than 35 either).

Therefore, the domain of the function is 0 ≤ x ≤ 35.

Answer: d

Step-by-step explanation:

By using the quadratic formula, the solutions of the quadratic equation include;

[tex]x = \frac{-13\; - \;3\sqrt{17}}{2}[/tex] and [tex]x = \frac{-13\; + \;3\sqrt{17}}{2}[/tex]

In Mathematics and Geometry, the standard form of a quadratic equation is represented by the following equation;

[tex]ax^2 + bx + c = 0\\\\x^2=13x-4\\\\x^{2} -13x+4=0[/tex]

where:

a = 1, b = -13, c = 4

Mathematically, the quadratic formula is represented by this mathematical equation:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\\\\x = \frac{-(-13)\; \pm \;\sqrt{(-13)^2 - 4(1)(4)}}{2(1)}\\\\x = \frac{-13\; \pm \;\sqrt{169 - 16}}{2}\\\\x = \frac{-13\; \pm \;\sqrt{153}}{2}\\\\x = \frac{-13\; + \;3\sqrt{17}}{2}\\\\x = \frac{-13\; - \;3\sqrt{17}}{2}[/tex]

The values 7/11 and 7/11, when considered slopes of two lines, indicate that these lines are parallel because they have identical slopes. For the lines to be perpendicular, one slope would need to be the negative reciprocal of the other, which is not the case here.

When faced with the values 7/11 and 7/11 in a mathematical context, we typically need additional information to determine a relationship such as whether lines or vectors are parallel, perpendicular, or neither. However, if we assume that the fractions 7/11 represent the slopes of two lines in a Cartesian coordinate system, we can determine the relationship between these lines.

If two lines have identical slopes, this indicates that they are parallel. Their steepness in the coordinate system will be the same, and they will not intersect, no matter how far they are extended. In our case, both slopes are 7/11, which means that these lines are indeed parallel to each other.

For lines to be perpendicular, the slope of one line must be the negative reciprocal of the other. In terms of angles, perpendicular lines intersect at a 90° angle. Since both slopes given here are identical, they do not satisfy the condition for perpendicularity.

Understanding the relationship between lines is essential for analyzing the structure of geometric figures and solving various problems in physics and engineering. Remember that irrespective of relative directions like 'forward' or 'backward,' parallelism is evaluated based on slope in a Cartesian plane.

y = A sin(Bx + C) + D

·        amplitude is A

Final answer:

To find the amplitude of a trigonometric function, identify the coefficient in front of the sine or cosine term in the wave equation. In the example equation y(x, t) = A sin(kx — wt), the amplitude is 0.2 meters, represented by A.

Explanation:

To find the amplitude of a trigonometric function, one must identify the coefficient of the sine or cosine function in the wave equation. Given the wave equation y (x, t) = A sin (kx — wt), the amplitude can be extracted directly as it is the absolute value of the coefficient A in front of the sine or cosine term. In the example provided, the amplitude of the wave is 0.2 meters because it is represented by A in y (x, t) = [tex]0.2 m sin (6.28 mx-1.57 s-t).[/tex]

Moreover, the characteristics of a sinusoidal wave such as wavelength (λ), period (T), and frequency (f) are related to the amplitude but represent different aspects of the wave's behavior. These can be determined using the wave number (k), angular frequency (ω), and initial phase shift, when present.

Answer:

25

Step-by-step explanation:

e2020

Answer:

A-10

Step-by-step explanation:

Answer: The initial number of transactions is neither an independent nor a dependent variable.

Step-by-step explanation:

Here, The initial number of transactions that took place in the first hour of day is 10 and the number of transactions doubles every hour after that.

If x represents the number of hours and y represents Number of transaction after x hours.

Therefore, The function which represents the situation is,

[tex]y = 10\times 2^x[/tex]

Where x is independent variable, while y is dependent variable.

Since initially x=0,   y=10 which is the initial transaction.

And, there is not any impact on the value of 10 by changing the values of x or y, Also 10 is not a variable( because it is a constant value)

Therefore neither it is dependent variable nor it is independent.

Answer:

The initial number of transactions is neither an independent nor a dependent variable.

Step-by-step explanation:

We know that the initial number of transactions that took place in the first hour of day is 10, i. e., a constant that is independent of the total number of transactions and the hour of the day. The independent variable is the time elapsed and the dependent variable is the total number of transactions made.

1 mile = 5280 feet

1 hour = 3600 seconds

72 * 5280 = 380160 feet per hour

380160/ 3600 = 105.6 feet per second ( round answer if needed)

To calculate the total miles, first convert 50000 inches to feet, then convert the result to miles. Approximately 0.790 miles are in 50000 inches.

To answer your question, "How many miles are in 50000 inches?" We need to convert inches to miles. We have to use the given conversion rates: 1 foot = 12 inches and 1 mile = 5280 feet.

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1) P = 9.4m, A = 4.8m^2

2) 27*14 /2 = 189 ft^2

3) 0.3^3 = 0.027

Answer:

1.0 x 10 ^ 8

Step-by-step explanation:

To find the parallel line's equation through the point (6, -5), we identify the slope of 9x - 2y = 7 as (9/2), and then use the point-slope form with the given point to derive the new line's equation. The final general form of this equation is 9x - 2y - 64 = 0.

To find the general form of an equation of the line that is parallel to the line 9x - 2y = 7 and passes through point a(6, -5), we first need to identify the slope of the given line. The slope-intercept form of the line can be found by rearranging the equation into y = mx + b, where m is the slope. For the given equation 9x - 2y = 7, we solve for y to get the slope:

2y = 9x - 7

y = (9/2)x - 7/2

The slope of the given line is (9/2). Since parallel lines have the same slope, our new line will also have a slope of (9/2). Using the point-slope form of a line's equation, we can insert the slope and the coordinates of point a to determine the equation of our new line:

y - y₁ = m(x - x₁)

y - (-5) = (9/2)(x - 6)

y + 5 = (9/2)x - 27

Finally, we rearrange this equation to its general form, Ax + By + C = 0:

(9/2)x - y - 32 = 0

or

9x - 2y - 64 = 0

This is the general form of the equation of the line that is parallel to 9x - 2y = 7 and passes through point (6, -5).

First, let's define the number we are looking for as n.

So "half a number" is (1/2)×n

Therefore, "four less than" this would be: ((12)×n)−4

And if this is or, in other words, = to #17 we can write the equation:

((12)×n)−4=17

Solving for n while keeping the equation balanced gives:

((12)×n)−4+4=17+4

(12)×n=21

(21)×(12)×n=21×(21)

((21)×(12))×n=421

1×n=42

n=42