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The area of a rectangle is 60 square inches. The length of the rectangle is 7 inches longer than the width. Which equation models this situation?

A: w + 7= 60
B: 7w = 60
C: w(w+7) = 60
D: w + 7w = 60

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

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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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).

Answer: d

Step-by-step explanation:

To find 60% off of $33.00, you multiply 33 by 60, then divide the product by 100. The result is $19.80, which is the discount amount. So after the discount, the cost is $13.20.

To find out what 60% off of $33.00 is, you need to multiply 33.00 by 60 and then divide that product by 100, as percentages are always out of 100. Here's the process:

So, 60% off of $33.00 equals $19.80. Hence, after a 60% discount, you would pay $13.20 (33 - 19.80), as this is the remaining cost after the discount has been applied.

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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

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: 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.

Answer:

1.0 x 10 ^ 8

Step-by-step explanation:

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.

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)

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]

Answer: 32 quarts

Step-by-step explanation:

We know that there area 4 quarts in one gallon.

i.e.[tex]1\text{ gallon}=4\text{ quarts}[/tex]

Now, to convert 8 gallons into quart we need to apply unitary method.

Using unitary method , to convert 8 gallons into quart , multiply 8 to 4 , we get

[tex]8\text{ gallon}=8\times4\text{ quarts}\\\\\Rightarrow\ 8\text{ gallon}=32\text{ quarts}[/tex]

Hence there are 32 quarts in 8 gallons.

There are 32 quarts in 8 gallons of quantity.

The given quantity is 8 gallons.

We know that, 1 gallon = 4 quarts

Here, 8 gallons = 8×4

= 32 quarts

Therefore, there are 32 quarts in 8 gallons of quantity.

To learn more about the metric conversion visit:

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Answer:

25

Step-by-step explanation:

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