Two candidates running for the same office received a total of 1,926 votes. If the winning candidate had 410 more votes than the other candidate, how many votes did the winner receive?

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.

The car will travel 300 miles while the bicycle travels 40 miles

Let's first calculate the ratio of distances traveled by the bicycle and the car in the given scenario:

Ratio of distances = Distance traveled by car / Distance traveled by bicycle

Ratio of distances = 30 miles / 4 miles = 7.5

This ratio represents the speed ratio between the car and the bicycle. Now, we can use this ratio to find the distance the car will travel while the bicycle travels 40 miles:

Distance traveled by car = Ratio of distances * Distance traveled by bicycle

Distance traveled by car = 7.5 * 40 miles = 300 miles

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The expression that can be used to represents the number of vehicles remaining in the bin is (b + c) - 1/3(b + c)

Total vehicles = b + c

Number of vehicles sold = 1/3 of total vehicles

= 1/3(b + c)

Number of vehicles remaining = (b + c) - 1/3(b + c)

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The expression that represents the number of vehicles remaining in the bin is 2/3 (b + c).

To determine the number of vehicles remaining in the bin after selling 1/3 of them, we start by calculating the total number of vehicles initially present. This total number is represented by b + c, where b is the number of bikes and c is the number of cars.

If the store sells 1/3 of the vehicles, the number sold can be represented as:

(b + c) / 3

The number of vehicles remaining in the bin would be the original total minus the number sold:

(b + c) - (b + c) / 3

We can simplify this expression by finding a common denominator:

(b + c) - (b + c) / 3 = 3(b + c)/3 - (b + c) / 3 = (3(b + c) - (b + c)) / 3 = (2(b + c)) / 3

Therefore, the expression that represents the number of vehicles remaining in the bin is 2/3 (b + c).

Answer:

1.0 x 10 ^ 8

Step-by-step explanation:

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.

39/4=9.

59/4=14.

add 14.+9.=23

now divide 23/4=5

40 is the first number evenly divided by 4 and is the 10th multiple of 4 (4*10=40)

56 is the last number evenly divisible by 4 and is the 14th multiple of 4 ( 4*14 =56)

14-10 = 4 +1 = 5

 there are 5 numbers evenly divisible by 4

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]

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.

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.

Let us say that:

x = pounds of $7 coffee

So that:

7 x + 2 * 20 = 5 * (x + 20)

7x + 40 = 5x + 100

2x = 60

x = 30 pounds

Therefore 30 pounds should be added.

To get a mixture of coffee worth $5 a pound, you should add 30 pounds of coffee worth $7 a pound to 20 pounds of coffee worth $2 a pound.

To solve this problem, we can use the method of mixtures. Let's assume that x pounds of coffee worth $7 a pound is added to 20 pounds of coffee worth $2 a pound. The total weight of the mixture will be (x + 20) pounds. The total value of the mixture will be the sum of the values of the two types of coffee.

The value of the 20 pounds of coffee worth $2 a pound is 20 * 2 = $40. The value of the x pounds of coffee worth $7 a pound is 7x. So, the total value of the mixture will be $40 + 7x.

Since we want the mixture to be worth $5 a pound, we can set up the equation:

(40 + 7x) / (20 + x) = 5

To solve this equation, we can cross-multiply:

(40 + 7x) = 5(20 + x)

Expanding the right side of the equation, we get:

40 + 7x = 100 + 5x

Subtracting 5x from both sides, we get:

2x = 60

Dividing both sides by 2, we get:

x = 30

Therefore, 30 pounds of coffee worth $7 a pound should be added to 20 pounds of coffee worth $2 a pound to get a mixture worth $5 a pound.

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

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

3) 0.3^3 = 0.027

Answer: d

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

e2020