Which triangle's unknown side length measures 7 units?

The electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.

The electrical resistance is the measure of the difficulty in passing electric current through a wire or an electrical component. It depends on various factors, such as the material, dimensions, and temperature of the wire.The given statement says that the electrical resistance varies directly as the square of the voltage and inversely as the electric power.

In mathematical terms, this relationship can be expressed as R ∝ V²/PR = kV²/P where R is the electrical resistance, V is the voltage, P is the electric power, and k is the constant of proportionality. The constant k depends on the material, dimensions, and temperature of the wire or component.

The given statement implies that the constant k is the same for the given wire or component, and it is not affected by the voltage or the power.To find the value of k, we can use the given values of V, P, and R.

According to the statement, if the voltage is 20 volts and the electric power is 5 watts, then the electrical resistance is 80 ohms. Therefore,R = kV²/PR = k(20²)/5R = 400k/5R = 80 ohms

Substituting the value of R in the equation, we get80 = 400k/5k = (80 x 5)/400k = 1. Therefore, the equation that relates the electrical resistance, voltage, and power isR = V²/PThe constant of proportionality k is 1 for the given wire or component.

Therefore, the electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.

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The model predicts that there are approximately 0.012456 (71/5700) restaurants per capita in the year 2016

To determine the number of restaurants per capita, we need to divide the number of restaurants (R) by the population (p). Given that R = 6t + 35 and p = 200t + 4500, we can substitute these values into the equation for restaurants per capita.

Restaurants per capita = R / p

Substituting the given equations, we get:

Restaurants per capita = \((6t + 35) / (200t + 4500)\)

To find the number of restaurants per capita for the year 2016, we need to calculate the value of t for that year. Since t represents years after 2010, in 2016, t would be 6 (2016 - 2010 = 6).

Restaurants per capita (2016) = \((6 * 6 + 35) / (200 * 6 + 4500)\)

= \((36 + 35) / (1200 + 4500)\)

= 71 / 5700

This means that, on average, there is roughly one restaurant for every 80 people in the town. Please note that this prediction is based on the given growth equations and assumes a linear relationship between population and the number of restaurants.

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Answer:

A: No, not correct, it comes out as 6.6666666

B: 8 plants

Therefore ,As a result, the region's problem with the suggested solution is the playing field area measures 118 yards by 56 yards.

Add length and breadth together to calculate area. The calculation for area is L times B. Radius or area equals r2(=3.14) With the use of these techniques, it is also possible to determine the area of various quadrilaterals, a specific type of polygon with 4 sides and an angle smaller than 90 degrees. Application. Geometry has been based on the concept of area from its inception.

Here,

We find w = 56, which indicates that the parallelogram has a length of 56 yards.

Since the width is identical to 2w + 6, we can make the computation simpler by changing w to 56 to find the rectangle's length.

The rectangle's length is shown to be 118 yards.

The size of the playing area is accordingly 118 yard by 56 yards.

As a result, the proportions of the playing field—118 yards by 56 yards—are the answer to the dilemma at hand.

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1. The x - intercepts of the parabola are

2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex of the parabola is at (5, 80).

A parabola is a curved shape

1. Given the parabola above, to find the x - intercepts, we proceed as follows.

The x-intercepts are the points at which the graph cuts the x-axis.

They are

2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.

The plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex is the maximum point on the graph.

So, we see that the vertex is at x = 5 s and y = 80 ft

So, the vertex is at (5, 80).

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Answer:

(i) She gives each student a pretest. Then she teaches a lesson using a computer program. Afterwards, she gives each student a posttest. The teacher wants to see if the difference in scores will show an improvement.

Step-by- Step

The situation is a case of matched or paired samples since the samples are dependent. The two measurements are drawn from the same pair of individuals The parameter that is tested using matched pairs is the population mean and this is what teacher intends to use a hypothesis test for.

For one to isolate the variable by using equation rules. Inverse inequality sign if multiplying/dividing by negative. Steps to isolate variable in inequality: Simplify, move constants with inverse operations. Divide coefficient to isolate variable. Reverse direction if using negative number.

Inequalities require you to apply the same principles as those used in equations when isolating a variable. For example, if there is an inequality 3x - 5 < 7. one can isolate the variable, by first:

Add 5 to both sides to be: 3x < 12.

Then divide both sides by 3: x < 4.

So, the variable x is one that is isolated, and the solution to the inequality is one where x < 4.

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Simplifying this equation, we get:

8 + 4k + 4k + 6 = 30

8k + 14 = 30

8k = 16

k = 2

Therefore, the value of k is 1.

In mathematics, a polynomial is an expression consisting of variables (usually represented by x), coefficients, and non-negative integer exponents, which are combined using the operations of addition, subtraction, and multiplication. For example,

\(3x^2 + 2x - 1\)

is a polynomial with three terms, or a "trinomial," where the variable x is raised to the powers of 2 and 1, and the coefficients are 3, 2, and -1.

The degree of a polynomial is the highest power of the variable in the expression. For example, the polynomial above has a degree of 2, since the highest power of x is 2.

Polynomials are used in many areas of mathematics, including algebra, calculus, and geometry, and are used to model many real-world phenomena.

We can use the remainder theorem, which states that if a polynomial f(x) is divided by (x - a), then the remainder is equal to f(a). In this case, we know that when the polynomial\(l x^3 + kx^2 + 2kx\) + 6 is divided by (x - 2), the remainder is 30. So, we can set up the following equation:

\(x^3 + kx^2 + 2kx + 6 = (x - 2)q(x) + 30\)

where q(x) is the quotient when. \(x^3 + kx^2 + 2kx + 6\) is divided by (x - 2). We don't need to know what q(x) is, since we're only interested in finding k.

Now, let's substitute x = 2 into the equation above:

\(2^3 + k(2^2) + 2k(2) + 6 = (2 - 2)q(2) + 30\)

Simplifying the left-hand side, we get:

\(8 + 4k + 4k + 6 = 30\)

\(16k = 16\)

\(k = 1\)

OR

8 + 4k + 4k + 6 = 30

8k + 14 = 30

8k = 16

k = 2

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The value of x is 6

2/5 = 6/21-x

Cross multiply both sides

2(21-x)= 30

42-2x= 30

collect the like terms

-2x= 30-42

-2x= -12

Divide both sides by the coefficient of x which is 2

2x/2 = 12/2

x= 6

Hence the value of x is 6

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First find the area of the square, then the triangle.

15 times 17 = 255 sq. yd

Triangle:

(5 times 5)/2 = 12.5 sq. yd

Your answer is 267.5 sq. yd

Hope this helps.

Answer:

Step-by-step explanation:

150 students/3 classes= 50 students per class

The percent decrease in the number of ponds that support brook trout would be approximately 47.37%.

To calculate the percent decrease in the number of ponds that support brook trout, we need to determine the difference between the initial number of ponds and the final number of ponds, and then express that difference as a percentage of the initial number of ponds.

Initial number of ponds: 19

Final number of ponds: 10

To calculate the percent decrease, we can use the following formula:

Percent Decrease = (Difference / Initial Value) * 100

Let's apply this formula to the given data:

Difference = Initial number of ponds - Final number of ponds

Difference = 19 - 10

Difference = 9

Percent Decrease = (9 / 19) * 100

Now, let's calculate the percent decrease:

Percent Decrease = (9 / 19) * 100

Percent Decrease ≈ 47.37%

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The length of the missing leg is given as follows:

40 units.

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

The parameters for this problem are given as follows:

Hence the missing leg x is obtained as follows:

30² + x² = 50²

x² = 1600

x² = 40²

x = 40.

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Answer:

i think that all of them EXCEPT the last one are correct. Explained below

Answer: 95

304/16=19

19X5=95

The expressions are simplified to;

1. 72n² + 63n

2. 18t - 18t²

3. -18b² - 18b

4. -56r - 21r²

5. -6m + 9m²

Algebraic expressions are simply described as expressions that are known to consist of coefficients of variables, variables, constants, terms, and factors.

These algebraic expressions are also made up of mathematical or arithmetic operations.

These operations are;

From the information given, we have;

1. -9n (-8n -7)

expand the bracket

72n² + 63n

2. -2t(-9 + 9t)

expand the bracket

18t - 18t²

3. -3b(6b + 6)

expand the bracket

-18b² - 18b

4. -7r(8 + 3r)

expand the bracket

-56r - 21r²

5. 3m(-2 + 3m)

expand the bracket

-6m + 9m²

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The straight-line distance between Akira's house and Cooper's house is 6.13 kilometers (rounded to the nearest tenth)

Given that,To get from home to his friend Akira's house, Jaden would have to walk 2.8 kilometers due east.The straight-line distance between Akira's house and Cooper's house is given by the distance between two points in a coordinate plane. Let the home be the origin (0, 0) of the coordinate plane and Akira's house be represented by the point (2.8, 4.7). Similarly, let Cooper's house be represented by the point (8.3, 7.4).The distance formula between the two points (2.8, 4.7) and (8.3, 7.4) is given by:distance = √[(8.3 - 2.8)² + (7.4 - 4.7)²]= √[5.5² + 2.7²]= √(30.25 + 7.29)= √37.54= 6.13 km (rounded to the nearest tenth)

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Answer:

2

Step-by-step explanation:

To find the interquartile range, subtract the lower quartile from the upper quartile.

The upper quartile is 7.

The lower quartile is 5.

Subtract.7–5=2

The interquartile range for Mike's teammates' shoe sizes is 2 sizes.

The interquartile range for Mike's teammates' shoe sizes is R = 2

The distance between the upper and lower quartiles is known as the interquartile range. Half of the interquartile range corresponds to the semi-interquartile range. Finding the values of the quartiles in a small data set is straightforward.

The spread of the data, or statistical dispersion, is measured by the interquartile range. The middle 50%, fourth spread, or H-spread are further names for the IQR. It is described as the spread between the data's 75th and 25th percentiles.

Given data ,

Let the interquartile range be represented as R

Now , the equation will be

Let the shoe sizes be represented as set A

A = { 2 , 4 , 6 , 8 , 10 }

Now , the upper range of the quartile is = 7

The lower range of the quartile is = 5

And , the interquartile range R = upper quartile - lower quartile

On simplifying , we get

The interquartile range R = 7 - 5 = 2

Hence , the interquartile range R = 2

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Answer:

  g(7) = 16

Step-by-step explanation:

The domain definitions in this piecewise function tell you that the third (bottom) piece applies when x=7.

  g(7) = (7+1)(7-5) = (8)(2)

  g(7) = 16

Answer:

$190.75 - cost of the units sold

Step-by-step explanation:

see picture

Given :

Initial length of electric cable needed, \(L=550\ ft\).

Later, Sally is told that the homeowner has decide to cut back from a​ three-car garage to a​ two-car garage, which will eliminate two branch​ circuits, one of 23 feet and the other of 34 feet.

To Find :

How many feet of wire will be needed​ now.

Solution :

Wire needed is given by :

Required = Total wire - ( length of 1nd branch + length of 2nd branch )

Required = 550 - ( 23 + 34 )

Required = 550 - ( 57 ) ft

Required = 443 ft

Therefore, length of wire required is 443 ft.

Hence, this is the required solution.

The length of the electric wire needed is 443 feet.

Mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the initial length of electric cable needed is 550 feet. Later, Sally is told that the homeowner has decided to cut back from a​ three-car garage to a​ two-car garage, which will eliminate two branch​ circuits, one of 23 feet and the other of 34 feet.

The wire needed is given by :

Required = Total wire - ( length of 1st branch + length of 2nd branch )

Required = 550 - ( 23 + 34 )

Required = 550 - ( 57 ) ft

Required = 443 ft

Therefore, the length of wire required is 443 ft.

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Step-by-step explanation:

To find the solution to the system of equations represented by the data in the table, we need to first write out the equations. Let's call the number of imports in a given month "x" and the number of exports "y". Then we have:

For January: 2x + 3y = total trade

For February: 4x + 4y = total trade

For March: 6x + 5y = total trade

For April: 8x + 6y = total trade

The simple interest formula for a future quantity is the following:

Where:

Solving for the present value we get:

Replacing the given values:

Solving the operations:

Therefore, she needs $57666

A Confidence Interval shows the joint or bivariate relationship between two categorized (nominal and/or ordinal) variables.

Data that is labeled without using quantitative data is known as nominal data.

A variable in mathematics is an alphabet or phrase that stands in for an unknowable amount, unknowable value, or unknowable number.

A variable is categorical unless it has a numerical value, in which case it is referred to as a quantitative variable.

The category and quantitative variables are now classified as follows:

Duration is a quantitative variable with interval as its unit of measurement.

Ratings are categorical variables with an ordinal level of measurement.

The degree of measurement for the categorical variable "voting status" is nominal.

Ordinal data are those that can be arranged.

The highest and smallest known values are continuous and discrete values for interval data, respectively. The order is clear here. Here, the distinction between two values means something.

All of the characteristics of interval data apply to ratio data, plus it has the definition of zero(0), meaning that no points are included. For instance, height, weight, etc.

Because ratio includes both continuous and discrete data, it is likely that the difference between any two numbers won't be the same.

It is interval data since everyone knows when a class starts and when it ends, and it also has these two times. for instance, between 9:00 to 10:00

Nominal because the information is categorical.

Ordinary, given that we may get quality products here. Good, acceptable, or poor.

Ordinal because the marks can be arranged.

Ordinary since we can arrange the ages.

Line symmetry; rotational symmetry; the reflection in the line x = 0, the reflection in the line y = 0 the reflection in the line y = x and the reflection in the line y = -x map the square onto itself; the rotations of 90°, 180°, 270° and  around the point ( 0 , 0 ) map the square onto itself.

Therefore,

A Confidence Interval shows the joint or bivariate relationship between two categorized (nominal and/or ordinal) variables.

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Mr. Carreon can give his students 243 different combinations of quizzes for a one-school week if he chooses to give a quiz in either math, science or history each day.

To find the number of different combinations of quizzes that Mr. Carreon can give his students for a one-school week, we can use the concept of permutations and combinations.

Since there are three subjects (math, science, and history) and Mr. Carreon can give a quiz in any of these subjects on each day of the week, the number of different combinations of quizzes for the week is given by the product of the number of choices for each day. That is,

Number of combinations = Number of choices on Monday * Number of choices on Tuesday * ... * Number of choices on Friday

Since there are 3 subjects to choose from for each day, the number of choices for each day is 3. Therefore, the number of different combinations of quizzes for the week is:

Number of combinations = 3 * 3 * 3 * 3 * 3 = 3^5 = 243

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The area of a circle having radius 2 is 12.57 square unit.

A circle is a round-shaped picture, that has no corners or edges, in geometrical figure it has the largest area for any given length or parameter.

Given that,

The radius of a circle = 2,

To find the area circle, use formula,

Area of circle = π×r²

Area = 22/7×2×2

Area = 88/7

Area = 12.57 square unit.

The area of circle is 12.57 square unit.

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The description of the area of a square is (c) as the length of the side increases, the area increases.

The table of values is given as:

Side Length (cm)        Area (cm²)

1                                       1

2                                      4

3                                      9

4                                      16

5                                    25

In the above table, we can see that:

As length increases, the area also increases

Hence, the description of the area is (c) as the length of the side increases, the area increases.

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