A neighborhood was given a vacant lot in the shape of a rectangle on which to build a park. The neighborhood is considering how to split up the area. Which statements about the formulas for finding areas are true? Check all that apply.

Part 1:

MyFone Cellular company: C = 30 + 0.05m

Cellphones R Us company: C = 35 + 0.03m

What does a math equation mean?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Part 2:

If your monthly budget is $50 for cell phone service, we can find the number of text messages that can be sent with each company by using the equation for each company's monthly bill and setting it equal to $50.

MyFone Cellular company: 50 = 30 + 0.05m, so m = 600

Cellphones R Us company: 50 = 35 + 0.03m, so m = 1250

In this scenario, Cellphones R Us company would give you the most text messages.

Part 3:

To find the number of text messages at which the monthly bill is the same for each company, we can set the two equations equal to each other and solve for m.

30 + 0.05m = 35 + 0.03m

0.02m = 5

m = 250

At 250 text messages, the monthly bill for both companies would be the same.

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Simple geometric forms are used to create composite figures. Divide a composite figure or any irregularly shaped figure into straightforward, non-overlapping figures to get its area. To determine the overall area of the composite figure, first calculate the areas of each simpler figure separately.

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Answer:

x = 15 , y = -5

Step-by-step explanation:

refer to attachment for answer

Hope this helps!

-Rishabh

The value of sinB using trigonometry ratio is 8/17 (optionB)

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

Sin(tetha) = opposite/ hypotenuse

cos ( tetha) = adjascent/ hypotenuse

tan (tetha) = opposite/adjascent

In the triangle 8 is the opposite to angle B and 15 is the adjacent to angle B and 17 is the hypotenuse.

sinB = opposite/ hypotenuse

sinB = 8/17

therefore the value of sinB = 8/17

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Using the sine ratio, sin B is calculated as: B. 8/17.

The sine ratio is a formula of the trigonometry ratios that is used to solve a right triangle. It is given as:

sin ∅ = length of opposite side / length of hypotenuse.

Given the following:

Length of opposite side = 8

Hypotenuse length = 17

Reference angle (∅) = B

Substitute the values into the sine ratio formula:

sin B = 8/17

Therefore, the value of sin B is expressed as: B. 8/17.

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Step-by-step explanation:

the volume of the cube at the beginning is

edge³ = 16³ = 4096 cm³

after 1 minute it is 4101 cm³

that means the edge is then

cubic root(4101) = 16.00650777... cm

the surface area of a cube is

6×edge²

at the beginning it was

6×16² = 1536 cm²

after 1 minute (and the increased volume) it is

6×16.00650777...² = 1,537.249746... cm²

at that moment the surface area is increasing at

1.249745825... cm²/ minute

The equation that could be used to find how many students are in the class is → {2x + 8 = 3x - 11}.

Given is that the teacher were to distribute sheets of paper so that each student got two sheets, there would be 8 sheets remaining. However, if three sheets were given to each student, the teacher would be 11 sheets short

Let the number of sheets be {y} and the number of students be {x}. We can write -

y = 2x + 8

y = 3x - 11

Equating both -

2x + 8 = 3x - 11

Therefore, the equation that could be used to find how many students are in the class is → {2x + 8 = 3x - 11}.

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MNP is a triangle, hence. MN and NP's midpoints are Q and R, respectively. MP is measured at 34.

Having three sides, three angles, and three vertices, a triangle is a closed, two-dimensional object. A polygon also includes a triangle. Triangle ΔABC is shown in the image above. Triangle illustrations.

Given:

MNP being a triangle, this. The midpoints of MN and NP are Q and R, respectively.

The lengths of QR and MP are 4x -11 and 9x - 29 respectively.

We must establish the MP's measurement.

x's value is:

The triangle midsegment theorem can be used to find the value of x.

Using the theorem, we've reached;

M P=2(Q R)

Substituting the lengths, we get;

9x - 29 = 2(4x - 11)

9x - 29 = 8x - 22

Subtracting both sides by  8 x, we have;

x - 29 = -22

Adding both sides of the equation by 29 , we get;

x = 7

As a result, x has a value of 7.

Measure of MP: The measure of MP can be obtained by changing x to equal 7 in the MP's length.

We therefore have;

MP = 9(7) - 29

MP = 63 - 29

The measure of MP is 34.

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Answer:

24x - 1/4

Step-by-step explanation:

Answer:

  6⁸ = 1679616

Step-by-step explanation:

You want to simplify the expression (6²)⁴.

The applicable rule of exponents is ...

  (a^b)^c = a^(bc)

Here, this means ...

  [tex](6^2)^4=6^{2\times4}=\boxed{6^8=1679616}[/tex]

__

Additional comment

Your calculator is good at evaluating numerical expressions.

<95141404393>

The curve at point P is approximately 0.88.

Slope is a measure of the steepness of a line or a surface and is represented by the letter m. It is calculated by dividing the vertical change in the line or surface by the horizontal change in the line or surface. Slope is used in mathematics, engineering, and other sciences to measure the rate of change between two points.

The slope of the curve at point P can be estimated by evaluating the function at the two points x=1.1 and x=1.3. At x=1.1, the value of y is 2.31 and at x=1.3, the value of y is 3.19. Therefore, the estimated slope of the curve at point P is (3.19-2.31)/(1.3-1.1) = 0.88.

This estimate indicates that the slope of the curve at point P is approximately 0.88.

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The graph for [tex]y=5\sqrt{x}-2x[/tex] has been attached below. The solution has been obtained using graphing the function.

What is graphing of a function?

Drawing the graph of an applicable function is the process of graphing a function. While graphing simple functions like direct, quadratic,etc. is fairly easy, complex functions like rational, logarithmic,etc. bear some complexity and an understanding of certain fine ideas. Every point on the curve will satisfy the function equation if the curve represents the function.

We are given [tex]y=5\sqrt{x}-2x[/tex]

The range is given as [0,12]

The graph obtained has been attached below.

It is observed that graph of the function is increasing gradually and then decreasing.

Hence, the graph of the function is increasing gradually and then decreasing.

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Answer:

area=262.5

Step-by-step explanation:

15x10=150

15x15=225

225÷2=112.5

150+112.5=262.5

At age 9, Tammy was taller than Leslie because she was 3.68 inches taller.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

as per the details stated above

that Leslie measured 50 inches at age 9

and Tammy's height may be predicted by the equation

y = 2.2x + 35.5,

where y represents Tammy's height at x years of age,

one must carry out the following computation to establish who was taller at that age:

Tammy = 2.2 x 9 + 35.5

= 18.18 + 35.5

= 53.68.

Tammy was 3.68 inches taller than Leslie at age 9 as a result, Tammy was taller at that age.

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By 3.68 inches, Tammy was taller than Leslie when she was nine years old.

As per the data given in the above question are as bellow,

The provided details are,

Given that Tammy's height can be predicted by the equation

y = 2.2x + 35.5,

where y is her height at age x, and Leslie's height at age 9 was 50 inches,

The following computation must be done to establish who was higher at that age:

Leslie is 50.

Tammy = 2.22 x 9.5 + 35.5 = 18.18 + 35.5 = 53.68

Consequently, Tammy was taller at age 9 than Leslie since she was 3.68 inches taller.

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Carlos have to travel 105 miles to reach the destination.

The path followed by an object to travel a predetermined distance at a predetermined speed from one place to another is called the distance traveled. As was previously said, the distance formula combines distance, speed, and time.

As per the details share in the above question are as bellow,

The details provided are as follow,

Carlos is traveling by automobile for more than 240 miles.

Carlos has traveled 135 miles so far.

How far must Carlos still travel?

We have to use subtraction method to determine the distance remaining.

Now subtract the total distance by the distance traveled,

Substitute the value in above we get,

=240-135

=105 miles

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The required value of z in the given system of equations is 4. Option D is correct.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
3x + 5y - z = 15 - - - - (1)

x + 2y = 8 - - - - -(2)

x - 3y + 2z = - 9 - - - - (3)

multiply equation 1 by 2 and add with equation 3,
6x + x + 10y -3y -2z + 2z = 30 - 9
7x + 7y = 21
x + y = 3 - - - -(4)

Subtract equation 4 from 2
y = 5
Now, from equation 4
x + 5 = 3
x = -2

From equation 1
3(-2) + 5(5) - z = 15
-6 + 25 - z = 15
z = 10 - 6
z = 4

Thus, The required value of z in the given system of equations is 4. Option D is correct.

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-1 is the negative integer.

Now, According to the question:

Let's know:

What are Integers?

Integers are the collection of whole numbers and negative numbers. Similar to whole numbers, integers also does not include the fractional part. Thus, we can say, integers are numbers that can be positive, negative or zero, but cannot be a fraction. We can perform all the arithmetic operations, like addition, subtraction, multiplication and division, on integers.

The word integer originated from the Latin word “Integer” which means whole or intact. Integers is a special set of numbers comprising zero, positive numbers and negative numbers.

Examples of Integers: – 1, -12, 6, 15.

So, According to the above statement is:

-1 is the negative integer.

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Skydiver took 15√3 seconds to freefall 1200 feet.

What is arithmetic?

Mathematical arithmetic is the study of the properties of the standard operations on numbers, such as addition, subtraction, multiplication, division, exponentiation, and root extraction.

Here, we have

Given: A skydiver falls at a rate of t = 0.75√x seconds to freefall x feet.

x = 1200 feet

Now, we put the value of x in t = 0.75√x and we get

t = 0.75×√1200

t = 0.75× 20√3

t = 15√3

Hence, Skydiver took 15√3 seconds to freefall 1200 feet.

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(2,-4), (-2, 3), (-3, 4), (-5, 0) is the transformation for the coordinates of the vertices of the given pairs of quadrilaterals.

In order to represent a quadrilateral visually, four line segments' ends are connected to form a closed geometric object. Each intersection point of every two line segments of a quadrilateral is referred to as a quadrilateral vertex because the ends of the four line segments cross at four separate places.

Triangle area equals 2 1

[x 1 (y 2 y 3 )+x 2 (y 3 y 1 )+x 3 (y 1 y 2 )]

Quadrilateral ABCD's area is equal to the sum of its sides, ACD and ABC.

(2,-4), (-2, 3), (-3, 4), (-5, 0) is the transformation for the coordinates of the vertices of the given pairs of quadrilaterals.

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An example of an extraneous solution in math is solving the equation 1/(x−2) + 1/(x+2) = 4/(x−2)(x+2) for x.

An extraneous solution is a root of a transformed equation that is not the root of the original equation because it was excluded from the domain of the original equation.

Solve the equation 1/(x−2) + 1/(x+2) = 4/(x−2)(x+2) for x

1/(x−2) + 1/(x+2) = 4/(x−2)(x+2)

(x−2)(x+2)/(x−2) + (x−2)(x+2)/(x+2) = 4(x−2)(x+2)/(x−2)(x+2)

(x−2) + (x+2) = 4

2x = 4

x = 2

But 2 is excluded from the domain of the original equation because it would make the denominator of one of the fractions zero--and division by zero is not allowed. Therefore, it cannot be the root of the original equation. So, 2 is an extraneous solution. So, the equation has no solutions.

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Answer: To reduce the fraction to lowest terms, we need to divide both the numerator and denominator by their greatest common factor.

In this case, the greatest common factor between the numerator and denominator is x^2y.

So we can divide the numerator and denominator by x^2y to get:

(4x^(4)y^(3))/(-8x^(2)y) = (4x^2y^2)/(-8) = -(1/2) x^2y^2

So the fraction reduced to lowest terms is -(1/2) x^2y^2, which corresponds with option B.

Step-by-step explanation:

The expression for the solution is 6x² - 18x - 4x + 12

We have different methods of solving quadratic equation, they include;

From the information given, we the quadratic equation;

6x² - 22x + 12 = 0

Let's solve the quadratic equation by using the factorization method, we have;

Multiply the coefficient of x² by the constant

Then find the pair factors of the product that adds up to -22, we get;

-18 and -4

Substitute the values into the formula to determine the expression, we have;

6x² - 18x - 4x + 12 =0

group in pairs

(6x² - 18x) - (4x + 12)  = 0

Hence, the expression is (6x² - 18x) - (4x + 12)

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In this study, weight loss would be the dependent variable, as it is being measured or observed as a result of the change in the independent variable, which is the calorie intake (1,300 calories/day).

The independent variable is the factor that is being manipulated or changed in the study, and the dependent variable is the factor that is being measured or observed as a result of that change.

Put simply, an independent variable is just what it sounds like it is. It's a separate factor that can't be affected by the others. One independent variable could be a person's age.

In research, the independent variable might be either (1) quantitative or (2) qualitative. Variables with numeric or scalar ranges are called quantitative. They can be thought of as numerical variables that provide answers to "how many?" or "how often?"

The three primary categories of research variables are the independent variable, the dependent variable, and the controlled variables. Take the case of an automobile driving along a variety of terrains.

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Answer: 3.76

Step-by-step explanation:

6.26 - 2.5 = 3.76

Answer:

3.76

Step-by-step explanation:

The kind of system and equation that has many solutions is a linear system of equations with infinitely many solutions.

Equation is an expression that states the equality of two things. It is usually written using mathematical symbols, and it typically contains an equals sign (=). An equation is used to describe a relationship between two or more variables, such as the relationship between the circumference of a circle and its radius, or the relationship between a certain amount of money and the amount of interest it will generate. Equations are used to solve problems in mathematics, chemistry, physics, engineering, and other disciplines.

This means that any combination of values for the unknowns that satisfies the equation will provide a solution. A linear system of equations can be written in the form of ax + by = c, where a, b, and c are all real numbers, and x and y are the unknown variables. When the equation has infinitely many solutions, it means that for any given value of a, b, and c, there is an infinite number of possible values for the unknowns x and y. This can be seen by looking at the graph of the equation, which will be a straight line that passes through the origin, and the line will have an infinite number of points on it.

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Step-by-step explanation:

I don't see any defined inequality here in the text.

but I can tell you what's in the picture. and how the correct inequality would look like.

the function, for which we need to define the range (all valid y-values) is moving between y = 2 and y = -2, including these 2 values.

the inequality shown is

-9 < y < -4

the values -4 and -9 are not included (indicated by the dotted lines).

so, we need to change that to

-2 <= y <= 2

please consider the "<=" signs, as both values have to be included, because the function is clearly also producing -2 and +2 values.

FYI

it would also be correct to write

2 >= y >= -2

Simply multiply the number of moles by 24 to obtain the volume of gas in dm3 at standard pressure and temperature.

According to the chemical formula 2 C2H6 + 7 O2 → 4 CO2 + 6 H2O + 3120 kJ, the full combustion of ethane releases 1559.7 kJ/mol, or 51.9 kJ/g, of heat along with carbon dioxide and water. Amorphous carbon and carbon monoxide can be produced when combustion doesn't involve too much oxygen.

Exothermic reactions, such as the combustion of hydrocarbons, provide heat energy. To find the volume of gas in dm3 at room temperature and pressure, simply multiply the number of moles by 24.

The typical scenario is that you are following a recipe that, for instance, calls for a 0.5 molar solution of NaOH. As you are aware, "0.5 M" refers to 0.5 moles per liter.

Therefore, the correct answer is option B 24 dm³.

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for k = 6, the pair of linear equations have infinitely many solutions.

n the above equation a1= k, a2 = 12, b1 = 3, b2 = k, c1 = -(k - 3) and c2 = -k

If a solution has infinitely many solutions, then

⇒ a1 / a2 = b1 / b2 = c1 / c2

For the above pair of equations,

⇒ k / 12 = 3 / k = k - 3 / k

⇒ k/ 12 = 3/ k

⇒ k2 = 36⇒ k = ± 6

Also

⇒ 3/ k = (k - 3)/ k

⇒ 3k = k(k - 3)

⇒ 3k = k2 -3k

Then,

⇒ k2 = 6k

⇒ k = 6

The value of k which satisfies both the equations is 6.

Thus, for k = 6, the pair of linear equations have infinitely many solutions.

The complete question is,

For what values of k will the following pair of linear equations have infinitely many solutions?

kx + 3y - (k – 3) = 0

12x + ky - k = 0

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