The sum of two numbers is twenty-one. one number is eighteen less than two times the other. find the numbers.

The definition of slope-intercept form y=mx+b is given below.

A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.

In geometry, there are two types of lines: straight and curved. Vertical and horizontal straight lines are further divided into categories. Parallel, intersecting, and perpendicular lines are further types of lines.

In the given question:-

The value of the steepness or the direction of a line in a coordinate plane is referred to as the slope of a line, also known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope may be determined using a variety of approaches.

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Answer:

Walmart has the better deal.

Step-by-step explanation:

Hi there!

To solve this question, we could find the final price of a bike from Walmart and Kmart, compare them, and identify which is less.

Walmart

Original price: $55

Deal: 20% off

55 × 0.8 = 11

A bike from Walmart costs $44.

Kmart

Original price: $65

Deal: 25% off

65 × 0.75 = 48.75

A bike from Kmart costs $48.75.

$44 < $48.75, so therefore, Walmart's deal is better.

I hope this helps!

Total number of songs downloaded: 48

Songs by his favourite band: 12

A. Divide the number of songs by his favorite band by the total number of songs:

12/48 = 0.25

B. is decimal terminating

0.65 is the correct one if not up there try 0.45 other possible one

Step-by-step explanation:

A rational number is defined as any number which can be expressed in fractional p/q of two integers, where 'p' is the numerator and 'q' is the denominator. 'q' can never be zero. A rational number can also be expressed as a terminating decimal. So, when 0.25 is added in 0.45 it becomes 0.65 which is rational.

Polynomials form a system like to that of integers hence they are closed under the operations of addition and subtraction.

Exponents of polynomials are whole numbers.

Hence the resultant exponents will be whole numbers , addition is closed for whole numbers. As a result, polynomials are closed under addition.

If an operation results in the production of another polynomial, the resulting polynomials will be closed.

The outcome of subtracting two polynomials is a polynomial. They are also closed under subtraction as a result.

The word polynomial is a Greek word. We can refer to a polynomial as having many terms because poly means many and nominal means terms. This article will teach us about polynomial expressions, polynomial types, polynomial degrees, and polynomial properties.

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The solution to the inequality 5x - 18 > 2(4x - 15) is x < 4.

To solve the inequality 5x - 18 > 2(4x - 15), we can simplify the expression and isolate the variable x.

First, distribute the 2 to the terms inside the parentheses:

5x - 18 > 8x - 30

Next, we want to isolate the x terms on one side of the inequality.

Let's move the 8x term to the left side by subtracting 8x from both sides:

5x - 8x - 18 > -30

Simplifying further, we combine like terms:

-3x - 18 > -30

Now, let's isolate the variable x.

We can start by adding 18 to both sides of the inequality:

-3x - 18 + 18 > -30 + 18

Simplifying further:

-3x > -12

To isolate x, we need to divide both sides of the inequality by -3. However, when we divide by a negative number, we need to flip the inequality sign:

(-3x) / (-3) < (-12) / (-3)

Simplifying gives us:

x < 4.

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Eddie's account can be modelled as a linear function.

Ely's account can be modelled as an exponential function.

Ely's account  would be higher than Eddie's account by $207.98.

A linear function is a function that has one variable that is raised to the power of 1. An example is 5x + 2.

Eddie's account can be modelled as a linear function because it increases by $240 every year. The linear function is $3000 + $240x. Where x is the number of years.

An exponential function is a function that is in the form y = \(a^{x}\).

Ely's account can be modelled as an exponential function because it increases by \(1.08^{x}\). The exponential function is $3000 x  \(1.08^{x}\). Where x is the number of years.

Value of Eddie's account in 5 years = $3000 + $240(5) = $4,200

Value of Ely's account in 5 years = $3000 x  \(1.08^{5}\) = $4,407.98.

Difference = $4,407.98 - $4,200 = $207.98

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The table is an illustration of a linear and an exponential function.

From the table, we can see that Eddie's balance increase by 240 each month.

This represents a linear function.

Also, we can see that Ely's balance increases at a rate of 8% each month.

This represents an exponential function.

So, we have:

\(y = 3000 + 240x\) -- Eddie's account

\(y = 3000(1.08)^x\) --- Ely's account

In (a), we have:

\(y = 3000 + 240x\) -- Eddie's account

\(y = 3000(1.08)^x\) --- Ely's account

So, their balance in 5 years is:

\(y =3000 + 240*5\)

\(y =4200\)

\(y = 3000(1.08)^5\)

\(y = 4408\)

Calculate the difference (d)

\(d = 4408 - 4200\)

\(d = 208\)

Hence, Ely's balance would be $208 greater than Eddie's

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The required matches for the given figures are 1.HI || EG, 2. AC⊥DB and ∠KFJ.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,
In the figure, we can see.

Line HI is parallel to line Eg so the correct choice is HI || EG.

Line AC is perpendicular to line AC, so the correct choice is AC⊥DB.
Angle made by points KFJ is ∠KFJ. so the correct choice is ∠KFJ.

Thus, the required matches for the given figures are 1.HI || EG, 2. AC⊥DB and ∠KFJ.

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Answer:

The correct option is;

C. Transformation

Step-by-step explanation:

In mathematics, transformation refers to the relocation of an object called the pre-image from initial position to another new location at which point the object will be known as the image whereby there is a one to one mapping from each point on the pre-image to the image

The types of transformation includes reflection, rotation, and translation which involve changes in position and dilation, which involves changes in the size of the pre-image.

Let us first draw the diagram given to understand the given information in the problem: The diagram above shows a quadrilateral ABCD, and point E is on segment AB. We are required to find the ratio of AB to BC and the ratio of AD to DC. To calculate the ratios in geometry:

Calculation of Ratio of AB to BC

In ΔABC, AB and BC are the sides that we want to find the ratio of. We can use the following formula to calculate the ratio of AB to BC:

Ratio of AB to BC = AB / BC

Using the diagram, we can see that AB = 7

and BC = 6. Substituting these values in the formula above, we get:

Ratio of AB to BC = AB / BC

= 7 / 6 = 1.1667

Rounding to the hundredths place, we get:

Ratio of AB to BC = 1.17

Calculation of Ratio of AD to DC

In ΔADC, AD and DC are the sides that we want to find the ratio of. We can use the following formula to calculate the ratio of AD to DC:

Ratio of AD to DC = AD / DC

Using the diagram, we can see that AD = 7

and DC = 11. Substituting these values in the formula above, we get:

Ratio of AD to DC = AD / DC

= 7 / 11 = 0.6364

Rounding to the hundredths place, we get:

Ratio of AD to DC = 0.64

Notice that the ratio of AB to BC is greater than 1, while the ratio of AD to DC is less than 1. Also, the sum of these ratios is greater than 1 (1.17 + 0.64 = 1.81). These observations indicate that the quadrilateral ABCD is not a parallelogram.

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The Paired samples t-test is the most suitable statistical technique for comparing the mean span of the dominant and non-dominant hands in this study.

To investigate whether the span of a person's dominant hand is greater than that of their non-dominant hand, the most appropriate statistical technique would be the Paired samples t-test.

The Paired samples t-test is used when comparing the means of two related groups or conditions. In this case, the dominant and non-dominant hands are related because they belong to the same individuals in the study. By comparing the means of the dominant and non-dominant hand spans, we can determine if there is a significant difference between the two.

The other options listed, ANOVA (Analysis of Variance), Independent samples t-test, Wilcoxon's matched-pairs signed rank test, and Mann-Whitney U test, are not suitable for this scenario because they are designed for different types of comparisons:

- ANOVA is used when comparing the means of three or more independent groups, which is not the case here.

- Independent samples t-test is used when comparing the means of two independent groups, which is not the case here as the measurements are paired.

- Wilcoxon's matched-pairs signed rank test and Mann-Whitney U test are non-parametric tests that are used when the data do not meet the assumptions of parametric tests. However, in this case, we have paired measurements, and the paired samples t-test is the appropriate parametric test.

Therefore, the Paired samples t-test is the most suitable statistical technique for comparing the mean span of the dominant and non-dominant hands in this study.

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a, b, and c are collinear points. b is the midpoint of ac .

The coordinate of c is 3. So, the coordinate of point c is 3.

If b is the midpoint of ac, it means that the coordinates of a, b, and c lie on the same line and b is exactly halfway between a and c.

Given that the coordinate of a is -8 and the coordinate of b is -2.5, we can determine the coordinate of c as follows:

The distance from a to b is equal to the distance from b to c. Since b is the midpoint, the distance from a to b is half of the distance from a to c. Mathematically, we can express this relationship as:

|a - b| = |b - c|

Substituting the given coordinates, we have:

|-8 - (-2.5)| = |-2.5 - c|

Simplifying further:

| -8 + 2.5 | = |-2.5 - c|

| -5.5 | = |-2.5 - c|

Since the absolute value of a number is always positive, we can drop the absolute value signs:

5.5 = 2.5 + c

Now we solve for c:

5.5 - 2.5 = c

3 = c

Therefore, the coordinate of c is 3. So, the coordinate of point c is 3.

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Answer:

8/10

Step-by-step explanation:

Answer:lol

Im a dude but you trying to pick up a girl on a school site is hilarious

Step-by-step explanation:

Hi

1) f(x)= 0.9 x

2) g(x) = x-100

3) f °g. is first apply g then f. so :

f°g = 0.9 ( x-100) = 0.9x-90

4) g°f. is first apply f then g

so g°f = (0.9x) -100 = 0.9x-100

I let you conclude which is the best deal :)

The length of the unknown leg of the right triangle is of 20 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 given as follows:

9.75² + x² = 22.25²

x = sqrt(22.25² - 9.75²)

x = 20.

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a) The binomial expansion of (1+12x)^1/2 is given by:

(1+12x)^1/2 = 1^1/2 + (1/2)(1^-1/2)(12x) + (1/2)(1^-1/2)(-1/2)*(12x)^2 + ...

Binomial expression: what is it?

A polynomial with only terms is a binomial. An illustration of a binomial is x + 2, where x and 2 are two distinct terms. Additionally, in this case, x has a coefficient of 1, an exponent of 1, and a constant of 2. As a result, a binomial is a two-term algebraic expression that contains a constant, exponents, a variable, and a coefficient.

The first four terms, in ascending powers of x, are:

1, (1/2)(12x), (1/8)(12x)^2, (1/16)*(12x)^3

b) To use x=1/36 in the expansion, you would substitute x=1/36 into the expansion, and keep only the terms up to x^3 (the fourth term in the expansion). This will give an approximation of the value of (1+12x)^1/2 when x=1/36.

This will be an approximation of √12 because x=1/36 corresponds to 12x = 1 and the initial value of the expansion is 1 + 12x .

We can use this approximation to approximate square root of 12 and also for other square roots by using appropriate x values.

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The equation of motion for this scenario is: dv/dt = (515.2 * x - 2.5 * v - 257.6) / 0.248.

To determine the equation of motion for this scenario, we need to consider the forces acting on the system. The weight exerts a gravitational force of 8 pounds, which can be converted to 8 * 32.2 = 257.6 lb*ft/s^2. The spring force opposes the weight and is given by Hooke's Law, which states that the force exerted by a spring is proportional to the displacement from its equilibrium position. The equation for the spring force is F_spring = k * x, where k is the spring constant and x is the displacement.

Since the weight stretches the spring by 0.5 feet, we can substitute the given values into the equation: 257.6 = k * 0.5. Solving for k, we find k = 515.2 lb/ft.

Next, we can consider the damping force. The damping force is given by F_damping = -2.5 * v, where v is the velocity. The negative sign indicates that the damping force opposes the velocity.

Now we can write the equation of motion: m * a = F_spring + F_damping + F_gravity, where m is the mass and a is the acceleration.

The mass is not given, but we can solve for it using the weight: 8 lb = m * 32.2 ft/s^2. Solving for m, we find m = 8 / 32.2 = 0.248 lb*s^2/ft.

With all the values known, we can write the equation of motion as: 0.248 * dv/dt = 515.2 * x - 2.5 * v - 257.6.

Simplifying the equation further, we have: dv/dt = (515.2 * x - 2.5 * v - 257.6) / 0.248.

This equation describes the motion of the system. To solve it, we can use numerical methods or techniques such as Laplace transforms, depending on the desired level of accuracy and complexity.

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Producing rDNA involves isolating and cleaving DNA, inserting fragments into a vector, and transforming host cells. rDNA can be introduced via transformation, transfection, or viral vectors. Clinical applications include protein production, gene therapy, vaccines, and diagnostics.

Producing a recombinant DNA (rDNA) vector involves several general steps. Here are the three main steps involved in the process:

Isolation and Cleavage of DNA:

The first step is to isolate the desired DNA fragments from the source organism. This can be done using various techniques such as PCR (Polymerase Chain Reaction) or restriction enzyme digestion. Restriction enzymes are enzymes that cut DNA at specific recognition sites. By using the appropriate restriction enzymes, the desired DNA fragment and a vector DNA can be cut at specific sites. The vector is usually a plasmid, which is a small circular DNA molecule.

Insertion of DNA Fragments into the Vector:

Once the DNA fragments and vector have been cut, they are mixed together and joined through a process called ligation. DNA ligase is used to catalyze the formation of covalent bonds between the ends of the DNA fragments and the vector. This creates a recombinant DNA molecule containing the desired DNA fragment within the vector. The recombinant DNA molecule is then introduced into host cells for replication.

Transformation of Host Cells:

The recombinant DNA molecules need to be introduced into host cells to produce multiple copies of the recombinant DNA. This is typically done using a process called transformation. Host cells, such as bacteria or yeast, are treated in a way that makes them more receptive to taking up the recombinant DNA. Methods for transformation include heat shock, electroporation, or using chemical agents. Once the host cells have taken up the recombinant DNA, they can be grown in culture to produce large quantities of the desired DNA fragment.

Introduction of rDNA into Cells:

Recombinant DNA can be introduced into cells using various methods, depending on the type of cells being targeted. Some common techniques include:

Transformation: As mentioned earlier, host cells, such as bacteria or yeast, can be treated to make them receptive to taking up the recombinant DNA. This can be achieved by exposing the cells to heat shock, electroporation, or using chemical agents.

Transfection: This method is used for introducing rDNA into eukaryotic cells, including animal cells. It involves the use of techniques such as calcium phosphate precipitation, liposome-mediated transfection, or electroporation.

Viral Vectors: Certain viruses, such as retroviruses, adenoviruses, or lentiviruses, can be modified to carry the recombinant DNA. These viral vectors can then infect target cells and deliver the rDNA into the host genome.

Clinical Applications of rDNA:

Recombinant DNA technology has revolutionized biomedical research and has led to numerous clinical applications. Some important applications include:

Production of Therapeutic Proteins: rDNA technology allows for the production of large quantities of therapeutic proteins, such as insulin, growth factors, clotting factors, and monoclonal antibodies. These proteins can be used to treat various diseases, including diabetes, cancer, and genetic disorders.

Gene Therapy: rDNA vectors can be used to deliver functional copies of genes into target cells to correct genetic defects. This holds promise for the treatment of inherited diseases caused by single gene mutations, such as cystic fibrosis and muscular dystrophy.

Vaccine Development: Recombinant DNA technology has been instrumental in the development of vaccines. By expressing specific antigens from pathogens, recombinant vaccines can be created to stimulate an immune response without causing disease.

Diagnostic Tools: Recombinant DNA techniques are used to produce specific DNA or RNA probes for diagnostic purposes. These probes can detect the presence of specific genes or mutations associated with diseases, aiding in early detection and personalized medicine.

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Answer:

$852

Step-by-step explanation:

From the given question, the following are given:

Present value, PV = $675

Rate, r = 6% = 0.06

Number of years, n = 2 years

Number of times per year, m = 2

The balance in his account is the future value (FV), so that;

Future value = PV\((1+r)^{nm}\)

                     = 675\((1+0.06)^{(2*2)}\)

                     = 675 x 1.26248

                     = 852.174

Future value = $852

Thus, the balance in Alex's account would be $852.

To achieve the maximum volume for the open-top bin, squares measuring 6 inches should be cut out of each corner of the 32-inch by 42-inch plastic piece.

To find the optimal size of the square cutouts, we need to consider the dimensions of the plastic piece and the volume of the resulting bin. Let's assume that the square cutouts have a side length of 'x' inches.

Step 1: Determining the dimensions of the bin:

When the squares are removed from each corner and the flaps are folded up, the resulting bin will have a length of (42 - 2x) inches and a width of (32 - 2x) inches. The height of the bin will be 'x' inches.

Step 2: Calculating the volume of the bin:

The volume of the bin can be obtained by multiplying its length, width, and height. Therefore, the volume V(x) can be expressed as follows:

V(x) = (42 - 2x) * (32 - 2x) * x

Step 3: Finding the maximum volume:

To determine the size of the square cutouts that will yield the maximum volume, we need to find the value of 'x' that maximizes the function V(x).

To find the maximum, we can take the derivative of V(x) with respect to 'x' and set it equal to zero. By solving this equation, we can find the critical point that corresponds to the maximum volume.

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On solving the provided question, we can say that Rounding to the nearest tenth of a square unit, the area of the circle is approximately 25.1 square units.

A circle seems to be a two-dimensional component defined as such collection of the all points in a jet that become equidistant from the hub. A circle is commonly portrayed with the capital "O" for centre and the lower section "r" for the radius, which is the distance from the origin to any point on the circle. Girth (the distance from around circle) is given by the formula 2r, where (pi) is a proportionality constant roughly equal to 3.14159. The formula r2 calculates the circle's circumference, which refers to the amount of room inside of the circle.

We can use the distance formula to find the radius of the circle, which is the distance between the center C(2, 5) and point D(4, 3):

\($r = \sqrt{(4-2)^2 + (3-5)^2} = \sqrt{8} = 2\sqrt{2}$\)

The area of the circle is given by the formula\($A = \pi r^2$\), so substituting in the radius we just found, we get:

\($A = \pi (2\sqrt{2})^2 = 8\pi \approx 25.1$\\\)

Rounding to the nearest tenth of a square unit, the area of the circle is approximately 25.1 square units.

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The required number is 936.

We have,

Since the number has 3 different digits and the hundreds and ones place digits are both divisible by 3, this means that the number must be in the form of ABC, where A and C are divisible by 3 and A ≠ C.

We also know that the hundreds place digit is the third multiple of 3, so it must be 9.

This leaves us with two options for the ones and tens place digits: 3 and 6.

However, since the digits must be different, the one's place digit must be 3, and the tens place digit must be 6.

Therefore,

The number is 936.

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The equivalent system of first-order differential equations is:

To transform the given differential equation into an equivalent system of first-order differential equations, we can introduce new variables. Let's define:

x1 = x

x2 = x'

x3 = x''

x4 = x'''

Now, we can rewrite the original equation in terms of these new variables:

x4 - 5x'' - 3x' + 53sin(3t) = 0

Replacing the derivatives with the new variables, we have:

x4 = x4

x3 = x'''

x2 = x'

x1 = x

Now, we have a system of first-order differential equations:

x1' = x2

x2' = x3

x3' = x4 - 5x2 - 3x1 + 53sin(3t)

x4' = ?

We need to find an expression for x4' by differentiating one of the equations. Let's differentiate the equation x3' = x4 - 5x2 - 3x1 + 53sin(3t) with respect to t:

x4' = x3'' = (x4 - 5x2 - 3x1 + 53sin(3t))'

Differentiating each term, we get:

x4' = x4' - 5x2' - 3x1' + 159cos(3t)

Simplifying, we have:

x4' = -5x2 - 3x1 + 159cos(3t)

Therefore, the equivalent system of first-order differential equations is:

x1' = x2

x2' = x3

x3' = x4 - 5x2 - 3x1 + 53sin(3t)

x4' = -5x2 - 3x1 + 159cos(3t)

Note: The given differential equation is of the fourth order, so the resulting system has four first-order equations to represent it.

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Answer:

46 feet below sea level

Step-by-step explanation:

First, we start at -50 feet, which is 50 feet below sea level. If he swims 8 feet up, we should add the 8 feet. -50 + 8 feet which would give us -42. If he descends another 4 feet from the point where he is at right now (-42 feet), it would leave us with the point where he would be which is -46 feet. This is because we are adding the -4 feet, he descends to the -46 feet which he is already at.

Las coordenadas de la escuela (rojo) son (4,3), las coordenadas de mi casa (rosado) son (6,5) las coordenadas del supermercado (verde) son (11,4) y las coordenadas del restaurante (amarillo) son (9,8).

Se refiere a una expresión, valor o magnitud sobre el plano cartesiano que muestra la ubicación de un punto o referencia.

Siempre se deben tener los valores de ambos ejes: el eje y (vertical)  y el eje x (horizontal). Para esto primero escriba el valor del eje x luego añada una coma y escriba el valor de y.

De acuerdo a lo anterior, los lugares ubicados en el mapa tiene las siguientes coordenadas:

(4,3)

(6,5)

(11,4)

(9,8)

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Answer:

does not clearly describe a word or phrase in a sentence

Step-by-step explanation:

Not sure that this is math but...

Answer:

The answer is B

Step-by-step explanation:

B) does not clearly describe a word or phrase in a sentence

Answer: h _<_ 46

there’s the line underneath the sign

Step-by-step explanation:

The four-sided geometric object known as a tetrahedron (WXYZ) has four triangle faces that are joined to one another at their edges. Its vertices are all linked, and its faces are all equilateral triangles.

The three-dimensional geometric structure known as a tetrahedron (WXYZ) has four triangle-shaped faces. The edges of each of the tetrahedron's faces are joined to one another. All of the faces are triangular shapes with equal sides, or equilateral triangles. The tetrahedron is a solid shape because all of its vertices are joined together. The tetrahedron's four vertices are joined to one another, forming a pyramid-like shape. The tetrahedron's four vertices are the only points that do not form the triangle faces. The tetrahedron's four faces come together to produce a point in the middle of the shape. The apex of the tetrahedron is where this point is located. The faces of the tetrahedron are all congruent, or identical, as they are a regular polyhedron.

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