How can you use equations to solve real-world problems? PLZ

Yes, all the numbers are multiples of prime numbers is a true statement as it get proved by prime factorization theorem.

As given in the question,

Given statement is written as:

All the numbers are representing multiples of prime numbers.

In the field of mathematics,

Using prime factorization theorem also known as fundamental theorem of arithmetic states that:

All the integers which are greater than one are represented as a multiple of prime numbers:

Example of the above stated theorem:

2 = 2×1

3 = 3 × 1

6 = 2 × 3

14 = 2 × 7 ( 2 and 7 both are prime numbers )

98 = 7 × 7 ×2 ..... and so on.

Therefore, all the numbers represents as a multiple of prime numbers is a true statement.

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We label sides as: the shorter leg is 30-degree angle, the longer leg is 60-degree angle and the hypotenuse is 90 degrees.

Any triangle with a 90-degree angle is considered a right triangle. A unique variety of right triangle with a 30-degree angle and a 60-degree angle in addition to the right angle is known as a 30-60-90 triangle.

Triangle Properties 30-60-90

A triangle with sides of 30-60-90 can be recognized by how they relate to the angles.

The shorter leg is the one that faces the 30-degree angle.

The longer leg is the one that faces the 60-degree angle.

The hypotenuse is the side that faces the right angle of 90 degrees.

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The simplification of the equation is 9y⁴/z³ - 3zy⁴.

Simplifying procedures is one way to achieve uniformity in work efforts, expenses, and time. It reduces diversity and variety that is pointless, harmful, or unnecessary.

Solving a math problem is the same thing as simplifying an expression. You basically strive to write an expression as simply as you can when you simplify it. In conclusion, there shouldn't be any more multiplying, dividing, adding, or removing to do.

Here, we have

Given: (36z²y⁶-12z⁶y⁶)/(4z⁵y²)

We have to simplify this equation.

= (36z²y⁶-12z⁶y⁶)/(4z⁵y²)

= 36z²y⁶/4z⁵y² - 12z⁶y⁶/4z⁵y²

= 9y⁴/z³ - 3zy⁴

Hence, the simplification of the equation is 9y⁴/z³ - 3zy⁴.

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Line graphs, bar graphs, pie charts, scatter plots, and histograms are examples of common graph types.

Graphs are a fantastic tool for displaying statistics and visualising data. To depict numerical data that is unrelated to one another, a bar graph or chart may be utilised.

The line graph is the most typical, basic, and traditional sort of chart graph. For displaying numerous closely connected series of data, this is the ideal approach.

Data that is readily apparent. appropriate unit-specific labelling for each axis. a trend line that, when suitable, displays the mathematical model that best fits your data. If there is more than one sort of information, there should be a legend.

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The measure of angles are,

m ∠K = 50°

m ∠L = 90°

m ∠M = 40°

m ∠LMN = 140°

What is triangle?

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

Let the triangle KLM is given.

We have to find the measure of each angle of triangle.

Since the measure of three angles of triangle is 180 degree.

⇒  m ∠K + m ∠L + m ∠M = 180°

                   5x + 9x + 4x = 180°

                                  18x = 180°

                                      x = 10°

⇒ m ∠K = 5x = 5(10°) = 50°

m ∠L = 9x = 9(10°) = 90°

m ∠M = 4x = 4(10°) = 40°

m ∠LMN = m ∠L + m ∠K

               = 90° + 50°

m ∠LMN = 140°

Hence,

m ∠K = 50°

m ∠L = 90°

m ∠M = 40°

m ∠LMN = 140°

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Answer:

(a) = $640

(b) = $8640.

Step-by-step explanation:

(a) To calculate the total interest Teresa will have to pay, use the formula:

Interest = Principal x Rate x Time

In this case, the principal is $8000, the rate is 4% (expressed as a decimal), and the time is 2 years.

So, Interest = $8000 x 0.04 x 2 = $640

(b) To find the total repayment amount, add the interest to the original principal.

In this case, the total repayment amount = $8000 + $640 = $8640.

The equation that represents the linear equation is t = 4d + 5.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

The table is given in the attached image.

To find the equation:

First, find the common difference.

So,

13 - 9 = 4

17 - 13 = 4

21 - 17 = 4

25 - 21 = 4

Here, the first difference 4 is common.

That means, the equation is a linear equation.

And the general form of the linear equation is,

t = md + c

Here, m = 4

So,

t = 4d + c

To find C:

Substitute the value of t = 9 and d = 1,

So, c = 5

So, the linear equation is t = 4d + 5.

Therefore, t = 4d + 5 is the linear equation.

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Instead of taking  6 miles south and 9 miles east to the house the shortest distance is 10.82 miles

The distance described  6 miles south and 9 miles east represents a right triangle with

opposite = 6 miles

adjacent = 9 miles

hypotenuse is the shortest distance

Using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

x² = 9² + 6²

x² = 81 + 36

x² =  117

x = √117

x = 10.82

the shortest distance is 10.82 miles

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The total distance it travels during one full cycle of motion is 4A. Hence, the correct answer is D.

When a block on the end of a spring is pulled to position x = A and released from rest, it begins to oscillate. The block will oscillate back and forth along the x-axis between the position x = A and the position x = -A.

In one full cycle of its motion, the block will travel from position x = A to position x = -A and back to position x = A. The total distance traveled by the block in one full cycle of its motion is the sum of the distance traveled in each direction.

The distance traveled by the block in one direction is A, and the distance traveled in the other direction is A. So, the total distance traveled by the block in one full cycle of its motion is:

It's important to note that the amplitude of the oscillation is equal to the distance from the equilibrium position to the position x = A. This means that the total distance the block moves in one full cycle is equal to twice the amplitude of the oscillation.

Therefore, the total distance traveled by the block in one full cycle of its motion is:

Hence, the correct answer is D, 4A.

This question should be provided with answer choices, which are:

The correct answer is D.

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The lengths of segments XY, XW, and YW in right triangle XYZ are given by:

XY = (1/2) * XZ

XW = (√3/2) * XZ

YW = (1 - √3/2) * XZ

To determine the lengths of segments XY, XW, and YW in right triangle XYZ, we can use the trigonometric ratios for the angles Y = 60° and Z = 30°.

Let's start with segment XY. The side opposite the 30° angle is half the length of the hypotenuse. Therefore, XY = (1/2) * XZ.

Next, let's find the length of segment XW. The side opposite the 60° angle is √3 times the length of the side opposite the 30° angle. Therefore, XW = √3 * XY = √3 * (1/2) * XZ = (√3/2) * XZ.

Finally, let's determine the length of segment YW. YW is the difference between XY and XW. Therefore, YW = XY - XW = (1/2) * XZ - (√3/2) * XZ = (1 - √3/2) * XZ.

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The graph of the given equation will be a straight line.

The equation of a straight line is y = m x + c m is the gradient and c is the height at which the line crosses the y-axis, also known as the y -intercept.

Given is an equation, y = -2x+1, we are asked to plot a graph for the same,

To plot the graph, we will firstly find the coordinates,

Therefore, the equation is y = -2x+1,

Put x = 0,

y = 1

The first coordinates = (0, 1)

Put y = 0

x = 1/2

The second coordinates = (1/2, 0)

Now, plot this points on the graph, and connect them, since the equation is linear, we will get a straight line, passing through these points, that will be the line of the equation given, (refer to graph attached)

Hence, the graph of the given equation will be a straight line.

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The ordered pairs which give the solutions of the system of equations are (-4, 1) and (-8, 9)

In order to determine the ordered pairs which give the solutions of the system of equations in a linear-quadratic graph, you need to find the points of intersection of the line and curve from the graph.

Then trace to the x and y-axes to find the ordered pairs values (Check the image attached)

Thus, the ordered pairs are (-4, 1) and (-8, 9)

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13 is considered as a prime number as there are only two factors of 13 which are equals to 1 and 13 itself.

As given in the question,

Given number is equal to 13,

Prime numbers are those numbers which has only two factors : one and the number itself.

Here is not divisible by any other number.

Factors of 13 are equals to :

1 and 13 itself.

There are only two factors of thirteen which are equals to one and number 13 itself.

Therefore, 13 is considered as a prime number because there are only two factors of 13.

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Answer: -1,0,1,2,3,4,5,6

Step-by-step explanation:

x<7

x>-2

Write that in one equation and you get

-2<x<7

The values of x that satisfy this inequality are

-1,0,1,2,3,4,5,6

The given equation f (n) = f ( n - 1) + 8; f (1) = -10; is a form of Recursive equation.

A recursive formula is one that specifies each term in a sequence by reference to the one before it (s).

The following parameters are defined using the recursive formulas:

The following is the recursive formula for calculating the nth term in an arithmetic sequence:

n2: a = an-1 + d

where,

For the given equation:

f (n) = f ( n - 1) + 8 and  f (1) = -10 are the form of recursive formula.

As, the common difference is added to the function as 8.

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The linear equation modeling the given relationship is y = 150 + 200x, where y is the fees and x is the time in hours.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Given that,

Registration fee for a new client = $150

There is also a fees of $200 per hour.

If x represents the hours, then the additional fees for x hours is 200x.

Total fees, y = 150 + 200x

If x = 0 hours, then y = $150

If x = 1 hour, y = 150 + (200 × 1) = $350

If x = 3 hours, y = 150 + (200 × 3) = $750

If x = 4 hours, y = 150 + (200 × 4) = $950

If x = 7 hours, y = 150 + (200 × 7) = $1550

Hence the linear equation modeling the situation is  y = 150 + 200x.

If x = 0, 1, 3, 4 and 7, the values of y are 150, 350, 750, 950 and 1550.

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11/3 is the additive inverse of 3/-11.. This means that the two numbers have an equal but opposite value. They have the same absolute value but opposite signs.

The additive inverse of a number is the number that when added to the original number, the sum is equal to zero. To find the additive inverse of 3/-11, we need to find the number that when added to 3/-11 will equal zero.

To begin, we need to know the signs of each number. The first number, 3, is a positive number, and the second number, -11, is a negative number. Because the signs of the two numbers are different, we will need to switch the signs in order to find the additive inverse.

11/3 is the additive inverse of 3/-11.. This means that the two numbers have an equal but opposite value. They have the same absolute value but opposite signs. To verify this, we can add 3/-11 and 11/3. When we do this, we find that the sum is zero. Therefore, 11/3 is the additive inverse of 3/-11.

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The cost of parkers tuition is $19090.9.

The percentage is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.

Given that,

The percent he pays with college tuition = 45%

The fee in percent which is not paid by scholarship = 100 - 45 = 55%

Let x be the total amount of parker's tuition, then the value of x:

55/100x = 10,500

55x = 10,50000

x= 19090.9

x = $19090.9

Thus, the cost of parkers tuition is $19090.9 if Parker was able to pay for 45 percent of his college tuition with his scholarship. The remaining $10,500 he paid for with a student loan.

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Class inequality refers to the unequal distribution of wealth, income, and social status among different groups within a society. This means that some individuals or groups have more resources, such as money, property, and access to education and job opportunities, while others have less.

Economic inequality is one of the main forms of class inequality, where a small group of individuals or families own a disproportionate amount of wealth and control the majority of resources, such as land, businesses, and investments. This can lead to a lack of economic mobility for those in lower classes, making it difficult for them to improve their economic situation.

Another form of class inequality is educational inequality, where individuals from lower socio-economic backgrounds have less access to quality education, which in turn limits their opportunities for higher-paying jobs and career advancement. This can also lead to a lack of social mobility, as education is often seen as a key factor in upward mobility.

Healthcare inequality also plays a role in class inequality, as those from lower socio-economic backgrounds often have less access to quality healthcare, leading to poorer health outcomes and increased health disparities.

These forms of class inequality can perpetuate a cycle of poverty and disadvantage for those in lower classes, while those in higher classes have greater access to resources and opportunities, leading to a widening gap between the rich and the poor.

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The probability that the selected marble will not be green is 21/25.

Probability is a measure of how likely something is to occur.

The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

So, we know that:

The bag contains: 2 red, 4 green, 10 yellow, and 9 purple

Probability formula: P(E) = favourable events/total events

Now, calculate as follows:

P(not green) = 21/25

Therefore, the probability that the selected marble will not be green is 21/25.

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Answer:

60%

Step-by-step explanation:

Answer: The answer to your question is 60%

Step-by-step explanation: The total number of marbles in Joseph's bag is:

2 (red) + 4 (green) + 10 (yellow) + 9 (purple) = 25

The probability of choosing one marble that is not yellow can be found by dividing the total number of marbles that are not yellow by the total number of marbles in the bag:

P(not yellow) = (2 red + 4 green + 9 purple) / 25

P(not yellow) = 15/25

P(not yellow) = 3/5

P(not yellow) = 0.6 or 60%

Therefore, the answer is 60%.

Answer:

49875 cm^3

Step-by-step explanation:

We use the formula, "V = bh" to find the volume of one cylinder (can), where "b" is the area of the circle base of the cylinder, and "h" is the height.

First, we can find the volume of one cylinder.

The base would be calculated by "πr^2", where "r" is the radius. To find the radius, we can use the information given in the diagram: four cans in a row have a length of 84 cm. Thus, if we divide 84 by 4, we get the diameter of one can. If we divide that diameter by 2, we get the radius of one can: 84/4/2 = 10.5 = r

πr^2 --> π10.5^2 = 110.25π

The height is shown in the diagram: one can fits perfectly inside the box, so the height dimension of the box is the same as the can's height dimension.

h = 12

Now, we can calculate the volume of one can: V = 12 * 110.25π = 1323π

As the problem calls for the volume of 12 cans, we can multiply the volume of one can by 12 to find the volume of 12 cans:

12 * 1323π = 15876π = 49875 cm^3

Answer:

Step-by-step explanation:

Firstly we have to find the dimensions of the can.

Height of can - 12 cm

Diameter of can - 21 cm

The radius of can - 21/2 = 10.5 cm

Volume of can - [tex]\pi r^2[/tex] * h ( height )

[tex]3.14 * 10.5^2[/tex] * 12

3.14* 110.25 *12

346.185 *12

4154.22

Volume of 12 cans - 4154.22 *12

Answer - [tex]49850.64cm^3\\[/tex]

The shortest distance between two lines in 3D represented by vectors can be found by using the dot product of the vector joining the two lines with the cross product of the direction vectors of the lines, divided by the length of the cross product vector.

To find the shortest distance between two lines in 3D space represented by vectors, you can use the following method:

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In the given expression, expression [tex]x^3[/tex]−5x+2 is a polynomial expression. So the option (i) is correct.

In the given question we have to find which of the following expression are polynomials.

As we know that,

The Greek words "polynomial" and "nominal" are the origins of the word polynomial, which is translated as "many phrases" when combined. There is no limit to the number of terms that a polynomial can have.

Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents. The expression is categorized as monomial, binomial, or trinomial depending on how many terms are present in it.

So if we see on the given expression then we can see that the option (i) [tex]x^3[/tex]−5x+2 have the degree 3 so [tex]x^3[/tex]−5x+2 is a polynomial expression.

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Answer: y=69x+b

Step-by-step explanation:

x=# of months of her cable bill

b=# movie fees

y=total bill

Answer:

A number line from -5 to 5 in increments of 1. An open circle is at 3 and a bold line starts from 3 and is pointing to the right

Answer: B

Step-by-step explanation:

Since they are all on one line, 27 + 90 + A = 180

Using this, we can get the value of A, which is 63 degrees.

Therefore, A is false.

C is equal to A since they are vertical angles.

Therefore, C is also false.

At this point, two statements are already wrong, so D is obviously false.

The correct statement is B, which we can test by subtracting 63 from 180. And sure enough, it's correct.

Answer:

4

Step-by-step explanation:

The value of x is 21° and y is 13°. The solution is obtained using the properties of parallel lines.

What are Parallel lines?

When two lines in a plane do not cross at any point, they are said to be parallel. In other words, lines that never cross paths with one another and do not have a common junction point are said to be parallel.

The characteristics of parallel lines with respect to transversal are listed below:

As shown in the figure, angles (2x+3)° and (6x+9)° denote the interior angles on the same side of the transversal.

Therefore, both the angles add upto 180°

So, (2x+3) + (6x+9)=180

8x+12=180

8x= 168

x= 21°

Also, angles (4y-7)° and (6x+9)° form a linear pair.

Therefore, both the angles add upto 180° and we know that x= 21°

So, (4y-7)+((6×21)+9)=180

4y+128=180

4y=52

y=13°

Hence, the value of x is 21° and y is 13°.

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Answer:

70

See explanation below

Step-by-step explanation:

The absolute value of a number is always its positive value

|-5| means absolute value of -5 which is 5

2|-5| becomes 2 · 5 = 10

- 5 · 4 = -20

-3(-5 · 4) becomes - 3 ( - 20 ) = + 60

So
2|-5| - 3(-5•4) = 10 + 60 = 70