What are the 3 steps to graph a line when given an equation?.

Answer:

X = 20

Step-by-step explanation:

The two quadrilaterals are similar to each other. So the ratio of  each side of the larger quadrilateral to the corresponding side of the smaller quadrilateral must be the same.

Examining the two figures we see the side which has  68° and 128° pf the smaller quadrilateral has length 2

The corresponding side of the larger quadrilateral on the right is 6

So each side of the larger quadrilateral =6/2 = 3 times each side of the smaller one

Side which has length 10 pf the smaller quadrilateral corresponds to the side with length x+10 of the larger one. This ratio must also be 1:3

So

[tex]\dfrac{10 + x}{10}= 3\\\\[/tex]

Cross-multiplying we get
10 + x = 10 x 3

10 + x = 30

x = 30-10

x =20

ANSWER

If there were 18 students in each group and they were asked to form six equal groups, then there would be a total of 108 students.

i.e. (18 students x 6 groups = 108 students)

When a group of students are asked to form a certain number of equal groups, the total number of students can be determined by multiplying the number of students in each group by the number of groups.

In this case, the students were asked to form six equal groups and there were 18 students in each group.

To find the total number of students, we simply multiply 18 by 6.

Therefore, there were 108 students in total.

This is because when you have x number of groups and y number of students in each group, the total number of students is xy.

In this case x=6 and y=18, so the total number of students is 6*18 = 108.

Question:

"In gym class, students were asked to form ix equal group. If there were 18 students in each group, then how many total students were there?"

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To calculate the composition of two functions, "F" and "G", represented by the notation "FG", you first need to have a specific input value, usually represented as "x".The first step is to apply the function "G" to the input "x", resulting in G(x).

The next step is to take the output of the function G, which is G(x), and use it as the input for the function F.

The final step is to apply the function F to the output of G(x) resulting in F(G(x)), which is the composition of the two functions F and G.

In other words, you apply the function G to the input x, and then you apply the function F to the result of G(x). The final result is the function F(G(x)), which is the composition of the functions F and G.

It's important to note that the order of the functions in composition matters and can change the result of composition. The notation "FG)(x)" is different from "GF)(x)" which means that the order of the functions matter in composition.

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Answer:

(0, 3 )

Step-by-step explanation:

y = 2x + 3 → (1)

3x + 2y = 6 → (2)

substitute y = 2x + 3 into (2)

3x + 2(2x + 3) = 6 ← distribute parenthesis and simplify left side

3x + 4x + 6 = 6

7x + 6 = 6 ( subtract 6 from both sides )

7x = 0 , then

x = 0

substitute x = 0 into (1) for y

y = 2(0) + 3 = 0 + 3 = 3

solution is (0, 3 )

On that particular night, there were 144 student tickets and 432 non-student tickets sold.

Let x be the number of student tickets sold that night

y be the number of non-student tickets sold that night

On that night, there were three times as many student as there were non-students. Hence, we can write that as an algebraic expression such that

3x = y

If tickets cost $5 for students and $9 for non-students, and on that night, they sold $4,608 in tickets, then we can express that as

$5x + $9y = $4608

5x + 9y = 4608

Substitute the value of y from the first expression to the second and solve for x.

5x + 9y = 4608

5x + 9(3x) = 4608

5x + 27x = 4608

32x = 4608

x = 144

Plug in the value of x into the first expression and solve for y.

y = 3x

y = 3(144)

y = 432

Hence, the number of tickets sold on that night to students and non-students were 144 and 432, respectively.

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Answer: 83r^2 - 59 + 60

Step-by-step explanation:

R^2 - 59R - 82r^2 + 60

= 83r^2 - 59 + 60

The 29.9-ounce package has a lower unit price of $0.2669 per ounce, making it the better buy.

To determine the unit price for the 10.5-ounce package, you would divide the cost of the package ($2.99) by the weight of the package (10.5 ounces). So:

$2.99 ÷ 10.5 ounces = $0.2847 per ounce

To find the unit price for the 29.9-ounce package, you would divide the cost of the package ($7.98) by the weight of the package (29.9 ounces). So:

$7.98 ÷ 29.9 ounces = $0.2669 per ounce

So, the 29.9-ounce package has a lower unit price of $0.2669 per ounce, making it the better buy.

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The difference in cost between Plumber W and Plumber T if the repair takes 5 hours will be $36.

From the information, Plumber W charges $95 per hour and an additional $32 for parts. Plumber T charges $86 per hour and an additional $41 for parts.

The difference in cost between Plumber W and Plumber T if the repair takes 5 hours will be:

= 86 + (41 × 5) - 95 + (32 × 5)

= 86 + 205 - 95 + 160

= 291 - 255

= 36

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Complete question

Plumber W charges $95 per hour and an additional $32 for parts. Plumber T charges $86 per hour and an additional $41 for parts.

What is the difference in cost between Plumber W and Plumber T if the repair takes 5 hours?

Answer: 11

Step-by-step explanation: (8/2.56) x 3.52 = 11 ounces

Answer:

6xˆ2 - x - 2 = 0

D = 1 + 1*2*6*4=49=7ˆ2;

using formula of discriminant you get

x1= -1/2

x2= 2/3

answer = x1, x2

Answer:

70.80

Step-by-step explanation:

40.00 increased by 77% is 70.80. The increase is 30.80.

Answer:

$70.80

Step-by-step explanation:

The dress was $40 to add the 77% increase, you would multiply 40 x .77= 30.80, then you would add the 30.80 to the original 40, giving you a total of $70.80

The shaded areas therefore cover a total area of 86.84 cm2.

Let's calculate the whole trapezoid's area. You multiply by the height after adding the top and bottom sides and dividing the result by two.

To get the length of the top side, we sum the values that make up that side.

6.4+5.2+9.6=21.2

The underside is 5.2.

The top and bottom sides are added.

21.2+5.2=26.4

We multiply by 2.

26.4/2=13.2

We increase by the height, which is 6.2 as we can see.

13.2×9.1=120.12

Next, we locate the rectangle's unlit portion.

6.4×5.2 = 33.28

To get the total area of the two shaded triangles, we deduct this from the trapezoid's overall area.

120.12 - 33.28 = 86.84

The shaded areas therefore cover a total area of 86.84 cm2.

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Answer:

A

Step-by-step explanation:

Angle A=Angle X

AB=XY

AC=XL

About once every 126 years, or every 31,560 days, there will be a 4-sigma event; A 5-sigma event occurs approximately once every 13,932 years (!!) or every 3,483,046 days.

The geniuses, or approximately 0.1 percent of the population, are 4 standard deviations from the mean. When attempting to determine a hypothesis's likelihood, the standard deviation emerges as an essential instrument.

4 Standard Deviations From The Mean: 99.99% (9999 out of 10000) of values in a data set with a normal distribution will be within 4 standard deviations of the mean. Therefore, the interval (S – 4E, S + 4E) will cover 9999 of the 10000 data points in the set.

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The number of atoms that can be laid end-to-end on a meter stick is equivalent to 10^8 atoms.

A meter is equivalent to 100 centimeters (cm), and an atom is about 10^-8 centimeters in length. So, when we divide the length of a meter stick (100 cm) by the length of one atom (10^-8 cm).

we are essentially dividing 100 by a decimal number on the order of 0.00000001.

This is the same as multiplying 100 by a number on the order of 100,000,000. In other words, we are multiplying 100 by 10^8.

So, 100 cm / (1*10^-8 cm) = 10^8 atoms

This means that the number of atoms that can be laid end-to-end on a meter stick is equivalent to 10^8 atoms which is a very big number, this is why we use scientific notation to represent it.

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Given that the polynomial is 12xy - 9x - 8y + 6, we must determine its fully factored form.

There are two variables in the given polynomial.

12xy - 9x - 8y - 6 = 3x(4y - 3) Now, 12xy - 9x - 8y - 6 = 3x(4y - 3) - 2(4y - 3) = (3x - 2)(4y - 3) The polynomial's fully factored form is (3x - 2)(4y - 3)

(3x - 2)(4y - 3) is the fully factored form of 12xy - 9x - 8y + 6.

One approach to factoring expressions is factoring by grouping. If the expression can be broken down into its component parts, this approach is helpful. On the other hand, we can employ additional strategies.

A polynomial is an expression made up of variables, constants, and exponents that are added, subtracted, multiplied, and divided using mathematical operations (no division by a variable).

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Full Question = What is the completely factored form of 12xy - 9x - 8y + 6?

No, the number 52 is not a perfect square. Because the square root of 52 is an irrational number.

An irrational number is a real number that cannot be expressed as a ratio of two integers, or in other words, as a fraction. Irrational numbers include numbers such as pi (π), the square root of 2, and the square root of 3, which are not terminating or repeating decimals. They cannot be written as a finite decimal or a fraction of integers. Irrational numbers have an infinite number of decimal places, which means they cannot be represented exactly as a decimal.

They are also non-repeating and non-terminating decimals. Irrational numbers have many important properties and applications in mathematics, such as in geometry, where they are used to calculate the lengths of curves and the areas of circles. They also appear in trigonometry and calculus. Irrational numbers are also important in physics and engineering as well as other branches of science and technology. They are often used to express the precise measurements and calculations that are essential in these fields.vb

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Test score of a student who does not study for the test 70%.

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The sign "%" is used to denote it.

Out of a hundred is what the word "percent" refers to. Percentages are used in mathematics to represent subsets of a whole, just like fractions and decimals are. The whole is thought of as being composed of 100 equal parts when using percentages. As a less common alternative, the abbreviation "pct" may be used to indicate that a number is a percentage.

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The degree of the polynomial p(x) = 3x²y³ - 4xy⁴ + x⁶ + y⁵ is 6.

A degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 2x^3 + 4x^2 - 5x + 7, the degree is 3 (the highest power of x is x^3). A polynomial of degree 0 is a constant polynomial and a polynomial of degree 1 is a linear polynomial.

To find the degree of a polynomial, you can do the following:

→ Write the polynomial in standard form, with the terms arranged in descending order of exponents.

→ Take the exponent of the term with the highest exponent. This exponent is the degree of the polynomial.

Given,

p(x) = 3x²y³ - 4xy⁴ + x⁶ + y⁵

Here,

Degree of polynomial is 6

As, 6 is highest of all the exponent given in p(x)

Hence, the degree of the polynomial p(x) = 3x²y³ - 4xy⁴ + x⁶ + y⁵ is 6.

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D) The quadratic equation's roots, 2x2 4x + 3 = 0, are imaginary in nature.

The quadratic formula, using square roots, factoring, and completing the square are the four ways to solve a quadratic problem.

Given a quadratic equation, it is 2x 2 + 4x + 3= 0.

∴ a=2,b=4,c=3

As a result, the discriminant of this equation is given by D=b 2 4ac.

∴D=(4) \s2 \s −4(2)(3) (3)

∴D=16−24

∴D=−8<0

The equation's roots are therefore fictitious.

The quadratic equation has the general form ax2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable. An example of a quadratic equation is x2 + 2x + 1.

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Full Question = The nature of the roots of the quadratic equation 2x ^2 + 4x + 3= 0 are

A. Real & Distinct

B. Real & Equal

C. No Real Roots

D. Imaginary

$656.25 is the difference between  the investor paid for the share and  the investor sold the share.

Two or more expressions with an Equal sign is called as Equation.

Given that At the beginning of 2017, the share was worth $1050.

From the beginning of 2015 to the beginning of 2017 the value of the share halved each year.

In 2017 it is 1050.

In 2016 , it is 2100

In 2015, it is 4200

Beginning of 2017 to the beginning of 2019, the value of the share increased by 1.5 times each year.

In 2017, 1050×1.5=1575

In 2018, 1575×1.5=2362.5

In 2019, 2362.5×1.5=3543.75

The investor paid for share is 4200 and the investor sold is 3543.75.

Difference =4200-3543.75

=656.25

Hence, $656.25 is the difference between  the investor paid for the share and  the investor sold the share.

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Answer:

To solve for g in terms of T, L, we can manipulate the formula T = 2π √(L/g) as follows:

First, we divide both sides by 2π:

T/2π = √(L/g)

Then, we square both sides:

(T/2π)² = (L/g)

Then, we multiply both sides by g^2 :

(T^2/4π^2) = L

Finally, we divide both sides by L:

(T^2/4π^2 * L) = g

So the formula for g in terms of T, L is g = (T^2/4π^2 * L)

Please note that this formula is only valid for simple pendulum and not for any complex pendulum, and also the result is in terms of acceleration due to gravity g.

The standard deviation is 4 The variance is equal to 16.

In information, the standard deviation is a degree of the quantity of variation or dispersion of a fixed of values. A low standard deviation indicates that the values tend to be near the implied (additionally called the predicted price) of the set, whilst an excessive preferred deviation suggests that the values are spread out over a wider variety.

Popular deviation can be abbreviated SD, and is maximum commonly represented in mathematical texts and equations by means of the decrease case Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample general deviation.

The standard deviation of a random variable, pattern, statistical population, statistics set, or possibility distribution is the square root of its variance. it's miles algebraically easier, even though in exercise less sturdy, than the common absolute deviation.

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Leslie's survey found that 58.75% of students had a dog, 21.25% had a cat, and 11.25% had neither.

This can be visualized in the following table:

Dog | Cat | Neither

 47  |   17  |   24

  9   |   0   |   0

Leslie's survey results showed that out of the 80 students surveyed, 47 of them had a dog, 17 of them had both a dog and a cat, 24 of them had a cat but no dog, and 9 of them had neither a dog nor a cat.

This shows that a higher percentage of students surveyed had a dog (58.75%) than a cat (21.25%). Furthermore, a higher percentage of students surveyed had either a dog or a cat (79%) than those that had neither (11.25%).

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The sum of two sides is always greater than the third side. So the side lengths 5, 12 and 13 can form a right triangle.

In the given question, we have to define the side lengths 5, 12 and 13 form a right triangle.

A side can form a right triangle if the sum of two sides is greater than the third side.

To check the given sides can from a right triangle or not we add them.

5 + 12 > 13

17 > 13 (True)

5 + 13 > 12

18 > 12 (True)

12 + 13 > 5

25 > 5 (True)

Hence, we can see that the sum of two sides is always greater than the third side. So the side lengths 5, 12 and 13 can form a right triangle.

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The relation's graph can be seen in the graphic at the bottom, where it is clear that it is   function.

The actual function can be specified using this "mapping" notation. Writing f:(x,y)x+y would allow us to define the above f(x, y). Real numbers are referred to as scalars to distinguish them from vectors. Each input is translated into a single output in a relation known as a function (input, output).

The horizontal axis is used for inputs, and the vertical axis is used for outputs. Here, we have the relationship shown below:

(-5,-1), (-4,1), (-3,3), (-1,5), (1,7) (1,7)

The figure below shows the graph of these points. Since there are no two points on the same vertical line, the relation is a function, as you can see.

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The value L that a function f(x) approaches when its input value x approaches a predetermined value c is referred to as the function's limit.

The limit of f(x) as x approaches c does not exist if, at the value c, there is no single value L that the function f(x) can be considered to approach.

The behavior of the function as it approaches c from both the right and the left must be examined in order to ascertain whether this is true of the function (that is, from x values that are larger and smaller than c, respectively).

A fundamental idea in calculus is the concept of limits. Limits help one to comprehend the connection that a function creates between its variables.

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Answer:This is a mathematical expression. To solve it, we can use the order of operations (PEMDAS)

First, we simplify the expressions inside the parentheses.

5+7 = 12

Then, we simplify the multiplication

12 * 200 = 2400

So the result of (5+7)*200 is 2400.

The first five multiplies of the denominator in each fraction in order of least to greatest are given below.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

There are two fractions,

2/5 and 3/2.

The first five multiplies of the denominator of 2/5:

5 x 1 = 5

5 x 2 = 10

5 x 3 = 15

5 x 4 = 20

5 x 5 = 25

The first five multiplies of the denominator of 3/2:

2x 1 = 2

2x 2 = 4

2x 3 = 6

2x 4 = 8

2x 5 = 10

Therefore, the first five multiplies of denominator are given above.

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The number of bacteria of type 3 that will be found on the Petri dish will be 36.84%.

The percentage of bacteria of type 3 on the Petri dish can be calculated using the percentage formula:

In this case, the final value is the number of bacteria of type 3 in the Petri dish, which is 7. The initial value is the total number of bacteria in the Petri dish, which is the sum of all the bacteria of all types, which is:

Hence:

Therefore, 36.84% of the bacteria in the Petri dish are of type 3.

This question should be provided as:

There are nine different types of bacteria on the Petri dish. A drawing shows some colonies of bacteria on the Petri dish. The number of bacteria in different colonies is as follows:

Colony  bacteria

   1          2

   2          1

   3          7

   4          4

   5          1

   6          1

   7          1

   8          1

   9          1

What percent of the bacteria on the Petri dish is of type 3?

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