X = 9 y = 4 is a solution of the linear equation (a) 2x+y=17 (b) x+y=17 (c) x+2y=17 (d) 3x-2y=17

The area of the quadrilateral ABCD for this case is of 4 square units.

The quadrilateral ABCD in the context of this problem represents a diamond, hence it's area is given by half the product of the diagonal lengths of the diamond.

The lengths for each diagonal of the diamond are given as follows:

The product of the diagonal lengths is given as follows:

AC x BD = 2 x 4 = 8 square units.

Hence half the product of these diagonal lengths, representing the area of the quadrilateral, is given as follows:

0.5 x 8 square units = 4 square units.

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Answer:

yes it is right now you can write it

The smallest positive integer n so that,

$$\renewcommand{\arraystretch}{1.5} \begin{pmatrix} -\frac{\sqrt{2}}{2} \frac{1}{n} \\ \frac{\sqrt{2}}{2} \frac{1}{n} \end{pmatrix}$$is a column matrix that contains integers,

we can write it as follows. $$\begin{pmatrix} -\frac{\sqrt{2}}{2} \frac{1}{n} \\ \frac{\sqrt{2}}{2} \frac{1}{n} \end{pmatrix} = \begin{pmatrix} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{pmatrix} \frac{1}{n}.$$Since n has to be an integer, we have to find the smallest positive integer n for which the right-hand side is a column matrix containing integers. Since the left-hand side has a factor of 1/n, we can see that the smallest value of n must be a divisor of the denominator of the left-hand side. The denominator of the left-hand side is $\sqrt{2}/2$. If we multiply this by 100, we get 70.710678.

Therefore, the smallest positive integer n that satisfies the equation is the smallest divisor of 70.710678. This is 2, and it gives us the column matrix $$\begin{pmatrix} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{pmatrix}.$$Therefore, the smallest positive integer n is 2.

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The calculated value of x in the similar triangles is 14 and it is calculated from the ratio 10 : x = 20 : 28

Given the triangle

The triangle is a superset of similar triangles

So, we have the following equivalent ratio that can be used to determine teh value of x

The set up of teh ratio is

10 : x = 10 + 10 : 28

Evaluating the like terms, we get

10 : x = 20 : 28

So, we have

x/10 = 28/20

Multiply both sides by 10

x = 14

Hence, the value of x is 14

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Therefore , the solution of the given problem of volume comes out to be the response is 900 cubic units.

A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. These symbols for cubic dimensions are liter and in3. However, understanding an object's volume is necessary to calculate its measurements. It is standard practice to convert the weight of an object into mass units like grams and kilograms.

Here,

The formula V = Bh, when B is the area of the bottom and h is the height of the prism, determines the volume of a right triangle prism.

The prism has an area of because its foundation is a right triangle with 8 and 15-foot-long legs.

=> B = (1/2)bh = (1/2)(8)(15) = 60

The prism's height is specified as 15 inches.

As a result, the prism's capacity is:

=>  900 cubic units are equal to V = Bh = 60(15).

Therefore, the response is 900 cubic units.

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Answer:

900 cubic units

Step-by-step explanation:

Answer:

58 degrees

Step-by-step explanation:

51+27=58 degrees

second one is 56 degrees

132-76=56 degrees

Step-by-step explanation:

a) Area=144m²

side²= 144

side=12m

b) perimeter=32m

4×side=32

side=32/4

side=8m

The answer of the given question based graph of function on finding the initial value of the function the answer is the initial value of the function is 2.

A graph is  visual representation of data that displays  relationship between variables. It consists of points or vertices connected by lines or arcs that represent relationships between  variables. Graphs can be used to represent various types of data, like numerical, categorical, and ordinal data.

Graph are commonly used in mathematics, science, engineering, and social sciences to help people understand complex data and relationships. Different types of graphs like  bar graphs, line graphs, scatter plots, pie charts, and histograms. Graphs are powerful tool for data analysis and visualization, and they can help people identify patterns, trends, and outliers in data.

If the function intersects both the x-axis and y-axis at the point (2,4), then the function can be written in the form:

y = a(x - 2)(x - 4)

where a is some constant.

To find the value of a, we can use the fact that the function passes through the point (0,2). Substituting x = 0 and y = 2 into the equation above, we get:

2 = a(0 - 2)(0 - 4)

2 = 8a

Solving for a, we get:

a = 2/8 = 1/4

Therefore, the function is:

y = (1/4)(x - 2)(x - 4)

To find the initial value of the function, we need to determine the value of the function when x is equal to zero. Substituting x = 0 into the equation above, we get:

y = (1/4)(0 - 2)(0 - 4)

y = (1/4)(8)

y = 2

Therefore,  initial value of  function is 2.

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Answer:

Step-by-step explanation:

This can be solved by taking X as the magnification

8*x = 12cm *10

x= 120/8

x= 30/2= 15

the magnification = 15 times

The numbers are as follows, going from lowest to highest:

-4.2, -3.5, -2.1, -1.5, -1, -0.5, 0.5, 3.5, 4.8.

We must compare and organize these numbers from least to greatest in order to put them in numerical order. The two smallest figures, which are -4.2 and -3.5, can be used as a starting point. Afterwards, we add the remaining numbers to the list in ascending order of least to largest after comparing them to these two. We arrive at the list above after continuing this approach.

Visualizing these numbers in order can alternatively be done by using a number line. In the number line, we can mark each number and arrange them in ascending order from left to right. We can see from the number line that the least number is -4.2.

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Compute P(x ≤ 15) = (15-10)/(20-10) = 5/10 = 0.5.

Compute P(12 ≤ x ≤ 18) = (18-12)/(20-10) = 6/10 = 0.6.

Compute E(x): The expected value of x is: E(x) = (a+b)/2 = (10+20)/2 = 15

Compute Var(x):The variance of x is: Var(x) = (b - a)^2/12 = (20 - 10)^2/12 = 100/12 = 8.33.

The probability density function is as follows: As the random variable x is uniformly distributed between 10 and 20. Thus, f(x) = 1/(20-10) = 1/10 for 10 ≤ x ≤ 20.Compute P(x ≤ 15):Thus, P(x ≤ 15) = (15-10)/(20-10) = 5/10 = 0.5.Compute P(12 ≤ x ≤ 18):Thus, P(12 ≤ x ≤ 18) = (18-12)/(20-10) = 6/10 = 0.6.Compute E(x):The expected value of x is: E(x) = (a+b)/2 = (10+20)/2 = 15.Compute Var(x):The variance of x is: Var(x) = (b - a)^2/12 = (20 - 10)^2/12 = 100/12 = 8.33.

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X = 2 is the solution of  the given equation for "x".

What does a math equation mean?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. For instance, 3x + 5 = 14 is an equation where 3x + 5 and 14 are two expressions separated by the 'equal' sign.

                           A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. By solving for x, we discover that x equals 7, which is the value for the variable.

8ˣ = (25)

 8ˣ =  (5)²

  X = 2

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Answer:

The following statements about Josiah's solution are true:

He found the proportion of rock songs to the total number of songs correctly: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction.

He solved the proportion correctly: StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction.

He correctly determined that the number of rock songs on his MP3 player is 300 (x = 300).

Therefore, the statements that are true are:

He found the proportion of rock songs to the total number of songs correctly.

He solved the proportion correctly.

He correctly determined that the number of rock songs on his MP3 player is 300 (x = 300).

The probability that the gambler has to play at least 3 rounds of the game before getting his first win is equal to 3/4.

The probability that the gambler has to play at least n rounds of the game before getting his first win is equal to 1 - (the probability of winning in the first n-1 rounds). To calculate the probability of winning in the first n-1 rounds, use the following formula:
P = (1/2)^(n-1)
Where P is the probability of winning in the first n-1 rounds.
For example, if the gambler has to play at least 3 rounds of the game, the probability of winning in the first 2 rounds is equal to (1/2)^(3-1) = (1/2)^2 = 1/4.

So, the probability that the gambler has to play at least 3 rounds of the game before getting his first win is equal to 1 - (1/4) = 3/4.

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The simplified polynomial, with each term written in standard form, is: 36a^3b - 6a^2b^3 + 11a^2b

To simplify the given polynomial, we need to expand and combine like terms.

First, we can distribute the coefficients of the first term:

12a^2 · 3ba = 36a^3b

Next, we can simplify the second term by multiplying the coefficients and adding the exponents:

-2ab · 3ab^2 = -6a^2b^3

Finally, we can combine the like terms:

36a^3b - 6a^2b^3 + 11a^2b

To write each term in standard form, we arrange the terms in decreasing order of exponents of 'a' and 'b':

36a^3b - 6a^2b^3 + 11a^2b

So, the simplified polynomial, with each term written in standard form, is:

36a^3b - 6a^2b^3 + 11a^2b

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The possible widths for the rectangular mural are between 10 and 15 feet. We can also list the number of possible widths within this range, which is six. They are 10 feet, 11 feet, 12 feet, 13 feet, 14 feet, and 15 feet.

To determine the possible widths for the rectangular mural with an area of 60 square feet, we can use the formula for the area of a rectangle, which is length multiplied by width. Since the area is given as 60 square feet and the length should be between 4 and 6 feet, we can set up inequality as follows:

4w ≤ 60 ≤ 6w

where w is the width of the mural in feet. Solving this inequality for w, we get:

10 ≤ w ≤ 15

It is important to consider the dimensions carefully to ensure that the mural meets the requirements and fits in the desired space. By having multiple possible widths, the class can select the most suitable one based on the available resources and space.

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Complete question:

Our class is planning to paint a rectangular mural with an area of 60 square feet, it should be at least 4 feet high but not more than 6 feet in length and width, and list a number of possible widths for our class. Planning to paint a rectangular mural with an area of 60 square feet, it should be at least 4 feet high but not more than 6 feet in length and width, and list the number of possible widths for it.

For equation a, x = 3

For equation b, x = -11/4.

For equation c, x = 1.

For equation d, x = -7/3.

For equation e, x = 9.

For equation f, x = 1/2.

To solve this equation, we need to isolate the variable x on one side of the equation.

7x - 6 = 6x + 3

Subtracting 6x from both sides:

x - 6 = 3

Adding 6 to both sides:

x = 9

Therefore, the solution to the equation is x = 9.

In the other equations:

a) 4x + 7 = 2x + 13

Subtracting 2x from both sides:

2x + 7 = 13

Subtracting 7 from both sides:

2x = 6

Dividing by 2:

x = 3

Therefore, the solution to the equation is x = 3.

b) x - 2 = 10 + 5x

Subtracting x from both sides:

-2 = 9 + 4x

Subtracting 9 from both sides:

-11 = 4x

Dividing by 4:

x = -11/4

Therefore, the solution to the equation is x = -11/4.

c) -3x - 8 = -7x - 4

Adding 7x to both sides:

4x - 8 = -4

Adding 8 to both sides:

4x = 4

Dividing by 4:

x = 1

Therefore, the solution to the equation is x = 1.

d) 2t + 5 = 5t + 12

Subtracting 2t from both sides:

5 = 3t + 12

Subtracting 12 from both sides:

-7 = 3t

Dividing by 3:

t = -7/3

Therefore, the solution to the equation is t = -7/3.

f) 15x = 7x + 4

Subtracting 7x from both sides:

8x = 4

Dividing by 8:

x = 1/2

Therefore, the solution to the equation is x = 1/2.

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Complete Question:

Find X for each equation.

A) 4 x + 7 = 2 x + 13 ;

b) x – 2 = 10 + 5 x ;

c) – 3 x – 8 = – 7 x – 4 ;

d) 2 t + 5 = 5 t + 12 ;

e) 7 x – 6 = 6 x + 3

f) 15 x = 7 x + 4

The answer of the given question based on the changing the denominator of fraction the answer is the fraction a+3/6-2a can be rewritten with a denominator of 2(a²-9) as (3 + a)/(2(a - 3)).

In mathematics,  formula is  mathematical expression or equation that describes  relationship between two or more variables or quantities. A formula can be used to solve problems or make predictions about particular situation or set of data.

Formulas often involve mathematical symbols and operations, like addition, subtraction, multiplication, division, exponents, and square roots. They may also include variables, which are typically represented by letters, and constants, which are fixed values that do not change.

To change the denominator of the fraction a+3/6-2a to 2(a²-9), we need to factor the denominator of the original fraction and then use algebraic manipulation to rewrite it in the desired form.

First, we can factor the denominator of the original fraction as follows:

6 - 2a = 2(3 - a)

Next, we can rewrite the denominator using the difference of squares formula:

2(a² - 9) = 2(a + 3)(a - 3)

Now, we can use the factored form of the denominator to rewrite the original fraction:

(a + 3)/(6 - 2a) = (a + 3)/(2(3 - a)) = -(a + 3)/(-2(a - 3)) = (3 + a)/(2(a - 3))

Therefore, the fraction a+3/6-2a can be rewritten with a denominator of 2(a²-9) as (3 + a)/(2(a - 3)).

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Answer:

Step-by-step explanation:

71/8*9 which it 639/8 feet long

Answer:

Show that, the sum of an infinite arithmetic progressive sequence with a positive common difference

is +∞

Step-by-step explanation:

To show that the sum of an infinite arithmetic progressive sequence with a positive common difference is +∞, we can use the formula for the sum of the first n terms of an arithmetic sequence:

Sn = n/2 [2a + (n-1)d]

where a is the first term, d is the common difference, and n is the number of terms in the sequence.

Now, if we let n approach infinity, the sum of the first n terms of the sequence will also approach infinity. This can be seen by looking at the term (n-1)d in the formula, which grows without bound as n becomes larger and larger.

In other words, as we add more and more terms to the sequence, each term gets larger by a fixed amount (the common difference d), and so the sum of the sequence increases without bound. Therefore, the sum of an infinite arithmetic progressive sequence with a positive common difference is +∞.

If a customer purchases 3 of the products, the probability of getting at least one that is defective is 38.59%.

In order to determine the probability of getting at least one defective product if a customer purchases three products with a defective rate of 7.5%, we can use the concept of complementary probability.

The probability of getting at least one defective product can be calculated as the complement of the probability of getting none defective products.

So, the probability of getting no defective products is:

P(none defective) = (1 - 0.075)³ = 0.6141

Therefore, the probability of getting at least one defective product is:

P(at least one defective) = 1 - P(none defective) = 1 - 0.6141 = 0.3859 or 38.59%

.So, the probability of getting at least one that is defective is 38.59%.

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The required value of EC is 5 units.

Since DE is parallel to BC, we can use the property of similar triangles to set up a proportion:

AD/DB = AE/EC

We know that AD + DB = AB = x + 5. Since D is a point on AB, we can express AD and DB in terms of x:

AD = x, DB = x + 5 - x = 5

We also know that AE = 3 and ED = x + 1. Using these values, we can express AD in terms of ED:

AD = ED - AE = (x + 1) - 3 = x - 2

Substituting these values into the proportion, we get:

(x - 2)/5 = 3/EC

Multiplying both sides by 5EC, we get:

x - 2 = 15/EC

Multiplying both sides by EC, we get:

EC(x - 2) = 15

Expanding the left side, we get:

ECx - 2EC = 15

Solving for EC, we get:

EC = 15/(x - 2)

We are given that EC = x, so we can set these expressions equal to each other:

x = 15/(x - 2)

Multiplying both sides by (x - 2), we get:

x(x - 2) = 15

Expanding the left side, we get:

x² - 2x = 15

Bringing all terms to one side, we get:

x² - 2x - 15 = 0

We can factor this quadratic equation:

(x - 5)(x + 3) = 0

Therefore, x = 5 or x = -3. We reject x = -3 since we are given that EC > 0. Thus, the length of EC is: EC = x = 5.

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Answer:

To indicate that we want both the positive and the negative square root of a radicand

Answer:

Because a negative number times a negative number has a positive answer

Step-by-step explanation:

The types of inferences that will be made about population parameters are causation, estimation, and regression on the basis of relationship.

Causation is the process of showing the cause-and-effect relationship between two variables. In this case, one variable influences the other variable. This type of inference is significant when making decisions because it helps us understand how a change in one variable leads to a change in another variable.

Estimation: In statistical analysis, estimation refers to determining the possible value of an unknown population parameter. It is impossible to calculate the population parameters directly, and hence we use sample statistics to estimate them.

Regression analysis is the statistical technique used to identify the relationship between two variables. It involves estimating the coefficients of the model that best fit the data.

This type of inference helps us predict the value of a dependent variable based on an independent variable.

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Answer:

5/37

Step-by-step explanation:

There are 37 possible outcomes when rolling a 37-sided die, so the probability of rolling any one specific number is 1/37.

To find the probability of rolling any of the given numbers (35, 25, 33, 9, or 19), we need to add the probabilities of rolling each individual number.

Probability of rolling 35: 1/37

Probability of rolling 25: 1/37

Probability of rolling 33: 1/37

Probability of rolling 9: 1/37

Probability of rolling 19: 1/37

The probability of rolling any one of these numbers is the sum of these probabilities:

1/37 + 1/37 + 1/37 + 1/37 + 1/37 = 5/37

So the probability of rolling any of the given numbers is 5/37, which is approximately 0.1351 when rounded to four decimal places.

Therefore, 15% of the beads on Tiana's necklace are blue.

Percentage is a way of expressing a fraction or a proportion out of 100. It is denoted by the symbol "%". For example, if we say that 50% of the students in a class are girls, it means that 50 out of every 100 students are girls.

Percentage can be calculated by dividing the given quantity by the total and multiplying by 100. For example, if there are 20 girls out of a total of 40 students in a class, the percentage of girls in the class can be calculated as follows:

Percentage of girls = (number of girls / total number of students) x 100%

= (20 / 40) x 100%

= 50%

by the question.

Tiana's necklace has a total of 3 + 17 = 20 beads.

To find the percentage of blue beads, we need to divide the number of blue beads by the total number of beads and then multiply by 100 to get the percentage:

percentage of blue beads = (number of blue beads / total number of beads) x 100

percentage of blue beads = (3 / 20) x 100

percentage of blue beads = 15

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Answer:

I hope this helps please rate my answer

Step-by-step explanation:

2/5×60

2×12=24

To prepare a buffer solution with a given pH, we need to choose a weak acid and its conjugate base, such that the pKa of the weak acid is close to the desired pH.

The pKa is related to the Ka value as follows:

pKa = -log(Ka)

So, for each of the weak acids given, we can calculate the pKa:

Phosphoric acid (H3PO4): Ka = 7.5 x 10^-3, so pKa = -log(7.5 x 10^-3) = 2.12

Acetic acid (CH3COOH): Ka = 1.8 x 10^-5, so pKa = -log(1.8 x 10^-5) = 4.74

Formic acid (HCOOH): Ka = 1.8 x 10^-4, so pKa = -log(1.8 x 10^-4) = 3.74

Now, let's consider the desired pH values and choose the best components for buffer solutions:

For a pH of 2.5, the best choice would be phosphoric acid (pKa = 2.12).

For a pH of 4.5, the best choice would be formic acid (pKa = 3.74) or a mixture of acetic acid and acetate ion (CH3COOH/CH3COO-, pKa = 4.76).

For a pH of 6.5, the best choice would be a mixture of acetic acid and acetate ion (CH3COOH/CH3COO-, pKa = 4.76).

Note that a buffer solution can be prepared by mixing a weak acid and its conjugate base in roughly equal amounts, so the appropriate salt can be added to the acid to form the buffer solution. For example, to prepare an acetate buffer, one could mix acetic acid with sodium acetate.

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The following equation can be used to represent the sentence:

7 + (x/4) = 5 where x stands for a number.

A straight line on a graph is represented by a linear equation. It has a constant slope and y-intercept, one or more variables, typically expressed by x and y. Several different real-world situations can be represented by linear equations, such as estimating the cost of goods based on the quantity purchased or calculating a car's distance traveled based on speed and time. Finding the value of the variable that causes the equation to be true is the first step in solving a linear equation. In mathematics, science, engineering, and economics, linear equations are frequently employed.

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The equation of line B is y = (1/5)x + 0, which can be simplified to y = (1/5)x.

An equation is a statement that shows the equality between two expressions. It typically contains one or more variables and may involve mathematical operations such as addition, subtraction, multiplication, division, exponentiation, or roots. An equation can be solved by finding the value(s) of the variable(s) that make the equation true. Equations are used extensively in mathematics, science, engineering, and other fields to describe relationships between different quantities and to make predictions or solve problems.

Here,

Since line B is perpendicular to line A, the product of their gradients is -1. Therefore, the gradient of line B is 1/5.

a) To find the y-intercept of line B, we need to know a point on the line. Since we don't have one, we can use the fact that the y-intercept is the point where the line intersects the y-axis. To find this point, we can set x = 0 in the equation of line B:

y = (1/5)x + c

0 = (1/5)(0) + c

c = 0

Therefore, the y-intercept of line B is (0,0).

b) The equation of line B is y = (1/5)x + 0, which can be simplified to y = (1/5)x.

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