If the angles of a pentagon are xº, x°, 2xº, (2x +
40), (2x+10)º, find the value of the biggest
angle

The greater number is [tex]$n^3+8$[/tex]

Let x be the greater number and y be the smaller number. We know that x-y=8.

We are also given that the smaller number is n³.

So we can set up the equation:

x = y + 8

x = n³ + 8

Therefore, the greater number is [tex]$n^3+8$[/tex].

The greater number is given as n³ + 8. If the smaller number we get is represented by the n³,  then by adding 8 to that value gives the greater number. The difference between the two numbers is always going to be 8, regardless of the value of n.

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30% percent of the students passed both Mathematics and English.

A rate, number, or amount in each hundred is known as a percentage

Let's use a Venn diagram to represent the information given in the problem. Let M be the set of students who passed Mathematics, E be the set of students who passed English, and F be the set of students who failed both.

We know that there are 40 students in the class, and 90% passed Mathematics, so the number of students who passed Mathematics is 0.9 × 40 = 36. Similarly, 75% passed English, so the number of students who passed English is 0.75 × 40 = 30.

We also know that 2 students failed both Mathematics and English, so we can label the F section with 2.

where the number in each section represents the number of students who passed the respective exam.

To find the percentage of students who passed both examinations (i.e., the intersection of M and E), we need to add the number of students in the M and E intersection to the F section, then subtract that from the total number of students (40), and finally divide by 40 to get the percentage. That is:

percentage of students who passed both exams = (M ∩ E + F) / 40 × 100%

= (28 + 2) / 40 × 100%

= 30%

Therefore, 30% of the students passed both Mathematics and English.

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I can give you with a general explanation of the functions of muscles, bones, and sensitive organs, as well as how they work together.

Muscles are responsible for movement and give the force needed to move bones. They're attached to bones via tendons and work in dyads or groups to produce coordinated movement. Muscles are also responsible for maintaining posture and generating heat.

Bones give a rigid frame for the body, cover internal organs, and serve as attachment points for muscles. They also store minerals similar as calcium and produce blood cells in the bone gist.

sensitive organs, similar as the eyes, cognizance, nose, and skin, descry and respond to stimulants in the terrain. They transmit information to the brain, which processes the information and generates an applicable response.

All three body corridor work together in the musculoskeletal system to produce movement, maintain posture, and respond to external stimulants. Muscles attach to bones and work together to produce coordinated movement. sensitive organs descry stimulants in the terrain and transmit information to the brain, which coordinates muscle movement and generates a response. Bones give the rigid frame and attachment points for muscles, as well as cover internal organs.

Three numbers have a product of 115 and a sum of 3(√115), which is the smallest possible sum.

In mathematics, a positive number is any number that is greater than zero. This includes all numbers that are written without a minus sign or are explicitly denoted as positive, such as 1, 2, 3, 4, 5, and so on

To find three positive numbers whose product is 115 and whose sum is as small as possible, we can use the AM-GM inequality. In other words, if we have three positive numbers x, y, and z, then:

(x + y + z)/3 ≥ (xyz)^(1/3)

If we rearrange this inequality, we get:

x + y + z ≥ 3(√(xyz))

Now, let's apply this inequality to the given problem. We want to find three positive numbers x, y, and z whose product is 115 and whose sum is as small as possible. Therefore, we want to minimize x + y + z while still satisfying the condition xyz = 115.

Using the AM-GM inequality, we have:

x + y + z ≥ 3(√(xyz)) = 3(√115) ≈ 16.75

Therefore, the sum of the three numbers is at least 16.75. To find three numbers that achieve this minimum sum, we can use trial and error or solve the system of equations:

xyz = 115

x + y + z = 3(√115)

One solution to this system is:

x = √(115/3)

y = √(115/3)

z = 3(√(115/3)) / 5

These three numbers have a product of 115 and a sum of 3(√115), which is the smallest possible sum.

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The complete question is Find three positive numbers whose product is 115.

Answer:

(-2,9)

Step-by-step explanation:

when moving it 5 units left on the x axis it would be 5-7

So in turn you would be given (-2,9)

Because the y stays the same you would still have (?,9)

Answer:

3x, 4x | 5, 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

kernel composition rules 2 1 point possible (graded) let and be two vectors of the same dimension. use the the definition of kernels and the kernel composition rules from the video above to decide which of the following are kernels. (note that you can use feature vectors that are not polynomial.) (choose all those apply. )

The mean number of burps after drinking root beer is between 0.66 and 4.24 burps fewer than after drinking cola.

Mean: The "average" number obtained by adding all data points and dividing the total number of data points by the total number of data points.

Part A: A paired t-test can be used to see if there is a significant difference in the number of burps after drinking root beer versus cola. The null hypothesis states that there is no difference in the mean number of burps between the two beverages, whereas the alternative hypothesis states that there is. Using a two-tailed test with a significance level of = 0.05, we find that the t-value is -3.365 and the p-value is 0.003. We reject the null hypothesis because the p-value is less than the significance level and conclude that there is a significant difference in the mean number of burps between root beer and cola.

Part B: We can use the paired t-test formula to generate a 95% confidence interval for the difference in the mean number of burps between root beer and cola:

(xd - d) / (sd / n) t

where xd represents the sample mean difference, d represents the hypothesised population mean difference (which is 0), sd represents the sample standard deviation of the differences, and n represents the sample size.

We calculate the sample mean difference to be -2.45 and the sample standard deviation of the differences to be 2.69 using the data in the table. We get a t-value of -3.365 with 19 degrees of freedom after plugging in these values. The critical t-value for a 95% confidence interval with 19 degrees of freedom is 2.093, according to a t-distribution table.

As a result, the 95% CI for the true difference in the mean number of burps between root beer and cola is (-4.24, -0.66). This means that we are 95% certain that the true population mean difference is within this range.

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Answer:

To solve the integral, we can use partial fractions and then integrate each term separately. The integrand can be written as:

[tex]\dfrac{x^4(1-x)^4}{1+x^2} = \dfrac{x^4(1-x)^4}{(x+i)(x-i)}[/tex]

Using partial fractions, we can write:

[tex]\dfrac{x^4(1-x)^4}{(x+i)(x-i)} = \dfrac{Ax+B}{x+i} + \dfrac{Cx+D}{x-i}[/tex]

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

[tex]x^4(1-x)^4 = (Ax+B)(x-i) + (Cx+D)(x+i)[/tex]

Substituting x=i, we get:

[tex]i^4(1-i)^4 = (Ai+B)(i-i) + (Ci+D)(i+i)[/tex]

Simplifying, we get:

[tex]16 = 2Ci + 2B[/tex]

Substituting x=-i, we get:

tex^4(1+i)^4 = (Ci+D)(-i-i) + (Ai+B)(-i+i)[/tex]

Simplifying, we get:

[tex]16 = 2Ai + 2D[/tex]

Substituting x=0, we get:

[tex]0 = Bi + Di[/tex]

Substituting x=1, we get:

[tex]0 = A+B+C+D[/tex]

Solving these equations simultaneously, we get:

A = -22/7 + π

B = 0

C = 22/7 - π

D = -2/5

Therefore, the integral can be written as:

[tex]\int_0^1 \dfrac{x^4(1-x)^4}{1+x^2}dx = \int_0^1 \left[\dfrac{-22/7+\pi}{x+i} + \dfrac{22/7-\pi}{x-i} - \dfrac{2/5}{1+x^2}\right]dx[/tex]

Integrating each term separately, we get:

[tex]\int_0^1 \dfrac{-22/7+\pi}{x+i}dx = [-22/7+\pi]\ln(x+i) \bigg|_0^1 = [\pi-22/7]\ln\left(\dfrac{1+i}{i}\right)[/tex]

[tex]\int_0^1 \dfrac{22/7-\pi}{x-i}dx = [22/7-\pi]\ln(x-i) \bigg|_0^1 = [22/7-\pi]\ln\left(\dfrac{1-i}{-i}\right)[/tex]

[tex]\int_0^1 \dfrac{-2/5}{1+x^2}dx = -\frac{2}{5}\tan^{-1}(x)\bigg|_0^1 = -\frac{2}{5}\tan^{-1}(1) + \frac{2}{5}\tan^{-1}(0) = -\frac{2}{5}\tan^{-1}(1)[/tex]

Therefore, the correct options are:

A) [tex]\pi-\frac{22}{7}[/tex]

B) [tex]\frac{2}{105}[/tex]

C) 0

D) [tex]\frac{71}{15}-\frac{3\pi}{2}[/tex]

Answer:

The answer is 657 and 365.

Step-by-step explanation:

Let the two numbers be x and y respectively

In first case,

x+y=1022

x=1022-y----------- eqn i

In second case

x-y=292

1022-y-y=292 [From eqn i]

1022-2y=292

1022-292=2y

730=2y

730/2=y

y=365

Substituting the value of y in eqn i

x=1022-y

x=1022-365

x=657

Hence two numbers are 657 and 365.

Pls mark me as brainliest if you got the answer

The conclusion which is correct about given situation is D) The p-value (0.001) is less than the significance level (0.01), which means we reject the null hypothesis that the proportion of boxes with broken glass is equal to or less than 8%.

We have convincing evidence to suggest that the actual proportion of boxes with broken glass is greater than 8%. Therefore, we can conclude that the glass manufacturer's belief is supported by the sample data.

This conclusion is based on the fact that the p-value is less than the significance level, indicating that the observed data is unlikely to have occurred by chance alone assuming the null hypothesis is true.

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The result (recurrent value), A = sum j=1 to 89 ln(j), is true for every n. This is the desired result.

As in T(n) = T(n/2) + n, T(0) = T(1) = 1, a recurrence or recurrence relation specifies an infinite sequence by explaining how to calculate the nth element of the sequence given the values of smaller members.

We can start by proving the base case in order to demonstrate the first portion through recurrence. Let n = 1. Next, we have:

Being true, ln(a1) = ln(a1). If n = k, let's suppose the formula is accurate:

Sum j=1 to k ln = ln(prod j=1 to k aj) (aj)

Prod j=1 to k aj * ak+1 = ln(prod j=1 to k+1 aj)

(Using the logarithmic scale) = ln(prod j=1 to k aj) + ln(ak+1)

Using the inductive hypothesis, the property ln(ab) = ln(a) + ln(b)) = sum j=1 to k ln(aj) + ln(ak+1) = sum j=1 to k+1 ln (aj)

(b), we can use the just-proven formula:

A = ln(1, 2,...) + ln + ln (89)

= ln(j=1 to 89) prod

sum j=1 to 89 ln = ln(prod j=1 to 89 j) (j).

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Add up the areas of all four strips to get an estimate for the distance traveled by the car in the first 40 seconds: Distance traveled = Area of strip 1 + Area of strip 2 + Area of strip 3 + Area of strip 4.

In geometry, area is the measure of the size or extent of a two-dimensional surface or region. It is typically measured in square units, such as square meters or square feet. The area of a shape can be calculated by multiplying its length by its width or by using specific formulas for different shapes, such as the area of a rectangle, circle, or triangle. Area is an important concept in many fields, including mathematics, physics, engineering, and architecture.

by the question.

Assuming the graph shows the speed of the car in meters per second (m/s) on the y-axis and time in seconds on the x-axis, we can estimate the distance traveled by the car in the first 40 seconds by dividing the area under the graph for that time period into four equal strips and calculating the area of each strip using the trapezium rule.

To do this, we need to find the speed of the car at four different times during the first 40 seconds, which we can do by reading off the graph. Let's say we choose the times t = 0, 10, 20, and 30 seconds.

Then we can estimate the distance traveled by the car in the first 40 seconds as follows:

Calculate the area of the first strip (from t = 0 to t = 10 seconds) using the trapezium rule:

Area of strip 1 = (1/2) x (speed at t = 0 seconds + speed at t = 10 seconds) x 10 seconds

Repeat for the other three strips, using the appropriate speeds and time intervals:

Area of strip 2 = (1/2) x (speed at t = 10 seconds + speed at t = 20 seconds) x 10 seconds

Area of strip 3 = (1/2) x (speed at t = 20 seconds + speed at t = 30 seconds) x 10 seconds

Area of strip 4 = (1/2) x (speed at t = 30 seconds + speed at t = 40 seconds) x 10 seconds

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An inequality representing the amount that the island of Martinique can received for hurricane relief efforts, where x is the number of days is y ≤ 32,000 + 4,500x.

Inequality is an algebraic statement that two or more mathematical expressions are unequal.

Inequalities can be represented as:

The total amount received by the island = $32,000

The daily receipt of donations = $4,500

Let the number of days = x

Let the funds raised for aid = y

y ≤ 32,000 + 4,500x

Thus, the inequality for the funds that the island can fundraise for hurricane relief aid by the end of the month is y ≤ 32,000 + 4,500x.

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Answer:

X+4

Step-by-step explanation:

Area = l *b

x^2 + 13x + 36 = (X+9) * b

x^2 + 9x + 4x + 36 = (X+9) * b

X(X+9) + 4(X+9) = (X+9) * b

(X+4) (X+9) = (X+9) * b

b = (X+4)

The volume of cylindrical tin is 1584 [tex]cm^3[/tex]. The depth of the oil in the tin is 9cm.

[tex]V_1 =[/tex] VOLUME OF CYLINDRICAL TIN

   [tex]= \pi r^2 h[/tex]

  [tex]=\frac{22}{7}[/tex] x 6 x 6 x 14

  = 44 x 36

  = 1584 [tex]cm^3[/tex]

[tex]V_2 =[/tex] VOLUME OF RECTANGULAR TIN

    = lbh = 1584

    = (16)(11)(h) = 1584

    = 176h =1584

    = h = 1584 / 176

    = h = 9 cm

A cylinder is a three-dimensional shape that consists of a circular base and a curved surface that extends upward to meet at a point known as the apex. The volume of a cylinder is the amount of space occupied by the shape and is given by the formula V = πr²h, Once we have calculated the area of the circular base, we can multiply it by the height of the cylinder to get the volume.

To calculate the volume of a cylinder, we need to know its dimensions, which are the radius and height. The radius is the distance from the center of the circular base to the edge, while the height is the distance between the two circular bases.

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The line x + y = 9 is y = -x + 6 is keeps through the point (5,1).

To find the equation of the line that passes through the point (5,1) and is parallel to the line x + y = 9, we need to first find the slope of the line x + y = 9.

Rearranging the equation in slope-intercept form, we get y = -x + 9

The slope of this line is -1, since the coefficient of x is -1.

Since the line we want to find is parallel to this line, it will have the same slope of -1.

Using the point-slope form of a line, the equation of the line passing through the point (5,1) and with a slope of -1 is: y - 1 = -1(x - 5)

Simplifying and rearranging the equation, we get:

y - 1 = -x + 5

y = -x + 6

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There are 1124 ways to choose a committee of 7 members with at least one member from each group and at least 3 artists.

Here, we have to solve this problem, we can use the concept of combinations, which involves counting the ways to choose a specific number of items from a larger set without regard to the order of selection.

Given the conditions that at least one member must be chosen from each group (artists, singers, writers) and there must be at least 3 artists, we can break down the problem into cases.

Case 1: Choosing 1 artist, 1 singer, and 5 members from the remaining groups (writers).

Case 2: Choosing 2 artists, 1 singer, and 4 members from the remaining groups (writers).

Case 3: Choosing 3 artists, 1 singer, and 3 members from the remaining groups (writers).

For each case, we will calculate the number of ways to choose members and then sum up the results from all three cases to get the total number of ways.

Let's calculate the number of ways for each case:

Case 1:

Number of ways to choose 1 artist: 6C1 (6 ways)

Number of ways to choose 1 singer: 4C1 (4 ways)

Number of ways to choose 5 writers: 5C5 (1 way)

Total ways for case 1: 6C1 * 4C1 * 5C5 = 6 * 4 * 1 = 24

Case 2:

Number of ways to choose 2 artists: 6C2 (15 ways)

Number of ways to choose 1 singer: 4C1 (4 ways)

Number of ways to choose 4 writers: 5C4 (5 ways)

Total ways for case 2: 6C2 * 4C1 * 5C4 = 15 * 4 * 5 = 300

Case 3:

Number of ways to choose 3 artists: 6C3 (20 ways)

Number of ways to choose 1 singer: 4C1 (4 ways)

Number of ways to choose 3 writers: 5C3 (10 ways)

Total ways for case 3: 6C3 * 4C1 * 5C3 = 20 * 4 * 10 = 800

Now, add up the total ways from all three cases:

Total ways = 24 + 300 + 800 = 1124

So, there are 1124 ways to choose a committee of 7 members with at least one member from each group and at least 3 artists.

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The volume of the solid whose base is the region inside the circle with radius 3 if the cross sections taken parallel to one of the diameters are equilateral triangles is 81/2*\sqrt3 by using the slicing method.

To find the volume of the solid whose base is the region inside the circle with radius 3, we need to integrate the area of the cross sections taken parallel to one of the diameters, which are equilateral triangles.

Let's consider a cross section of the solid taken at a distance x from the center of the circle.

Since the cross section is an equilateral triangle, all its sides have the same length.

Let  this length be y. Since the triangle is equilateral, its height can be found using the Pythagorean theorem as follows:

[tex]height = \sqrt{(y^2 - (y/2)^2)} = \sqrt{(3/4y^2)}= \sqrt{3/2y}[/tex]

Therefore, the area of the cross section at a distance x from the center of the circle is:

[tex]A(x) = (1/2)y\sqrt{3/2y} = \sqrt{3/4y^2}[/tex]

Now, we need to integrate this area over the range of x from -3 to 3 (since the circle has radius 3):

[tex]V = \int\ [-3,3]\sqrt{3/4*y^2} dx[/tex]

To find the limits of integration for y, we need to consider the equation of the circle:

[tex]x^2 + y^2= 3^2[/tex]

Solving for y, we get:

[tex]y =\pm\sqrt{(3^2 - x^2)}=\pm\sqrt{(9^2 - x^2)}[/tex]

Since we want the cross sections to be equilateral triangles, we know that y is equal to the height of an equilateral triangle with side length equal to the diameter of the circle, which is 2*3 = 6. Therefore, we can write:

[tex]y = 3*\sqrt{3}[/tex]

Substituting this into the integral, we get:

[tex]V = \int\ [-3,3] \sqrt{3/4*(3\sqrt3)^2} dx[/tex]

[tex]= \int\ [-3,3] 27/4*\sqrt{3} dx[/tex]

Integrating, we get:

[tex]V = [27/4\sqrt{3x}]*[-3,3][/tex]

[tex]= 81/2*\sqrt{3}[/tex]

Therefore, the volume of the solid is [tex]81/2*\sqrt3[/tex]cubic units

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The correct statement explain for the given ratio of boys to girls of 3:4 is - this fraction of girls in the class is found to be 4/7.

Irrespective whatever how a ratio is expressed, it is crucial to reduce it to the fewest whole numbers, just like with any fraction. To accomplish this, divide the integers by their largest common factor after discovering it.

Ratios can also be expressed as a fraction because they are straightforward division problems. Some folks prefer to use merely words to express ratios.

Class contains a ratio of boys to girls of 3: 4.

So, Boys / Girl = 3 / 4

Total students = boys  + girls.

Total students = 3 + 4 = 7

So,

Girl / Total = 4/7

Thus, the correct statement explain for the given ratio of boys to girls of 3:4 is - this fraction of girls in the class is found to be 4/7.

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The complete question is-

A class has a ratio of boys to girls 3:4.

Select correct option:

a) The fraction of boys in the class is 3/4

b) The fraction of girls in the class is 4/7

c) The number of boys in the class is 6

d) The number of pupils in the class is 12

In response to the stated question, we may state that To conclude, the function problem's relation is a function for all x values except x between 3 and 4.

In mathematics, a function is a connection between two sets of numbers in which each member of the first set (known as the domain) corresponds to a single element in the second set (called the range). In other words, a function takes inputs from one set and produces outputs from another. Inputs are commonly represented by the variable x, whereas outputs are represented by the variable y. A function can be described using an equation or a graph. The equation y = 2x + 1 represents a linear function in which each value of x yields a distinct value of y.

If and only if each input has precisely one output, a relation is a function. To determine whether the connection stated in the issue is a function, we must examine whether any x values have more than one output.

We may achieve this by putting the specified points on a graph and looking for vertical lines that cross the graph more than once. If so, the relationship is not a function.

We may create the following graph with the supplied points:

    |                    

8  |                    

    |                    

7  |              ●      

    |                    

6  |           ●        

    |                    

5  |                    

    |                    

4  |          ●          

    |                    

3  |              ●      

    |                    

2  |    ●                

    |                    

 1  |                    

    |                    

0  |                    

    |                    

-1 |                    

    |                    

-2 |                    

    |                    

-3 |                    

    |                    

-4 |                    

    |                    

    |_____________________

       -4  -3  -2  -1  0  1  2  3  4

Apart for the line travelling through the points (3, 2) and (4, 2), there is no vertical line that intersects the graph in more than one spot (4, -3). As a result, if x is between 3 and 4, the relation specified in the issue is not a function.

To conclude, the problem's relation is a function for all x values except x between 3 and 4.

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Answer:

Step-by-step explanation:

To solve this problem, we can use the formula for calculating simple interest:

I = P * r * t

where:

I = interest earned

P = principal (initial amount of money)

r = rate of interest

t = time (in years)

We can rearrange the formula to solve for the principal:

P = I / (r * t)

In this case, we know that Gill earned $2306 in interest after one year at a rate of 6%. So:

I = $2306

r = 0.06

t = 1 year

Substituting these values into the formula, we get:

P = $2306 / (0.06 * 1)

P = $38,433.33

Therefore, the initial amount of money that Gill deposited into her account was $38,433.33.

The decoration's volume, to the closest tenth of an inch cubic, is: 308.9 cubic inches make up V.

The quantity of space that an object or substance occupies is measured by its volume. Usually, it is expressed in cubic measures like cubic metres, cubic feet, or cubic inches. By multiplying an object's length, width, and height, or by applying a formula unique to the shape of the object, one can determine the volume of the object.

given

The cylinder's radius is equal to half of its diameter, or 14/2, or 7 inches. The new water level is 9 + 2 = 11 inches because the initial water level was 9 inches and the decoration raised the water level by 2 inches.

The decoration's volume is equivalent to the volume of water it removed from the area.

We can determine the volume of the ornamentation by using the following formula: V = r2h.

V = (72/2), which equals 98 cubic inches.

The decoration's volume, to the closest tenth of an inch cubic, is: 308.9 cubic inches make up V.

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The probability of getting tails in the three coins would be 0.125 or 12.5%.

To calculate the probability of an event happening, first, we need to identify the rate of the desired outcome versus the total possible outcomes. Moreover, to determine the total probability of two or more events happening we need to calculate the probability of each event and then multiply the results.

Probability of getting tails in any of the three coins:

1 / 2 = 0.5

Total probabilityy:

0.5 x 0.5 x 0.5 = 0.125 or 12.5%

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Answer:

[tex]\large\boxed{\textsf{x = 7}}[/tex]

Step-by-step explanation:

[tex]\textsf{For this problem, we are asked to find the value of x.}[/tex]

[tex]\textsf{We should simply isolate the x so that it's only on one side.}[/tex]

[tex]\large\underline{\textsf{How?}}[/tex]

[tex]\textsf{Simply use the Distributive Property for the right side of the equation.}[/tex]

[tex]\textsf{Simplify the equation to where x is by itself.}[/tex]

[tex]\large\underline{\textsf{What is the Distributive Property?}}[/tex]

[tex]\textsf{The Distributive Property is a Property that allow us to distribute expressions further.}[/tex]

[tex]\textsf{Commonly, the form is a(b+c); Where b and c are multiplied by a.}[/tex]

[tex]\large\underline{\textsf{Use the Distributive Property;}}[/tex]

[tex]\mathtt{5x-2=3(x+4)}[/tex]

[tex]\mathtt{5x-2=(3 \times x)+(3 \times 4)}[/tex]

[tex]\mathtt{5x-2=3x+12}[/tex]

[tex]\large\underline{\textsf{Add 2 to Both Sides of the Equation;}}[/tex]

[tex]\mathtt{5x-2 \ \underline{+ \ 2}=3x+12 \ \underline{+ \ 2}}[/tex]

[tex]\mathtt{5x=3x+14}[/tex]

[tex]\large\underline{\textsf{Subtract 3x from Both Sides of the Equation;}}[/tex]

[tex]\mathtt{5x-3x=3x-3x+14}[/tex]

[tex]\mathtt{2x=14}[/tex]

[tex]\large\underline{\textsf{Divide the Whole Equation by 2;}}[/tex]

[tex]\mathtt{\frac{2x}{2} = \frac{14}{2} }[/tex]

[tex]\large\boxed{\textsf{x = 7}}[/tex]

Answer:

[tex] \sf \: x = 7[/tex]

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 5x - 2 = 3(x + 4)

Then the value of x will be,

→ 5x - 2 = 3(x + 4)

→ 5x - 2 = 3(x) + 3(4)

→ 5x - 2 = 3x + 12

→ 5x - 3x = 12 + 2

→ 2x = 14

→ x = 14 ÷ 2

→ [ x = 7 ]

Hence, the value of x is 7.

Answer:

When it was purchased (year 0) the coin was worth $7

Step-by-step explanation:

we have

[tex]f(t) = 7(2)^t[/tex]

This is a exponential function of the form

[tex]y=a(b)^x[/tex]

where

a is the initial value

b is the base

In this problem we have

[tex]a=\$7[/tex]

[tex]b=2[/tex]

[tex]b=1+r[/tex]

so

[tex]2=1+r[/tex]

[tex]r=1[/tex]

[tex]r=100\%[/tex]

The y-intercept is the value of the function when the value of x is equal to zero

In this problem

The y-intercept is the value of a rare coin when the year t is equal to zero

[tex]f(0)=7(2)^0[/tex]

[tex]f(0)=\$7[/tex]

therefore

The meaning of y-intercept is

When it was purchased (year 0) the coin was worth $7

Answer:

Value of the coin when it was first released

-------------------------------

The y-intercept is the value of f(0).

Substitute t = 0 and find the y-intercept:

This is representing the value of the coin when it was released.

The new position of Rhombus ABCD after the translation can be described as follows: point A is now at (-1,-8), point B is at (2,-3), point C is at (7,0), and point D is at (4,-5).

To translate Rhombus ABCD using the rule (x, y) = (x+2, y-6), we add 2 to the x-coordinate and subtract 6 from the y-coordinate for each vertex.

Thus, the new vertices for the translated rhombus are:

A' = (-3+2, -2-6) = (-1, -8)

B' = (0+2, 3-6) = (2, -3)

C' = (5+2, 6-6) = (7, 0)

D' = (2+2, 1-6) = (4, -5)

Therefore, the coordinates for the translated Rhombus ABCD are A'(-1,-8), B'(2,-3), C'(7,0), and D'(4,-5).

Learn more about Rhombus here: brainly.com/question/27870968

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