What is the discriminant of 3x^2-10 x = -2

The value of the expression given as (9x-26) (4x+43) (2x-12) is 72x³ + 134x²  -5642x + 13416

From the question, the expression is given as

(9x-26) (4x+43) (2x-12)

Next, we evaluate the expression in pairs

So, we have

(9x-26) (4x+43) (2x-12) = (9x-26) (4x+43) (2x-12)

Evaluate the first two factors

So, we have

(9x-26) (4x+43) (2x-12) = (36x² + 387x - 104x  - 1118) (2x-12)

Evaluate the like terms in the expression

So, we have

(9x-26) (4x+43) (2x-12) = (36x² + 283x  - 1118) (2x-12)

Evaluate the first two factors

So, we have

(9x-26) (4x+43) (2x-12) = (72x³ - 432x² + 566x² - 3396x  - 2246x + 13416)

Evaluate the like terms

So, we have

(9x-26) (4x+43) (2x-12) = (72x³ + 134x²  -5642x + 13416)

Remove the bracket

(9x-26) (4x+43) (2x-12) = 72x³ + 134x²  -5642x + 13416

Hence, the solution is 72x³ + 134x²  -5642x + 13416

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Answer:

$1654.20

Step-by-step explanation:

There are 12 months in a year. There are 36 months in 3 years. If he gets charged $45.95 each month for 3 years or 36 months, he pays:

$45.95×36=

$1654.20 for three years.

The sum of the interior angles for a pentagon is 540°

Sum of Interior Angles of a Pentagon :

The interior angles of a pentagon sum up to 540 degrees.. Regardless of how regular or irregular the pentagon is, this is true. By dividing the whole amount by 5, we can calculate the size of each internal angle in the case of regular pentagons. To determine the measure of a missing angle in the situation of irregular pentagons, we must first know the measurements of other angles.

Any pentagon's internal angles add up to 540° in the same way. This holds true regardless of how regular or irregular the pentagon is. By using the polygon angle sum formula, the following sum is obtained:

(n-2)180(n−2)×180°

where n represents the polygon's number of sides. We have n = 5 in the case of a pentagon. Consequently, utilizing the formula:

=(n-2)180=(n−2) ×180°

= (5-2) 180= (5−2) ×180°

= (3) 180= (3) ×180°

= 540=540°

Consequently, a pentagon's interior angles add up to 540 degrees.

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Answer:

1.x=12

2.y=2

3.x=2

Step-by-step explanation:

Solving an Inequality with No Solution

Write the inequality.

Distributive Property

Subtract 8x from each side

Simplify.

The unit rate in metric tons per hour is 1 metric ton per hour.

The unit rate will be calculated by simply performing the division of amount of dirt by amount of time.

Keep the values in formula to find the value of the unit rate in metric tons per hour.

Unit rate = 1/4÷1/4

Performing division on Right Hand Side of the equation to find the value of the unit rate in metric tons per hour.

Unit rate = 1 metric ton per hour

Thus, the unit rate to remove dirt from construction site is 1 metric ton per hour.

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Answer:

If a line has an undefined slope, it means it is a vertical line. A vertical line passing through the point (12, -20) would have all points on the line with an x-coordinate of 12. Therefore, the equation of the line would be:

x = 12

So, any point of the form (12, y) would be on this line, where y can be any real number.

Answer:

x=12

Step-by-step explanation:

since 12 is the x coordinate, and an undefined slope is vertical that means x has to equal to 12

The value of a(t) is -1 and b(t) is 55 + \(e^t\)

No, the given equation y' - y = 55 + \(e^t\) is not in the standard form of a first-order linear differential equation.

In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.

For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:

μ(t) = e^∫a(t)dt

To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.

To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).

Comparing the given equation with the standard form, we can identify:

a(t) = -1

b(t) = 55 + \(e^t\)

Therefore, The value of a(t) is -1 and b(t) is 55 + \(e^t\)

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Answer:

C

Step-by-step explanation:

To find which of the given choices are solutions for the system of equations, we need to:

-substitute x, and y with the given coordinates and

-check if they are solutions for both equations.

7x+y= 6

x+ 2y = -1

A. (x = -1, y = 0) ❌

7(-1)+0= 6; -7 =6 FALSE

-1+ 2*0 = -1; -1= -1 TRUE

B. (x = 1, y = 0)❌

7*1+ 0= 6; 7= 6 FALSE

1+ 2*0 = -1; 1 =-1 FALSE

C. (x =1, y= -1)✅

7*1 -1= 6; 6=6 TRUE

1+ 2(-1) = -1; -1=-1 TRUE

D. None of these choices are correct ❌

because one choice is correct

Therefore, the train journey from Telford Central to Shrewsbury should take approximately 22 minutes. a) The first train to Oakengates arrives at 0815.

To determine the time, we look at the timetable for Oakengates and find the earliest arrival time listed. In this case, the timetable shows that the first arrival time at Oakengates is 0815.

b) If you catch the 0852 train from Telford Central, it should take approximately 27 minutes to reach Shrewsbury.

To calculate the travel time, we examine the timetable for Shrewsbury. The 0852 train departure from Telford Central is the relevant starting point. From the timetable, we can see that the train arrives at Shrewsbury at 0914. To find the travel time, we subtract the departure time from the arrival time:

0914 - 0852 = 22 minutes.

Therefore, the train journey from Telford Central to Shrewsbury should take approximately 22 minutes.

It's important to note that the calculated travel time is an estimation based on the timetable provided. Actual travel times may vary depending on factors such as delays, stops, and the specific train schedule. It is advisable to refer to the most up-to-date timetable and consider any potential disruptions or changes in train services.

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Answer:

X + 5 =  X + 5

Step-by-step explanation:

The answer is X + 5 because they both are different simbuls, wich means you cant add them. The answer just stayes x + 5.

Answer:

We do this by first converting all terms into fractions, finding the least common denominator (LCD), then rewriting each term as an equivalent fraction with the LCD. Then we compare the numerators of each fraction and put them in correct order from least to greatest or greatest to least.

Step-by-step explanation:

hope this helps!

Answer:

8n=8×5=40

..............

The consecutive integers are 12 , 13 ,14, and 15 .

Of the four consecutive integers let us consider the smallest integer be x.

Therefore the other 3 integers are x+1 , x+2 and x+3 .

Therefore the sum of the integers are:

x +(x+1)+(x+2)+(x+3)=4x+6

The sum of the integers is given 54.

∴4x + 6 = 54

or, 4x = 54 - 6

or, 4x = 48

or, x = 48 ÷ 4

or, x = 12

Therefore the three other integers are 13,14 and 15.

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Answer:

man can u send the pic of the diagram I will solve it

Answer: He rode on the bus for 3 hours

Step-by-step explanation:

1. We add 15 miles and 3 miles to get 18 miles.

2. Then 66/18 is 3.6666

3. Convert to whole number

Then 15x3 is 45

66-45 is 21

21/3=7

so he walked for 7 hours and rode the bus for 3 hours

Answer:

C ≈ 251.33

Step-by-step explanation:

The circumference of a circle is C = 2πr

Radius = r = 40 is given in the problem

C = 2* 3.14 * 40

C ≈ 251.33

Answer:

251.2

Step-by-step explanation:

Given,

Radius ( r ) = 40

To find : Circumference of a circle = ?

Formula : -

Circumference of a circle = 2πr

Note : -

The value of π is :

Solution : -

Circumference of a circle = 2πr

= 2 x 3.14 x 40

Circumference of a circle = 251.2

Therefore,

Circumference of a circle is 251.2

a. The MRS is constant (not diminishing) at 1/3.

U(x,y) = 3x + y

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = 1 / 3

The MRS is constant (not diminishing) at 1/3.

b. The MRS is diminishing because as y increases, the MRS decreases.

U(x,y) = x * y

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = 1 / y

The MRS is diminishing because as y increases, the MRS decreases.

c. The MRS is diminishing because as y increases, the MRS decreases.

U(x,y) = x * y

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = 1 / y

Similar to the previous case, the MRS is diminishing because as y increases, the MRS decreases.

d. The MRS depends on the ratio of y to x and can vary.

U(x,y) = x^2 - y^2

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = -2y / 2x = -y / x

The MRS depends on the ratio of y to x and can vary. It is not necessarily diminishing.

e. The MRS depends on the values of x and y and can vary.

U(x,y) = x + y / (x * y)

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = -1 / (y^2) + 1 / (x^2 * y)

The MRS depends on the values of x and y and can vary. It is not necessarily diminishing.

Now let's move on to the second part of the question:

For parts a, b, and c, we need more specific information about the utility functions, such as the values of α and β, to calculate the demand curves for x and y, the indirect utility function, and the expenditure function.

To show that the demand curve is homogeneous in degree zero in terms of income and prices, we need the specific functional form of the utility functions and information about the prices of x and y. Please provide the necessary details for parts A, b, and c to continue the analysis.

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By using the formula, Quantity = Percent × Whole, 20 is 50% percent of 40.

In Mathematics, a percentage can be defined as any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

In order to determine the percentage which 20 is of a whole number (40), we would apply the following mathematical expression (formula);

Quantity = percent × whole number

Substituting the given parameters into the percentage and quantity formula, we have the following;

20 = percent × 40

Percent = 20/40

Percent = 0.5

Next, we would multiply the resulting decimal value by 100 as follows;

Percentage = 0.5 × 100

Percentage = 50%.

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Answer:

7x

Step-by-step explanation:

Answer:

7x

Step-by-step explanation:

4x+3x

4+3=7

add x, same answer of 7x

Answer:

your answer is 242 in^2

A=22+52+168

Using  both and levels of significance and the critical value, we can conclude that the percentage of spam emails sent by the huge firm is different from the percentage in a recent month.

The population proportion of spam emails in a recent month is p = 0.718.

A random sample of emails from a large corporation has a sample proportion of spam emails, p'= 0.645.

We want to test the hypothesis that the population proportion of spam emails in the large corporation is different from p = 0.718.

We will use both 0.05 and 0.01 levels of significance and the critical value method.

To test this hypothesis using the critical value method, we can follow these steps:

The null hypothesis is that the population proportion of spam emails in the large corporation is equal to 0.718:

H0: p = 0.718

The alternative hypothesis is that the population proportion of spam emails in the large corporation is different from 0.718:

Ha: p ≠ 0.718

We will use both 0.05 and 0.01 levels of significance. Since we have a large sample (np > 10 and n(1-p) > 10), we can use the z-test for proportions. The test statistic is calculated as:

z = ( p' - p) / sqrt(p(1-p)/n)

where n is the sample size.

Using a standard normal distribution table, the critical values for a two-tailed test at the 0.05 and 0.01 levels of significance are:

At the 0.05 level: ±1.96

At the 0.01 level: ±2.58

Step 4: Calculate the test statistic and p-value.

Using the formula for the test statistic and the given values, we get:

z = (0.645 - 0.718) / sqrt(0.718(1-0.718)/n)

Since we don't know the population standard deviation, we use the standard error estimated from the sample:

z = (0.645 - 0.718) / sqrt(0.718(1-0.718)/n) = -2.546 / sqrt(0.718(1-0.718)/n)

Using n = 1000 (a reasonable sample size for an email server), we get:

z = -2.546 / sqrt(0.718(1-0.718)/1000) = -9.386

The corresponding p-value for this test statistic is very small (less than 0.0001), indicating strong evidence against the null hypothesis.

At the 0.05 level of significance, the critical value is ±1.96, which does not include the calculated test statistic of -9.386. Therefore, we reject the null hypothesis and conclude that the population proportion of spam emails in the large corporation is different from 0.718.

At the 0.01 level of significance, the critical value is ±2.58, which also does not include the calculated test statistic of -9.386. Therefore, we reject the null hypothesis at this level of significance as well.

In conclusion, we have strong evidence to suggest that the proportion of spam emails in the large corporation is different from the proportion in a recent month (0.718).

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Step-by-step explanation:

Probability

Probability is a measure of the likelihood that an event will happen.

When dealing with probability, the outcomes of a process are the possible results. For example, when a die is rolled, the possible outcomes are 1, 2, 3, 4, 5, and 6. In mathematical language, an event is a set of outcomes, which describe what outcomes correspond to the "event" happening. For instance, "rolling an even number" is an event that corresponds to the set of outcomes {2, 4, 6}. The probability of an event, like rolling an even number, is the number of outcomes that constitute the event divided by the total number of possible outcomes. We call the outcomes in an event its "favorable outcomes".

Probability =

A parametric representation of the solution set of the linear equation 3x - 6y = 0 is given by the equations:

x = 2t , y = t

To find a parametric representation of the solution set of the linear equation 3x - 6y = 0, we can express x and y in terms of a parameter t. Let's solve the equation:

3x - 6y = 0

First, we can divide both sides by 3 to simplify the equation:

x - 2y = 0

Now, let's express x and y in terms of t:

x = 2t

y = t

Therefore, a parametric representation of the solution set of the linear equation 3x - 6y = 0 is given by the equations:

x = 2t , y = t

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True. Exception reports show a greater level of detail than is included in routine reports.

Exception reports are reports that help in identifying data that does not conform to expected patterns. Exception reports show information about an exception in the data set.

This helps to identify irregularities or anomalies in data or system operations.Exception reports are used to analyze system performance, monitor resource consumption, and to detect unusual activity.

This type of report is important to identify issues or errors, where the routine reports or standard reports would not provide enough detail or insight to do so.

It provides detailed information on any unusual event or anomaly that occurred beyond the usual course of events or processes.Exception reports are generated and distributed when the data is not expected or when an event occurs that is outside of what is considered typical.

For example, a financial system might generate an exception report if a transaction is entered that exceeds the maximum allowed amount. This report would show the details of the transaction and highlight the exception.

The purpose of exception reports is to provide users with a higher level of detail than they would find in routine reports. Exception reports are used to highlight significant data, which will be used for further analysis or action.

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Complete question :

The latter is leaning against the building so that the distance from the ground to the top of the ladder is 9 feet less than the length of the ladder finally put the ladder in the distance from the bottom of the ladder to the building 15 feet. Find length of the ladder.

Answer:

17

Step-by-step explanation:

From Pythagoras :

Hypotenus = sqrt(opposite² + adjacent²)

From the diagram

l = sqrt((l-9)² + 15²)

l² = (l² - 18x + 81 + 225)

Square both sides

l² = l² - 18x + 306

l² - l² = 306 - 18x

18l = 306

l = 306/18

l = 17

Answer:

47.5

Step-by-step explanation:

19÷2=9.5x5=47.5

Answer:

it's 4 1/3

Step-by-step explanation:

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Answer:

x^5+5x^4+10x³+10x²+5x+1

Step-by-step explanation: