a) Find the simplified form of the difference quotient for the function f(x) = 4x² - 2x + 1.

Answer:

[tex]\Huge \boxed{\boxed{\bf{Volume = 848.23 cm^3}}}[/tex]

Step-by-step explanation:

To calculate the volume of a cone with a height of 10 cm and a diameter of 18 cm, we can use the formula:

[tex]\LARGE \boxed{\tt{V = \frac{1}{3} \times \pi \times r^2 \times h}}[/tex]

➤V = volume

➤r = radius

➤h = height

Since the diameter is 18 cm, the radius is half of that, which is 9 cm. Now, we can plug in the values:

The volume of the cone is [tex]\tt{270\pi \approx 848.23 \texttt{ cm}^3}[/tex]

__________________________________________________________

The fraction that, when subtracted from 5/12, yields the same result as the difference between 2/3 and 1/2, is 1/4.

To find the fraction that, when subtracted from 5/12, gives the same result as the difference between 2/3 and 1/2, we need to compute both the difference and the subtraction, and then find the fraction that represents their equality.

The difference between 2/3 and 1/2 can be found by subtracting the two fractions:

2/3 - 1/2 = (4/6) - (3/6) = 1/6

Now, let's represent the fraction we are looking for as "x." We can set up the equation:

5/12 - x = 1/6

To solve for "x," we need to isolate it on one side of the equation. We can do this by subtracting 5/12 from both sides:

-x = 1/6 - 5/12

To simplify the right side, we need a common denominator, which is 12:

-x = 2/12 - 5/12

Now we can combine the numerators:

-x = (2 - 5)/12 = -3/12 = -1/4

To solve for "x," we multiply both sides of the equation by -1:

x = 1/4

For more such questions on fraction

https://brainly.com/question/78672

#SPJ8

3x-15=x+33

or, 3x-2x=33+15

THEREFORE X=48 UNITS

THIS IS THE CORRECT QNSWER

Answer:

PQ=20

Step-by-step explanation:

1) 11+x+2+3x-1+10+2x=64

2) 6x+22=64

3) 6x=42

4) x=7

5) PQ = 3(7)-1 = 20

Answer:

a.  0.00166

b. 0.00200

Overall B is correct because it has the prossibilty of getting more votes. 0.00200

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the slope and y-intercept of a linear function, we need to use the formula y = mx + b, where "m" is the slope of the line and "b" is the y-intercept.

Given points in the linear function are not provided in the question, but if you are given two points on a line, you can find the slope of the line by using the slope formula:

slope = (change in y)/(change in x)

Assuming the given points of the linear function are (x1, y1) and (x2, y2), then the slope of the line is:

slope = (y2 - y1)/(x2 - x1)

Once we have the slope of the line, we can use any point on the line and the slope to find the y-intercept, b, using the formula:

y = mx + b

b = y - mx

Therefore, we can find the slope and y-intercept of a linear function, given two points on the line.

Answer:

A: A^-1 = [[-2,-3,-1.5],[-2,-4,-2.5],[-1,1,-.5]]

Step-by-step explanation:

Answer:

To find the inverse of the matrix A, we will use the row reduction method. We will augment matrix A with the identity matrix I and perform row operations until A is transformed into the identity matrix. The resulting matrix on the right side will be the inverse of A.

Step-by-step explanation:

Augment the matrix A with the identity matrix I:

[ 1  0 -3 | 1  0  0 ]

[ 3  1 -4 | 0  1  0 ]

[ 4  2 -4 | 0  0  1 ]

Perform row operations to transform the left side of the augmented matrix into the identity matrix:

R2 = R2 - 3R1

R3 = R3 - 4R1

[ 1  0 -3 | 1  0  0 ]

[ 0  1  5 | -3  1  0 ]

[ 0  2  8 | -4  0  1 ]

Perform row operations to further transform the left side of the augmented matrix into the identity matrix:

R3 = R3 - 2R2

[ 1  0 -3 | 1  0  0 ]

[ 0  1  5 | -3  1  0 ]

[ 0  0 -2 | 2  -2  1 ]

Multiply the third row by -1/2 to make the pivot element of the third row equal to 1:

R3 = (-1/2) * R3

[ 1  0 -3 | 1  0  0 ]

[ 0  1  5 | -3  1  0 ]

[ 0  0  1 | -1  1  -1/2 ]

Perform row operations to further transform the left side of the augmented matrix into the identity matrix:

R1 = R1 + 3R3

R2 = R2 - 5R3

[ 1  0  0 | 2  0  3/2 ]

[ 0  1  0 | 2  -4  5/2 ]

[ 0  0  1 | -1  1  -1/2 ]

The resulting matrix on the right side of the augmented matrix is the inverse of matrix A:

[ 2  0  3/2 ]

[ 2  -4  5/2 ]

[ -1  1  -1/2 ]

Therefore, the inverse of matrix A is:

[ 2  0  3/2 ]

[ 2  -4  5/2 ]

[ -1  1  -1/2 ]

Answer:

30.7

Step-by-step explanation:

30.725 to one decimal place is 30.7.  To round/correct to one decimal place, it would be the tenths.  So, look at the hundredths place number (2), and if its greater than 5, add 1 to the tenths place (7 changes to 8), and if its less than 5, don't do anything (7 stays as 7).

Hope this helps! :)

Answer:

The value corrected to one decimal place is 30.7

Step-by-step explanation:

The value 30.725 has three decimal places. The number 7 is in the one's place, the number 2 is in the tenth place, and the number 5 is in the hundredth place.

To round off, if the value in a place is equal to or above 5, the previous place number is increased by one; else it remains the same. In this case, the hundredth place is 5, so we add 1 to the tenth place. This gives us 2 + 1 = 3. Therefore, the number is expressed with two decimal places as 30.73.

To express it as one decimal place, we look at the value in the tenth place, which is 3. As 3 is less than 5, the one's place remains the same.

Thus, the value is 30.7 when expressed with one decimal place.

Learn more about decimal places,

https://brainly.com/question/20563248

Answer:

17.85$

Step-by-step explanation:

Let x be 1 shirt price

Let y be 1 pant price

we have the following equation

3x+2y = 104.81$ (1)

2x+y = 61.33$ => multiply two sides by 2 => 4x + 2y = 122.66 (2)

=> (2) - (1) => x = 17.85$

So one shirt is 17.85$

Answer:

A. x+y+z=35,000

4x+6y+12x-194,000

2y-z=0

Step-by-step explanation:

The system of equations is:

x + y + z = 35,000 (total investment is $35,000) 4x + 6y + 12z = 19,400 (the investor wants an annual return of $1940 on the three investments) y = 2z (the client wants to invest twice as much in A bonds as in B bonds)

The answer is A.

The first equation represents the total amount of money invested in the three types of bonds. The second equation represents the total annual return on the investments, which is equal to the sum of the individual returns on each type of bond. The third equation represents the client's preference for investing in A bonds over B bonds.

The system of equations can be used to solve for the values of x, y, and z, which represent the amounts invested in AAA, A, and B bonds, respectively.

Answer:

[tex]\textsf{A.} \quad \begin{cases}x+y+z=35000\\4x+6y+12z=194000\\2z-y=0\end{cases}[/tex]

Step-by-step explanation:

A system of equations is a set of two or more equations with the same variables. It allows us to model and solve problems that involve multiple equations and unknowns.

An investment firm recommends that a client invest in bonds rated AAA, A, and B. The definition of the variables are:

The average yield on each of the three bonds is:

We have been told that the total investment is $35,000. Therefore, the equation that represents this is the sum of the three investments equal to 35,000:

[tex]x+y+z=35000[/tex]

To find the annual return on each investment, multiply the number of bonds by the average yield (in decimal form). Given the investor wants a total annual return of $1940 on the three investments, the equation that represents this is the sum of the product of the investment amount for each bond type and its corresponding yield, equal to $1940.

[tex]0.04x+0.06y+0.12z=1940[/tex]

Multiply all terms by 100:

[tex]4x+6y+12z=194000[/tex]

Finally, given the client wants to invest twice as much in A bonds as in B bonds, the equation is:

[tex]y=2z[/tex]

Subtract y from both sides of the equation:

[tex]2z-y=0[/tex]

Therefore, the system of equations the models the given scenario is:

[tex]\begin{cases}x+y+z=35000\\4x+6y+12z=194000\\2z-y=0\end{cases}[/tex]

Answer:

The rational form of the ratio 2:3 is 2/5

Step-by-step explanation:

For those of us who don't know or don't remember what rational means, it just means fraction, and in this case is asking as to convert ratio 2:3 into a fraction.

-First thing is to add the ratio:

2+3=5

-Now, we are going to place 5 as the denominator of the fraction, and we are going to keep the 2 from the ratio (it will always be the first number of our ratio, for example, if the ratio is 6:1 we'd be keeping the 6), and place it on the numerator place:

2:3 = 2/5

-So, that would be pretty much it, by the way, I know that the question was upgraded, but I don't mind to have 5 points more.

Answer:

Step-by-step explanation:

ACTUAL ANSWER

(-5¼)/(3/2)

= -{(20+1)/4}/(3/2) //CONVERTING INTO IMPROPER FRACTION

= (-21/4)/(3/2)

= (-21/4) x (2/3) // MULTIPLYING BY RECIPROCAL

 = (-21x2)/(4x3)

= -42/12

= -(7x6)/(2x6) TAKING 7 AS COMMON FACTOR

= -7/2

STEPS FOLLOWED BY ESMERELDA

(-5¼)/(3/2)

= -{(20+1)/4}/(3/2)

= -(21/4)/(3/2)

= -(21/4) x (3/2)

= -(21+3)/(4+2)

= - (24/6)

= -4

HENCE THE ERRORS COMMITTED BY HER ARE:-

1. ESMERALDA ADDED THE NUMERATORS

2. ESMERALDA ADDED THE DENOMINATORS

3. ESMERALDA DID NOT USE THE RECIPROCAL OF THE DIVISOE

The correct answer is Part 1: The 99% confidence interval for the population proportion is approximately (0.4716, 0.5416).Part 2: With 99% confidence, the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.

Part 1:

To construct a 99% confidence interval for the population proportion, we can use the formula:

Confidence Interval = Sample Proportion ± Margin of Error

where the margin of error is determined by the level of confidence and the standard error.

First, let's calculate the sample proportion:

Sample Proportion = (Number of adults who say they have started paying bills online) / (Total number of adults surveyed)

Sample Proportion = 1436 / 2837 ≈ 0.5066 (rounded to four decimal places)

Next, we need to calculate the standard statistics error, which is the measure of the variability in the sample proportion:

Standard Error = sqrt((Sample Proportion * (1 - Sample Proportion)) / Sample Size)

Standard Error = sqrt((0.5066 * (1 - 0.5066)) / 2837) ≈ 0.0136 (rounded to four decimal places)

Now, we can calculate the margin of error:

Margin of Error = Critical Value * Standard Error

The critical value is based on the desired confidence level. For a 99% confidence level, the critical value is approximately 2.576 (obtained from a standard normal distribution table).

Margin of Error = 2.576 * 0.0136 ≈ 0.0350 (rounded to four decimal places)

Finally, we can construct the confidence interval:

Confidence Interval = Sample Proportion ± Margin of Error

Confidence Interval = 0.5066 ± 0.0350

Confidence Interval ≈ (0.4716, 0.5416) (rounded to four decimal places)

Part 2:

The correct interpretation is:

C. With 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.

This means that we are 99% confident that the true proportion of adults who have started paying bills online falls within the range of 0.4716 to 0.5416. The survey results suggest that approximately 47.16% to 54.16% of the population of adults have started paying bills online in the last year.

Learn more about statistics here:

https://brainly.com/question/15525560

#SPJ8

a. The marginal profit function Py is Py = -30x + 47y - 915 and

b. Change in profit if price increase by 1 cent is 831 cents.

To find the marginal profit functions Px and Py, we need to find the partial derivatives of the profit function P(x, y) with respect to x and y, respectively.

Given:

P(x, y) = (x - 40)(55 - 4x + 5y) + (y - 45)(70 + 5x - 7y)

a. Marginal profit function Px:

To find Px, we differentiate P(x, y) with respect to x while treating y as a constant:

Px = ∂P/∂x = (∂/∂x) [(x - 40)(55 - 4x + 5y) + (y - 45)(70 + 5x - 7y)]

Expanding the terms and simplifying:

Px = (55 - 4x + 5y) + (x - 40)(-4) + (70 + 5x - 7y)(5)

Simplifying further:

Px = 55 - 4x + 5y - 4x + 40 + 350 + 5x - 7y

Combining like terms:

Px = 355 - 3x - 2y

b. Marginal profit function Py:

Similarly, to find Py, we differentiate P(x, y) with respect to y while treating x as a constant:

Py = ∂P/∂y = (∂/∂y) [(x - 40)(55 - 4x + 5y) + (y - 45)(70 + 5x - 7y)]

Expanding the terms and simplifying:

Py = (x - 40)(5) + (70 + 5x - 7y)(-7) + (y - 45)(5)

Simplifying further:

Py = 5x - 200 - 7y - 490 - 35x + 49y + 5y - 225

Combining like terms:

Py = -30x + 47y - 915

This is the profit function Py.

b. Estimating the daily change in profit:

To estimate the daily change in profit, we need to evaluate Px and Py at the given prices and calculate the change in profit when the prices are increased as specified.

Given initial prices:

First brand price (x) = 70 cents

Second brand price (y) = 73 cents

To estimate the change in profit, we substitute the initial prices into Px and Py and calculate the results:

Px(70, 73) = 355 - 3(70) - 2(73)

          = 355 - 210 - 146

          = -1

Py(70, 73) = -30(70) + 47(73) - 915

          = -2100 + 3431 - 915

          = 416

The daily change in profit can be estimated by multiplying the changes in price (1 cent for the first brand and 2 cents for the second brand) with the respective marginal profit functions:

Change in profit = ΔP ≈ Px(70, 73) * 1 + Py(70, 73) * 2

               ≈ -1 * 1 + 416 * 2

               ≈ -1 + 832

               ≈ 831 cents

Therefore, the estimated daily change in profit when the salesperson increases the price of the first label by 1 cent and the price of the second label by 2 cents is 831 cents.

Learn more about profit function here:

https://brainly.com/question/16866047

#SPJ1

The presence of the Purple Party and the Chartreuse Party in the Houses of Parliament in Ghyronmia reflects the diversity of views and opinions in society. It creates a dynamic political environment that encourages debate, discussion, and better decision-making, and ensures that the interests of all sections of society are represented.

In Ghyronmia, a hypothetical small country, the Houses of Parliament have two political parties: the Purple Party and the Chartreuse Party. These two parties may have different political ideologies and values which reflect on their stances on various issues. The presence of different political parties in Parliament creates a dynamic political environment where different ideas are debated and discussed, and this leads to better decision-making and representation of different sections of society.
The Purple Party may represent a certain section of society that values conservatism, tradition, and stability. They may be more inclined to support policies that uphold traditional values, promote law and order, and preserve the status quo. On the other hand, the Chartreuse Party may represent a section of society that values progress, social justice, and reform.

They may be more inclined to support policies that aim to bring about change, promote equality, and challenge the status quo.
The presence of these two parties in Parliament means that different views and opinions are represented, and this creates healthy competition in the political sphere. It also ensures that decisions are not taken without due consideration and debate, and that policies are subject to scrutiny from different angles.

This, in turn, helps to prevent any one party or ideology from dominating the political discourse.

for more search question dynamic

https://brainly.com/question/14975027

#SPJ8

To order the fractions from least to greatest, we need to compare their values. The given fractions are 11/4, -2, and -1/8. The answer of the given question -2, -1/8, 11/4

Let's start by converting the mixed number -2 into a fraction. A mixed number consists of a whole number and a fraction. To convert it to a fraction, we multiply the whole number by the denominator of the fraction part and add the numerator. Then, we place the result over the original denominator. In this case, -2 can be written as -2/1.

Now we have the following fractions: 11/4, -2/1, and -1/8.

To compare these fractions, we can find a common denominator. The least common multiple (LCM) of the denominators 4, 1, and 8 is 8. So, we will rewrite the fractions using 8 as the common denominator:

11/4 = 22/8

-2/1 = -16/8

-1/8 remains the same

Now we have 22/8, -16/8, and -1/8. We can see that -16/8 is the smallest, followed by -1/8, and finally 22/8.

Therefore, in order from least to greatest, the fractions are:

-16/8, -1/8, 22/8

Simplifying further, we have:

-2, -1/8, 11/4

Note that we simplified the fractions, but the order remains the same. The fractions are ordered based on their numerical values, with the least value first and the greatest value last.

For more such questions on fractions

https://brainly.com/question/17220365

#SPJ8

The answer to four decimal places, the probability is approximately 0.6481.

To find the probability that a randomly chosen student is either female or received an "A," we need to calculate the sum of the probabilities of these two events occurring individually and subtract the probability of both events occurring simultaneously.

Let's start by calculating the probability of selecting a female student. From the given information, we know that there are 29 female students out of a total of 54 students. Therefore, the probability of selecting a female student is 29/54.

Next, we need to determine the probability of selecting a student who received an "A." Looking at the table, we can see that there are a total of 8 students who received an "A" grade out of 54. Hence, the probability of selecting a student who received an "A" is 8/54.

To find the probability of both events occurring, we need to consider the intersection of the two events, which is the set of female students who also received an "A." According to the table, there are 2 female students who received an "A." Therefore, the probability of selecting a female student who received an "A" is 2/54.

Now, we can calculate the probability of selecting a female student OR a student who received an "A" by summing the individual probabilities and subtracting the probability of both events occurring simultaneously:

Probability (Female OR "A") = Probability (Female) + Probability ("A") - Probability (Female AND "A")

= 29/54 + 8/54 - 2/54

= 35/54

For more such questions on probability

https://brainly.com/question/25839839

#SPJ8

Answer:

This is not the answer but if u have Spanchat you can go to the AI and ask him to fill in the table using this function rule, list x, and then put the equation and he'll give you the table

Step-by-step explanation:

[tex] \huge{ \tt{ \boxed{ \tt{answer}}}}[/tex]

★Refer the attachment mate!! Follow for more★

The graph which shows the interval notation of the inequality 3 > - x > - 7 is option C.

3 > - x > - 7

Break the compound inequality into two and solve each

3 > - x

divide both sides by -1

-3 < x

- x > - 7

divide both sides by -1

x < 7

So the solution to the inequality is

-3 < x < 7

Therefore, it can be interpreted that x is greater than -3 and less than 7

Read more on inequality?

https://brainly.com/question/25275758

#SPJ1

Given statement solution is :- The manager will have enough funds, and the amount set aside ($10,000) is sufficient to cover the payroll for the next four weeks.

To determine if the manager will have enough funds to cover the nightly payroll for the next four weeks, we need to calculate the total cost for four weeks and compare it to the amount set aside.

The nightly payroll has a mean of $2200 and a standard deviation of $300. Since there are seven nights in a week, the weekly payroll can be calculated as:

Weekly Payroll = Nightly Payroll * Number of Nights in a Week

= $2200 * 7

= $15,400

To calculate the total cost for four weeks, we multiply the weekly payroll by four:

Total Cost for Four Weeks = Weekly Payroll * Number of Weeks

= $15,400 * 4

= $61,600

Now, let's calculate the z-score using the formula:

z = (X - μ) / σ

Where:

X = Total Cost for Four Weeks

μ = Mean of the distribution

σ = Standard deviation of the distribution

z = ($61,600 - $2200) / $300

z = $59,400 / $300

z ≈ 198

To determine if the manager will have enough funds to cover the payroll, we need to find the proportion of the distribution that is less than or equal to the z-score. This can be done by consulting a standard normal distribution table or using statistical software.

For a z-score of 198, the proportion in the tail of the distribution is essentially 1 (or 100%). This means that the manager is virtually guaranteed to have enough funds to cover the payroll for the next four weeks.

Since the manager has set aside $10,000, which is less than the calculated total cost of $61,600, he will indeed have enough funds to cover the payroll.

Therefore, the manager will have enough funds, and the amount set aside ($10,000) is sufficient to cover the payroll for the next four weeks.

For such more questions on Funds Cover Payroll: Confirmed

https://brainly.com/question/32039603

#SPJ8

Answer: -6

Step-by-step explanation:

1. Evaluate the expressions inside the innermost brackets and braces first:

 [tex]\((-2)^2 \cdot 2 - 6 = 4 \cdot 2 - 6 = 8 - 6 = 2\)[/tex]

  So, the expression becomes:

  [tex]\(14 - \{7 + 4 \cdot 3 - 2\}+ (2^2 + 6 - 5 \cdot 3) + 3 - (5 - 2^3 / 2)\)[/tex]

2. Continue evaluating the expressions inside the braces:

  [tex]\(7 + 4 \cdot 3 - 2 = 7 + 12 - 2 = 17\)[/tex]

  So, the expression becomes:

[tex]\(14 - 17 + (2^2 + 6 - 5 \cdot 3) + 3 - (5 - 2^3 / 2)\)[/tex]

3. Now, evaluate the expressions inside the parentheses:

[tex]\(2^2 + 6 - 5 \cdot 3 = 4 + 6 - 15 = -5\)[/tex]

 [tex]\(5 - 2^3 / 2 = 5 - 8 / 2 = 5 - 4 = 1\)[/tex]

  So, the expression becomes:

[tex]\(14 - 17 - 5 + 3 - 1\)[/tex]

4. Finally, perform the remaining operations:

[tex]\(14 - 17 - 5 + 3 - 1 = -3 - 5 + 3 - 1 = -6\)[/tex]

So, the result of the expression is -6.

The standard form of the polynomial x^2 - x^6 + x^8 - 5 is:

x^8 - x^6 + x^2 - 5

To express the polynomial x^2 - x^6 + x^8 - 5 in standard form, we arrange the terms in descending order of their exponents.

The given polynomial can be rewritten as:

x^8 - x^6 + x^2 - 5

In the standard form of a polynomial, the terms are arranged in descending order of their exponents. So, let's rearrange the terms:

x^8 - x^6 + x^2 - 5

The standard form of the polynomial x^2 - x^6 + x^8 - 5 is:

x^8 - x^6 + x^2 - 5

for such more question on polynomial

https://brainly.com/question/15702527

#SPJ8

Answer:

B

Step-by-step explanation:

Answer:

OK, HERE IS YOUR ANSWER

Step-by-step explanation:

AI-generated answer

We are given a demand curve in the form of a graph, and we are asked to find the area of the triangle shown on the diagram. The formula for finding the area of a triangle is:

Area = 1/2 x base x height

In this case, the base of the triangle is the quantity in thousands of units per unit of time, and the height of the triangle is the price in dollars per unit.

The base of the triangle can be calculated as the difference between the quantities at the two endpoints of the demand curve. From the graph, we can see that the quantity at the left endpoint is 20, and the quantity at the right endpoint is 50. Therefore, the base of the triangle is:

Base = 50 - 20 = 30

The height of the triangle can be calculated as the difference between the prices at the two endpoints of the demand curve. From the graph, we can see that the price at the left endpoint is $90, and the price at the right endpoint is $70. Therefore, the height of the triangle is:

Height = 90 - 70 = 20

Now, we can use the formula to find the area of the triangle:

Area = 1/2 x base x height

Area = 1/2 x 30 x 20

Area = 300

Therefore, the area of the triangle shown on the diagram is $300. Hence, the correct answer is 300.

The area of the triangle in the demand curve diagram can be found using the formula for the area of a triangle which is 1/2 * base * height. From the points provided, we are able to calculate an area of 2450 dollars.

To answer this question, we need to understand how to calculate the area of a triangle which is represented by the equation: Area = 1/2 * base * height. From the diagram, we can find these values:

Base: The quantity 1,000s of units per unit of time which is the x-axis,

Height: Price per unit (dollars) which is the y-axis.

Assuming that the triangle's points intersect at 10 (on the y-axis) and 70 (on the x-axis) with a hypotenuse ending at 80 on the y-axis. The base would be 70 - 0 = 70, and the height would be 80 - 10 = 70.

Plugging these values into our formula, we get Area = 1/2 * 70 * 70 = 2450 dollars. So the area of the triangle is 2450 dollars.

Learn more about area of the triangle here:

https://brainly.com/question/34237015

#SPJ2

The probable question may be:

The diagram to the right illustrates a hypothetical demand curve representing the relationship between price (in dollars per unit) and quantity (in 1,000s of units per unit of time).

The area of the triangle shown on the diagram is $. (Enter your response as an integer.) 100 90- 80- 70-67 60 50- 40 30- 20-17 10- D 23 73 20 30 40 50 60 70 80 90 Quantity (1,000s of units per unit of time) 10 100

Answer:

f(x) = x² - 4x + 10

Step-by-step explanation:

the standard form of a quadratic function is

f(x) = ax² + bx + c ( a ≠ 0 )

given

f(x) = (x - 2)² + 6 ← expand the factor using FOIL

     = x² - 4x + 4 + 6 ← collect like terms

    = x² - 4x + 10 ← in standard form

Answer:

Slope = -7

Step-by-step explanation:

Take any two points from the table:

   (39 , 36) ⇒ x₁ = 39 & y₁ = 36

    (41 , 22) ⇒ x₂ = 41 & y₂ = 22

Substitute the points in the below formula:

                    [tex]\boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

                                 [tex]\sf = \dfrac{22-36}{41-39}\\\\\\=\dfrac{-14}{2}\\\\=-7[/tex]

The value of x that satisfies the equation x² + x - 6 = 0 is x = 2 or x = -3.

To find the value of x that satisfies the equation x² + x - 6 = 0, we can solve the quadratic equation by factoring or using the quadratic formula.

Option 1: Factoring

To factor the quadratic equation, we need to find two numbers whose product is -6 and whose sum is +1 (the coefficient of x).

The numbers that satisfy this condition are +3 and -2.

Therefore, we can rewrite the equation as (x + 3)(x - 2) = 0.

Setting each factor equal to zero, we have x + 3 = 0 or x - 2 = 0.

Solving these equations gives x = -3 or x = 2.

Option 2: Quadratic Formula

The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b² - 4ac)) / (2a).

In our equation, a = 1, b = 1, and c = -6.

Substituting these values into the formula, we have:

x = (-1 ± √(1² - 4(1)(-6))) / (2(1)).

Simplifying the expression inside the square root, we get:

x = (-1 ± √(1 + 24)) / 2.

x = (-1 ± √25) / 2.

x = (-1 ± 5) / 2.

This gives us two solutions: x = (-1 + 5) / 2 = 4 / 2 = 2, and x = (-1 - 5) / 2 = -6 / 2 = -3.

For similar question on equation.

https://brainly.com/question/30645878  

#SPJ8