If the sum of the zeroes of the polynomial 5x2-px+7 is 9, the find the value of 'p'.​

Answer:

Part A:

Using the Factor Theorem, we know that f(x) can be written as:

f(x) = a(x - 6)(x + 1)(x + 3)

where a is a constant that we need to determine.

To find the value of a, we can use one of the given zeros of f(x), for example, x = 6. When x = 6, we know that f(x) = 0, so we can substitute these values into the equation above:

0 = a(6 - 6)(6 + 1)(6 + 3)

Simplifying, we get:

0 = 189a

Therefore, a = 0.

So, the polynomial f(x) is:

f(x) = 0(x - 6)(x + 1)(x + 3)

Simplifying, we get:

f(x) = 0

Part B:

To divide f(x) by (x² - x - 2), we can use long division:

0

___________

x² - x - 2 | 0x³ + 0x² + 0x + 0

- (0x³ - 0x² - 0x)

_______________

0x² + 0x

- (0x² - 0x - 2)

_______________

2x + 2

Therefore, the rational function g(x) in simplest factored form is:

g(x) = (2x + 2)/(x² - x - 2)

To find the vertical asymptotes, we need to find the roots of the denominator:

x² - x - 2 = 0

(x - 2)(x + 1) = 0

Therefore, the vertical asymptotes are x = 2 and x = -1.

To find the horizontal asymptote, we can use the fact that the degree of the numerator is less than the degree of the denominator. Therefore, the horizontal asymptote is y = 0.

Part C:

The function g(x) has two vertical asymptotes at x = 2 and x = -1.

To check for any holes, we can simplify the function by factoring the numerator:

g(x) = 2(x + 1)/(x - 2)(x + 1)

Since we factored the numerator and denominator of g(x), we can see that there is a hole in the graph at x = -1. This is because the factor (x + 1) cancels out in both the numerator and denominator, leaving a hole at that point.

To find the x-intercepts, we need to solve for when the numerator is equal to zero:

2x + 2 = 0

x = -1

Therefore, the x-intercept is (-1, 0).

To find the y-intercept, we can substitute x = 0 into the equation for g(x):

g(0) = 2(0 + 1)/(0 - 2)(0 + 1)

g(0) = -1

Therefore, the y-intercept is (0, -1).

To sketch the graph of g(x), we can use the information we have gathered so far. The graph has two vertical asymptotes at x = 2 and x = -1, a hole at x = -1, an x-intercept at (-1, 0), and a y-intercept at (0, -1). The horizontal asymptote is y = 0.

We can also use the factored form of g(x) to determine the end behavior of the graph. As x approaches positive or negative infinity, the function approaches zero. Therefore, the graph approaches the x-axis on either side of the vertical asymptotes.

Putting all of this information together, we can sketch the graph of g(x) as follows:

[insert graph of g(x) here]

Answer: 61 degrees

Step-by-step explanation:

A triangle has an internal angle sum of 180. So subtract 67 and 52, and you get x which is 61 degrees.

Answer:

Step-by-step explanation:

that it is 30 degrees above and its a triangle

The total amount the man had = 52,200 rupees. Out of this, he gave 21,750 rupees to his son, 13,050 rupees to his daughter, and 17,400 rupees to his wife , the total amount given away by the man = 21,750 + 13,050 + 17,400 = 52,200 rupees.

A man gave 5/12 of his money to his son, 3/7 of the remainder to his daughter, and the remaining to his wife. If his wife gets Rs. 8,700, what is the total amount?

The given problem can be solved using the concept of ratios and fractions. Let us solve the problem step-by-step.Assume the man had x rupees with him.The man gave 5/12 of his money to his son.

The remaining amount left with the man = x - 5x/12= (12x/12) - (5x/12) = (7x/12)The man gave 3/7 of the remainder to his daughter.'

Amount left with the man after giving it to his son = (7x/12)The amount given to the daughter = (3/7) x (7x/12)= (3x/4)The remaining amount left with the man = (7x/12) - (3x/4)= (7x/12) - (9x/12) = - (2x/12) = - (x/6) (As the man has given more money than what he had with him).

Therefore, the daughter's amount is (3x/4) and the remaining amount left with the man is (x/6).The man gave all the remaining amount to his wife.

Therefore, the amount given to the wife is (x/6) = 8700Let us find the value of x.x/6 = 8700 x = 6 x 8700 = 52,200

Therefore, the man had 52,200 rupees with him.He gave 5/12 of his money to his son. Therefore, the amount given to his son is (5/12) x 52,200 = 21,750 rupees.

The remaining amount left with the man = (7/12) x 52,200 = 30,450 rupees.He gave 3/7 of the remainder to his daughter. Therefore, the amount given to his daughter is (3/7) x 30,450 = 13,050 rupees.

The amount left with the man = (4/7) x 30,450 = 17,400 rupees.The man gave 17,400 rupees to his wife.
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Answer:

Question 5: <ACB=<DFE

Question 6:AB=DE

Question 1: SSS (side side side)

Question 2: SAS (side angle side)

Step-by-step explanation:

All of these questions are talking about congruency theorems.  There are many theorems including SAS, SSS, AAS, etc, that help with congruency.

SAS=side angle side

SSS = side side side

AAS = angle angle side

HL (right triangles only)= hypotenuse and a leg are congruent

ASA=angle side angle

Question 5:

In this case, they are asking for AAS, which stands for Angle-Angle-Side.  We are already given 1 angle, and 1 side, so we need another angle.  The answer to this would be to show that <ACB and <DFE are congruent.

Question 6:

They are asking for the same thing (triangle congruency), but by using SAS, which is Side-Angle-Side.  We are given 1 angle, 1 side, so we need another side.  The answer to this would be AB=DE.

Question 1:

We are given 3 sides, which means that the congruence theorem would be SSS (Side-Side-Side).

Question 2:

We are given a side, an angle, and another side.  This means that the congruence thorem would be SAS (Side-Angle-Side).

Hope this clarifies!  Let me know if you have more questions :)

Answer:

x² - 4x + 4 = (x - 2)²

The vertex is (2, 0). It follows that 2 is a double root (a root of multiplicity 2).

Answer:

Two angles are supplementary if the sum of their measures is 180°. For example, two angles whose measures are 35° and 145° are supplementary angles.

Two angles are complementary if the sum of their measures is 90°. For example, two angles whose measures are 35° and 55° are complementary angles.

Answer:

The expression 20!/1! is not directly related to the binomial distribution.

The expression 20!/1! represents the number of ways to arrange 20 distinct objects in a specific order, where each object is used exactly once. This is known as a permutation, and the number of permutations of n objects is given by n!.

On the other hand, the binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success. The probability of getting k successes in n trials, each with probability p of success, is given by the binomial probability mass function:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where (n choose k) represents the number of ways to choose k items from a set of n items, and is given by the formula:

(n choose k) = n!/k!(n-k)!

So, while the expression 20!/1! is not directly related to the binomial distribution, the binomial distribution does involve calculating combinations (i.e., choosing k items from a set of n items), which are related to permutations.

Answer:

5069.1875

Step-by-step explanation:

Area is found by using Length x Width, for this the length is 91.75 and width 55.25. Thus the answer is 91.75x55.25=5069.1875

Answer:

Step-by-step explanation:

√25=5

side of the smaller square enlarged by 5 times.

To find the missing value in an arithmetic sequence, there are a few methods that can be used. Here are the ways to find the missing value in the table:

1. Use the common difference: In an arithmetic sequence, the difference between consecutive terms is constant, known as the common difference.

To find the missing value, you can calculate the common difference by subtracting any two consecutive terms given in the table. Once the common difference is determined, you can add it to the previous term or subtract it from the following term to find the missing value.

2. Use the arithmetic sequence formula: The arithmetic sequence formula allows you to find any term in the sequence given the first term (a1), the common difference (d), and the position of the term (n). If you know the first term and the common difference, you can use the formula an = a1 + (n-1)d to calculate the missing value.

3. Use the pattern: Sometimes, there may be a noticeable pattern in the given terms of the arithmetic sequence. By observing the sequence and identifying the pattern, you may be able to determine the missing value without relying on explicit calculations.

It is important to note that in order to accurately find the missing value, at least two consecutive terms are required. With only one term given, it is not possible to determine the missing value as there is no information about the common difference or the pattern.

By utilizing the common difference, the arithmetic sequence formula, or by recognizing patterns, you can find the missing value in an arithmetic sequence table.

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Use the percent formula, A =PB: A is P percent of B, 22% of approximately 170 is equal to 37.4.

To find the number, let's use the percent formula:

A = P * B

where A is the value we are trying to find, P is the percentage (in decimal form), and B is the total.

In this case, we are given that 22% of a certain number is equal to 37.4. So we have:

A = 0.22 * B

We want to solve for B, so we can rearrange the formula:

B = A / 0.22

Substituting A = 37.4 into the equation:

B = 37.4 / 0.22

Calculating this:

B ≈ 170

Therefore, 22% of approximately 170 is equal to 37.4.

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The number of years N(r) since two independently evolving languages split off are as follows;

a. N(0.9) = 526.8.

b. N(0.4) = 4581.5.

c. N(0.3) = 6019.9.

d. 2554.1 years have elapsed since the split.

e. r = 0.9.

Based on the information provided above, the number of years N(r) since two independently evolving languages split off from a common ancestral language can be approximated by the following equation:

N(r) = -5000Inr

Part a.

When r = 0.9, we have:

N(0.9) = -5000In(0.9)

N(0.9) = 526.8 years.

Part b.

When r = 0.4, we have:

N(0.4) = -5000In(0.4)

N(0.4) = 4581.5 years.

Part c.

When r = 0.3, we have:

N(0.3) = -5000In(0.3)

N(0.3) = 6019.9 years.

Part d.

When r = 60% or 0.6, we have:

N(0.6) = -5000In(0.6)

N(0.6) = 2554.1 years.

Part e.

When N(r) = 500 years, we have:

500 = -5000lnr

-500/5000 = lnr

-0.1 = lnr

[tex]r = e^{-0.1}[/tex]

r = 0.9.

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Answer:

y = 0.30x + 0.70

Step-by-step explanation:

Assuming that the options are

A.

y = 1.90x + 0.40

B.

y=0.30x +0.70

C.

y= 0.90x + 0.30

D.

y= 1.30x + 1.70

(these might be in a random order for different people)

the answer would be B. y=0.30x +0.70

The bank reconciliation reveals various errors and discrepancies between ABC Company's records and the bank statement, including missing deposits, incorrect check charges, outstanding checks, unrecorded interest proceeds, fees, NSF charges, and recording errors.

Upon analyzing the bank reconciliation for ABC Company, several discrepancies between the company's records and the bank statement are identified:

A deposit of Br. 410.90 made after banking hours does not appear on the bank statement. This indicates that the deposit was not processed by the bank before the statement was generated.

A check drawn for Br. 79 was charged by the bank as Br. 973. This suggests an error by the bank in processing the check, resulting in an incorrect charge to ABC Company.

Outstanding checks are checks issued in July but have not yet been paid by the bank. The checks include check numbers 801, 888, 890, and 891, with respective amounts of Br. 100.00, Br. 10.25, Br. 294.50, and Br. 205.00.

A check written for Br. 210 was charged by the bank as Br. 120, indicating an error in the bank's recording.

The proceeds from the collection of an interest-bearing note receivable from David, with a face amount of Br. 500, are not reflected in the bank statement.

A Br. 24.75 interest earned on the average account balance during July is included in the bank statement.

A check for Br. 10, which was recorded in the check register as Br. 100, was returned with the statement. This discrepancy could be due to an error in recording the check amount.

A Br. 5.00 fee was charged by the bank for handling the collection of a note receivable.

A Br. 50.25 check from customer John, deposited by ABC Company, was charged by the bank as Non-Sufficient Funds (NSF), indicating that the customer's check bounced.

A Br. 12.70 service charge was imposed by the bank for the month of July.

Check number 875 was issued on July 20 for Br. 85 but was erroneously recorded in the cash payment journal as Br. 58 for the payment of telephone expenses.

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The x-coordinate represents the cosine of the angle, and the y-coordinate represents the sine of the angle. Coordinates of point B: (cos((1/8) * 2π), sin((1/8) *.

a) To determine the angles of rotation in standard position from point A to each of the points B through H in radians, we need to understand the concept of radian measure. In a unit circle, the circumference is equal to 2π (approximately 6.28318) units.

Since the circumference is divided into 8 arcs of equal length, each arc will have a length of (2π / 8) units, which simplifies to (π / 4) units.

Starting with point B, we can measure the angles in radians as follows:

Angle from A to B: (1/8) * 2π = (1/8) * π radians

Angle from A to C: (2/8) * 2π = (2/8) * π radians = (1/4) * π radians

Angle from A to D: (3/8) * 2π = (3/8) * π radians

Angle from A to E: (4/8) * 2π = (4/8) * π radians = (1/2) * π radians

Angle from A to F: (5/8) * 2π = (5/8) * π radians

Angle from A to G: (6/8) * 2π = (6/8) * π radians = (3/4) * π radians

Angle from A to H: (7/8) * 2π = (7/8) * π radians

Angle from A back to A: 2π radians

b) The arc length from point A to each of the other points on the circle can be calculated by multiplying the angle (in radians) by the radius of the circle, which is 1 in a unit circle.

Arc length from A to B: (1/8) * 2π * 1 = (1/8) * π

Arc length from A to C: (1/4) * 2π * 1 = (1/4) * π

Arc length from A to D: (3/8) * 2π * 1 = (3/8) * π

Arc length from A to E: (1/2) * 2π * 1 = (1/2) * π

Arc length from A to F: (5/8) * 2π * 1 = (5/8) * π

Arc length from A to G: (3/4) * 2π * 1 = (3/4) * π

Arc length from A to H: (7/8) * 2π * 1 = (7/8) * π

Arc length from A back to A: 2π * 1 = 2π

Rounded to three decimal places:

Arc length from A to B: 0.393

Arc length from A to C: 0.785

Arc length from A to D: 1.178

Arc length from A to E: 1.571

Arc length from A to F: 1.963

Arc length from A to G: 2.356

Arc length from A to H: 2.749

Arc length from A back to A: 6.283

c) The exact coordinates of each point can be determined using the unit circle and the trigonometric functions cosine and sine. In a unit circle, the x-coordinate represents the cosine of the angle, and the y-coordinate represents the sine of the angle.

Coordinates of point B: (cos((1/8) * 2π), sin((1/8) *

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Answer:

Expert-Verified Answer

= 166.59 cm³ (approx.)

Step-by-step explanation:

The volume of the hemisphere is derived by Archimedes. The volume of a hemisphere = (2/3)πr3 cubic units. Where π is a constant whose value is equal to 3.14 approximately.

Answer:

166.5 [tex]cm^{3}[/tex]

Step-by-step explanation:

The volume of a sphere is 4/3 [tex]\pi r^{3}[/tex].  A hemisphere is half of a circle.

V = 1/2(4/3)[tex]\pi[/tex][tex]4.3^{2}[/tex]

v = 2/3 [tex]\pi[/tex] (79.507)                                

v = 166.519071406

Helping in the name of Jesus.                    

The four strategies that can be effective in raising awareness, promoting change, and addressing the issue are mentioned below.

Awareness Campaigns and Education: Communities can organize awareness campaigns to educate the public about gender-based violence, its impact, and the importance of preventing and addressing it. This can include public rallies, marches, workshops, and community dialogues. Education initiatives can focus on promoting gender equality, challenging harmful gender norms and stereotypes, and fostering empathy and respect.

Support and Empower Survivors: Creating support systems for survivors of gender-based violence is crucial. Communities can establish safe spaces, helplines, or support groups where survivors can share their experiences, access resources, and receive emotional and practical support. Empowering survivors through counseling, legal aid, and vocational training can help them regain control of their lives and raise awareness about the issue.

Advocacy for Policy Change: Community members can engage in advocacy efforts to influence policy changes related to gender-based violence. This can involve lobbying for stricter laws, improved enforcement, and increased funding for support services. Collaborating with local NGOs, women's rights organizations, and other stakeholders can strengthen advocacy efforts and amplify voices.

Engaging Men and Boys: Engaging men and boys as allies in the fight against gender-based violence is essential. Community initiatives can promote positive masculinity, challenge harmful attitudes, and encourage men to actively participate in prevention efforts. Engaging men as role models, mentors, and advocates can help shift social norms and contribute to a more inclusive and violence-free community.

These strategies can be interconnected and reinforce each other. Building a strong community network and fostering partnerships with relevant organizations and stakeholders will enhance the impact of these efforts. It is important to tailor strategies to the specific needs and cultural context of the community, ensuring that they are inclusive, respectful, and sustainable in the long term.

The need for engaging in strategies to protest gender-based violence in communities arises from several important reasons: Human Rights: Gender-based violence is a violation of human rights. Every individual has the right to live a life free from violence, discrimination, and harm. By addressing gender-based violence, communities can uphold the principles of human rights and work towards creating a society where everyone can thrive with dignity and equality.

Safety and Well-being: Gender-based violence has severe physical, emotional, and psychological consequences for survivors. It creates an environment of fear, insecurity, and trauma. By protesting gender-based violence, communities aim to create safer environments where individuals can live without the constant threat of violence and can access the support they need for healing and recovery.

Social Justice and Equality: Gender-based violence is rooted in gender inequality and harmful social norms. It perpetuates power imbalances, discrimination, and the marginalization of individuals based on their gender. Protesting gender-based violence is essential for challenging these oppressive structures, promoting gender equality, and working towards a more just and inclusive society.

Prevention and Intervention: By engaging in strategies to protest gender-based violence, communities aim to prevent future acts of violence and intervene in existing cases. Awareness campaigns, education, and support services play a crucial role in creating a culture that rejects violence and promotes respectful relationships.

Addressing gender-based violence is not only a moral imperative but also essential for building healthy, inclusive communities. By raising awareness, supporting survivors, advocating for policy changes, and engaging men and boys as allies, communities can play a vital role in eradicating gender-based violence and creating a more equitable and just society for all.

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The equation of a line parallel to 2x - 5y = 10 with a y-intercept of (0,1) is 2x - 5y = -5 in standard form.

Equation of a line passing through (2,6) and (2,4) in slope-intercept form:

To find the equation of a line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b).

Given points:

Point 1: (2,6)

Point 2: (2,4)

Since the x-coordinate is the same for both points, we can conclude that the line is vertical, and its equation will be in the form x = c, where c is the x-coordinate of any point on the line.

In this case, x = 2 is the equation of the line passing through the points (2,6) and (2,4).

Equation of a line parallel to 2x - 5y = 10 with a y-intercept of (0,1) in standard form:

To determine the equation of a line parallel to a given line, we need to keep the same slope. The given line has the equation 2x - 5y = 10, which can be rearranged to the slope-intercept form y = (2/5)x - 2.

Since the parallel line has the same slope, the equation will be in the form y = (2/5)x + b, where b is the y-intercept.

Given y-intercept: (0,1)

Substituting the values into the equation, we have y = (2/5)x + 1.

To convert the equation into standard form (Ax + By = C), we multiply through by 5 to eliminate the fraction:

5y = 2x + 5

Rearranging the terms:

2x - 5y = -5

Therefore, the equation of a line parallel to 2x - 5y = 10 with a y-intercept of (0,1) is 2x - 5y = -5 in standard form.

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Answer:

y = -4/3x + 13/3, A

Step-by-step explanation:

To find the line that is perpendicular to another line, the intersection of both lines must be at 90 degrees. Both slopes when multiplied should equate to -1. Since you have a slope of 3/4, to get the product of -1, you must multiply by -4/3 which would be the slope perpendicular to the given line. Now, we can use the point-slope formula to find the equation of the line. We can treat (-5,11) as (x₁,y₁) and plug it into the point-slope formula.

y-y₁=m(x-x₁) ; y-11=-4/3(x-(-5))

y = -4/3x - 20/3 + 11

y = -4/3x + 13/3, A

Answer: A ( -4, -7)Step-by-step explanation:if you translate -1, three units to the left u get -4 and then when u go nine units down

Step-by-step explanation:

Answer:

OK, Here is your answer

Step-by-step explanation:

Let's assume the capacity of the drum be C litres.Since the drum is initially 3/4 full, the amount of water in it is 3/4 × C = (3/4)C liters.When 9 liters of water are drawn from the drum, the remaining amount of water is (3/4)C - 9 liters.Since the drum is now half full, the amount of water remaining in it is (1/2)C liters.Therefore, we can write the equation: (3/4)C - 9 = (1/2)CTo solve for C, let's first get rid of the fractions by multiplying both sides by 4.(3/4)C - 9 = (1/2)C → 3C - 36 = 2C → C = 36Therefore, the capacity of the drum is 36 liters.Hence, the drum holds 3/4 × 36 = 27 liters of water initially and after 9 liters of water are drawn, the remaining amount of water in it is 27 - 9 = 18 liters.

Answer:

18 Lieters.

Step-by-step explanation:

found the answer in his answer. ↑↑↑↑

Step-by-step explanation:

The bisection method is a root-finding algorithm that repeatedly bisects an interval and then selects a subinterval in which a root must lie for further processing. To apply the bisection method to the equation x^3 - x - 9 = 0, you need to find two initial values a and b such that f(a) and f(b) have opposite signs. This means that there is at least one root of the equation in the interval [a, b].

Let’s take a = 2 and b = 3 as our initial interval. We can see that f(2) = 2^3 - 2 - 9 = -1 and f(3) = 3^3 - 3 - 9 = 18, so f(a) and f(b) have opposite signs.

Now we can apply the bisection method as follows:

Calculate the midpoint c = (a + b)/2 = (2 + 3)/2 = 2.5.

Evaluate f© = 2.5^3 - 2.5 - 9 ≈ 5.625.

Since f© > 0 and f(a) < 0, there must be a root in the interval [a, c]. So we set b = c and repeat the process.

Calculate the new midpoint c = (a + b)/2 = (2 + 2.5)/2 = 2.25.

Evaluate f© ≈ 1.765625.

Since f© > 0 and f(a) < 0, there must be a root in the interval [a, c]. So we set b = c and repeat the process.

We can continue this process until we reach the desired level of accuracy.

The values of the functions (u + w)(5) and (u - w)(5) are 18 and -32 respectively.

Given that :

1.)

(u + w)(5) can be calculated thus:

(u + w) = -2x + 3 + 5x = 3x + 3

substitute x = 5 into the equation

Hence,

(u + w)(5) = 3(5) + 3 = 15 + 3 = 18

2.)

(u - w)(5) can be calculated thus:

(u - w) = -2x + 3 - 5x = -7x + 3

substitute x = 5 into the equation

Hence,

(u - w)(5) = -7(5) + 3 = -35 + 3 = -32

Therefore, the values of (u + w)(5) and (u - w)(5) are 18 and -32 respectively.

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Answer:

There are 72 ways to order AI meals.

Step-by-step explanation:

1. Calculate the number of ways Al could order his lunch: 2 x 3 = 6 ways.

2. Calculate the number of ways Al could order his dinner if he orders a different appetizer than he did for lunch: 1 x 2 x 4 = 8 ways.

3. Calculate the number of ways Al could order his dinner if he orders the same appetizer as he did for lunch: 1 x 1 x 4 = 4 ways.

4. Calculate the total number of ways Al could order his meals: 6 x (8 + 4) = 72 ways.

Answer:

[tex]y=\frac{1}{5}x-3[/tex]

Step-by-step explanation:

[tex]y-y_1=m(x-x_1)\\y-(-4)=\frac{1}{5}(x-(-5))\\y+4=\frac{1}{5}(x+5)\\y+4=\frac{1}{5}x+1\\y=\frac{1}{5}x-3[/tex]

Plot that into Desmos and you got your graph :)

The answer is:

below

Work/explanation:

First, we need to find the equation of the line. We're given that:

its slope = 1/5

a point it goes through = (−5,−4)

Plug the data into point-slope

[tex]\rm{y-y_1=m(x-x_1)}[/tex]

where m = slope and the point is (x₁, y₁).

Plug in:

[tex]\rm{y-(-4)=\dfrac{1}{5}(x-(-5)}[/tex]

Simplify fully

[tex]\rm{y+4=\dfrac{1}{5}(x+5)}[/tex]

Now let's graph it. I'll use Desmos - the graphing calculator.

Based on the information, it should be noted that the value of 3x + 2y when x = 4 and y = 7, 3x + 2y equals 26.

To find the value of 3x + 2y when x = 4 and y = 7, we substitute these values into the expression and perform the calculations.

3x + 2y = 3(4) + 2(7)

= 12 + 14

= 26

Therefore, when x = 4 and y = 7, 3x + 2y equals 26.

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What does 3x+2y equal if x = 4 y = 7

The result matches the given after-tax total, confirming that the pre-tax subtotal is indeed $1,000.00.To calculate the pre-tax subtotal, we need to reverse-engineer the calculation based on the given after-tax total and tax rate.

Let's denote the pre-tax subtotal as "x." The tax rate is 7%, which can be written as 0.07 in decimal form. The after-tax total is $1,070.00.

We know that the tax amount is calculated by multiplying the tax rate by the pre-tax subtotal. So, the tax amount can be expressed as 0.07x.

The after-tax total is obtained by adding the pre-tax subtotal and the tax amount:

After-tax total = Pre-tax subtotal + Tax amount

$1,070.00 = x + 0.07x

To solve for x, we can combine like terms:

$1,070.00 = 1.07x

Now, let's isolate x by dividing both sides of the equation by 1.07:

$1,070.00 / 1.07 = x

Simplifying the calculation:

$1,000.00 = x

Therefore, the pre-tax subtotal is $1,000.00.

To verify the result, we can calculate the tax amount by multiplying the pre-tax subtotal by the tax rate:

Tax amount = 0.07 * $1,000.00 = $70.00

Adding the tax amount to the pre-tax subtotal:

$1,000.00 + $70.00 = $1,070.00

The result matches the given after-tax total, confirming that the pre-tax subtotal is indeed $1,000.00.

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Answer:

no

Step-by-step explanation:

if the room is a square, then all sides are equally long (19 in).

in any case, Pythagoras applies to calculate the length of the diagonal :

(side1)² + (side2)² = diagonal²

if both sides are equally long, that would mean

19² + 19² = 20.62²

361 + 361 = 425.1844

722 = 425.1844

that is not true, so the assumption that the room is a square is not true.