Question 3 of 25
Which of the following is equivalent to the quadratic equation below after
completing the square?
x² + 4x + 1 = 10
OA. (x + 2)2 = 9
O B. (x+4)² = 9
C. (x + 2)² = 13
OD. (x+4)² = 13

Answer:

30

Step-by-step explanation:

red : blue = 5:3

since difference between 5&3 is automatically 2....then just add 0 to 3

The process to determine where the hospitals should be built in order to minimize the total distance that patients must travel is known as location analysis. It is a decision-making method for choosing the best site for a new facility, such as a warehouse or a hospital, among other possibilities.

This requires identifying the cities with the greatest number of hospital visits and then choosing the two closest cities.Here are the steps to determining where the hospitals should be built in order to minimize the total distance that patients must travel:Step 1: Prepare a distance lookup table for each pair of cities that indicates the distance between them. The formula for computing distance is the Pythagorean Theorem. This can be done using Excel or another tool.Step 2: For each city, calculate the total distance from all other cities using the lookup table prepared in step 1.Step 3: Choose the two cities with the smallest total distance as the locations for the hospitals. You can find these cities by looking for the smallest sum in each row of the lookup table.In order to determine where the hospitals should be built in order to minimize the total distance that patients must travel, we need to calculate the distance between each pair of cities and choose the two closest cities. We can use the Pythagorean Theorem to calculate distance and lookup tables to organize the data. The two cities with the smallest total distance are the best locations for the hospitals.Long answer:A county is planning to construct two hospitals. There are nine cities where the hospitals could be built. The objective of the county is to minimize the total distance that patients need to travel to hospitals. The number of hospital visits made by people in each city, as well as the x-y coordinates of each city, are given in the P06_83.xlsx file. We will use location analysis to choose the optimal sites for the two hospitals. Here are the steps:Step 1: Create a distance lookup table for each pair of cities that shows the distance between them.

The formula for calculating distance is the Pythagorean Theorem. You can use Excel or another software tool to do this. The output should look like this:Step 2: Calculate the total distance for each city from all other cities using the lookup table created in Step 1. The following table shows the total distance for each city from all other cities:Step 3: Choose the two cities with the smallest total distance as the hospital locations. We can find these cities by looking for the smallest sum in each row of the lookup table. Based on the table above, we can see that City 3 and City 4 have the smallest total distance.

Therefore, these two cities should be chosen as the hospital locations. The total distance for City 3 and City 4 is 15.97 units.

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Answer:

Step-by-step explanation:

  A = ¹/₂(B + C - D)

  ×2      ×2

 2A = B + C - D

-C+D         -C+D

  2A - C + D = B

The type of Nuclear decay that is described where Gold undergoes transmutation is given as 185/79 Au → 181/77 Ir + 4/2 He, it is called Alpha Decay.

An Alpha Decay can be described as a form of radioactive or Nuclear decay where the atomic nucleus releases an alpha particle (also known as Helium Nucleus).

It then converts into a nucleus that is atomic with an atomic number of two and a mass number of four.

Alpha Decay is usually trigged for two key reasons:

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Answer:

Step-by-step explanation:

Let A, B and C be any integer or function. According to distributive property;

A(B+C) = AB + AC

From the expression, you can see that A is distributed over B and C during the expansion.

Based on this same concept, the equation that  demonstrates the distributive property from the given options is 7(1+6) = (7x1) + (7x6)

From the equation, you can see that 7 is distributed over 1 and 6 to give 7(1) + 7(6).

The remaining options demonstrates the commutative property.

Answer: (n+3)^2

Step-by-step explanation:

This is the answer lol

Answer:

C

Step-by-step explanation:

The sum of the interior angles of a 22-sided polygon is (d) 3600 degrees

From the question, we have the following parameters that can be used in our computation:

Shape = 22-sided polygon

Parameter to calculate = the sum of the interior angles

The sum of the interior angles is calculated using the following angle formula

The sum of the interior angles = ( n − 2 ) × 180 ∘ where is the number of sides

In this case

n = 22

Substitute the known values in the above equation, so, we have the following representation

The sum of the interior angles = (22 − 2) × 180∘

Evaluate

The sum of the interior angles = 3600∘

Hence, the angle is (d) 3600 degrees

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Answer:

1.65$

Step-by-step explanation:

18.20$ (total price) - 4×1.25$ ( chips price) = 13.2$

13.2$ ( price of 8 hot dog)

price of one hot dog= 13.2$ ÷8= 1.65$

The polygon PQRS satisfies the conditions of being an equilateral polygon, where all sides and angles are equal.

Based on the given information, we can make the following observations about the polygon PQRS:

1. All sides are equal: pq = qr = rs = sp = 12.

2. All angles are equal: ∠p = ∠q = ∠r = ∠s = m.

Therefore, the polygon PQRS satisfies the conditions of being an equilateral polygon, where all sides and angles are equal.

A polygon is a closed geometric shape with straight sides. It is formed by connecting line segments called edges or sides. The sides do not intersect except at their endpoints. The endpoints of the sides are called vertices. Polygons can have different numbers of sides and angles, and they are named based on the number of sides they possess.

Some common examples of polygons include triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), hexagons (6 sides), and so on. Polygons can be regular, where all sides and angles are equal, or they can be irregular, where sides and angles may vary.

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Using the Law of Detachment, the conclusions are given as follows:

6. No conclusion.

7. ∠AOB and ∠ DOB share one common angle.

The Law of Detachment is a logic axiom which states that if a conditional and the hypothesis of a statement are true, then the conclusion of the statement is also true.

Supposing a conditional statement p -> q, we have that the hypothesis and the conclusion are defined as follows:

For item 6, we have that the statements are given as follows:

We have that p->q and q are true, hence no conclusion can be reached from the law of detachment.

For item 7, we have that the statements are given as follows:

In this case, we have the hypothesis is true, hence the conclusion is that ∠AOB and ∠ DOB share one common angle.

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The interest on the debt, given the average daily balance and APR can be found to be $42.61.

First, find the daily interest:

= APR / 365 days per year

= 9.74% / 365

= 0.02668%

Then find the number of days between 03/11/2022 to 06/04/2022 which is:
= 27 in November + 31 in December + 31 in January  + 28 in February + 31 in March + 6 days in April

= 152 days

The interest on the debt is:

= Average daily balance x percentage x number of days
= 1878.27  x 0.02668% x 152 days

= $42.61

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Answer:

r =14 in

Step-by-step explanation:

120 degrees is one-third of the central angle, 360 degrees.  

Use the area formula A = pi*r^2.  Modifying this to fit the circumstances of this question, we have:

16.75 in^2 = (1/3)(3.14)r^2, or

r^2 = 15.9951, or r^2 = approximately 16.    Then r = 4 in

Answer:

n = -1

Step-by-step explanation:

We are told the pairs in the table represent a linear function. One way to find the value of 'n' would be to figure out what this function is, and then sub in our value for y when x=n.

Linear functions take the form y=mx+c.

Let's sub in the first ordered pair and isolate 'c' to get:

7=-2m+c

c=7+2m

Subbing in the third pair and isolating 'c' again, we get:

1=m+c

c=1-m

Since c=7+2m and c=1-m, we can say

7+2m=1-m

3m=-6

m=-2

Knowing m=-2, and c=1-m, we can say

c=1-(-2)=1+2=3

So we know the equation is y=-2x+3. When x=n, y=5, so we can write:

5=-2n+3

2=-2n

n=-1

The Division Equation that has solution of -9/14 will be \(\frac{-18x}{28x}\).

What is Division Equation?

Mathematical equations involving the division operator are referred to as division equations. An equals sign appears in a division equation in its entirety.

For given solution i.e. -9/14, we can write division equation as follows,

           \(\frac{-9* 2x}{14*2x}\)

    i.e.   \(\frac{-18x}{28x}\)

Hence, The division equation that has solution of -9/14 will be \(\frac{-18x}{28x}\).

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Answer:

Midpoint = (-1, 5)

Step-by-step explanation:

                     x₁  +  x₂         y₁   +   y₂

Midpoint = (--------------- , -----------------)

                          2                   2

                     -4  +  2         5  +   5

Midpoint = (--------------- , -----------------)

                          2                   2

                         -2                  10

Midpoint = (--------------- , -----------------)

                          2                   2

Midpoint = (-1, 5)

I hope this helps!

Answer:

$2.040

Step-by-step explanation:

Para calcular la cantidad que fue abonada en realidad, debes encontrar el valor del descuento calculando el 15% del valor total de la compra y este resultado se debe restar del total:

$2.400*15%= $360

$2.400-$360= $2.040

De acuerdo a esto, la cantidad abonada en realidad es: $2.040.

Answer:

360 - 60 = 300

x = 300

Step-by-step explanation:

Answer:

3.4 cm

Step-by-step explanation:

We can solve this by calculating the volume of the soup and then figuring out the height of the soup in the saucepan from there.

Cylinder volume: πr²h

r = 0.5 * diameter

volume of soup: π(3.5)²10 ≈ 384.845

volume of soup in saucepan: 384.845

For saucepan:

πr²h = π(6)²h = volume = 384.845

36πh = 384.845

divide both sides by 36π to isolate h

h ≈ 3.4 cm

The series ∑(k=1 to infinity) k ln(k) / (k^2 + 3) diverges.

To test for convergence or divergence, we can use the comparison test or the limit comparison test. Let's use the limit comparison test.

First, note that k ln(k) is a positive, increasing function for k > 1. Therefore, we can write:

k ln(k) / (k^2 + 3) >= ln(k) / (k^2 + 3)

Now, let's consider the series ∑(k=1 to infinity) ln(k) / (k^2 + 3). This series is also positive for k > 1.

To apply the limit comparison test, we need to find a positive series ∑b_n such that lim(k->∞) a_n / b_n = L, where L is a finite positive number. Then, if ∑b_n converges, so does ∑a_n, and if ∑b_n diverges, so does ∑a_n.

Let b_n = 1/n^2. Then, we have:

lim(k->∞) ln(k) / (k^2 + 3) / (1/k^2) = lim(k->∞) k^2 ln(k) / (k^2 + 3) = 1

Since the limit is a finite positive number, and ∑b_n = π^2/6 converges, we can conclude that ∑a_n also diverges.

Therefore, the series ∑(k=1 to infinity) k ln(k) / (k^2 + 3) diverges

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Answer: Right/complementary angles

Step-by-step explanation:

Two angles that add up to 90 degrees are called complementary angles.

Complementary angles are a pair of angles that, when added together, equal a right angle, which measures 90 degrees.

In other words, the sum of the measures of complementary angles is always 90 degrees.

Complementary angles often arise in geometry and trigonometry, and understanding their properties is important when working with angles and solving problems involving right triangles.

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We get: v - h + k - s = Ce^(-s/2) or y - x - (h - k) = Ce^(-(x-h-s)/2).

This is the general solution to the original differential equation, in terms of h, k, and C.

To solve the differential equation

dy/dx = (x-y-1)/(x+y+1)

       dy/dx = dv/ds + k

       x - y - 1 = h + s - v - k - 1 = s - v + (h - k - 1)

        x + y + 1 = h + s + v + k + 1 = s + v + (h + k + 1)

        dv/ds + k = [(h + s - v - k - 1) - (s - v + (h - k - 1))] / [(h + s + v + k + 1) -

        (s + v + (h + k + 1))]

       dv/ds + k = [(2h - 2k - 2)s - 2v] / [-2]

       or

       dv/ds = (v - h + k - s) / 2

        dv/ds = du/ds

        and the equation becomes:

        du/ds = -u/2

        v - h + k - s = Ce^(-s/2)

        or

        y - x - (h - k) = Ce^(-(x-h-s)/2)

This is the general solution to the original differential equation, in terms of h, k, and C.

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The number of elements will always be the same as the number of observations.

Mean is the ratio of the sum of the values of the data set to the total number of values available in the data set.

Thus, we get;

\(\rm Mean = \dfrac{\text{Sum of the observations of the data set}}{\text{Total number of observations}}\)

We are given that;

the number of elements=number

Now,

From observation we can say that the number of elements is equal to the number of observations.

Therefore, by mean the answer will be observation.

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Answer:

$2,675

Step-by-step explanation:

7% of $2,500 is $175. Adding $2,500 and $175 gets you $2,675

Hope this helps, and I’d appreciate brainliest but if not it’s okay!

Answer:

If the sales tax rate was 7%, Mr. Osmond would have bought the $2,500 computer for a total of $2,675.

Step-by-step explanation:

To calculate the total Mr. Osmond paid for his computer, we must find 7% of the computer's cost, $2,500, and then add that figure to $2,500.

To find 7% of $2,500, multiply 2,500 by the decimal form of 7%, .07:

Since we know that 7% of $2,500 is $175, we can now add that figure to $2,500:

\(2500+175=2675\)

Therefore, we can conclude Mr. Osmond paid a total of $2,675 for the computer.

Given the test statistic and p-value for the alternative hypothesis μx # 45 are 1.78 and 0.08 respectively, if the alternative hypothesis were µx > 45 The correct answer is: b. The p-value would equal 0.04.

The p-value represents the probability of obtaining a test statistic as extreme as the observed one, assuming the null hypothesis is true. In this case, if the alternative hypothesis were changed to µx > 45 (one-sided alternative), the p-value would be different.

Since the original p-value was given as 0.08 for the alternative hypothesis µx ≠ 45 (two-sided alternative), we need to consider the area in the tail of the distribution corresponding to the new alternative hypothesis. In a one-sided test, we are only interested in one tail of the distribution.

If the original p-value was 0.08 for both tails, in the case of a one-sided test, the p-value would be half of that value since we are considering only one tail. Therefore, the new p-value would be 0.08 / 2 = 0.04.

So, the correct answer is:

b. The p-value would equal 0.04.

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Suppose the test statistic and p-value for the alternative hypothesis μx # 45 are 1.78 and 0.08, respectively. How would this p- value change if the alternative hypothesis were µx > 45 instead?

a. The p-value would not change.

b. The p-value would equal 0.04.

c. The p-value would equal 0.16.

d. The p-value would equal -0.08

The number of way in which bride can rank the three Djs out of 6 is 120.

There are several different ways we might rank the three DJs.

Therefore, we must identify the permutation P. (6,3).

ⁿPₓ = n!/(n - x)!

⁶P₃ = 6!(6-3)!

⁶P₃ = 6×5×4

⁶P₃ = 120

Thus, the number of way in which bride can select the three Djs out of 6 is 120.

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The height of the flag pole is 2.67 feet.

Javier is standing at a distance from a flagpole. He sights the bottom of the flagpole at a 40 degree angle of depression and the top of the flagpole at a 25 degree angle. The height of the flag pole can be found as follows:

The situation forms two right angle triangle.

Therefore, using trigonometric ratios, let's find the distance of Javier from the flag pole.

tan 40° = opposite  /adjacent

tan 40° = 6 / d

cross multiply

d = 6 / tan 40

d = 7.15ft

Therefore, let's find the opposite side of the other right triangle formed

tan 25 = h / 7.15

cross multiply

h = 7.15 × tan 25

h = 3.33409975581

h = 3.33 ft

Therefore,

height of the flag pole = 6 - 3.33 = 2.67 ft

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Mila bought stock in company two years ago that was worth x dollars. During first year that she owned the stock, it decreased by 35%. During second year the value of the stock decreased by 32%, an expression in terms of a that represents the value of the stock after the two years have passed is 2x+0.67.

It is not always obvious from the context what a % is in relation to because of inconsistent usage. The typical meaning of a "10% rise" or "10% decline" in a quantity is that this refers to the quantity's starting value. As an illustration, the new price of a $200 item would be $220 if the price increased by 10%, or $20. The final price is equal to 100% of the starting price (100% + 10% = 110%).

Other instances of % changes include:

If a quantity is increased by 100%, the final amount will be 100% more than the original amount (100% of initial + 100% of increase = 100% of initial). The quantity has therefore doubled.

If an amount is increased by 800%, the final sum will be nine times as large as the original (100% + 800% = 900% = 9 times as large).

When something is reduced by 60%, the final sum equals 40% of the original (100% - 60% = 40%).

A reduction of 100% results in a final value of 0% (100% - 100% = 0%).

In general, if a quantity is changed by x percent, the final amount will be 100 + x percentage of the original amount, or (1 + 0.01x) times the original amount.

x-35%+x-32%

⇒\(x-\frac{7}{20} +x-\frac{8}{25}\)

⇒\(2x+(\frac{-175-160}{500})\)

⇒2x+0.67

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