Solve this quadratic equation by completing the square.
x² + 6x = 18
OA. x= -3± √27
OB. x= -3± √18
OC. x= -6± √18
OD. x = -6± √27
SUBI

The triangles ABE and CED are similar in figure 1 by SAS similarity criteria whereas in figure 2 the triangles PST and RPQ are not similar.

The triangles are similar if all angles in one triangle are congruent to corresponding angles in other triangle and sides are proportional. There are different criterias for similarity of triangles namely SSS, SAS, ASA/AAS and RHS. According to the criteria/rule

SSS(SIDE-SIDE-SIDE):triangles are similar, if all three sides of one triangle are proportional to the three sides of another triangle.

SAS(SIDE-ANGLE-SIDE):The b are similar if two sides are proportional and an angle included  is congruent to two sides and included angle of another triangle.

ASA(ANGLE-SIDE-ANGLE):The triangles are similar if two angles are equal and an side between the angles is proportional  to the two angles and side between the angles of another triangle.

Q13) Consider ΔABE and ΔCED ,

∠AEB = ∠CED = 90°

and,

AE=21 units ;BE= 26+16=42 units

CE=16 units ; ED=32 units

and

∴ Sides are proportional

Hence ΔABE is similar to ΔCDE by SAS criteria.

Q14)Consider triangles ΔPQR and ΔPST,

Given that ∠QPT=42°, and PR bisects ∠QPT

∴∠QPR=∠RPT=21°

Given that ∠PTS=102°,

In ΔPST, by angle sum property of triangle:

∠SPT+∠PTS+∠TSP=180°

21 + 102 + ∠TSP=180°

∠TSP=180° - 102 -21

∠TSP=57°

Given that ∠PRQ=58°

In ΔPRQ, by angle sum property of triangle:

∠RPQ+∠QRP+∠PQR=180°

21 + 58 + ∠PQR=180°

∠PQR=180°- 58 - 21

∠PQR=101°

In  ΔPRQ the three angles are 21°,101° and 58° whereas in ΔPST the three angles are 21°,102° and 57°. As the angles are not congruent, the triangles are not similar.

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Our first equation yields p = 0. We obtain q = 3p = 0 by substituting this in the second equation. Hence, p = q = 0. As a result, the values of p and q are both zero.

A polynomial is a mathematical equation composed of variables and coefficients that is solved using mathematical operations like combination, deletion, multiplication, and quel integer exponents.

given

The result of dividing the same polynomial by x + 2 is

(p[tex]x^{2}[/tex] + (2p-q)x + (5q-2))(x+2) + (q[tex]x^{3}[/tex] + q[tex]x^{2}[/tex]+ 4[tex]x^{2}[/tex]) (12p-9q-2)

p+2q-2 = 12p-9q-2

When we simplify this equation, we obtain:

11p + 2q = 0

=> 3p - q = -4 (by adding 22p to both sides and multiplying both sides by 2)

Now, we also understand that the polynomial, when divided by x – 2, leaves a remainder of -18. Synthetic division or polynomial long division yields the following results:

= (p (x-2)³ + (7p-2q)(x-2) (x-2)² + (18q-8p)(x-2)) - 18

When we compare coefficients, we find:

p = 7p - 2q = 18q - 8p = 0

Our first equation yields p = 0. We obtain q = 3p = 0 by substituting this in the second equation. Hence, p = q = 0. As a result, the values of p and q are both zero.

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The volumes of the figures are 728 cubic meters, 47.14 cubic yards, 1260 cubic centimeters, 5581.71 cubic inches and 860.07 cubic inches

Figure 1:

The volume is calculated as

Volume = Product of dimensions/3

So, we have

Volume = 13 * 8 * 21/3

Volume = 728 cubic meters

Figure 2:

The volume is calculated as

Volume = πr²h

So, we have

Volume = 22/7 * 5² * 3/5

Volume = 47.14 cubic yards

Figure 3:

The volume is calculated as

Volume = Product of dimensions

So, we have

Volume = 14 * 18 * 5

Volume = 1260 cubic centimeters

Figure 4:

The volume is calculated as

Volume = 1/3πr²h

So, we have

Volume = 1/3 * 22/7 * 12² * 37

Volume = 5581.71 cubic inches

Figure 5:

The volume is calculated as

Volume = 1/3h(a² + b²)

So, we have

Volume = 1/3 * 13.3 * (16 * 6 + 14 * 7)

Volume = 860.07 cubic inches

Other dimensions are not clear

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Answer:

The measure of angle 14 is 83°.

Step-by-step explanation:

Angles 6 and 14 are congruent so if angle 6 is 83° so is angle 14.

Answer:

To solve this equation for the coefficient of the x term, we need to first simplify the equation by solving for x. 5x^2 + 3x - 2 = x/3 Multiplying both sides by 3 to eliminate the fraction, we get: 15x^2 + 9x - 6 = x Bringing all terms to one side: 15x^2 + 8x - 6 = 0 Now, we can use the quadratic formula to solve for x: x = [-b ± √(b^2 - 4ac)] / 2a where a = 15, b = 8, and c = -6 x = [-8 ± √(8^2 - 4(15)(-6))] / 2(15) x = [-8 ±

[tex]f(x) = (2/3)(x - 6)/(x + 3)[/tex]

What is triangle?

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed.

The given information is an acute angle ∠A, and sides a and b, along with the height of the triangle h = b sin A. The criteria for the number of possible triangles that can be formed are as follows:

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A nurse should empty a Hemovac wound suction device when it is half full to ensure proper functioning and prevent discomfort or injury to the patient due to the device becoming too heavy.

The rationale for a nurse to empty a Hemovac wound suction device when it is half full is to ensure the device is functioning correctly and to prevent it from becoming too heavy and potentially causing discomfort or injury to the patient.

When a Hemovac wound suction device is half full, it may start to lose suction, which can result in less efficient drainage of fluid from the wound site. By emptying the device, the nurse can ensure that the device is functioning correctly and that the suction pressure is maintained.

Additionally, allowing the device to become too full can make it heavy and uncomfortable for the patient, potentially causing discomfort or injury to the wound site. Therefore, emptying the device when it is half full can help prevent these complications and ensure that the patient remains comfortable throughout the healing process.

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Answer:

To calculate the distance or length of XY, YZ, and XZ, we can use the distance formula: Distance = √[(x2 - x1)^2 + (y2 - y1)^2] For XY: Distance = √[(7 - 7)^2 + (5 - 0)^2] Distance = √[0 + 25] Distance = √25 Distance = 5 units For YZ: Distance = √[(0 - 7)^2 + (5 - 5)^2] Distance = √[49 + 0] Distance = √49 Distance = 7 units For XZ: Distance = √[(0 - 7)^2 + (5 - 0)^2] Distance = √[49 + 25] Distance = √74 Therefore, the length

AB thus has a 12 unit length as the triangle ABE is a right triangle with hypotenuse AE and legs AB and 5 in length.

A closed triangle is a two-dimensional geometric shape having three straight edges and three angles. The shorter of a triangle's two sides is known as the hypotenuse, while its long sides are known as the triangle's legs. The longest side's opposing angle is referred to as the greatest or "opposite" angle in triangles. Angles are given names based on where they are in relation to the sides. An essential component of geometry is the study of triangles, and there are numerous varieties with distinctive characteristics. An equilateral triangle, on the other hand, has three equal edges and 3 equal angles that are each 60 degrees in length. A right triangle, for instance, has one angle that is 90 degrees in length.

given

The Pythagorean theorem can be used to determine the length of AB.

We can see from the diagram that triangle ADE is a right triangle with hypotenuse AE and legs measuring 12 and 5 (DE - AE = AD = 13 - 8 = 5). Well, here we are:

[tex]AD^2 + DE^2 = AE^2\\AE^2 = 5^2 + 12^2\\AE^2 = 169[/tex]

AE = 13

In a similar way, we can observe that triangle ABE is a right triangle with hypotenuse AE and legs AB and 5 in length. Well, here we are:

AB2 = 169 - 25 when AE2 = AB2 + BE2 132 = AB2 + 5

AB^2 = 144

AB = 12

AB thus has a 12 unit length as the triangle ABE is a right triangle with hypotenuse AE and legs AB and 5 in length.

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The total length of the parallelogram-shaped cross-country course is equal to 26 miles.

We can calculate the total length of the cross-country course using the formula for the perimeter of a parallelogram, which is twice the sum of the lengths of its adjacent sides. In this case, the adjacent sides are the base of length 7 mi and the side of length 6 mi.

So, we can find the total length by first finding the sum of these two sides:

7 mi + 6 mi = 13 mi

Then, we can multiply this sum by 2 to get the total length:

2 x 13 mi = 26 mi

Therefore, the total length of the cross-country course is 26 miles.

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Answer:

approximately 1.81 meters.

Step-by-step explanation:

Let's call the height of the tree "h". We can set up a proportion based on the similar triangles formed by Nicole, her shadow, the tree, and the tree's shadow:

(height of Nicole) / (length of Nicole's shadow) = (height of tree) / (length of tree's shadow)

Substituting the given values, we get:

1.55 / 25.6 = h / 30.05

Simplifying and solving for h, we get:

h = (1.55 / 25.6) * 30.05

= 1.81181640625

Rounding to the nearest hundredth, we get:

h ≈ 1.81 meters

the height of the tree is approximately 1.81 meters.

Given:

The number rounded to the nearest tenth is 59.6.

To find:

The approximate value of the given number to the nearest tenth.

Solution:

The required values shown in the below table:

Number               Nearest tenth                                    

59.58333333             59.6

Answer:

Sure! To find the diameter of the garden, we can use the formula: circumference = π x diameter Given that the circumference of the garden is 39.25 feet and π is approximately 3.14, we can plug in the values and solve for diameter: 39.25 = 3.14 x diameter diameter = 39.25 ÷ 3.14 diameter ≈ 12.5 feet (rounded to the nearest hundredth) Therefore, the approximate diameter of the garden is 12.5 feet.

Answer:

You are correct

Step-by-step explanation:

Answer:

Sure, I can help you with that! To find the value of g(7), we simply need to substitute x=7 into the expression for g(x): g(7) = (7/8)*7 - 1/2 g(7) = 49/8 - 1/2 g(7) = 95/8 Therefore, g(7) = 95/8.

0 / 350

Answer:

9. The weights, in pounds, of five pumpkins from a pumpkin patch are 17, 18, 17, 15, and 13.

What is the MAD of the weights?

Step-by-step explanation:

9. The weights, in pounds, of five pumpkins from a pumpkin patch are 17, 18, 17, 15, and 13.

What is the MAD of the weights?

a. The time at which the population is at a maximum is 25 hours. b. The maximum population is 1,182,500.

A polynomial function of degree 2 is a quadratic function, while one of degree 1 is a linear function. The formula for a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants and an is not equal to 0. A parabola, a U-shaped curve, is the graph of a quadratic function. Depending on the sign of the leading coefficient, the function's minimum or maximum value is located at the parabola's vertex.

a) The highest value of the population function, which is a quadratic function with a negative leading coefficient, occurs near the parabola's vertex.

Thus, t = -b/2a.

Substituting the values  a = -1698, b = 85,000, and c = 10,000 we have:

t = -85000 / 2(-1698) = 25

Therefore, the time at which the population is at a maximum is 25 hours.

b) To determine the maximum population we substitute the value of t = 25.

p(25) = -1698(25)² + 85,000(25) + 10,000 = 1,182,500

Therefore, the maximum population is 1,182,500.

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Answer:

D. [tex]\sqrt{3}[/tex] ; 2

Hope this helps!

Step-by-step explanation:

The procedure used to analyze the given data is intention-to-treat analysis.

The procedure to analyze data according to the original assignment of the treatment regardless of the actual treatment received is called the intention-to-treat (ITT) analysis. It is considered the gold standard in clinical trial analysis because it preserves the randomization and avoids bias that may arise from differential dropouts or non-compliance. By analyzing all patients according to their randomized group, the ITT analysis provides an unbiased estimate of the treatment effect and better reflects the real-world effectiveness of the intervention.

The intention-to-treat (ITT) analysis is different from other types of analyses because it includes all patients according to their original randomized group, regardless of whether they received the assigned treatment or not. This is in contrast to per-protocol analysis, where only patients who completed the study without any major protocol deviations are included, or as-treated analysis, where patients are analyzed according to the actual treatment received.

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The equation to model the statement is [tex]-8(y + 3) = 32[/tex] and the value of y is -7.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given statement is the product of – 8 and [tex](y + 3)[/tex] is 32.

Product means the operation is multiplication.

So the equation can be written as,

[tex]-8 (y + 3) = 32[/tex]

Dividing both sides by 8,

[tex]-(y + 3) = 4[/tex]

[tex]y + 3 = -4[/tex]

[tex]y = -4 - 3 = -7[/tex]

Hence the value of y is -7.

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The statement "The empirical rule assumes that the distribution of data follows a normal curve." is True.

The empirical rule, also known as the 68-95-99.7 rule, is a statistical rule that states that for a normal distribution, approximately 68% of the data will fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. This implies that the distribution of data follows a normal curve.

A normal distribution is a type of probability distribution that follows a symmetrical bell-shaped curve. It is also known as the Gaussian distribution and is a continuous probability distribution. The normal distribution is defined by its mean, which is the average of the values, and its standard deviation, which is a measure of the spread of the values from the mean.

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To multiply 7(b-5)(b-4), you can follow these steps:

1.

Start by distributing the 7 to the terms inside the parentheses:

7(b-5)(b-4) = 7 * b * (b-4) - 7 * 5 * (b-4)

2.

Simplify each term using the distributive property:

= 7b^2 - 28b - 35b + 140

3.

Combine like terms:

= 7b^2 - 63b + 140

So, the final answer is 7b^2 - 63b + 140.

Answer: 1 and 5

Step-by-step explanation:

the mean of 41, 52, 56, 65, 65, 76, and 89 is 63.43.

Step-by-step explanation:

Answer:  The probability that Travis will choose a mystery book is 1/3.

Step-by-step explanation: To find the probability that Travis will choose a mystery book, we need to determine the ratio of the number of mystery books to the total number of books on Travis's shelf.

Travis has 6 mystery books, and the total number of books on his shelf is 6 + 5 + 4 + 3 = 18.

Therefore, the probability (in fraction form) that Travis will choose a mystery book is 6/18.

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 6.

6 ÷ 6 = 1

18 ÷ 6 = 3

So, the simplified fraction is 1/3.

(a) The probability of having at least 10 defective chips is approximately 0.9131. (b) The probability of having between 15 and 20 defective chips is approximately 0.4135.

First, we need to find the mean (μ) and standard deviation (σ) for the binomial distribution.
μ = np = 500 * 0.03 = 15
σ = sqrt(np(1-p)) = sqrt(15*0.97) ≈ 3.66

(a) To find the probability of at least 10 defective chips, we'll calculate the Z-score and use a Z-table:

Z = (X - μ) / σ = (10 - 15) / 3.66 ≈ -1.36

P(X ≥ 10) = 1 - P(X ≤ 10) = 1 - 0.0869 = 0.9131

So, the probability of having at least 10 defective chips is approximately 0.9131

(b) To find the probability of between 15 and 20 defective chips (inclusive), we'll calculate the Z-scores and use a Z-table:

Z1 = (15 - 15) / 3.66 ≈ 0

Z2 = (20 - 15) / 3.66 ≈ 1.36

P(15 ≤ X ≤ 20) = P(Z1 ≤ Z ≤ Z2) = P(0 ≤ Z ≤ 1.36) = 0.4135

So, the probability of having between 15 and 20 defective chips is approximately 0.4135.

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The probability that no two adjacent people would stand is option C: 49/256, as there are 256 distinct counting rotations.

First, we assume that one person stands up. There are 8 possible ways to select which person does. We can, next, assume that no two adjacent people stand up. There are 4 ways to choose which of the remaining 7 people will stand up (since no two adjacent people can stand up).

Then, we can assume that no two adjacent people stand up again. There are 3 ways to choose which of the remaining 6 people will stand up (since no two adjacent people can stand up).

We continue this process until there is only one person left who can stand up.

The number of arrangements according to the number of people standing.

Therefore, the number of arrangements that no two adjacent people will stand.

n(S) = 1 + 8 + 20 + 16 + 2 + 2 = 49

The total number of possible outcomes is:

2⁸ = 256

So, the probability that no two adjacent people will stand would be:

= 49/256.

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Complete question is:

Eight people are sitting around a circular table, each holding a fair coin. All eight people flip their coins and those who flip heads stand while those who flip tails remain seated. What is the probability that no two adjacent people will stand?

(a) 47/256

(b) 3/16

(c) 49/256

(d) 25//128

(e) 51/256

Answer:

-5, -12

Step-by-step explanation:

We just have to find somthing colder than -4f so it has to be less than -4 so it would be -5 and -12.

The correct answers to your question would be -5 and - 15.

Based on the given data, there are a total of 13 packets and 5 of them are spicy. Therefore, the probability that the next packet Cooper pulls out of the box will be spicy is 5/13 or approximately 0.385 (rounded to three decimal places).

To calculate the probability of the next packet being spicy, we need to know how many packets of each flavor are in the box. Assuming that Cooper doesn't put back the packets he has pulled out, we can count the number of spicy packets and divide it by the total number of packets he pulled out.

In this case, out of the 13 packets he pulled out, 5 were spicy. Therefore, the probability of the next packet being spicy is 5/13, or approximately 0.38, or 38%. However, if the box is refilled with packets of different flavors, this probability may not hold.

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Answer: 4/13

Step-by-step explanation: i did this IXL and this was the correct answer

Surface area of this right triangular prism=96in²

A right triangular prism is a three-dimensional geometric shape that has two parallel triangular bases and three rectangular faces that connect the bases. The triangular bases of a right triangular prism are always perpendicular to its rectangular faces. The prism is called "right" because the rectangular faces meet the bases at right angles, meaning the edges connecting the triangular and rectangular faces form right angles.

In the given  right triangular prism

S₁=5in

S₂=5in

S₃=8in

l=4in

b=8in

h=3in

Total surface area of this right triangular prism = (S₁+S₂+S₃)l+(b×h)

=(5+5+8)×4+8×3

=96

Hence, surface area of this right triangular prism=96in².

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