ERROR ANALYSIS Describe and correct the error in solving the equation.
X -2x²-8=0
-2x²=8
x² = -4
x = ±2
BIU E = T²
T² T₂

Answers:

A, B, D, E

Nearly everything except choice C is true.

====================================================

Explanation:

9514 1404 393

Answer:

  A. Side lengths of 4 units and 2 units and a nonincluded angle of 30°

Step-by-step explanation:

Both triangles have sides marked 2 units and 4 units, but the angle is not between them. The angle is opposite the short side in one triangle (which will be a right triangle), and opposite the long side in the other triangle (which will be an obtuse triangle). The sides and angles of the two triangles will not have the same measures, and neither will have an angle of 100°.

The first description is appropriate:

  Side lengths of 4 units and 2 units and a nonincluded angle of 30°

Total miles driven by DeAndre on the rented truck is 2020 miles .

What is rented object?

A car/truck rental, hire car/truck , or car hire agency is a company that rents automobiles to the general public for short periods of time, typically ranging from a few hours to a few weeks.

Main body:

According to question:

Base fee for truck rent = $19.99

Additional charge for each mile = $0.92

Total he had to pay = $205.83

Let the total no. of miles driven = x

The equation becomes ⇒

Total paid = base fee + no. of miles * rent for each mile

205.83 = 19.99 + 0.92*x

205.83 - 19.99 = 0.92 x

185.84 = 0.92 x

x= 185.84/ 0.92

x = 2020 miles

Hence the total miles driven by DeAndre are 2020 miles.

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The number of different frames you can create, if There are 4 different styles, each available in 5 different colors, there are 3 different shades of blue to choose from, is 12.

A combination is a choice of items from a group of different items, where the order of the choices is irrelevant.

Given:

There are 4 different styles, each available in 5 different colors, there are 3 different shades of blue to choose from,

Calculate the total number of frames, we can create as shown below,

The number of frames = different styles available for blue color × shades of blue

The number of frames = 4 × 3

The number of frames = 12

Thus, the number of frames you can create is 12.

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The value of y in the triangle is 2√10 units.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

The value of y can be found using the similar triangle ratios as follows:

Hence,

8 / y = y / 5

cross multiply

y² = 8 × 5

y²= 40

square root both sides of the equation

y = √40

Therefore,

y = 2√10 units

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Answer:

5/7

Step-by-step explanation:

ratio of boys to girls---> 2:5

ratio sum: 2+5=7

girls ratio =5/7

OR

total of people in 7th grade choir=28

hence, no of girls in 7th grade choir=5/7 × 28

=20

proportion of girls in choir= 20/28 = 5/7

Answer:

1 1/8

Step-by-step explanation:

The solutions to the questions are

The area of a shape is the amount of space on the shape

For most regular quadrilaterals, you multiply the side lengths to determine the area

The area expression is given as

Area = ▢ × 102 + ▢ × 101 + 6

From the question, we can use any number

However, this number must be positive

Assume the number is 5

So, we have

Area = 5 × 102 + 5 × 101 + 6

In (a), we have:

Area = 5 × 102 + 5 × 101 + 6

Evaluate

Area = 1021

The perfect square number closest to this is

Closest = 1024

In (b), we have

Closest = 1024

Rewrite as

Area = 1024

Take the square roots

Length = 32

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In order for the relationship zyx ~ wvu to be correct, the following conditions must be true:

Corresponding angles are congruent: The angles formed by matching vertices should have the same measures in both triangles. This ensures that the corresponding angles are equivalent.

Corresponding sides are proportional: The lengths of the sides that connect the corresponding vertices of the triangles should have a consistent ratio. This implies that the corresponding sides are proportional to each other.

These conditions are based on the definition of similarity between two triangles. If both the corresponding angles are congruent and the corresponding sides are proportional, then the triangles zyx and wvu are considered similar (denoted by ~).

Therefore, in order for zyx ~ wvu to be correct, the congruence of corresponding angles and the proportionality of corresponding sides must hold true.

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Answer:

width = 4in

length = 8in

Step-by-step explanation:

A = LxW = 32

L = W + 4

W(W+4) = 32

W² + 4W - 32 = 0

(W + 8)(W - 4) = 0

W ≠ -8 (dimensions cannot be negative)

W = 4in

L = W+4 = 4+4 = 8in

I believe its 2 ^ -3

because

1/8 = 1/2^3 = 2^-3

The Polynomial x⁵ + x³ - 5 is divided by x - 2, the quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

The quotient and remainder when the polynomial x⁵ + x³ - 5 is divided by x - 2, we can use polynomial long division. Here's the step-by-step process:

1. Write the dividend (x⁵ + x³ - 5) and the divisor (x - 2).

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

2. Divide the first term of the dividend (x⁵) by the first term of the divisor (x) to get x⁴. Write x⁴ above the line. x⁴

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

3. Multiply the divisor (x - 2) by the quotient term (x⁴) to get x⁵ - 2x⁴. Write this under the dividend and subtract it.  x⁴

  x - 2 | x⁵ + x³ + 0x² + 0x - 5

 - (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

4. Bring down the next term (-5) from the dividend.

x⁴ + 3x³

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

5. Divide the first term of the new dividend (3x⁴) by the first term of the divisor (x) to get 3x³. Write 3x³ above the line.

 x⁴ + 3x³

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

 - (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

6. Multiply the divisor (x - 2) by the new quotient term (3x³) to get 3x⁴ - 6x³. Write this under the new dividend and subtract it.

x⁴ + 3x³

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

- (3x⁴ - 6x³)

6x³ + 0x² + 0x - 5

7. Repeat steps 4-6 until you have subtracted all terms.

x⁴ + 3x³ + 6x² + 12x + 24

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

- (3x⁴ - 6x³)

6x³ + 0x² + 0x - 5

- (6x³ - 12x²)

12x² + 0x + 0

 - (12x² - 24x)

 24x + 0

- (24x - 48)

 48

8. The quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

Therefore, when the polynomial x⁵ + x³ - 5 is divided by x - 2, the quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

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To answer this question, we have that both singers generated $438 million in tickets sales.

Then, we can rewrite it in algebraic expressions as follows:

However, we know that singer B took in $22 million less than singer A:

Now, we can substitute this expression in the original one as follows:

And to solve this equation, we can add the like terms, and then add 22 to both sides of the equation as follows:

Then, to find the earnings of singer B, we have:

Then, B is equal to:

Then, we can check that A + B is:

And we can see that singer B took in $22 million less than singer A:

In summary, therefore, we can say that each tour generated:

Singer A generated $230 million in ticket sales and Singer B generated $208 million.

Points A, B, C, D, and E are collinear and in that order. The value of Ac is 18.

According to the segment addition postulate, if two points on a line segment, A and C, are given, a third point, B, will only be found on line segment AC if and only if the distances between the points satisfy the conditions of the equation AB + BC = AC.

Keep in mind that a line segment is a portion of a line that has two distinct end points. There are many points between the two end points that make up the object.

The segment addition postulate can be stated more simply by saying that if point B lies on line segment AC, then AB + BC will equal AC.

by the segment addition postulate,

AC + CE = AE so AC = AE - CE

AC = (x+50) - (x+32)

AC = x+50-x-32

AC = 18

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Answer:

It was used as the multiplier because the 5 represents the hours she's worked. If she uses the 1/5 graph she will find the unit rate of each time she gets paid an hour.

Answer:

A

B

E

Explanation:

The first, third and fifth options are valid as it mentions the three edges; no matter what the order is as long as the three points are mentioned its considered as the valid name

Answer:

29.4°

Step-by-step explanation:

The equation can be rearranged to give C directly.

 C = arccos((a^2 +b^2 -c^2)/(2ab))

 C = arccos((90^2 +55^2 -50^2)/(2·90·55))

 C = arccos(8625/9900) ≈ 29.4002°

 C ≈ 29.4°

The measure of angle C is approximately 29.46 degrees.

To find the measure of angle C (cos(C)) using the given values a = 55, b = 90, and c = 50, we can use the Cosine Rule formula:

cos(C) = (a² + b² - c²) / (2 * a * b)

Substitute the given values:

cos(C) = (55² + 90² - 50²) / (2 * 55 * 90)

Now, calculate the numerator:

cos(C) = (3025 + 8100 - 2500) / (2 * 55 * 90)

cos(C) = 8625 / 9900

Now, divide to get the final value of cos(C):

cos(C) ≈ 0.8707

To find the measure of angle C itself, we can take the inverse cosine (arccos) of this value:

C ≈ arccos(0.8707)

Using a calculator, you'll find:

C ≈ 29.46 degrees (rounded to two decimal places)

So, the measure of angle C is approximately 29.46 degrees.

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A confidence interval that will capture the true population mean with 95% confidence. The value is ( 23.6459    , 24.8293 ) .

What is population mean?

A population in statistics is a group of comparable objects or occurrences that are relevant to a particular topic or experiment. A statistical population can be a collection of real things or a hypothetical, possibly limitless collection of objects derived from experience.

Data: 18

for given data

\($$\begin{aligned}\bar{X} & =\frac{\sum X i}{n} \\& =2448 / 101 \\& =24.2376\end{aligned}$$\)

as population variance is unknown so we used sample variance

\($$\begin{aligned}S^2 & =\frac{1}{n-1}\left(\sum X i^2-n \times \bar{X}^2\right) \\S^2 & =\frac{1}{100}\left(60232-101 \times 24.2376^2\right) \\& =8.9830\end{aligned}$$\)

Now

\(\frac{\bar{X}-\mu}{S / \sqrt{n}} \sim t_{n-1}$$\)

hence 95 % of population mean is

As n=101 which is large so critical value is 1.98397

\($$\begin{aligned}& =\left(\bar{X}-\sqrt{\frac{S}{n}} \times t_{(n-1, \alpha / 2)}, \bar{X}+\sqrt{\frac{S}{n}} \times t_{(n-1, \alpha / 2)}\right) \\& =\left(24.2376-\sqrt{\frac{8.9830}{101}} \times 1.98397,24.2376+\sqrt{\frac{8.9830}{101}} \times 1.98397\right) \\& =(23.6459,24.8293)\end{aligned}$$\)

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The approximate x-values for the local maximum and the local minimum are given as follows:

D) max ≈ -0.3 , min ≈ 2.3.

Hence the critical points of the graphed function are given as follows:

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Answer:

Length W+9

Width W

Step-by-step explanation:

Answer:

I have completed the answers and attached them to the explanation.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question asks for a subtraction expression:

length is always a positive number so bigger number first here.

OB = 4-(-1)              >only moves in x direction so subtract x's

AB = 4-(-2)             >only moves in y direction so subtract y's

The average (mean) score for each of the innings is 64 runs for the first inning and 78 runs for the second inning.

To find the average (mean) score for each of the innings in two-innings cricket, we need to calculate the total runs scored in each inning and divide it by the number of innings played.

Given:

First inning score = 64 runs

Second inning score = 78 runs

To find the average for each inning, we divide the total runs by the number of innings played.

For the first inning:

Average score = First inning score / Number of innings

Average score = 64 runs / 1 inning

Average score = 64 runs

For the second inning:

Average score = Second inning score / Number of innings

Average score = 78 runs / 1 inning

Average score = 78 runs

It's worth noting that in two-innings cricket, the average score is calculated separately for each inning, as the total runs and the number of innings are considered independently for each inning.

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Answer:

The customers are wrong.

Step-by-step explanation:

Apple juice is wayyyyyyyyy better than orange juice.

The operating characteristics of the customer waiting line shows that the average service rate per hour is 5 customers per hour.

The average service rate per hour will be:

= 60/12 = 5

The average number of customers waiting will be:

= (2.2)²/5(5 - 2.2)

= 4.84/14

= 0.3457

The average number of customers in the system will be:

= 0.3457 + 2.2/5

= 0.7857

The average time that a customer spends waiting in the system will be:

= 0.3457/2.2

= 0.1571

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In conclusion, none of the given statements are correct based on the information provided.

To determine the correct statement, let's analyze the given information and the regression equation:

The regression equation for estimating the number of customers on a given day is y = 1.03x + 229.4, where x represents the day number and y represents the number of customers served.

We are also given that the restaurant has been making a net profit of $5.82, on average per customer:

Now let's evaluate each statement:

A. On day 7, the owner can expect 15 more customers than she has served on day 6.

To determine the number of customers on day 7, we substitute x = 7 into the regression equation:

y = 1.03(7) + 229.4 = 7.21 + 229.4 = 236.61

So, the number of customers on day 7 is approximately 237, which is not 15 more than the number of customers served on day 6.

Therefore, statement A is incorrect.

B. If the number of customers continues to follow the current trend, the restaurant will make a net profit of $1,377 on day 7.

To calculate the net profit on day 7, we need to multiply the average net profit per customer ($5.82) by the number of customers on day 7:

Net profit on day 7 = $5.82 \(\times\) 237 ≈ $1,379.34

So, statement B is incorrect as the net profit on day 7 is not expected to be $1,377.

C. On day 12, the owner can expect a net profit of $1,300.

Since the question only provides information about the number of customers served for the first 6 days, we cannot determine the net profit on day 12.

Therefore, statement C is incorrect.

D. Net profit for days 6 and 7 combined is expected to be less than the earned net profit on day 1.

To calculate the net profit for days 6 and 7 combined, we need to calculate the number of customers on both days using the regression equation and then multiply it by the average net profit per customer.

Let's substitute x = 6 into the regression equation:

y = 1.03(6) + 229.4 = 6.18 + 229.4 ≈ 235.58

Now, let's calculate the net profit for days 6 and 7 combined:

Net profit on days 6 and 7 = ($5.82 \(\times\) 235) + ($5.82 \(\times\) 237) ≈ $2,735.2

Comparing this to the earned net profit on day 1, we cannot determine if it is less or greater without the information provided.

Therefore, statement D is incorrect.

In conclusion, none of the given statements are correct based on the information provided.

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The sum represents an infinite geometric sequence, and it's result is given by: \(\frac{3}{16}\).

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term.

The sum of an infinite sequence in which |q| < 1 is given by:

\(S = \frac{a_1}{1 - q}\)

In this problem, we have that the first term and the common ratio are given, respectively, by:

\(a_1 = \frac{1}{4}, q = -\frac{1}{3}\)

Hence:

\(S = \frac{\frac{1}{4}}{1 + \frac{1}{3}} = \frac{\frac{1}{4}}{\frac{4}{3}} = \frac{3}{16}\)

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Answer:

c - edge2022

Step-by-step explanation:

Solution

Given

Answer:

1:7

Step-by-step explanation:

There was originally 28 students. Since 4 of them are gone. There are 24 students.
the ratio of students to markers is now:

24:168

Now you have to simplify it by finding the lowest common denominator:

24 and 168 both share 1 so:

24/24 = 1, 168/24 = 7

1:7

Therefore, for every student on that day, there is 7 markers

7 markers per student