Solve the absolute value equation −|x − 2| + 3 = 0.

1)

We note that the quadratic can be factored into \((2x-1)(x-1)\).

The quadratic is greater than \(0\) if both of its factors are positive, or they are both negative.

Case: both positive

We need to solve the system of inequalities:

\(2x-1>0\\x-1>0\).

The first inequality gives \(x>\frac{1}{2}\).

The second inequality gives \(x>1\).

Taking the points where the inequalities coincide gives \(x>1\).

(Note: 1 is a root of the quadratic. Coincidence? If not, try and prove it!)

Case: both negative

We need to solve the system of inequalities:

\(2x-1<0\\x-1<0\).

The first inequality gives \(x<\frac{1}{2}\).

The second inequality gives \(x<1\).

Taking the points where the inequalities coincide gives \(x<\frac{1}{2}\).

(Note: \(\frac{1}{2}\) is the other root of the quadratic. Coincidence? If not, try and prove it!)

Taking the union of both cases gives the solution set: \(\boxed{x\in (-\infty, \frac{1}{2}) \cup (1, \infty)}\)

2)

We bring over the \(15\) to get \(x^2-2x-15<0\).

Note that the quadratic factors into \((x-5)(x+3)\).

The quadratic is less than \(0\) if 1 of its factors is negative, but not both.

Case: first factor is negative, second positive

We have that \(x-5<0\) and \(x+3>0\).

We get that \(x<5\) and \(x>-3\), which has the solution set \(-3<x<5\).

Case: second factor is negative, first positive

We have that \(x+3<0\) and \(x-5>0\).

We get that \(x<-3\) and \(x>5\), which has no solutions.

So, the solution set is \(\boxed{x\in (-3, 5)}\)

Step-by-step explanation:

Odpowiedź:

9.75zł :3 = 3.25zł

3.25zł x 4 = 13zł - Prawda

3.25zł x 10 = 32.50zł - Prawda

Liczę na najlepsze.

The values of a, b, c are 152°, 28°, 152° respectively.

Angles around a point describes the sum of angles that can be arranged together so that they form a full turn.

The sum of angles at a point will give 360°.

This means that a + b + c + 28 = 360

c +28 = 180° ( angle on a straight line)

c = 180 -28

c = 152°

c = a( alternate angles are equal)

therefore the value of a = 152°

b = 28( alternate angles are equal)

therefore the value of b is 28

therefore the values of a, b, c are 152°, 28°, 152° respectively

learn more about angle at a point from

https://brainly.com/question/25716982

#SPJ1

Answer:

Domain: {3,5,6,9}

Range: {1,2,8}

Step-by-step explanation:

In a relation, the domain is the x-values while the range is the y-values. To find them simply list the values in order from least to greatest while not repeating any values. This relation would also not be considered a function because x-values repeat.

If the correlation coefficient has a negative value, then the coefficient of determination: b. must be positive.

A regression line is a statistical line that best describes the behavior of a data set and such, it is a line that best fits a set of data.

A positive correlation can be defined as a terminology that is used to described a scenario (situation) in which two variables move in the same direction and are in tandem.

This ultimately implies that, a positive correlation exist when two variables have a linear relationship or are in direct proportion. Thus, when one variable increases, the other increases, as well.

Read more on positive correlation here: brainly.com/question/3753830

#SPJ4

Complete Question:

If the correlation coefficient has a negative value, then the coefficient of determination:_________.

a. can take on either a negative or positive value.

b. must be positive.

c. will also have a negative value.

d. will equal zero.

A triangle has all three angles summing up to 180. If two of the sides measure 40 degrees and 50 degrees, then the third side measures as follows;

The third angle, which is labelled as angle A measures 90 degrees, and that means the triangle is a "right angled triangle."

The official is approximately \(\sqrt{(13)\)  meters from the center of the discus circle.

The official is standing 2 meters from the edge of the discus circle and 3 meters from a point of tangency. To find how far the official is from the center of the discus circle, we can use the properties of a tangent line.

First, let's draw a diagram. We have a discus circle with a center, a point of tangency, and the official standing outside the circle.

The official is standing 2 meters from the edge of the circle, so we can draw a line from the official to the point of tangency. This line is a tangent line, and it is perpendicular to the radius of the circle that passes through the point of tangency.

We also know that the official is 3 meters from the point of tangency.

To find the distance from the official to the center of the discus circle, we can form a right triangle. One leg of the triangle is the radius of the circle, and the other leg is the distance from the official to the point of tangency.

Using the Pythagorean theorem, we can find the length of the hypotenuse of the right triangle, which is the distance from the official to the center of the circle.

Let's call the distance from the official to the center of the circle x.

Using the Pythagorean theorem: \(x^2 = 2^2 + 3^2\)
Simplifying the equation: \(x^2 = 4 + 9\)

Combining like terms: \(x^2 = 13\)

Taking the square root of both sides: \(x = \sqrt{(13)\)

to learn more about Pythagorean theorem

https://brainly.com/question/14930619

#SPJ11

a. Sally can feed her pets in different orders by considering the concept of permutations. The number of different orders she can feed her pets can be calculated by finding the number of permutations of her 7 pets (3 dogs and 4 cats).

b. The probability that her first three pets to be fed are her cats can be determined by considering the total number of possible orders and the number of orders where the first three pets are her cats.

a. To calculate the number of different orders, we use the concept of permutations. The number of permutations of 7 objects (Sally's 3 dogs and 4 cats) is given by 7 factorial (7!). So the number of different orders Sally can feed her pets in is 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040.

b. Since Sally has 4 cats, the probability of the first three pets being her cats can be calculated by considering the number of ways the first three positions can be occupied by her cats (which is 4!) divided by the total number of different orders (which is 7!). So the probability is 4! / 7! = 24 / 5040 = 1 / 210, or approximately 0.0048.

Therefore, Sally can feed her pets in 5040 different orders, and the probability that her first three pets to be fed are her cats is approximately 0.0048.

Learn more about  probability : brainly.com/question/31828911

#SPJ11

Written in Standard Form: 5u^(2)v^(2)+5u^(2)u+4uv^(2)-4uv

Simplified: 5u^(2)v+4uv^(2)+5u^(2)v^(2)-4uv

Brainliest or a thank you please this took me a while to type :)) <3

Step-by-step explanation:

lo siento, no tengo idea de cómo explicarte esto. Ummm, hay una aplicación que puedes descargar en tu teléfono para tomar una foto de la hoja de trabajo o el papel y luego la traducirá para ti. Se llama buena traducción o algo en. buena suer

Answer:

Slope=3

y-intercept=4

Step-by-step explanation:

the line intercepts the y axis at 4.

Answer:

slope = 3

y-intercept = 4

Step-by-step explanation:

From the graph, we can automatically tell that the y-intercept is at (0,4) so the y-intercept is 4. Now, we just need to find the slope and to do that we can choose 2 points. I am choosing (-2,-2) and (0,4).

The slope formula is m = y2-y1/x2-x1. I am going to plug in the points in the formula.

m = (4 - (-2))/(0 - (-2))

m = 6/2

m = 3

slope = 3

y-intercept = 4

Answer:

Variables- x, y and z

Constants- 2 and 8

Coefficients- 3, 7, and 4

Step-by-step explanation:

Variables - The numbers we don't know/trying to find.

Constants- The numbers that remain fixed

Coefficients- The numbers in front of the variables

Answer:

47*

Step-by-step explanation:

Using the vertical angle rule, I can get CBD as 47*

The solutions are given below.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

Part A

the dotted line formes the thrid side of the triangle.

part B

The length is the unknon side increases while kepping the known side lenths fixed, measuremnt of anggle Z will increas. So, the tringle will not fir the given conditions anymore.

part c

If the length of he unknown side decrases while keeping h known side lengths fixed,the measure of angle will decrease so he tringle will not fit the given conditions anymore.

part D

You know the given conditions for the triangle are fixed you also know the unknown side length is fixed. What dose the this tell you angles adjacent to the unknown side.

part e

The given condiction are fixed and the unknown side lenghtis fixed, the angles adjacent to the unknown side must much also be fixed.

part f

Given two side lengths and the measurement of the angle between them, only one triangle can be constructed. Part G The length of the unknown side (c) is 9.76 centimeters

To learn more on triangle click:

brainly.com/question/29126067

#SPJ1

Answer:

10 times

Step-by-step explanation:

The value of the 7 in 70,048 is 70,000

The value of the 7 in 17,992 is 7,000.

If you divide 70,000 by 7,000, you get 10.

The first 7 is 10 times greater than the 2nd.

I hope this helps!

pls ❤ and mark brainliest pls!

Answer:10 times

Step-by-step explanation:

The value of 7 in 70,048 stands for 7 Ten thousand  which is equal to 70,000

Also 7 in 17,992 stands for 7 thousand which is equal to  7,000

So we divide to know how much the lesser value is in the grater vale giving us

70,000/7,000 =10

Therefore, the value of 7 in 70,048 is 10 times  than the value of 7 in 17,992

See similar answer here: https://brainly.com/question/13200619

The installation fee for 150 square feet of carpet is $148.60.

The cost to purchase x square feet of carpet is given by the function:

f(x) = 5.6x

The installation fee is $115 more than 4% of the cost of the carpet. Let C be the cost of the carpet.

Then the installation fee can be represented by the function:

g(x) = 0.04C + 115

We can substitute the expression for the cost of the carpet, f(x), into the expression for C:

C = f(x) = 5.6x

Substituting this into the expression for g(x), we get:

g(x) = 0.04(5.6x) + 115

= 0.224x + 115

To find the installation fee for 150 square feet of carpet, we can substitute x = 150 into the expression for g(x):

g(150) = 0.224(150) + 115

= 33.6 + 115

= $148.60

Therefore, the installation fee for 150 square feet of carpet is $148.60.

Learn more about   cost from

https://brainly.com/question/25109150

#SPJ11

Answer:

6,942 steps left!

Step-by-step explanation:

OK so this is easy so we know that if 1 / 19 = 0.052 we minus that by - 3 because - 3 is our exponent that gives us 3.052 so now we just take 3.052 - 10,000 which gives us exactly 6942 you two steps so he needs 6942 steps left

Answer:

3,141 steps

Step-by-step explanation:

Let x be equal to the number of steps he needs to reach his goal

10,000 = \((\frac{1}{19} )^{-3}\)+ x

10,000 = 6,859 + x

3,141 = x

Answer:

3637, 3638, 3639?

Step-by-step explanation:

i just drew 4 boxes and then worked it out

Answer:

-4

Step-by-step explanation:

This is according to my sense. please consider other answers as well

Triangle \(PQR\) is a scalene acute triangle based on the given side lengths and angles.

Based on the given measurements and angles of triangle \(PQR\), we can determine the type of triangle it is.

First, let's analyze the side lengths. \(PQ\) is \(7.96\), \(PR\) is \(3.96\), and \(RQ\) is \(8.41\). Since all three sides have different lengths, the triangle cannot be equilateral or isosceles.

Next, let's consider the angles. \(PQR\) is \(28\) °, \(QRP\) is \(70\)°, and \(RPQ\) is \(82\)°. None of these angles are right angles (\(90\)°), so the triangle is not a right triangle.

Now, let's examine the remaining possibilities. Since none of the side lengths are equal, the triangle cannot be isosceles. Additionally, since the largest angle \(RPQ\) is \(82\)°and is greater than \(90\)°, the triangle cannot be obtuse.

By process of elimination, we can conclude that the triangle \(PQR\) is a scalene acute triangle. This means it has three different side lengths and all angles are less than \(90\)°.

In summary, triangle \(PQR\) is a scalene acute triangle based on the given side lengths and angles.

For more such questions on scalene acute triangle: https://brainly.com/question/16589630

#SPJ11

Answer:

r = -2

s = 13

Step-by-step explanation:

Given quadratic equation is,

11x² - 44x - 99 = 0

Divide this equation by 11,

x² - 4x - 9 = 0

x² - 2(2)x - 9 = 0

x² -2(2)x + 2² - 2² - 9 = 0

[x² - 2(2)x + 2²] - 4- 9 = 0

(x - 2)² - 13 = 0

(x - 2)² = 13

[x + (-2)]² = 13

By comparing this equation with  (x + r)² = s

Values of the constants r and s will be,

r = (-2) and s = 13

To determine whether there is enough evidence to reject the null hypothesis, we need to compare the computed test statistic to the critical value.

In this case, the computed test statistic is 2.50 and the critical value is 2.33. If the computed test statistic falls in the rejection region beyond the critical value, we can reject the null hypothesis. Conversely, if the computed test statistic falls within the non-rejection region, we fail to reject the null hypothesis.In this scenario, since the computed test statistic (2.50) is greater than the critical value (2.33), it falls in the rejection region. This means that the observed data is unlikely to occur if the null hypothesis were true.

Therefore, based on the given information, there is enough evidence for the emergency room nurse to reject the null hypothesis. This suggests that there is sufficient evidence to support the claim that the average number of cases of upper respiratory infections per day at the hospital is over 21 cases.

Learn more about statistic here

https://brainly.com/question/15525560

#SPJ11

There is enough evidence to reject the null hypothesis in this case because the computed test statistic (2.50) is higher than the critical value (2.33). This suggests the average number of daily respiratory infections exceeds 21, providing substantial evidence against the null hypothesis.

Yes, there is enough evidence for the emergency room nurse to reject the null hypothesis. The null hypothesis is typically a claim of no difference or no effect. In this case, the null hypothesis would be an average of 21 upper respiratory infections per day. The test statistic computed (2.50) exceeds the critical value (2.33). This suggests that the average daily cases indeed exceed 21, hence providing enough evidence to reject the null hypothesis.

It's crucial to understand that when the test statistic is larger than the critical value, we reject the null hypothesis because the observed sample is inconsistent with the null hypothesis. The statistical test indicated a significant difference, upheld by the test statistic value of 2.50. The significance level (alpha) of 0.05 is a commonly used threshold for significance in scientific studies. In this context, the finding suggests that the increase in respiratory infection cases is statistically significant, and the null hypothesis can be rejected.

https://brainly.com/question/32386318

#SPJ11

By applying sample space concept, it can be concluded that the sample space for this experience is {(0,g), (0,f), (0,s), (1,g), (1,f), (1,s)}.

Sample space is the collection of all possible outcomes of an experiment.

Complement of a set A is a set whose members are members of the sample space but are not members of set A. It is mathematically written as \(A^{c}\).

Some code used in the problem:

1 = have insurance

0 = not have insurance

g = good

f = fair

s = serious

The sample space (S) for this experience describes all possible outcomes, combining the insurance possession and the condition.

S = {(0,g), (0,f), (0,s), (1,g), (1,f), (1,s)}

If A = event that the patient is in serious condition, then the outcomes in A = {(0,s), (1,s)}

If B = event that the patient is uninsured, then the outcomes in B = {(0,g), (0,f), (0,s)}

The outcomes in event \(B^{c}\) ∪ A can be obtained by determining the outcomes of \(B^{c}\).

\(B^{c}\) = {(1,g), (1,f), (1,s)}

so \(B^{c}\) ∪ A = {(1, g), (1, f), (1, s), (0, s)}

Original question:

A hospital administrator codes incoming patients suffering gunshot wounds according to whether they have insurance (coding 1 if they do and 0 if they do not) and according to their condition, which is rated as good (g), fair (f), or serious (s). Consider an experiment that consists of the coding of such patients.  

(a) Give the sample space of this experiment.  

(b) Let A be the event that the patients is in serious condition. Specify the outcomes in A.  

(c) Let B be the event that the patients is uninsured. Specify the outcomes in B.  

(d) Give all the outcomes in the event \(B^{c}\) ∪ A

To learn more about sample space, click here: https://brainly.com/question/24652200

#SPJ4

(a) The probability that all 4 missiles will fire is 0.2098 and (b) The probability that at most 2 will not fire is 0.0099.

Here we need to use the concept of combinations to get our required answer.

Here we have been given that 4 out of 14 missiles are defective.

Hence 10 missiles are working.

A sample of 4 missiles was chosen

Hence the simple can be chosen in ¹⁴C₄ ways

a)

The probability that all 4 missiles will fire is

¹⁰C₄/¹⁴C₄

= 0.2098

b)

The probability that at most 2 will not fire is

1 - the probability of including all three defective missiles

= 10³C₃/¹⁴C₄

= 0.0099

To learn more about Probability visit

https://brainly.com/question/30034780

#SPJ4

(a) Probability all 4 fire: 0.3297. (b) Probability at most 2 not fire: 0.9591.

(a) To track down the chance that all of the 4 rockets will fire, we actually need to do not forget the quantity of methods we can select 4 operating rockets out of the eleven that are not unsuitable, isolated by the all out range of approaches we will select four rockets out of the whole component.

The amount of ways of selecting four operating rockets out of the eleven that aren't improper is given by way of the combination recipe:

C(eleven,four) = 330

The absolute quantity of methods of selecting four rockets out of the entire part is given via:

C(14,4) = 1001

Subsequently, the chance that each one of the four rockets will hearth is:

P(all four hearth) = C(11,four)/C(14,4) = 330/1001 ≈ zero.3297

(adjusted to 4 decimal spots)

(b) To find the likelihood that at most 2 rockets might not fire, we need to remember every one of the potential conditions in which 0, 1, or 2 poor rockets are selected, and afterward song down the likelihood of every case and upload them up.

Case 1: No defective rockets are selected

The amount of ways of selecting four working rockets out of the eleven that are not faulty is given through the mixture recipe:

C(11,four) = 330

Subsequently, the chance of choosing no defective rockets is:

P(0 inadequate) = C(eleven,4)/C(14,four) ≈ 0.3297

Case 2: One defective rocket is chosen

The quantity of ways of selecting three operating rockets out of the eleven that are not poor is given with the aid of the combo equation:

C(eleven,three) = 165

The amount of ways of selecting 1 damaged rocket out of the three that are available is given through the mix equation:

C(three,1) = 3

Subsequently, the all out number of approaches of selecting 1 insufficient and three running rockets is:

C(eleven,three) × C(3,1) = 495

Thusly, the probability of choosing one deficient rocket and three running rockets is:

P(1 deficient) = C(eleven,three) × C(three,1)/C(14,4) ≈ 0.4655

Case three: Two poor rockets are selected

The amount of approaches of choosing 2 poor rockets out of the three which might be handy is given through the combination recipe:

C(3,2) = 3

The amount of ways of choosing 2 running rockets out of the 11 that aren't faulty is given via the mix recipe:

C(11,2) = 55

In this way, the all out number of methods of selecting 2 broken rockets and 2 working rockets is:

C(3,2) × C(eleven,2) = one hundred sixty five

Subsequently, the chance of choosing two incorrect rockets and two operating rockets is:

P(2 insufficient) = C(3,2) × C(11,2)/C(14,four) ≈ 0.1638

Subsequently, the likelihood that at maximum 2 rockets might not fireplace is:

P(at maximum 2 don't fire) = P(zero imperfect) + P(1 blemished) + P(2 deficient) ≈ 0.9591

(adjusted to 4 decimal spots).

To learn more about probability, refer:

https://brainly.com/question/1581511

#SPJ4

Answer:

32. C

34.C

36. 2

Answer:

32. C, 34. C, 35. C, 36. 2 miles

Step-by-step explanation:

32. C because you can see the ratio is 7:1. There is only one answer that has a ratio of 7:1 which is C

34. C because the ratio of batches of cookies to cooking oil is \(1:\frac{2}{3}\) since you want 4 batches of cookies, multiply 4 by \(\frac{2}{3}\) to get C

35. C because the ratio of butter to sauce is \(\frac{2}{3}:2\frac{1}{2}\) multiply \(\frac{2}{3}\) by 4 to get C

36. 2 miles because the ratio of miles to hours is \(\frac{1}{2} :\frac{1}{4}\) multiply \(\frac{1}{2}\) by 4 to get 2 miles

Quantitative data can be further classified as continuous or nonsequential is false.

Can continuous quantitative data exist?

To know more about quantiative check the below link:

https://brainly.com/question/14037311

#SPJ1

Answer: 9%

Step-by-step explanation: as all the marks are out of 100 i suppose

so Ali got 58% at eng and 49% at math

so 58-49=9%

and that is how we get the answer

Answer:

9%

Step-by-step explanation:

because 58-49=9 and then add the percentage and then u get the answer

Answer:

8.125 inches

Step-by-step explanation:

Ok so basically what you needed to do was this

Find out what was the value like this 3 1/4 = 3.25 and 2 1/2 = 2.5

Then you will do

3.25 x 2.5 and get your answer

8.125

There you go! Have a Wonderful Day

Answer:

Avery needs to pay $14.84

Step-by-step explanation:

When there's a tax we need to sum the original value of the product with the tax's value. To find the amount of money Avery needs to pay in taxes we can apply a rule of three as shown below:

\(\frac{14}{x} = \frac{100}{6} \frac{\%}{\%}\)

Where "x" is the tax value, and $14 represents 100%, since it's the value used to calculate the tax. We have:

\(x = \frac{14*6}{100}\\x = \frac{84}{100}\\x = 0.84\)

The value to be paid is the product value plus the tax, therefore:

\(\text{paid} = 14 + 0.84 = 14.84\)

Avery needs to pay $14.84