What are the domain and range of the function f(x) = -
OD: {X E R | X + -2},R: {ye Rly +-8}
E
OD: (x = R X
4),R: {ye Rly -2}
OD: {x € R | x # 2},R: {y = R | y + 8)
x² - 4x-12?
X+2
OD:{X = R | x # -4},R: {y = R | y + 2}

The measures of the angles BCA and ABD are equal because they are both right angles.

The line segment BD is a tangent to the circle with diameter AB. We need to find out the reason why the measure of angle BCA must be equal to the measure of angle ABD. The diagram is attached below.

Since AB is the diameter of the circle, it makes an angle equal to 180 degrees at the center of the circle. So the measure of the angle BCA is half of the angle produced by the diameter.

∠BCA = (1/2)×180° = 90°

Since the line BD is tangent to the circle, it will be perpendicular to the diameter. Hence, the angle formed by the diameter and the tangent must be the right angle.

∠ABD =  90°

Hence, both the angles are equal to each other.

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The slopes of the given lines are:

1. 2/5.

2. -1.

If a line passes through points on a graph, [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex], the formula that can be employed to find the slope of a line is given as:

Slope (m) = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

1. Using two points on the line, (3, 1) and (-2, -1):

Slope of the line = m = (-1 - 1)/(-2 - 3)

Slope of the line (m) = -2/-5

Slope of the line (m) = 2/5

The slope of the graph is 2/5.

2. Using two points on the line, (-3, 2) and (2, -3):

Slope of the line = m = (-3 - 2)/(2 -(-3))

Slope of the line (m) = -5/5

Slope of the line (m) = -1

The slope of the graph is -1.

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The polynomial f(x) = 2x³ + ax² + bx + 6 is exactly divisible by 2x - 3. The values of a and b are a = 131/27 and b = -71/9

To solve the problem, use the polynomial remainder theorem. If a polynomial f(x) is divided by a linear function with zero x = a, then the remainder r = f(a).

The given polynomial is:

f(x) = 2x³ + ax² + bx + 6

- The polynomial is exactly divisible by (2x-3) means:

f(3/2) = 0

2. (3/2)³ + a(3/2)² + b(3/2) + 6 = 0

27 + 9a + 6b + 24 = 0

9a + 6b = - 51 (equation 1)

- f(x) divided by (x+3) has remainder -28

f(-3) = -28

2. (-3)³ + a(-3)² + b(-3) + 6 = -28

9a - 3b = 20  (equation 2)

Substract equation 2 from equation 1

9a + 6b = -51

9a - 3b =  20 _

      9b = -71

         b = -71/9

9a - 3(-71/9) = 20

9a = 131/3

a = 131/27

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The width, labelled x in the figure is 162.5 meters

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

Length = 650 - 2x

Width = x

The area of a rectangle is the product of its dimensions

So, we have

Area = Length x Width

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

A = (650 - 2x) * x

Evaluate

A = 650x - 2x²

Differentiate and set to 0

650 - 4x = 0

So, we have

4x = 650

Divide by 4

x = 162.5

Hence, the width is 162.5 meters

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The answer is 4/15

2/5 * 2/3 = 2 · 2/5 · 3 = 4/15

Multiply the numerators and denominators together. Keep the result fraction to the smallest possible denominator GCD(4, 15) = 1. It cannot further simplify the fraction result by canceling in the following intermediate step.

In other words, two fifths times two thirds equals four fifteenths.

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Answer:

5/3

Step-by-step explanation:

"of" means times so so so often. It is not a hard math rule/definition. But more like a soft English-Math translation.

So, "2/5 of what"

means 2/5x (but make sure the 2/5 is a fraction beside the x, NOT the x on the bottom with the 5)

"is" means equals.

2/5x = 2/3

Multiply both sides by 5/2.

5/2 • 2/5x = 2/3•5/2

x = 2/3 • 5/2

x = 5/3

You get 5/3 either by "cancelling" the 2's OR by

fraction multiplication where you times top×top and bottom×bottom and simplify.

x = 10/6

x = 5/3

2/5 of 5/3 is 2/3.

The "what" in the question is 5/3.

During the problem disaggregation process, the logic trees should have branches that are both mutually exclusive and collectively exhaustive.

Problem disaggregation refers to the process of breaking down the larger higher-level operation into smaller plans and shorter periods. It refers to the use of analysis, logic, and facts to evaluate and understand each element of the problem in terms of causes and driver of the situation using logic trees. Logic trees improve the problem definition and aid in understanding an issue in more detail. There are different types of logic trees used in the process – factor logic tree, inductive logic tree, deductive logic tree, hypothesis tree, and decision tree. The logic trees should have branches that are MECE – mutually exclusive and collectively exhaustive. It is the second and an important step in the seven steps bulletproof problem-solving process used for complex solving.

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The test statistic is -2.60 as a sample of 380 patients found that 95 were uninsured.

A statistic used in statistical hypothesis testing is known as a test statistic. A test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single value that can be used to conduct the hypothesis test, is how a hypothesis test is typically expressed. For instance, the Z-statistic, which has the typical normal distribution under the null hypothesis, is the test statistic for a Z-test. Here,

n=380

x=95

p=95/380

p=0.25

test=(0.25-0.31)/√(0.28(1-0.28)/380)

test=-2.60

The test statistic is -2.60 because 95 out of 380 patients in the sample did not have insurance.

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The equation of a line in point- slope form, that passes through (1, -7) and has a slope of -2/3 is (y + 7) = -2/3 (x - 1)

Information gotten from the question include

a slope of -2/3

points (1, -7)

A linear function consists of functions where the variables has exponents of 1.

The equation of a line in point- slope form is expressed in the form.

(y - y₁) = m (x - x₁)

Definition of variables

(y and y₁) = refers to variables in the y direction

m = slope

x and  x₁ = refers to variables in the x direction

substituting into the slope and point (1, -7) equation gives

()y + 7) = -2/3 (x - 1)

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Events A and B are non-overlapping. Option(2) is correct.

When two sets A and B have at least one element in common, they are said to be overlapping.

The sets of photographs that don't overlap are the sets where no two pictures (correctly) don't overlap. They are the expansion of the cross-bifix-free sets of strings to two dimensions is called non-overlapping.

A red die and a blue die are rolled.

Assume that Event A is receiving the number 9.

Event B: You receive a double.

Whether events A and B overlap or not is what we want to determine.

When two red dice and two blue dice are thrown, a sample space is then provided by,

S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5),(3,6), (4,1), (4,2), (4,3), (4,4),(4,5),(4,6) (5,1), (5,2), (5,3), (5,4),(5,5),(5,6),(6,1), (6,2),(6,3)(6,4),(6,5),(6,6)}

The two dice are rolled, and there are a total of 36 outcomes.

n(S)=36

Assume that Event A is receiving the number 9.

The probable results for A = (3,6), (4,5), (5,5), (5,6), (6,3)

And let's say that you receive a double in Event B.

The events that may occur if B=(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)

We can observe that the two events are distinct from one another since there is no overlap in the potential outcomes of the two events.

Therefore events A and B are non-overlapping

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A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables.

Hence, the correlation coefficient is [tex]-0.9[/tex], i.e., [tex]x[/tex] and [tex]y[/tex] have a strong, negative correlation

What is a correlation coefficient?

A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables.

The variables may be two columns of a given data set of observations, often called a sample or two components of a multivariate random variable with a known distribution.

As we know that the correlation coefficient is a measure of the strength of the straight line or linear relationship between two variables. Correlation coefficients are expressed as values between [tex]+1[/tex] and [tex]-1[/tex].

So,

[tex](1,8),(2,3),(3,0),(4,1),(5,2),(6,1)[/tex]

As per the Excel tools i.e., CORREL function the correlation coefficient is [tex]-0.9[/tex].

Hence, the correlation coefficient is [tex]-0.9[/tex], i.e., [tex]x[/tex] and [tex]y[/tex] has a strong, negative correlation.

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40 freezers could be shipped in the container.

What is a variable?

A variable is a quality that may be measured and take on several values.

We are given that

A railroad container can hold weight=42,000 pounds

Total number of ovens for ship=90

Weight of each oven=200 lbs

Weight of each freezer=600 pounds

We have to find the number of freezers that can be shipped in the container.

Let x be the number of freezers that can be shipped in the container.

According to the question,

42000=90(200)+600x

42000=18000+600x

600x=42000-18000=24000

x=24000/600=40

Hence, 40 freezers can be shipped in the container.

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Answer:

4 tons of its body weight

Step-by-step explanation:

In this situation you must find 2% of 200. This is simply 4.

Answer: 4 tons

Step-by-step explanation:

the whale eats 2% of itself everyday, so it would be x/200= 2/100 and the whale would eat x tons, which equals 4 so it eats 4 tons of krill a day

Using percentages we calculate in the beginning there were 125 jellybeans in the jar.

Let the number of jellybeans in the jar was x.

Now student ate 20% of the jellybeans.

Number of jellybeans students ate = 20% of x = 0.2x

Number of jellybeans left = x - 0.2x = 0.8x

But the number of jellybeans is given as 100.

Therefore 0.8x = 100

or, x = 100 /0.8 = 125

Hence there were 125 jellybeans in the jar.

The English word "percentage" derives from the Latin phrase "per centum," which means "by the hundred." Percentages are fractions with a denominator of 100.

In other words, that is a relationship where it is always assumed that the value of the whole is 100.

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The pool will have 14, 477 gallons of water.

The amount of water that has leaked in 91 days = rate of leakage × number of days

Keep the values in formula

The amount of water that has leaked in 91 days = 11 × 91

Performing multiplication

The amount of water that has leaked in 91 days = 1001 gallons

Amount of water remaining after 91 days = total amount of water - the amount of water that has leaked in 91 days

Amount of water remaining after 91 days = 15,478 - 1001

Performing subtraction

Amount of water remaining after 91 days = 14, 477 gallons

Hence, after 91 days there will be 14, 477 gallons of water in the pool.

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If the common difference between every term in a sequence is the same, the sequence is arithmetic. If all of the terms in a sequence have the same common ratio, the sequence is geometric.

Take a look at the sequence 2,4,6,8, and note how each new term is created by adding a constant term, in this case 2, to the one before it.

For instance, the number 4 is created by adding 2 to the previous phrase, in this case the number 2.

Similar to how 2 + 4 = 6, another number is obtained by adding 2 to 4.

As a result, the sequence is arithmetic since there is a common difference between the sequences, which in this case is 2.

Take the numbers 3, 6, 12, etc.

Keep in mind that the ratio of the following and preceding terms is the same (6/3=2 and 12/6=2).

Such a sequence is referred to as a geometric sequence, and the constant ratio is known as the common ratio of the sequence and is typically indicated by the symbol r.

What is arithmetic sequence?

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence.

What is geometric sequence?

Every term in a geometric series is obtained by multiplying the term before it by the same number.

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Using the angle of elevation formula, the distance between John and Fred from the building is 1.2m and 1.67m.

So, the distance of the building from John and Fred is:

Now, we get the formula:

Calculate as follows:

John's distance:

Fred's distance:

Therefore, using the angle of elevation formula, the distance between John and Fred from the building is 1.2m and 1.67m.

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Using the concepts of straight line, we got 7 movies did marc watch between the beginning of week 1 and the beginning of week 5.

From the diagram given, we got that during the week 1 number of movies watch by marc is 2,while at the beginning of the week 5 the number of movies watch by marc is 9.

So, we need total  number of movies watched by marc in between week 1 and week 9 which is given by-

Number of movies watch at the beginning of week 5-Number of movies watch at the beginning of week 1

Number of movies=9-2

=>Number of movies watched by marc=7.

Hence, the number of movies marc watch between the beginning of week 1 and the beginning of week 5 is 7.

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(Complete question)

Marc is keeping track of the total number of movies he has watched over time. The line graph below actually shows the data where the number of movies corresponds to  number of movies that had been watched at the beginning of  week shown on the horizontal axis.

How many movies did Marc watch between  beginning of week 1 and the beginning of week 5? Do not include the unit in your answer.

A graph of the inequality (-2x + y ≥ -6) is shown in the image attached below.

A graph simply refers a type of chart that is typically used for the graphical representation of data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate.

Next, we would rearrange and simplify the given equation in slope-intercept form as follows:

-2x + y ≥ -6

Adding 2x to both sides of the inequality, we have the following equation:

-2x + y + 2x ≥ -6 + 2x

y ≥ -6 + 2x

Rearranging the equation in slope-intercept form, we have the following equation:

y ≥ 2x - 6

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17576000 courses can be given unique catalog numbers.

There are three numbers and three English letters.

Each of three numbers can be chosen from 0 to 9, so the ways to choose each number is  = 10

So the total number to choose three numbers = 10*10*10 = 1000

Each of letters can be chosen from A to Z.

Number of choice for the each letter = 26

So, the outcomes of letter combination = 26*26*26 = 17576

Hence the total possible catalog numbers = 1000*17576 = 17576000

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17.5 litres of must be added to 14 litres of a 90% acid solution to obtain a 40% acid solution.

A percentage is a number or ratio expressed as a fraction of 100.

Given that, there are 14 litres of a solution which is 90% acidic,

Let water added be x, then according to question,

0.90*14 = 0.40(x+14)

12.6 = 0.40x + 5.6

0.40x = 7

x = 17.5

Hence, 17.5 litres of must be added to 14 litres of a 90% acid solution to obtain a 40% acid solution.

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Answer:

He has to sell 5000 to earn $1000

Step-by-step explanation:

1000/0.2 = 5000

The proof that shows that lines DC and AB are parallel is shown below.

The SSS congruence theorem states that two triangles that have three corresponding congruent sides are congruent to each other.

When two triangles are proven to be congruent triangles, invariably, we can state that the corresponding parts of both triangles are also equal to each other by CPCTC.

The following proof shows lines DC and AB are parallel lines:

Statement                                              Reasons                                                    

1. AB = CD                                             1. Given

AD = CB                                    

2. Line AC = Line AC                            2. Reflexive property

3. Triangle ADC ≅ Triangle ABC         3. SSS

4. Angle 1 ≅ Angle 4                             4. CPCTC

5. DC║AB                                              5. Converse of alternate interior ∠s theorem

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The two positive numbers are 5 , 5.

Given:

Product of two positive numbers = 25

sum of these number is minimum.

Let a and b be the two positive numbers.

a*b = 25

b = 25/a

sum s = a+b

= a + 25/a

apply derivation on both sides.

ds/da = 1 - 25/[tex]a^{2}[/tex]= 0.

1 = 25/[tex]a^{2}[/tex]

a = [tex]\sqrt{25}[/tex]

a = 5 , -5

since given are positive numbers so 5 is considered.

b = 25/5

b = 5

Therefore the two positive numbers are 5 , 5.

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Answer:

22.479411764705882352941176470588

Step-by-step explanation:

76.43/3.4

=22.479411764705882352941176470588

Considering an exponential function, it is found that:

a) The half-life of the element is of 39.63 days.

b) The time needed is of 51.82 days.

A decaying exponential function is modeled by the equation presented as follows:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which the variables of the equation are:

In this problem, the parameters are given as follows, from the text:

A(0) = 120, A(11) = 99.

Hence the decay rate r is obtained as follows:

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]120 = 99(1 - r)^{11}[/tex]

[tex](1 - r)^{11} = \frac{99}{120}[/tex]

[tex]1 - r = \sqrt[11]{\frac{99}{120}}[/tex]

[tex]1 - r = \left(\frac{99}{120}\right)^{\frac{1}{11}}[/tex]

1 - r = 0.98266367982

Hence the equation is:

[tex]A(t) = A(0)(0.98266367982)^t[/tex]

The half-life is the value of t for which:

A(t) = 0.5A(0).

Hence:

[tex]A(t) = A(0)(0.98266367982)^t[/tex]

[tex]0.5A(0) = A(0)(0.98266367982)^t[/tex]

[tex](0.98266367982)^t = 0.5[/tex]

[tex]\log{(0.98266367982)^t} = \log{0.5}[/tex]

[tex]t\log{(0.98266367982)} = \log{0.5}[/tex]

[tex]t = \frac{\log{0.5}}{\log{(0.98266367982)}}[/tex]

t = 39.63 days.

For item b, the time is obtained as follows:

[tex]A(t) = 99(0.98266367982)^t[/tex]

[tex]40 = 99(0.98266367982)^t[/tex]

[tex](0.98266367982)^t = \frac{40}{99}[/tex]

[tex](0.98266367982)^t = 0.40404040[/tex]

[tex]t = \frac{\log{0.40404040}}{\log{(0.98266367982)}}[/tex]

t = 51.82 days.

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The required answer in mixed number for a given operation is [tex]8\frac{4}{9}[/tex]

What are mixed numbers?

A whole number and a proper fraction are both expressed together as a mixed number. A number between any two whole numbers is typically represented by it.

Given,     [tex]2\frac{8}{9} + 5\frac{5}{9}[/tex]

             [tex]= \frac{(2*9)+8}{9} +\frac{(5*9)+5}{9}[/tex]

             [tex]= \frac{18+8}{9} +\frac{45+5}{9}[/tex]

              [tex]= \frac{26}{9} +\frac{50}{9}[/tex]

               [tex]= \frac{26+50}{9} = \frac{76}{9} = 8\frac{4}{9}[/tex]

Hence, the required answer for the given term is  [tex]8\frac{4}{9}[/tex] .

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The corresponding estimate for numbers in 1,2,3 and 4 are 10, 24, 21 and 153

Estimation and approximation is the process of using rounded values when presenting numerical data and making rough calculations.

The digits 1,2,3 and are rounded down and digits 5,6,7,8 and 9 are rounded up

1.  2.1 x 5.12 =  2 x 5 = 10

Explanation: The number after the digit 2 in 2.1 is 1, we will round down 2.1 to 2. Also, the number after the digit 5 in 5.12 is 1, we will round down 5.12 to 5

2. 12.3 x 1.6 = 12 x 2 = 24

Explanation: The number after the digit 12 in 12.3 is 3, we will round down 12.3 to 12. Also, the number after the digit 1 in 1.6 is 6, we will round up 1.6 to 2

3. 6.5 x 3.1 = 7 x 3 = 21

Explanation: The number after the digit 6 in 6.5 is 5, we will round up 6.5 to 7. Also, the number after the digit 3 in 3.1 is 1, we will round down 3.1 to 3

4. 51.3 x 2.7 = 51 x 3 = 153

Explanation: The number after the digit 51 in 51.3 is 3, we will round down 51.3 to 51. Also, the number after the digit 2 in 2.7 is 7, we will round up 2.7 to 3

Therefore, the estimate for 1,2,3 and 4 are 10, 24, 21 and 153 respectively

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Answer:

Step-by-step explanation:

Let's find the equation in the form of y=mx+b that fits the data.  m is the slope and b is the y-intercept (the value of y when x=0).  Slope, m, the the Rise/Run of the line.  It can be found by taking any two points from the table.  Let's choose (0,15) and (2,35), although any two will work.

x    y

0   15

1    25

2   35

3   45

4   55

(0,15)   (2,35)

The Rise is the change in y:  (35 - 15) = 20.

The Run is the change in x for the same points:  (2 - 0) = 2

The slope is the Rise/Run = (20/2) or 10.

The equation has the form y = 10x + b.

Let's find b.  Just enter any of the points in the above equation and solve for b.  I'll choose (3,45).

  y = 10x + b

  45 = 10*(3) + b

b = 45 - 30

b = 15

[Note:  since b is the value of y when x equals zero, we really didn't need to calculate b as we just did.  There is a data point already that tells us the value of y when x = 0:  (0,15)]