Find a and b such that the function is differentiable everywhere. f(x) x2 -2x+ 2 if x s -2 ax b if x> -2.

Applying the distance formula, to calculate the coordinates of B, use: 3 =√[(x-4)² + (y-2)²]  

The distance formula, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], is used to find the distance between two points on a coordinate plane.

We are given one point A(4, 2), let:

B (x, y) = (x2, y2)

A(4, 2) = (x1, y1)

d = 3 units

Plug in the values into the distance formula to find how to calculate the coordinates of B:

3 =√[(x-4)² + (y-2)²]  

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The record that represents an outlier in this data set is John's weight.

An outlier is a data point that differs significantly from other observations.

In other words, an outlier is a value or point that differs substantially from the rest of the data.

Therefore, the record that represents an outlier in this data set is  John's weight. This is because it is on the

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The results of the survey best illustrate the framing effect.

People make choices based on whether possibilities are given with positive or negative connotations, such as as a gain or a loss, according to a cognitive bias known as the framing effect.

When provided with a positive frame, people tend to avoid danger, but when offered with a negative frame, they tend to seek out hazards.

The scenario of framing effect defines gain and loss as descriptions of results.

The idea aids in the development of framing effect understanding in social movements as well as in the creation of political opinion, where spin plays a significant role in political opinion polls that are framed to encourage a response advantageous to the group that commissioned the poll. It has been asserted that the framing effect is invalidating political polls.

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A and B are independent events if the probability of getting a red convertible is 0.08

The given parameters are:

P(A) = 0.20

P(B) = 0.40

The events are independent, if

P(A and B) = P(A) * P(B)

So, we have:

P(A and B) = 0.20 * 0.40

Evaluate

P(A and B) = 0.08

Hence, A and B are independent events if the probability of getting a red convertible is 0.08

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Complete question

A video game randomly chooses your car color and type. The probability of getting a red car is 0.20, and the probability of getting a convertible is 0.40.

Event A = You get a red car.

Event B = You get a convertible.

A and B are independent events if _____.

A.The probability of getting a red car or a convertible is 0.60.

B.The probability of getting a red car or a convertible is 0.08.

C.The probability of getting a red convertible is 0

D.The probability of getting a red convertible is 0.08

#6

Yes

Direct variation because Time increases cupcakes increases and vice versa

#B

Constant of proportionality represents the amount of time required per cupcakes

#7

Yes we can find it

We have to check the x and y values of the ordered pairs (x,y)

If y is decreasing with respect to increase in x then it's inverse variation

Comparing with the original expression, the value that will go into the green box is 5

Given the indices expression below;

[tex]\frac{4^{-5}}{4^4}[/tex]

Since 4^-5 is equivalent to 1/4^5, hence the given expression will be equivalent to;

[tex]\frac{1}{4^5\times4^4}[/tex]

Comparing with the original expression, the value that will go into the green box is 5

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Answer:

x=1/3

Step-by-step explanation:

(2/x)+4=3^3+1

(2/x)+4=10

(2/x)=6

2=6x

1/3=x

x=1/3

There is also a possibility that you meant to write 2/(x+4)=3^2+1

2/(x+4)=3^2+1

2/(x+4)=10

2=10x+40

-38=10x

x=-3.8

Answer: -35/16

Step-by-step explanation:

i just took the test:)

Whenever two or more lines intersect at a point, an angle is usually produced. And some of these angles formed may have common properties, and thus be congruent.

The appropriate reasons for the given statements in the question are given below:

         STATEMENT                                          REASON

1. <1 ≅ <2                                                Vertical Angle theorem

2. <1 and <2 are complementary            

   <2 and <3 are complementary        Congruent Complements Theorem

3. <1 and <2 are supplementary              

   <2 and <3  are supplementary        Congruent Supplements

4. <1 and <2 are right angles               All Right Angles are Congruent

5. <1 ≅ <2,

   <1 and <2    are supplementary         If two angles are congruent and

                                                               supplementary, then each angle is

                                                               a right angle.

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Answer:

5/2

Step-by-step explanation:

Answer:

1 3/4 or 1.75

Step-by-step explanation:

Formula: y1-y2/x1-x2

Plug in the given coordinates: y1 = -3, y2 = 4, x1 = 2, x2 = 6

-3-4/2-6 = -7/-4 = 7/4 = 1 3/4 or 1.75

The value of the expression ((-3)^4)^2 when simplified is 6561

Expressions are mathematical statements represented by numbers, arithmetic operations and variables

The expression is given as:

((-3)^4)^2

Start by expanding the inner bracket

((-3)^4)^2 = ((-3)*(-3)*(-3)*(-3))^2

Next, we evaluate the product (-3)*(-3)*(-3)*(-3)

This gives

((-3)^4)^2 = (81)^2

Next, expand the exponent

((-3)^4)^2 = (81) * 81

Next, we evaluate the product

This gives

((-3)^4)^2 = 6561

Hence, the value of the expression ((-3)^4)^2 when simplified is 6561

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The NBA league exhibits more competitive balance.

The chance that each team in a league has of winning the title is referred to as competitive balance. The championship would be won by each team on a regular basis in an ideal competitive environment. In contrast, if there was no balance between the two types of competition, the same team would consistently prevail.

Competitive balance is often regarded as a desirable trait because too much predictability makes fans of the lesser franchises angry and fans of the defending champions complacent, which lowers interest in the sport as a whole.

The "Noll-Scully" measure is the competitive balancing metric that is most frequently used in sports. The winning percentage of each league team's standard deviation (SD) is used to compute it. The SD is then divided by what it would be if all teams had equal talent and the outcomes were entirely random.

For NBA team, competitive balance = 0.134/32*82 = 0.343

For EPL team, competitive balance = 0.158/20*38 = 0.30

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Answer:

Step-by-step explanation:jneke

There is no such value of 'a' such that f(x) = 9x² + 4 and g(x) = (3x - a)² are equivalent.

Two polynomials are said to be equivalent only when the coefficients of all powers of x are equal for both the polynomials.

In the question, we are asked is there a value of 'a' such that f(x) = 9x² + 4 and g(x) = (3x - a)² are equivalent.

We know that two polynomials are said to be equivalent only when the coefficients of all powers of x are equal for both the polynomials.

Thus to check, we expand g(x), using the formula (p - q)² = p² + q² - 2pq.

g(x) = (3x - a)²,

or, g(x) = (3x)² + (a)² - 2(3x)(a),

or, g(x) = 9x² + a² - 6ax.

For f(x) = 9x² - 4, and g(x) = (3x - a)² to be equivalent,

As we need two different values of, 'a' at the same time, which ain't possible, thus we can say that there is no such value of 'a' such that f(x) = 9x² + 4 and g(x) = (3x - a)² are equivalent.

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Kira's time exercising every day can be represented as t  ≥ 40 because she exercises for 40 minutes or more.

This situation can be represented with an inequality. An inequality is an expression that is used to represent variables. This type of expression uses symbols such as >, < or ≥ to represent different variable values.

The inequality represented in this situation implies that Kira exercises is equal or more time than 40 minutes every day.

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Answer:

sin-1 (24/25).

Step-by-step explanation:

We are given the opposite side  to the given angle (24 ft) and the hypotenuse (25 ft) .

sin = opposite / hypotenuse

- so it is  sin-1 (24/25).

Answer:

Step-by-step explanation:

I'm not entirely sure that this is correct, but it seems so to me from what I've  read.

The Coordinate system uses N,S,E,W to denote plus and minus. N (north) and E (east) are plus, and S (south) and W (west) are minus. North is + y and S is - y. E (east is plus x W is minus x)

(4,-7) = 4 east 7 south is what I would use as my answer.

It takes 4 weeks at minimum for each pair to hug at least once if they sit in random order.

Analyzing the Given Information

As per the given information,

Number of people = 8

It is given that they sit in random order every week.

W e assume that the order is not repeated.

There are 4 pairs and since a person hugs both the persons on his immediate left and right.

Determining the Number of Weeks

Total number of people to be hugged by each person = 7

Number of people hugged by a person in one week = 2

So, number of weeks taken by each to huge every other person = 7/2

⇒ It will take (3 +1) for every pair to hug.

It takes 4 weeks at a minimum for every pair to hug if we assume that  their order is not repeated.

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The rule which describe the composition of transformations that

maps ΔBCD to ΔB"C"D" is:

Reflection across the y-axis composition translation of 6 units x,

negative 5 units y ⇒ last answer

Step-by-step explanation:

Let us revise the reflection across the y-axis , horizontal translation

and vertical translation

1. If point (x , y) is reflected across the y-axis, then its image is (-x , y)

2. If point (x , y) is translated h units to the right, then its image is

  (x + h , y), if translated h units to the left, then its image is (x - h , y)

3. If point (x , y) is translated k units up, then its image is (x , y + k),

  if translated k units down, then its image is (x , y - k)

∵ The vertices of triangle BCD are (1 , 4) , (1 , 2) , (5 , 3)

∵ The vertices of triangle B'C'D' are (-1 , 4) , (-1 , 2) , (-5 , 3)

∵ The x-coordinates of the vertices of Δ B'C'D' have the same

  magnitude of x-coordinates of Δ BCD and opposite signs

∴ Δ B'C'D' is the image of Δ ABC after reflection across the y-axis

∵ The vertices of triangle B'C'D' are (-1 , 4) , (-1 , 2) , (-5 , 3)

∵ The vertices of triangle B''C''D'' are (5 , -1) , (5 , -3) , (1 , -2)

∵ The image of -1 is 5 and the image of -5 is 1

∴ The x-coordinates of the vertices of triangle B'C'D' are added by 6

∵ The image of 4 is -1 , image of 2 is -3 and the image of 3 is -2

∴ The y-coordinates of the vertices of triangle B'C'D' are subtracted

  by 5

∴ Δ B"C"D" is the image of Δ B'C'D' by translate 6 units to the right

 and 5 units down ⇒ (x + 6 , y - 5)

The rule which describe the composition of transformations that

maps ΔBCD to ΔB"C"D" is:

Reflection across the y-axis composition translation of 6 units x,

negative 5 units y

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The composition of transformations that maps BCD to B"C"D" is described by the following rule:

Composition translation of 6 units x, negative 5 units y across the y-axis last response

Let us rewrite the y-axis reflection, horizontal translation, and vertical translation.

1. If point (x, y) is mirrored across the y-axis, the image of that point is (-x , y)

2. If point (x, y) is translated h units to the right, its image is (x + h, y), and if it is translated h units to the left, its image is (x + h, y) (x - h , y)

3. If point (x, y) is translated k units up, its image is (x, y + k), but if it is translated k units down, its image is (x , y - k)

∵ Triangle BCD has (1, 4) vertices, (1, 2) vertices, and (5, 3) vertices. Triangle B'C'D' has (-1, 4) vertices, (1, 2) vertices, and (5, 3) vertices. The x-coordinates of the B'C'D' vertices have the same magnitude as the x-coordinates of BCD and opposite signs. B'C'D' is the picture of ABC after it has been reflected across the y-axis.

The vertices of triangle B'C'D' are (-1, 4), (-1, 2), (-5, 3), (1, -2)

The vertices of triangle B"C"D" are (5, -1), (5, -3), (1, -2)

The x-coordinates of the triangle B'C'D' vertices are added by 6.

The image of 4 is -1, the image of 2 is -3, and the image of 3 is -2.

The y-coordinates of triangle B'C'D' vertices are subtracted by 5.

∴ Δ B"C"D" is the image of Δ B'C'D' by translating 6 units to the right

and 5 units down ⇒ (x + 6 , y - 5)

The rule which describe the composition of transformations that

maps ΔBCD to ΔB"C"D" is:

Reflection across the y-axis composition translation of 6 units x,

negative 5 units y

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The stock worth when she sells it eight years later $545, If the stock decreases at a rate of 15% per year for eight years.

According  to the question,

Petra opens her mail one day to find that an anonymous donor has given her $3000 cash. She sets aside $1000 to refurnish her apartment, and decides to invest the other $2000.

If the stock decreases at a rate of 15% per year for eight years. In order to find the stock worth when she sells it eight years later we have the formula

Value of stock after 'n' years = Principal[1-Rate/100]ⁿ

Value of stock after '8' years = 2000[1-15/100]⁸

= 2000[1-0.15]⁸

=2000[0.85]⁸

=2000[0.2725]

=545$

Hence, the stock worth when she sells it eight years later $545, If the stock decreases at a rate of 15% per year for eight years.

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Answer:

5 days

(the exact number of days below)

Step-by-step explanation:

65/7=9.28571429

9.28571429 sec = 1 dollar

464285.715 seconds=50000 dollars

464285.715 seconds=5.373677256944 days

Answer:

3/5

Step-by-step explanation:

the chance of landing on an even number (2 or 4) is 2/5

the chance of landing on the unshaded section (3) is 1/5

add the 2 together since the problem said "or" to get 3/5

The probability that one would have selected 2 five-dollar bills is; 1/4.

It follows from the task content that the piggy bank contains; 4 one-dollar bills and 4 five-dollar bills to make a total of 8 bills.

Hence, provided the probability events are carried out with replacement, the probability to have selected 2 five-dollar bills is;

= 4/8 × 4/8

= 1/4.

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Answer:

1/4

Step-by-step explanation:

Because we have a vertical asymptote at x = 0 and a horizontal asymptote at y = -1, we conclude that the correct option is the last one.

Here we have the function:

[tex]f(x) = \frac{1}{x} - 1[/tex]

First notice that we have a vertical asymptote at x = 0, because we can't divide by zero.

Now, notice that when x tends to infinity or negative infinity, the first term becomes zero, then we have a horizontal asymptote at y = -1.

Then the correct option is the last one:

"On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 0, and the horizontal asymptote is at y = negative 1."

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Answer:

Last option

Step-by-step explanation:

Hello,

Pythagorean theorem :

x² = 8² + 8²

x² = 64 + 64

x² = 128

x = √128

x = √(64 × 2)

x = √(8² × 2)

x = 8√2

→ Answer D

The equation that can be used to represent total tickets sales is 2170 = 5s + 2f + 10a

let

Expression for number of students tickets sold;

s = f + 15

Expression for number of faculty tickets sold;

f = 2a

Expression for number of alumni tickets sold;

f = 2a

a = f/2

2170 = 5s + 2f + 10a

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Percentages are used to show the fraction of a thing. For example, if 5 students out of 20 like math, the percentage is 5/20 x 100= 25%

This refers to the number of ratios that is described as a fraction of 100 and is denoted by the sign %.

Hence, we can see that although your question is incomplete, I gave you a general overview of percentages for a better understanding of the concept.

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Yes, (3, -2) is a solution for the linear system y = 2x - 8 and 2x + 4y = -2

In mathematics, the theory of linear systems is the foundation and core part of linear algebra, a subject that is used in most parts of modern mathematics. When the number of equations is the same as the number of variables, there is likely to be a solution. Not guaranteed, but likely.

If there is no solution, the equations are called "inconsistent".

One or infinitely many solutions are called "consistent"

In mathematics, a system of linear equations is a set of one or more linear equations involving the same variables

We need to find whether (3, -2) is a solution for the linear system y = 2x - 8 and 2x + 4y = -2 or not

Let y = 2x - 8.......(1)

From equation (1) we get, y - 2x = -8.....(2)

2x + 4y = -2.........(3)

Put (3,-2) in equation (2) , we get

-2 - 2(3) = -2 -6 = -8

LHS = RHS

Put (3,-2) in equation (3) , we get

2(3) + 4(-2) = 6 - 8 = -2

LHS = RHS

Hence,(3, -2) is a solution for the linear system y = 2x - 8 and 2x + 4y = -2

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The equation of a trend line that passes through the points (7, 450) and (14, 401) is y = -7x+99.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.

Points are: (7, 450) and (14, 401)

Slope(m)=(401-450)/(14-7)

              = -49/7

              = -7

Equation of trend line:

(y-450)= -7(x-7)

y-450= -7x+49

y= -7x+49+450

y= -7x+499

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The Number of people is 12 when time taken is 2 hours.

According to the statement

Time taken when 10 people works is 3 hours

Time taken when 5 people works is 8 hours

Then we have to find the number of peoples when time taken is 2 hours.

So, average time that for which single person works is 180 min/ 10 = 18 min.

It means the average time for single person works is 18 min in case of 10 people.

and one thing is clear that the number of people is greater than 10 people when time taken is 2 hours.

So, The Number of people is 12 when time taken is 2 hours.

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Answer:

50000

Step-by-step explanation:

Using

[tex]P(percentage) \times CP(cost \: price) = Sales \: Tax[/tex]

Putting the given values

P × 25000 = 1750

[tex]P = \frac{1750}{25000} [/tex]

[tex]P = 0.07 \times 100[/tex]

[tex]P = 7\%[/tex]

Now

For purchase price of a new car.

[tex]P \times CP=Sales \: Tax[/tex]

[tex]7 \times CP = 3500[/tex]

[tex]CP = 50000[/tex]

Hope it helps you, any confusions you may ask!