Where is this function discontinuous? Justify your answer. f(x)= {−(x+2)2+1x+1(x−3)2−1​ if x≤2 if −23​.

The scalar triple product is not zero, we can conclude that the points A(1, 3, 2), B(3, 21, 6), C(5, 2, 0), and D(3, 6, 24) do not lie in the same plane.

To determine whether the points A(1, 3, 2), B(3, 21, 6), C(5, 2, 0), and D(3, 6, 24) lie in the same plane, we can use the scalar triple product.

The scalar triple product is defined as the dot product of the cross product of three vectors. In this case, we can form two vectors from the given points: AB and AC. If the scalar triple product of AB, AC, and AD is zero, then the points are collinear and lie on the same plane.

First, let's calculate the vectors AB and AC:

Vector AB = B - A = (3, 21, 6) - (1, 3, 2) = (2, 18, 4)

Vector AC = C - A = (5, 2, 0) - (1, 3, 2) = (4, -1, -2)

Next, we will calculate the scalar triple product using the vectors AB, AC, and AD:

Scalar Triple Product = AB · (AC x AD)

The cross product of AC and AD can be calculated as follows:

AC x AD = |i j k|

|4 -1 -2|

|2 3 22|

Expanding the determinant, we have:

AC x AD = (3 * -2 - 22 * 3)i - (2 * -2 - 22 * 4)j + (2 * 3 - 4 * 3)k

= (-66)i + (88)j + (2)k

= (-66, 88, 2)

Now, we can calculate the scalar triple product:

Scalar Triple Product = AB · (AC x AD)

= (2, 18, 4) · (-66, 88, 2)

= 2 * (-66) + 18 * 88 + 4 * 2

= -132 + 1584 + 8

= 1460

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Answer:

12.8 is how many kilometers drew runs

Answer:

0.62*8=4.96

happt to help

1/2 gallons of water rush down the slide each seconds.

For the given question-

Rate of running water = 1 half gallon every 3 seconds.

Rate of running water = 1 1/2 = 3/2 gallon every 3 seconds.

It means-

In every 3 seconds ----> 3/2 gallons water flows.

Thus for 1 sec, divide both side by 3.

1 seconds ----> 1/2 gallons water flows.

Therefore, 1/2 gallons of water rush down the slide each seconds.

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Answer:

b is not a linear function

Step-by-step explanation:

any equation with an x∧2 is not a linear function they produce a curved line.

Answer:

86 in.

Step-by-step explanation:

The height of the rectangular prism whose volume is 9 cubic inches and the base area is 4 square inches will be 2.25 inches.

Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.

The volume of the prism is given as,

Volume = (Base area) x (Height)

The rectangular prism has a volume of 9 cubic inches. The area of the base is 4 square inches.

Then the height of the rectangular prism is given as,

9 = 4 h

h = 9 / 4

h = 2.25 inches

The height of the rectangular prism whose volume is 9 cubic inches and the base area is 4 square inches will be 2.25 inches.

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Answer:

Two angles are said to be complementary when the sum of the two angles is 90°. Two angles are said to be supplementary when the sum of the two angles is 180°. When a transversal intersects with two parallel lines eight angles are produced. The eight angles will together form four pairs of corresponding angles.

Step-by-step explanation:

Brainlest plz!

Answer:

It's difficult to explain, so I added a photo. If you have any questions, dm me <3

Step-by-step explanation:

Answer:

\(12w^7 z^6\)

Step-by-step explanation:

\(2w^5 z(6w^2 z^5)=(2)(6)w^5 w^2 z^5 z=12w^7 z^6\)

Answer:

1: 16x11=176

2: 16x0.5=8

3: 16x1/16=1

4: 1/5x5=1

5: 2/5x2 1/2=1

Step-by-step explanation:

1: 176/16=11

2: 8/16=0.5

3: 1 by  16  and simplify: 1/16 or 0.0625

4: Solve for   by simplifying both sides of the equation, then isolating the variable.   5

5: Exact Form:    5/ 2  Decimal Form:  2.5  Mixed Number Form: 2  1 /2

Answer:

terminating

Step-by-step explanation:

when you divide 3/4 you get 0.75 which terminating means there is no remainder (0)

Answer:

30

Step-by-step explanation:

Answer:

A) 8cm

B) 12cm

Step-by-step explanation:

A) Perimeter = 4 × L

where L is the length of the sides

32 = 4 × L

32/4 = L

L = 8cm

B) Area = L^2

144 = L^2

L = square root of 144

L = 12cm

a)

The length of each side is 8 cm.

d)

The length of each side is 12 m.

A square is a two-dimensional figure that has four sides and all four sides are equal.

The area of a square is given as side².

We have,

The perimeter of the square = 32 cm

Area of the square = 144 m²

Now,

Perimeter = 32 cm

4 Side = 32 cm

Side = 32 /4

Side = 8 cm

Area = 144 m²

Side² = 144

Side = 12 m

Thus,

The length of the side is 8 cm.

The length of the side is 12 m.

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The simplified expression for the given algebraic expression \(a^{2} c^{2} -b^{2} c^{2} -4a^{2} d^{2} +4b^{2} d^{2}\) is \((a+b)(a-b)(c+2d)(c-2d)\)

As per the question statement, we are given an algebraic expression

\(a^{2} c^{2} -b^{2} c^{2} -4a^{2} d^{2} +4b^{2} d^{2}\) and we are supposed to solve and simplify it.

Solution:

\(a^{2} c^{2} -b^{2} c^{2} -4a^{2} d^{2} +4b^{2} d^{2}\\c^{2} (a^{2} -b^{2})-4d^{2}(a^{2} -b^{2})\\(a^{2} -b^{2})(c^{2}-4d^{2})\\(a^{2} -b^{2})(c^{2}-(2d)^{2})\\\)

Have used Distributive property for solving and simplifying the above algebraic expression.

Now using the property, \(a^{2} -b^{2} =(a+b)(a-b)\)

We get,

\((a+b)(a-b)(c+2d)(c-2d)\)

Therefore \((a+b)(a-b)(c+2d)(c-2d)\) is our required answer.

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Since we know that the equation has the solutions  \(x = 4\) and \(x = -4\) the value of a could be either  \(8\) or  \(-8\) .

We know that the product of two factors is equal to zero only when at least one of the factors is zero.

\((x + 4) \ (2x - a) = 0\)

This equation has two factors:  \((x + 4)\) and \((2x - a)\) . We can set each of these factors equal to zero and solve for x to find the values that make the equation true.

Setting  \((x + 4)\) equal to zero, we get:

\(x + 4 = 0\)

\(x = -4\)

This means that  \(-4\) is one of the solutions of the equation.

Setting  \((2x - a)\) equal to zero, we get:

\(2x - a = 0\)

\(2x = a\)

\(x = a/2\)

This means that \(a/2\) is another solution of the equation.

Since we know that the equation has the solutions  \(x = 4\) and \(x = -4\)  , we can substitute these values into the expression we found for x in terms of a to get:

\(a/2 = 4\) or  \(a/2 = -4\)

Solving for a in each case, we get:

\(a = 8\) or \(a = -8\)

Therefore, the value of a could be either  \(8\) or  \(-8\) .

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Step-by-step explanation:

Least common multiple of 66 and 88 is 2424. Convert -\frac{5}{6}−

6

5

and \frac{83}{8}

8

83

to fractions with denominator 2424.

-\frac{20}{24}+\frac{249}{24}−

24

20

+

24

249

Step 2

Since -\frac{20}{24}−

24

20

and \frac{249}{24}

24

249

have the same denominator, add them by adding their numerators.

\frac{-20+249}{24}

24

−20+249

Step 3

Add -20−20 and 249249 to get 229229.

\frac{229}{24}

24

229

answer:222/24 = 9.5419999967

what kinda question is this lol

First let's find how many kilometers the jeep traveled, by subtracting the odometer readings:

Now, to find the miles per gallon, we just need to divide the kilometers by the amount of gallons of gasoline:

So Harry got 17.8 miles per gallon with the Jeep.

In a supermartingale , the current variable (\(X_{t}\)) is an overestimate for the upcoming \(X_{t + 1}\).

A sequence of random variable (\(X_{t}\)) adapted to a filtration (\(F_{t}\)) is a martingale (with respect to (\(F_{t}\))) if  all the following holds for all t :

(i)   E|\(X_{t\)| < ∞

(ii) E[ \(X_{t + 1}\)|\(F_{t}\)] = \(X_{t}\)

If instead of condition (ii) we have E [\(X_{t + 1}\)|\(F_{t}\)]  ≥ \(X_{t}\) for all t , we then say that (\(X_{t}\))  is submartingale with respect to (\(F_{t}\)).

If instead of condition (ii) we have E [ \(X_{t + 1}\) | \(F_{t}\)] ≤\(X_{t}\) for all t , we then say that (\(X_{t}\)) is supermartingale with respect to (\(F_{t}\)).

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Answer:

Step-by-step explanation:

17-8=9 but if 18-7=11 then 19-8=7

Answer:

800 flyersOn Earth day, a local community wants to distribute 800 flyers, 300 banners, and 250 badges to volunteers in packets containing the three items. What is the greatest number of packets that can be made using all these items if each type of item is equally distributed among the packets?

To find the area of the surface obtained by rotating the given curve, x = t sin(t), y = t cos(t), about the x-axis over the interval 0 ≤ t ≤ π/4, we can set up the integral as follows:

∫[0,π/4] 2πy√(1 + (dx/dt)²) dt.

To calculate the surface area, we use the formula for surface area of revolution, which involves integrating 2πy√(1 + (dx/dt)²) with respect to t over the given interval. In this case, y = t cos(t) represents the height of the curve, and (dx/dt) = sin(t) + t cos(t) represents the derivative of x with respect to t.

Plugging these values into the integral and integrating from 0 to π/4 will give us the desired area of the surface.


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Answer: 8575/2

Step-by-step explanation:

Answer:

cant see it

Step-by-step explanation:

Answer:

5/16

Step-by-step explanation:

The equation of line in slope intercept form is y = -0.5x -3.

What is slope intercept form?

The graph of the equation y = mx + b is a line with slope m and y-intercept b. The slope-intercept method is used to depict the linear equation, where m and b are real numbers.

We are given a line on the graph.

Taking two points as (2, -4) and (-2, -2), we get the slope as

⇒m = \(\frac{-2 +4 }{-2-2}\)

⇒m = \(\frac{2 }{-4}\)

⇒m = \(\frac{-1 }{2}\)

⇒m = -0.5

Similarly,

b = -3

We know that slope intercept form is given by

y = mx + b

On substituting, we get

y = -0.5x -3

Hence, the equation of line in slope intercept form is y = -0.5x -3.

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A useful graphical method of constructing the sample space for an experiment is a tree diagram that is option A.

A tree diagram is a useful graphical method of constructing the sample space for an experiment. It is a type of diagram used to represent the possible outcomes of an event. The diagram is structured in a way that each branch of the tree represents an event that can occur, and each level of the tree represents a stage in the experiment. By using a tree diagram, it is easier to visualize and understand all the possible outcomes of an experiment and the probabilities associated with each outcome. Therefore, option A is the correct answer.

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Answer:

b

Step-by-step explanation:

(i) The average values for the variables andre, pri gpa, and act is sum of all the values divided by the total number of values.

(ii) The model atenderte 5 b0 1 b1 prigpa 1 b2act 1 u in equation form  is atenderte = b₀ + b₁ x prigpa + b₂ x act + u

(iii) The slope coefficients is  b₁ and b₂

(iv) The predicted atenderte if prigpa 5 3.65 and act 5 20 is atenderte = b₀ + b₁ x 3.65 + b₂ x 20 + u

(v) if student a has prigpa 5 3.1 and act 5 21 and student b has prigpa 5 2.1 and act 5 26, then the predicted difference in their attendance rates is  0.5

In this exercise, we will be exploring a regression model that predicts the attendance rate of students based on their academic performance variables. We will be using three variables to predict the attendance rate: "andre", "pri gpa", and "act". Here are the answers to the questions:

(i) To obtain the minimum, maximum, and average values for the variables "andre", "pri gpa", and "act", we need to first look at the data. The minimum value is the smallest value for each variable, the maximum value is the largest value for each variable, and the average value is the sum of all the values divided by the total number of values.

(ii) The regression model that predicts the attendance rate is written in equation form as

=> "atenderte = b₀ + b₁ x prigpa + b₂ x act + u".

This equation means that the predicted attendance rate (atenderte) is equal to the intercept (b₀) plus the product of the coefficient for "pri gpa" (b₁) and the value of "pri gpa" plus the product of the coefficient for "act" (b₂) and the value of "act".

(iii) The estimated slope coefficients (b₁ and b₂) tell us the expected change in the attendance rate for each one-unit increase in "pri gpa" or "act". If b₁ is positive, it means that as "pri gpa" increases, the attendance rate is expected to increase. Similarly, if b₂ is positive, it means that as "act" increases, the attendance rate is expected to increase.

(iv) To find the predicted attendance rate if "pri gpa" is 3.65 and "act" is 20, we can substitute these values into the regression equation:

atenderte = b₀ + b₁ x prigpa + b₂ x act + u

atenderte = b₀ + b₁ x 3.65 + b₂ x 20 + u

This will give us the predicted attendance rate for a student with "pri gpa" of 3.65 and "act" of 20. If there are any students in the sample with these values of the explanatory variables, then their actual attendance rate should be close to the predicted value.

(v) To find the predicted difference in attendance rates between student A (with "pri gpa" of 3.1 and "act" of 21) and student B (with "pri gpa" of 2.1 and "act" of 26), we can first use the regression equation to predict the attendance rates for each student:

Student A:

atenderteA = b0 + b1 x 3.1 + b2 x 21 + u

Student B:

atenderteB = b0 + b1 x 2.1 + b2 x 26 + u

Then, we can take the difference between the predicted attendance rates for each student:

=> atenderteA - atenderteB

=> 52.6 - 52.1 = 0.5

This will give us the predicted difference in attendance rates between the two students.

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Answer:

A

Step-by-step explanation:

5/8=0.625

0.42=0.42^2