Simplify the expression

the vector (2, -17, 13) is a nonzero vector orthogonal to the plane through the points P, Q, and R.

To find a nonzero vector orthogonal to the plane through the points P(3, 0, 3), Q(-2, 1, 4), and R(6, 2, 5), we can use the cross product of two vectors in the plane.

Let's first find two vectors in the plane. We can use the vectors PQ and PR.

PQ = Q - P = (-2, 1, 4) - (3, 0, 3) = (-5, 1, 1)

PR = R - P = (6, 2, 5) - (3, 0, 3) = (3, 2, 2)

Now we can take the cross product of PQ and PR to get a vector orthogonal to the plane:

N = PQ x PR

N = (-5, 1, 1) x (3, 2, 2)

N = (2, -17, 13)

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Answer:

The slope is undefined

Step-by-step explanation:

Since x doesn't have an existing value it leaves the slope as undefined.

Answer:

x=-2, y=3

Step-by-step explanation:

substitute 11 + 4x into the second equation for y

3x + 2(11+4x) =0

3x +22+8x=0

11x=-22

To solve for y: y=11+4(-2)

Answer: 10x+14

Step-by-step explanation: In a equation like this one you just add like terms. So 10 and 4 are added and make 14. Since there are no like terms for 10x then you just leave it be.

Answer:2000

Step-by-step explanation:They are asking for the value not the digit .The digit is 2 .It’s in the thousands place .So 2000is the value of 2.

Answer:

9

Step-by-step explanation:

f(x)=2^x +1, then f(3)

Replace the x with 3

f(3)=2^3 +1

(2*2*2)+1 = f(3)

9= f(3)

Answer:

1. a worker who works for the company from home or somewhere else

2. Going to college to get a degree for your career.

3. teacher

4. False

5. job/occupation

6. There are plenty of jobs for x-ray technicians in the area.

7. shift supervisor (Not 100% sure)

8. working toward a goal

9. Health Sciences

10. True

11. at the competing company across the street (not sure like 30%)

12. student teaching in middle school

13. They work for someone else.

14. taking classes on how medical drugs interact with one another

15. outsourcing.

Step-by-step explanation:

The two equations that represent circles with a diameter of 12 units and a center that lies on the y-axis are:

(x - 4)² + y² = 36

(x + 6)² + y² = 144

(x - 4)² + y² = 36:

This equation represents a circle with center (4, 0) since the x-coordinate of the center is 4, indicating it lies on the y-axis. The radius of this circle is √36 = 6 units. Therefore, it satisfies the given conditions.

(x + 6)² + y² = 144:

This equation represents a circle with center (-6, 0) since the x-coordinate of the center is -6, indicating it lies on the y-axis. The radius of this circle is √144 = 12 units. Hence, it also satisfies the given conditions.

x² + (y - 3)² = 36:

This equation represents a circle with center (0, 3) since the y-coordinate of the center is 3, indicating it does not lie on the y-axis. Therefore, it does not meet the given conditions.

x² + (y + 8)² = 36:

This equation represents a circle with center (0, -8) since the y-coordinate of the center is -8, indicating it does not lie on the y-axis. Thus, it does not fulfill the given conditions.

x² + (y - 5)² = 6:

This equation represents a circle with center (0, 5) since the y-coordinate of the center is 5, indicating it does not lie on the y-axis. Hence, it does not meet the given conditions.

Based on this analysis, the equations that represent circles with a diameter of 12 units and a center that lies on the y-axis are options 1 and 2:

(x - 4)² + y² = 36

(x + 6)² + y² = 144.

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We need to evaluate the expressions x^2j0''(x), xj0'(x), and x^2j0(x), where j0(x) represents the Bessel function of the first kind of order 0.

The Bessel function j0(x) can be expressed as a power series. The expressions x^2j0''(x), xj0'(x), and x^2j0(x) involve different differentiations and multiplications of the Bessel function.

To evaluate x^2j0''(x), we differentiate j0(x) twice with respect to x, multiply the result by x^2, and substitute the value of x. Similarly, for xj0'(x), we differentiate j0(x) once, multiply by x, and substitute the value of x. For x^2j0(x), we multiply j0(x) by x^2 directly.

The evaluation of these expressions requires numerical methods or specialized mathematical software as the Bessel function involves an infinite series. Analytically expressing the expressions may not be feasible.

Therefore, to obtain the specific numerical values for x^2j0''(x), xj0'(x), and x^2j0(x), it is recommended to use a mathematical software such as MATLAB, Python's scipy.special module, or Wolfram Alpha, which provide built-in functions to compute Bessel functions and their derivatives.

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Answer:

you are the only person I can be of assistance to

Step-by-step explanation:

ok is the best friends to come in the medicine and the

The coordinates of point T' is (2, -2)

A dilation is a transformation that changes the size of a figure but not its shape.

In a dilation with respect to the origin, a point (x, y) is transformed to a point (kx, ky) where k is a scale factor.

In this case, the point T (3, -3) is transformed under a dilation of 2/3 with respect to the origin.

So the image point is (kx, ky) = (3 * 2/3, -3 * 2/3) = (2, -2)

So the image point of T under a dilation of 2/3 with respect to the origin is (2, -2)

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After ten years, you will have approximately $34,448.12.

To calculate the future value of an amount invested at a certain interest rate, we can use the compound interest formula:

Future Value = Present Value * (1 + interest rate)^number of periods

In this case, we will receive $15,500 in three years and then invest it for seven more years at a 9% interest rate.

Step 1: Calculate the future value after three years.

Future Value after three years = $15,500 * (1 + 0.09)^3

Step 2: Calculate the future value after ten years (three years plus the additional seven years).

Future Value after ten years = Future Value after three years * (1 + 0.09)^7

Let's calculate the future value using the given values:

Future Value after three years = $15,500 * (1 + 0.09)^3

= $15,500 * (1.09)^3

= $15,500 * 1.295029

= $20,045.45

Future Value after ten years = $20,045.45 * (1 + 0.09)^7

= $20,045.45 * (1.09)^7

= $20,045.45 * 1.71899

= $34,448.12

Therefore, after ten years, you will have approximately $34,448.12.

It's important to note that this calculation assumes that the interest is compounded annually. If the interest is compounded more frequently (e.g., semi-annually or quarterly), the calculation would be slightly different.

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Answer: The answer is 7/12

Step-by-step explanation:

First, multiply the denominators by each other (4*3) and you get 12. Then 12 is the main denomanator. Then multiply the numberators by the opposite numberator. (3*1 and 4*1). Then you will put (4/12+3/12) which you add the numberators together but keep the same denomerator and you will get (7/12)

Since the provided equation is inconsistent, it cannot intersect.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

we can see that the second set of equation,

4x+2y=12

20x+10y=30

4/20=2/10≠12/30

1/5=1/5≠2/5

The given equation is inconsistent so it does not intersect.

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Answer:

a=1  b=2

Step-by-step explanation:

a+2b=5

3a-b=1

Multiply the second equation by 2

6a-2b=2

Add the two equations together

a+2b=5

6a-2b=2

-------------------

7a    = 7

Divide by 7

7a/7 = 7/7

a=1

Now find b

3a-b =1

3(1) -b =1

3-b=1

Subtract 3 from each side

3-b-3=1-3

-b = -2

Multiply by -1

b=2

Answer:

please mark me brainliest

Step-by-step explanation:

a+2b=5...equ 1

3a-b=1...equ 2

3a+6b=15...equ 3

3a-b=1...equ 4

elimination method

3a has been cancelled

so 6b+b=7b

15-1=14

7b=14

b=14/7

b=2

substitute 2 for b in equ 2

3a-b=1

3a-2=1

3a=1+2

3a=3

a=3/3

a=1

a=1,b=2

Based on this data, for every inch in height, the arm span increases by 1.1 inches.

Here, we have,

I put the height of people on the x-axis because this is what I am trying to correlate the arm span to. I put the arm span on the y-axis because it is dependent on height.

I used point (60,61) and (70,72) to draw the line of best fit and to get the equation. First, to get the slope I would use the slope formula of m = 72-61/70-60 or 11/10 to get a slope of approximately 1.1. Then I used (60,61) to get the rest of the equation by plugging it in: y-61 = 1.1(x -60). This becomes y-61 = 1.1x - 66. Add 61 to both sides and the final equation is y = 1.1x – 5.

The slope represents the rate of change arm span based on height. The y intercept is the arm span.

Using points (66,68) and points (70,72) I plug each into the equation y=1.1x-5 to figure each out based on the difference from the actual points and get .4 for (66,68) and 0 for point (70,72) so I would say, based on .4 and 0 for these two points that this is a good line of best fit.

Based on this data, for every inch in height, the arm span increases by 1.1 inches.

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complete question:

There are many measurements of the human body that are positively correlated. For example, the length of one's forearm (measured from elbow to wrist) is approximately the same length as the foot (measured from heel to toe). They are positively correlated because, as one measurement increases, so does the other measurement.

To estimate the integral √(ln(2)) ln(x) dx within an accuracy of 0.01 using upper and lower sums for a uniform partition of the interval [1, e], we need to divide the interval into at least n subintervals. The answer is obtained by finding the minimum value of n that satisfies the given accuracy condition.

We start by determining the interval [1, e], where e is approximately 2.718. The function ln(x)^2 is increasing, meaning that its values increase as x increases. To estimate the integral, we use upper and lower sums with a uniform partition. In this case, the width of each subinterval is (e - 1)/n, where n is the number of subintervals.

To find the minimum value of n that ensures the accuracy condition S - S < 0.01, we need to evaluate the difference between the upper sum (S) and the lower sum (S) for the given partition. The upper sum is the sum of the maximum values of the function within each subinterval, while the lower sum is the sum of the minimum values.

Since ln(x)^2 is increasing, the maximum value of ln(x)^2 within each subinterval occurs at the right endpoint. Therefore, the upper sum can be calculated as the sum of ln(e)^2, ln(e - (e - 1)/n)^2, ln(e - 2(e - 1)/n)^2, and so on, up to ln(e - (n - 1)(e - 1)/n)^2.

Similarly, the minimum value of ln(x)^2 within each subinterval occurs at the left endpoint. Therefore, the lower sum can be calculated as the sum of ln(1)^2, ln(1 + (e - 1)/n)^2, ln(1 + 2(e - 1)/n)^2, and so on, up to ln(1 + (n - 1)(e - 1)/n)^2.

We need to find the minimum value of n such that the difference between the upper sum and the lower sum is less than 0.01. This can be done by iteratively increasing the value of n until the condition is satisfied. Once the minimum value of n is determined, we have the required number of subintervals for the given accuracy.

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The relation symbol that is to be placed on the blank to make the numerical sentence correct is "<". (Option B) Thus, the correct numerical statement is: -75 < 4.

The above statement is suggestive of the fact that -75 is less than 4. Note that the relational symbol for "less than" is "<".

Relational symbols are mathematical symbols that are used to represent relationships between two or more quantities. Some common examples include "=", "≠", ">", "≥", "<", and "≤". These symbols are used to express equality, inequality, and relative magnitude in mathematical statements and equations.

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Full Question:

Which of the relation symbol is to be placed on the blank to make the numerical sentence correct? -75 ___ 4

A >

B <

C =

D all o the above

Based on the definition of an equilateral triangle, the measure of angle KML is: d 60.

An equilateral triangle can be described as a triangle that has three sides that are equal and also equal interior angles that measures 60 degrees each.

The image shows that the three sides of triangle KML are marked equally by three strokes. This shows that the three sides of triangle KML are congruent to each other. Since they are congruent, they have equal length.

Therefore, triangle KML is an equilateral triangle that has interior angles that measures 60 degrees.

Angle KML is an interior angle of the equilateral triangle, therefore:

The measure of angle KML is: d. 60 degrees.

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To determine whether the given series converges or diverges, we will use the Comparison Test.

The series we are analyzing is:

Σ(1/(n^2 + 1)^(1/2)) from n=1 to infinity.

First, we can observe that (n^2 + 1) > n^2 for all n, which means that:

1/(n^2 + 1) < 1/n^2 for all n.

Now, taking the square root of both sides:

(1/(n^2 + 1)^(1/2)) < (1/n^2)^(1/2) = 1/n.

We know that the series Σ(1/n) is a harmonic series and it diverges. Since the given series is smaller term-by-term than a divergent series, we can use the Comparison Test to conclude that the given series converges.

Your answer: The series Σ(1/(n^2+1)^(1/2)) from n=1 to infinity converges.

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Answer:

(x + 11)²

Step-by-step explanation:

x² + 22x + 121

consider the factors of the constant term (+ 121) which sum to give the coefficient of the x- term (+ 22)

the factors a + 11 and + 11 , since

11 × 11 = 121 and 11 + 11 = 22 , then

x² + 22x + 121 = (x + 11)(x + 11) = (x + 11)² ← in factored form

Answer:

hot dog= $2.25

juice= $1.50

Step-by-step explanation:

Let the price of a hot dog be $H and that of a juice be $J.

H +J= 3.75 -----(1)

2H +3J= 9 -----(2)

(1) ×2:

2H +2J= 7.5 -----(3)

(2) -(3):

2H +3J -(2H +2J)= 9 -7.5

Expand:

2H +3J -2H -2J= 1.5

J= 1.5

Substitute J= 1.5 into (1):

H +1.5= 3.75

H= 3.75 -1.5

H= 2.25

∴ The price of a hot dog and a juice is $2.25 and $1.50 respectively.

Theoretically, there is 0 chance of turning a 9 in this probability.

The probability is the proportion of favourable results to all results in the sample area. Probability of an occurrence P(E) = (Number of favourable outcomes) is how it is stated. (Sample space). In cases where it is impractical or financially unfeasible to perform repeated experiments, theoretical probability is necessary.

When calculating the probability of 9, in chance

(assuming the probability is the same on each spin) is (0/6) .

P(E)=(Number of favorable outcomes)÷(Sample space).

= 0 ÷ 6

= 0.

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if a kite is also a parallelogram, then it must be a rhombus is the correct statement

Is A rhombus a parallelogram?

Also, every rhombus is considered as a parallelogram but the converse is always not true. Parallelogram: A parallelogram is a flat-shaped figure. It has four sides. The pair of opposite faces/sides of a parallelogram are parallel and congruent to each other.

The only set of two parallelograms is the third one: square and rhombus.

Parallelograms are quadrilaterals (polygons with 4 sides) whose opposite sides are parallel.

Square, rhombus and rectangle are parallelograms.

Some kites may be parallelograms but not all the kites are parallelograms and trapezoid are not parallelograms.

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Answer:

b

Step-by-step explanation:

Answer:

-32

Step-by-step explanation:

The differences between two samples are more likely to be statistically significant if the samples are and the standard deviations of the samples are: large and the standard deviations of the samples are small.

Now,

Hence, The differences between two samples are more likely to be statistically significant if the samples are and the standard deviations of the samples are: large and the standard deviations of the samples are small.

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Answer:

I think -$111.21 soB i am really bad at math

Step-by-step explanation:

Answer:

5765/574

Step-by-step explanation:

there u go lol