Find the equation of the line.
Use exact numbers.
y =_x+7

The vector orthogonal to the plane through the points P, Q, and R is (8, -8, 12), and the area of triangle PQR is \($\sqrt{301}$\).

For part (a), we can find a nonzero vector orthogonal to the plane through the points P, Q, and R by constructing a normal vector to the plane using the cross product of two vectors in the plane. The two vectors in the plane are \($\vec{PQ} = (1- (-2), 0-1, 1-3) = (3, -1, -2)$\) and \($\vec{PR} = (1-4, 0-2, 1-5) = (-3, -2, -4)$\). Taking the cross product of the two vectors gives us the normal vector to the plane, \($\vec{n} = \vec{PQ} \times \vec{PR} = (8, -8, 12)$\). Therefore, the vector orthogonal to the plane is \($\vec{n} = (8, -8, 12)$.\)

For part (b), the area of triangle PQR can be found using the formula for Heron's Formula, which states that the area of a triangle with sides a, b,and c is given by

\($A = \sqrt{s(s-a)(s-b)(s-c)}$\)

where \($s = \frac{a+b+c}{2}$\) . In this case, the sides are \($a = \|\vec{PQ}\| = \sqrt{3^2 + (-1)^2 + (-2)^2} = \sqrt{14}$, $b = \|\vec{QR}\| = \sqrt{(-2-4)^2 + (1-2)^2 + (3-5)^2} = \sqrt{14}$\), and\($c = \|\vec{PR}\| = \sqrt{(-3)^2 + (-2)^2 + (-4)^2} = \sqrt{29}$\). Plugging these values into the formula, we get

\(= \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{\frac{7(7-\sqrt{14})(7-\sqrt{14})(7-\sqrt{29})}{4}} = \sqrt{7(7-\sqrt{14})^2(7-\sqrt{29})} = \sqrt{7(7-\sqrt{14})^2(\sqrt{14}+\sqrt{29})} = \sqrt{7(7-\sqrt{14})^2\sqrt{43}} = \sqrt{301}$\)Therefore, the area of triangle PQR is \($\sqrt{301}$\)

The vector orthogonal to the plane through the points P, Q, and R is (8, -8, 12), and the area of triangle PQR is \($\sqrt{301}$\).

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I don't have gotten any answer of this question

Answer:

Prime

Step-by-step explanation:

Answer:

\(1.)\\\frac{{6\choose3}*{10\choose4}}{{16\choose7}}= 36.7133\\2.)\\\frac{{5\choose3}*{11\choose4}}{{16\choose7}}= 28.8462\\3.)\\\frac{{7\choose4}}{{18\choose4}}= 1.1438\\4.)\\\frac{{4\choose4}*{48\choose1}}{{52\choose5}}= .0018\\5.)\\\frac{{13\choose5}}{{52\choose5}} = .0495\\6.)\\\frac{{12\choose4}*{40\choose1}}{{52\choose5}}= .7618\\7.)\\\frac{{4\choose2}*{4\choose2}*{44\choose1}}{{52\choose5}}= .0609\\8.)\\\frac{{4\choose1}*{48\choose4}}{{52\choose5}}= .2995\)

all numbers were intended to % attached at the end, i just don't know how to do it.

Answer:

take away 8 from 14 then see if the answer works for x by doing 28 - that answer

Step-by-step explanation:

Answer:

w = x+2/a−3

Step-by-step explanation:

Let's solve for w

aw−x=3w+2

Step 1: Add -3w to both sides

aw−x+−3w=3w+2+−3w

aw−3w−x=2

Step 2: Add x to both sides

aw−3w−x+x=2+x

aw−3w=x+2

Step 3: Factor out variable w

w(a−3)=x+2

Step 4: Divide both sides by a-3

w(a−3)/a−3 = x+2/a−3

w = x+2/a−3

The value of w is (2+x)/ (a-3).

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

aw-x=3w+2

Now, solving for w

aw - 3w = 2 + x

w(a-3 )= 2+x

w= (2+x)/ (a-3).

Hence, the value of w is (2+x)/ (a-3).

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The ratio of dividends to the average number of common shares outstanding is known as the dividend yield. It is a measure of the return on an investment in the form of dividends received relative to the number of shares held.

To calculate the dividend yield, you need to divide the annual dividends per share by the average number of common shares outstanding during a specific period. The annual dividends per share can be obtained by dividing the total dividends paid by the number of outstanding shares. The average number of common shares outstanding can be calculated by adding the beginning and ending shares outstanding and dividing by 2.

For example, let's say a company paid total dividends of $10,000 and had 1,000 common shares outstanding at the beginning of the year and 1,500 shares at the end. The average number of common shares outstanding would be (1,000 + 1,500) / 2 = 1,250. If the annual dividends per share is $2, the dividend yield would be $2 / 1,250 = 0.0016 or 0.16%.

In summary, the ratio of dividends to the average number of common shares outstanding is the dividend yield, which measures the return on an investment in terms of dividends received per share held.

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Answer:

369 cans

Step-by-step explanation:

Add the two numbers of cans collected by each:

Alan:   154 cans

Betty:  215 cans

Total:  369 cans

The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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Extrapolation is the use of the regression line to estimate a mean of y-values for an x-value that is far outside the x-range of data.

What is extrapolation?

A statistical technique called extrapolation aims to understand the unknown data from the known data. It uses historical data to attempt to predict future data. For instance, using the current population size and growth rate to project the size of a population in a few years.

Predicting hypothetical values outside of a specific data set is the goal of extrapolation.

Contrary to interpolation, which typically focuses on estimating past values, extrapolation is used to predict unknown future values due to its predictive nature.

Hence, extrapolation is the use of the regression line to estimate a mean of y-values for an x-value that is far outside the x-range of data.

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Answer:

4

Step-by-step explanation:

because 5 times 5 is 25 which 25 is how many cards fit in one section so 100-25=75 and so you could say that 100 divided by 25 is 4 so he will need 4 sections hope you find this helpful! :D

Answer:

A receipt is a record of a transaction that apready happened.

Answer:

(4,2),(5,−3),(−1,7),(0,9)

Step-by-step explanation:

Answer:

this is correct answer

Step-by-step explanation:

you supports to write this

The values of x and y in the triangle are x = 100 degrees and y = 50 degrees

The possible figure that completes the question is added as an attachment

From the figure, we have the following properties

The above highlights mean that

Angle y = 50

Rewrite as

y = 50

Also by the opposite external angle theorem, we have

x= y + 50

This gives

x = 50 + 50

Evaluate

x = 100

Hence, the angles are x = 100 degrees and y = 50 degrees

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The major variable in this statistics class is considered a nominal variable.

The major variable is considered a nominal level of measurement because it represents a categorical characteristic that cannot be ordered or measured in a quantitative manner.

In other words, the values assigned to different majors (e.g. Engineering, English, History) do not represent numerical quantities or differences.

The level of measurement of a variable determines the type of statistical analyses that can be conducted with that variable. In this case, the major variable is considered a nominal variable because it represents a categorical characteristic that cannot be ordered or measured in a quantitative manner.

Nominal variables are often used to categorize or group data based on non-numeric characteristics, such as gender, race, or occupation. By collecting data on both GPA and major, the statistics instructor can explore relationships between these variables, such as whether certain majors tend to have higher or lower GPAs.

In conclusion, the major variable in this statistics class is considered a nominal variable.

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Understanding a set’s nature or properties is made easier by its closure property

The set is closed if it has the closure property. This means that any operation performed on an element within a set will provide a result that belongs to that element’s set.

Why Closure Property is important?

Understanding a set’s nature or properties is made easier by its closure property. Mathematical applications of closure are numerous. Any operation that adheres to this condition is said to be “closed” or to have “fulfilled the operation’s closure property.”

Example – The set of even number is closed under subtraction

                   Even – Even = Even

                   6 – 4 = 2

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Answer:

no

Step-by-step explanation:

substitute the x- coordinate 5 into the equation and if the result is equal to the y- coordinate 0 then it is a solution

y = 5 + 5 = 10 ≠ 0

Then (5, 0 ) is not a solution to the equation

Answer:

This means it is between 22000000 m and 44000000 m.

Step-by-step explanation:

From the question, the UAE Hope Pobe is between 22 000 km and 44 000 km away from Mars.

Since,

1 000 m = 1 km

Then,

22 000 km = 22 000 x 1000 m

                   = 22000000 m

also,

44000 km = 44000 x 1000 m

                  = 44000000 m

Therefore, the Probe is between 22000000 m and 44000000 m.

The square of given expression √1 ( square root of 1 ) is equal to 1.

As given in the question,

Given expression is equal to √1 ( square root of 1 )

To calculate the square of √1 we have,

Let us consider variable x is equal to √1

x = √1

Now take square on both the sides of the given expression we get,

x² =  (√1 )²

⇒ x² = √1  × √1

Multiplying square root of 1 to square root of 1 is equal to 1 we get,

or use law of exponent :

√1 × √1 = \(1^{\frac{1}{2} + \frac{1}{2} }\)

            = 1

⇒ x² = 1

Therefore, the square of the given expression √1 ( square root of 1 )is equal to 1.

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The concentration of the solution prepared by adding 15.00 mL of 2.07 M into a 50.00 mL volumetric flask and diluting to the mark is approximately 0.621 M.

To calculate the concentration of the solution, we can use the formula: C1V1 = C2V2. Where: C1 = initial concentration of the solution; V1 = initial volume of the solution ; C2 = final concentration of the solution;  V2 = final volume of the solution. In this case: C1 = 2.07 M; V1 = 15.00 mL; C2 = ?; V2 = 50.00 mL. Plugging in the values into the formula, we have: (2.07 M)(15.00 mL) = C2(50.00 mL).

Now, solve for C2: C2 = (2.07 M)(15.00 mL) / (50.00 mL). C2 = 0.621 M. Therefore, the concentration of the solution prepared by adding 15.00 mL of 2.07 M into a 50.00 mL volumetric flask and diluting to the mark is approximately 0.621 M.

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Answer:

32

Step-by-step explanation:

V=\(\pi\)r^2

5120=\(\pi r^{2}\)x20

5120/20 = 256

\(\sqrt{256}\)=16

16+16 ( 16x2) = 32

32in.

Answer:

- 2x - 8

Step-by-step explanation:

\( - 7x + 4 - 5x - 12\)

Collect like terms

-7x - 5x +4 - 12

= -2x - 8

Answer: C

Step-by-step explanation:

i just took a test

Answer:Answer:

x + y = 10

6x + 8y = 72

Step-by-step explanation:

Number of packages = 10

Total batteries = 72

For AA:

batteries per package = 6

Let number of packages = x

For AAA:

batteries per package = 8

Let number of packages = y

Number of AA packages + number of AAA packages = 10

Sum of AA + sum of AAA equals 72 batteries

x + y = 10

6x + 8y = 72

Step-by-step explanation:

Answer:

10,600 cookies will be made in 8 hours

Step-by-step explanation:

1325 × 8 = 10,600

We can use Coulomb's law to calculate the magnitude of the electric field at a distance r away from a point charge Q:

E = k * Q / r^2

where k is Coulomb's constant, Q is the charge of the point charge, and r is the distance from the point charge.

In this problem, we have a point charge Q of -10 nC located at (1.2 cm, 0 cm), and we want to find the x-component of the electric field at a distance r = 5.3 cm away at position (-4.1 cm, 0 cm).

To find the x-component of the electric field, we need to use the cosine of the angle between the electric field vector and the x-axis, which is cos(180°) = -1.

So, the x-component of the electric field at position (-4.1 cm, 0 cm) is:

E_x = - E * cos(180°) = - (k * Q / r^2) * (-1)

where k = 9 x 10^9 N*m^2/C^2 is Coulomb's constant.

Substituting the given values, we get:

E_x = - (9 x 10^9 N*m^2/C^2) * (-10 x 10^-9 C) / (0.053 m)^2

E_x ≈ -30,566.04 N/C

Rounding this to two significant figures and including the appropriate units, we get:

The x-component of the electric field is about -3.1 x 10^4 N/C (to the left).

Answer:

first dice-4/6

second dice-5/6

Step-by-step explanation:

if you have six possible outcomes for the first dice and you want it to roll 1 thru 4 then you have a four out of six chance and you have a 5 out of six chance for the second dice

Answer:

960 dollars

Step-by-step explanation:

Your welcome