consider the plane determined by the points a(3, 0, -2), b(11, -5, 2), and c(3, 7, 4) find the normal equation of the plane

Answers

Answer 1

The normal equation of the plane is: 20x - 48y + 56z = 0

To find the normal equation of the plane determined by points A(3, 0, -2), B(11, -5, 2), and C(3, 7, 4), we can use the cross product of the vectors formed by two sides of the plane.

Let's first find two vectors on the plane:

Vector AB = B - A = (11, -5, 2) - (3, 0, -2) = (8, -5, 4)

Vector AC = C - A = (3, 7, 4) - (3, 0, -2) = (0, 7, 6)

Next, we calculate the cross product of AB and AC:

N = AB × AC

The cross product is given by:

N = (AB_y * AC_z - AB_z * AC_y, AB_z * AC_x - AB_x * AC_z, AB_x * AC_y - AB_y * AC_x)

Substituting the values:

N = (8 * 6 - 4 * 7, 4 * 0 - 8 * 6, 8 * 7 - (-5) * 0)

N = (48 - 28, 0 - 48, 56 - 0)

N = (20, -48, 56)

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Related Questions

food safety guidlines recommend that a beef rib roast should cook for 23 minutes per pound based on 325f oven setting. how many hours should it take to cook a 5.17 pound roast?

Answers

It should take approximately 1.98 hours, or around 1 hour and 59 minutes, to cook a 5.17 pound beef rib roast based on the recommended guideline of 23 minutes per pound at a 325°F oven setting.

To calculate the cooking time for a 5.17 pound roast, we can use the recommended guideline of 23 minutes per pound. First, we need to convert the weight from pounds to minutes, and then convert minutes to hours.

Cooking time in minutes = 5.17 pounds * 23 minutes/pound

Cooking time in minutes = 118.91 minutes

To convert minutes to hours, we divide the total minutes by 60:

Cooking time in hours = 118.91 minutes / 60

Cooking time in hours ≈ 1.98 hours

Therefore, it should take approximately 1.98 hours to cook a 5.17 pound beef rib roast based on the recommended guideline of 23 minutes per pound at a 325°F oven setting.

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Can anyone help me? I’ll give Brainly!!!

Can anyone help me? Ill give Brainly!!!

Answers

Answer:

Step-by-step explanation:

its 12 yd

Answer:

This is your answer. If I'm right so,

Please mark me as brainliest. thanks!!!

Can anyone help me? Ill give Brainly!!!

On a coordinate plane, a line goes through (0, negative 1) and (3, 1). a point is at (negative 3, 0). what is the equation of the line that is parallel to the given line and has an x-intercept of â€"3? y = two-thirdsx 3 y = two-thirdsx 2 y = negative three-halvesx 3 y = â€"three-halvesx 2

Answers

The equation of the line that is parallel to the given line and has an x-intercept of 3 is y = 2/3x - 2

What is the equation of the line that is parallel to the given line and has an x-intercept of 3?

The given parameters are

Point =(0, -1) and (3, 1)

Calculate the slope using

m = (y₂ - y₁)/(x₂ - x₁)

Where m represents the slope

So, we have:

m = (1 -- 1)/(3 -0)

Evaluate

m = 2/3

Parallel lines have equal slopes

So, the slope of the other line is

m = 2/3

Linear equations are represented as:

y = mx + c

Where m represents the slope and c represents the y-intercept

So, we have

y = 2/3x + c

An x-intercept of 3 means

0 = 2/3 * 3 + c

So, we have

c = -2

Substitute c = -2 in y = 2/3x + c

y = 2/3x - 2

Hence, the equation of the line that is parallel to the given line and has an x-intercept of 3 is y = 2/3x - 2

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precalculus b dba given a vertical asymptote and a horizontal asymptote, how would you begin to find an expression for a rational function?

Answers

By finding the vertical and horizontal asymptotes, you can use them to help find an expression for the rational function

To find an expression for a rational function given a vertical asymptote and a horizontal asymptote, start by recognizing that the general form of a rational function is f(x) = (ax + b)/(cx + d), where a, b, c, and d are all constants.

Next, use the given information to solve for a, b, c, and d in the equation. The vertical asymptote represents the x-values at which the denominator of the equation equals zero, so set cx + d equal to zero and solve for x. Similarly, the horizontal asymptote can be found by setting ax + b equal to the asymptote’s y-value.

Once both equations are solved for x, substitute the x-values back into the equation for the rational function and solve for the corresponding a, b, c, and d values.

A vertical asymptote occurs when the denominator of the rational function is equal to zero, so you can set the denominator equal to zero and solve for the variable to find the vertical asymptote.

A horizontal asymptote occurs when the degree of the numerator and denominator are equal, so you can look at the leading coefficients of the numerator and denominator to find the horizontal asymptote.

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Kaun ha R 5,400. 00 on hand to be depoited in two account. He ha depoited part
of it in a fixed depoit at 3% annual interet and the ret in a aving account that earn
2% annual interet. If the imple interet earned from both account i R 140. 00 for
the year, then how much doe he have in each account

Answers

Based on simultaneous equations, Kaun has deposited in each account the following:

Account A = R 3,200Account B = R 2,200.

What are simultaneous equations?

When two or more algebraic equations are solved concurrently, we call them simultaneous equations.

We can solve simultaneous equations by graphing, elimination, or substitution methods.

The total deposit in the two accounts = R 5,400

The annual interest in Account A = 3% or 0.03

The annual interest in Account B = 2% or 0.02

The total interest earned from both accounts for the year = R 140

Let Account A be designated as a and Account B be designated as b.

Equations:

a + b = 5,400 ... Equation 1

0.03a + 0.02b = 140 ... Equation 2

Eliminate a by multiplying Equation 1 by 0.03:

0.03a + 0.03b = 162 ... Equation 3

Subtract Equation 2 from Equation 3:

0.03a + 0.03b = 162

-

0.03a + 0.02b = 140

= 0.01b = 22

b = 2,200

From Equation 1, substitute b:

a + 2,200 = 5,400

a = 3,200 (5,400 - 2,200)

Check:

In equation 2:

0.03a + 0.02b = 140

0.03(3,200) + 0.02(2,200) = 140

96 + 44 = 140

140 = 140

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may u answer this with equation im very confused pls

may u answer this with equation im very confused pls

Answers

Answer:

See explanation below.

Step-by-step explanation:

1. (-1, -1) and (2, -2)

  m = -2+1 / 2+1

  m = -1/3

2. (-1, -4) and (0, -1)

  m = -1+4 / 0+1

  m = 3/1

  m = 3

3. (-4, 0) and (-2, -3)

  m = -3-0 / -2+4

  m = -3/2

4. (2, 0) and (0, -3)

  m = -3-0 / 0-2

  m = -3/-2

  m = 3/2

5. (-1, 2) and (-4, -3)

  m = -3-2 / -4+1

  m = -5/-3

  m = 5/3

6. (4, 3) and (1, -4)

  m = -4-3 / 1-4

  m = -7/-3

  m = 7/3

I need help on this question!

I need help on this question!

Answers

The answer I am not sure but will try
Ans: 110

Answer:

110 cookies in 180 minutes

Step-by-step explanation:

To solve the system of linear equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 by using the linear combination method, Henry decided that he should first multiply the first equation by –3 and then add the two equations together to eliminate the x-terms. When he did so, he also eliminated the y-terms and got the equation 0 = 0, so he thought that the system of equations must have an infinite number of solutions. To check his answer, he graphed the equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 with his graphing calculator, but he could only see one line. Why is this?

Answers

Henry could only see one line since both lines had the same slope, which means that the graphs of both equations will be identical and hence overlap.

Identify the linear equation?

Linear equations in a system 3x + 2y = 4, and 9x + 6y = 12

We must demonstrate why Henry could only make out one line when he plotted the equations 3x-2y=4 and 9x-6y=12 on a graph.

Take the provided linear equation system into consideration.

3x - 2y = 4 ................(1)

9x - 6y = 12 ..................(2)

Due to the fact that equation (2) is a multiple of equation (1), 3 (3x - 2y = 4) = 9x - 6y = 12

The slopes of the provided equations are also same.

Difference with regard to x for equation (1) yields,

additional to equation (2),

With regard to x, we can differentiate to get,

The graphs of both equations will overlap since both lines have the same slope and hence have the same appearance on the graph.

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based on the following results, conclude whether to reject or not reject h0. h0 : p=0.75; ha : p>0.75 α=0.05 (significance level) the test statistic is 2.59. the critical value is z0.05=1.65.

Answers

Reject H0.

To determine whether to reject or not reject H0 (null hypothesis), we compare the test statistic to the critical value. In this case, the test statistic is 2.59, and the critical value at a significance level of 0.05 is 1.65.

Since the test statistic is greater than the critical value, we have sufficient evidence to reject the null hypothesis. This suggests that there is significant evidence to support the alternative hypothesis (Ha: p > 0.75).

The result indicates that the proportion being tested is significantly greater than the hypothesized value of 0.75.

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is 132 divisible by 3

Answers

Answer:

yes clearly

Step-by-step explanation:

using rules of divisibility it is divisible

using your calculator it is divisible

the answer is 44

Yes 132 is divisible by 3

if you type 132 divided by 3 into your calculator you’ll get 44. You could do this with any 2 numbers. If your answer is a whole number, then the numbers are divisible.

pls hurry. 10. Select all numbers that represent a solution of the equation below.

pls hurry. 10. Select all numbers that represent a solution of the equation below.

Answers

\(x^2=196\\x=-\sqrt{196} \vee x=\sqrt{196}\\x=-14 \vee x=14\)

Therefore, it's A and D.

Help now Twenty-seven is 25% of a0.

Answers

Answer:

27  is  25 %  of  108

Step-by-step explanation:

x*25/100=27 or x=(27*100)/25=108

27
is
25
%
of
108
Explanation:
Let the number be
x
. Then
x

25
100
=
27
or
x
=
27

100
25
=
108

27
is
25
%
of
108
[Ans]

11.) The sum of four consecutive even
integers is 68. Find the four consecutive
even integers. What is the 3rd integer
in the sequence?

Answers

Answer:

Four consecutive even integers are 14, 16, 18 and 20
Third number in the sequence is 18

Step-by-step explanation:

Let N be the first even integer

Each consecutive integer is 2 away from the previous integer

Next consecutive integer = N + 2, next one = N+4 and the last one = N +6

Add these expressions together, set them equal to 68 to solve for N

==> N + (N +2) + (N +4) + (N + 6) = 68

==> N + N +2 + N +4 + N + 6 = 68

==> 4N + 12 = 68

==> 4N = 68-12

==> 4N = 56

N = 56/4 = 14

So the integers are 14, 16, 18 and 20

Third integer in the sequence is 18

What is the value of -112.84-54.14-(29.18)?

Answers

−196,16

.....................

In exponential growth functions, the base of the exponent must be greater than 1. How would the function change if the base of the exponent were 1

Answers

If the base of the exponent in an exponential growth function were 1, the function would become constant, with a fixed value of 1 regardless of the value of x.

In exponential growth functions, the base of the exponent represents the factor by which the function grows at each step. When the base is greater than 1, the function experiences exponential growth, with the values increasing rapidly over time. However, if the base of the exponent were 1, the function would change significantly.

When the base of the exponent is 1, the function becomes constant. This is because any number raised to the power of 1 remains unchanged. Therefore, if the base is 1, the exponential function will have a constant value and will not exhibit any growth or decay.

Mathematically, an exponential function with a base of 1 can be represented as:

f(x) = 1^x

No matter what value of x is used, the result will always be 1. For example, if we substitute different values for x, such as x = 2 or x = -3, we get:

f(2) = 1^2 = 1

f(-3) = 1^(-3) = 1

In both cases, the result is always 1.

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Hannah has liabilities totaling $30,000 (excluding her mortgage of $100,000 ). Her net worth is $45,000. What is her debt-to-equity ratio? 0.75 0.45 0.67 1.30 1.00

Answers

Hannah's debt-to-equity ratio when her liabilities was $30,000 (excluding her mortgage of $100,000 ) and her net worth is $45,000 is 0.75.

Debt-to-equity ratio is a financial ratio that measures the proportion of total liabilities to shareholders' equity. To calculate the debt-to-equity ratio for Hannah, we need to first calculate her total liabilities and shareholders' equity.

We are given that Hannah has liabilities of $30,000 excluding her mortgage of $100,000. Therefore, her total liabilities are $30,000 + $100,000 = $130,000.

We are also given that her net worth is $45,000. The net worth is calculated by subtracting the total liabilities from the total assets. Therefore, the shareholders' equity is $45,000 + $130,000 = $175,000.

Now we can calculate the debt-to-equity ratio by dividing the total liabilities by the shareholders' equity.

Debt-to-equity ratio = Total liabilities / Shareholders' equity = $130,000 / $175,000 = 0.74 (rounded to two decimal places)

Therefore, Hannah's debt-to-equity ratio is 0.74, which is closest to option 0.75.

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Solve the equation for x. 2/3x-1/9+5=20

Answers

Answer:  x = 68/3

Step-by-step explanation: 2/3x - 1/9 + 5 = 20

Combine the fractions:   5 - 1/9 = 44/9

44/9 + ⅔x = 20

Subtract 44/9 from both sides:   44/9 + ⅔x - 44/9 = 20 - 44/9

Simplify:  ⅔x = 136/9

Multiply both sides by 3:    3 x ⅔x = 136 x 3 divided by 9

Simplify:   2x = 136/3

Divide both sides by two:   2x/2 = 136/3 divided by two

Simplify:   x =  68/3

 

Lebron runs 3 miles in 14 minutes at a constant speed . Stephon runs 1 mile in (3/4) the amount of time Lebron runs 1 mile . How long does it take for Stephon to run 1 mile ?

Answers

Speed generally refers to the rate at which an object moves, typically measured in units of distance per unit of time, such as miles per hour or meters per second.

To solve this problem, we need to first figure out how long it takes LeBron to run one mile. We know that he runs three miles in 14 minutes, so we can set up a proportion:

3 miles / 14 minutes = 1 mile / x minutes

Cross-multiplying, we get:

3x = 14

x = 4.67 minutes

So LeBron runs one mile in 4.67 minutes.

Next, we need to figure out how long it takes Stephon to run one mile. We know that he runs one mile in (3/4) the amount of time it takes LeBron to run one mile, so we can set up another proportion:

(3/4)x = 1

Cross-multiplying, we get:

3x = 4

x = 4/3 = 1.33 minutes

So it takes Stephon 1.33 minutes to run one mile.

In summary, LeBron runs one mile in 4.67 minutes and Stephon runs one mile in 1.33 minutes.

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solve the system of equations y=8x+5 y=6x+25​

Answers

Answer:

(10,85)

Step-by-step explanation:

x=10

y=85

For a science experiment, maria threw an egg 88.2 meters in 3 seconds. what was the average rate of speed of the egg? a. 88.2 m/sec. b. 44.1 m/sec. c. 29.4 m/sec. d. 9.8 m/sec.

Answers

Answer: its not A its b c or d sorry i could not help more

Answer:

The answer is C. 29.4 m/sec.

Step-by-step explanation:

I got it right ^w^

HELP!!!
WHAT IS THE AREA OF THE POLYGON IN SQUARE UNITS?

A- 180 square units
B- 108 square units
C- 70 square units
D- 64 square units

HELP!!!WHAT IS THE AREA OF THE POLYGON IN SQUARE UNITS?A- 180 square unitsB- 108 square unitsC- 70 square

Answers

Answer: C

Step-by-step explanation:

area of rectangle = (5--2) × (2--2) = 7 × 4 = 28

area of triangle = ((12-5) × (6--6)) ÷ 2 = (7 × 12) ÷ 2 = 84 ÷ 2 = 42

total area = 28 + 42 = 70

the t distribution is a family of similar probability distributions T/F

Answers

The statement "the t distribution is a family of similar probability distributions" is True.

The t-distribution is indeed a family of similar probability distributions. It is used in statistics to model the distribution of a random variable when the sample size is small and the population standard deviation is unknown. The shape of the t-distribution depends on the degrees of freedom, which is determined by the sample size. As the degrees of freedom increase, the t-distribution approaches the shape of the standard normal distribution.

The t-distribution is symmetric and bell-shaped like the normal distribution, but it has heavier tails, which means it has more probability in the tails and less in the center compared to the normal distribution. The t-distribution plays a crucial role in hypothesis testing and constructing confidence intervals when working with small samples.

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3. The x-intercept of a line is -5 and the y-intercept is -2. What is the equation of the line?
A y = -5/2x -5
B y = 2/5x +2
C y = 5/2x -2
D y = -2/5x -2

4. What is the slope- intercept form of the equation y- 7 = -5/2(x+4)?
A y - 2 = -5/2(x+2)
B y + 7 = -x + 5/2
C y = -4/7 +2
D y = -5/2x -3

5. What is the standard form of the equation y = -3/2x +5?
A 3x + 2y = 10
B 3x - 2y = 10
C -2y - 3x = 26
D 3x + 2y = 26

Answers

Answer:

1)D

2)D

3)A

Step-by-step explanation:

A plane flies from Dubbo on a bearing of 139° for 852 km, then turns and flies on a bearing of 285° until it is due west of Dubbo. How far from Dubbo is the plane, to the nearest km?

Answers

Answer:

Step-by-step explanation:

So first you add them together which gives you infinity and then you divide infinity by (139+285) then keep doing it until you realise this is a scam

please help asap, it's for homework ​

please help asap, it's for homework

Answers

Answer:

The slope is 10/1 so +10

Step-by-step explanation:

Hope this helps !!!

Answer:

10.

Step-by-step explanation:

Picking out 2 convenient points, (3, 30) and (0, 0):

Slope = (30-0)/(3-0)

= 30/3

= 10.

Karen exchanged BDS$2000 and received EC$2700. How much is the value of one BDS$ in EC$

Answers

Answer:

Bds$ 1 EC$ 1.34

Step-by-step explanation:

Which property can be changed to affect the natural frequency of an object?
responses

color

length

elasticity

pressure

Answers

Length can be changed to affect the natural frequency of an object. (option 2).

The natural frequency of an object refers to the frequency at which it vibrates when subjected to a disturbance. It is determined by the object's mass and stiffness, with a long object having a lower natural frequency than a shorter one. Changing the length of an object directly affects its mass, stiffness, and natural frequency.

For example, if a spring is made longer, its natural frequency will decrease, causing it to oscillate more slowly. Conversely, if the length of a spring is reduced, its natural frequency will increase, making it oscillate more quickly. Other properties such as color, elasticity, and pressure do not affect the natural frequency of an object in the same manner as length.

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Complete Question:

Which property can be changed to affect the natural frequency of an object?

colorlengthelasticitypressure

plz i need help for my exam 100 points

What is the solution to this system?
x= 7 - 2y
2x + y = 5

(3,1)
(4,-1)
(1,3)
(-1,4)

Answers

I believe that the answer would be (1,3)

The temperature at noon was 5.6 F. During the afternoon the temperature dropped 2.8 F and then dropped another 2.2 F in the evening.
Part A: Estimate the new temperature

Part B: Find the actual new temperature

Part C: Peter got an exact new temperature of 11.63 F. Explain how peter can use the estimate to determine that his answer is wrong

-If the answer is correct, I'll give brainiest

Answers

A. To estimate the temperature I would follow the trend of a -2.8 drop plus .6. So the estimated new temperature would be 5.6-2.8= 2.8-2.2= .6- 1.6= -1
B. To calculate it, you would do the same math as above as I believe my answer is correct.
C. Peter can use the estimate to determine his answer is wrong because it follows the opposite of the trend in where the temperature goes. The trend is negative and decreasing, therefore, numbers higher than 5.6 would not be possible anywhere in the graph

Which value of x makes this equation true? -12x - 2(x+9) = 5(x+4)

Answers

x = -2

−12x−2(x+9)=5(x+4)

Use the distributive property to multiply −2 by x+9.

−12x−2x−18=5(x+4)

Combine −12x and −2x to get −14x.

−14x−18=5(x+4)

Use the distributive property to multiply 5 by x+4.

−14x−18=5x+20

Subtract 5x from both sides.

−14x−18−5x=20

Combine −14x and −5x to get −19x.

−19x−18=20

Add 18 to both sides.

−19x=20+18

Add 20 and 18 to get 38.

−19x=38

Divide both sides by −19.

x=  

−19

38

 

Divide 38 by −19 to get −2.

x=−2

The required simplified value of x for the given equation is -2/19.

To determine the value of x that makes equation -12x - 2(x + 9) = 5(x + 4) true.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

What is simplification?

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.

-12x - 2(x + 9) = 5(x + 4)
-12x -2x  - 18 = 5x + 20
-14x - 18 = 5x  + 20
-14x - 5x = 20 - 18
-19x  = 2
x = -2/19

Thus, the required simplified value of x for the given equations is -2/19.

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