Find an equation of the plane.The plane through the point(4, −3, −1)and parallel to the plane 6x − y − z = 6

Answers

Answer 1

Both planes have the same normal vector:

[tex]6x-y-z=6\implies\mathbf n=\langle6,-1,-1\rangle[/tex]

The plane we want must contain the point (4, -3, -1), so its equation would be

[tex]\mathbf n\cdot\langle x-4,y+3,z+1\rangle=0[/tex]

[tex]\implies 6(x-4)-(y+3)-(z+1)=0[/tex]

[tex]\implies\boxed{6x-y-z=28}[/tex]


Related Questions

4 - m/2 = 10

Please help!!

Answers

Answer:

M=3

Step-by-step explanation:

4-m/2=10subtract 4 from each sideget m/2=6then divide 2 from 6 and get m=3

Hope this helps:)

The correct answer is M=3

What is 78 divided by 4.68

Answers

Answer:

16.67

Step-by-step explanation:

78 / 4.68

= 7800 / 468

= 16.67

When 78 is divided by 4.68 it gives 16.67 as a result.

Division

From the four basic operations of arithmetic, the division is one. The division is generally done when we want to distribute something in equal portions.

therefore, 78 divided by 4.68 can be solved as,

Given to us

78 divided by 4.68

[tex]78\div 4.68\\\\=\dfrac{78}{4.68}\\\\=\dfrac{78}{\dfrac{468}{100}}\\\\\\=\dfrac{78 \times 100}{468}\\\\=\dfrac{7800}{468}\\\\=16.6667 \approx 16.67[/tex]

Hence, when 78 is divided by 4.68 it gives 16.67 as a result.

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One leg of a right triangle has a length of 3 m. The other sides have lengths that are consecutive integers. Find these lengths.

The other leg is ___ m.

Answers

Answer:

The other leg is 4 m long, and the hypotenuse is 5 m long

Step-by-step explanation:

Recall that the longest side of a right angle triangle is its hypotenuse, and that the legs and hypotenuse must verify the Pythagorean identity:

[tex]hyp^2=leg_1^2+leg_2^2[/tex]

so, we know that the other two sides have consecutive integers for lengths. That is: if one is "x" in length, the other one must be "x+1"

So we can assume that the largest of this is the hypotenuse: "x+1"

Not, they must verify the Pythagorean identity:

[tex]hyp^2=leg_1^2+leg_2^2\\(x+1)^2=x^2+3^2\\x^2+2\,x+1=x^2+9\\2\,x+1=9\\2\,x=8\\x = 4[/tex]

then, the other side is of length 4 m, and finally the hypotenuse is of length 4+1 = 5 m

Evaluate the expression when a=2 and b=20

Answers

50(2) -2(20) +6 = ?
100 - 40 + 6 = ?
60 + 6 = ?
66

Given A is between Y and Z and YA= 14x, AZ= 10x, and YZ= 12x + 48, find AZ

Answers

Answer:

96

Step-by-step explanation:

The value of AZ will be 40.

A is a point between Y and Z and YA = 14x , AZ = 10x and YZ = 12x + 48.

We have to calculate the value of AZ.

What is the value of MP , if N is the midpoint of M and P ?

The value of MP will be equal to the summation of NM and NP i.e., MP = NP + NM .

As per the question ;

A is the midpoint of Y and Z.

⇒ AZ + YA = YZ

⇒ 10x + 14x = 12x + 48

24x = 12 x + 48

⇒ 12x = 48

x = 4

So ,

The value of AZ will be ;

AZ = 10 × 4

AZ = 40

Thus , the value of AZ will be 40.

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choose all the expression with a difference less than 5

8.3
- 4.07

9.33
-3.99

7.1
- 2.603

12.3
- 7.08

7.005
- 2.005

Answers

Answer:

a and c

a and c are the expressions with a difference less than 5

Step-by-step explanation:

a) 8.3-4.07=4.23

b) 9.33-3.99=5.34

c) 7.1-2.603=4.497

d) 12.3-7.08=5.22

e)7.005-2.005=5

Hope this helps ;) ❤❤❤

Simon used 13 pears and 9 apple to make fruit salad. What was the ratio of the number of apple to the number of fruit in the fruit salad?

Answers

Answer:

13:9

Step-by-step explanation:

The ratio of the number of apples to the number of fruits in the fruit salad is given by the equation A = 9 : 22

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the ratio of number of apples to the number of fruits be A

Now , the proportion will be

The number of pears = 13 pears

The number of apples = 9 apples

Now , the number of fruits = number of pears + number of apples

Substituting the values in the equation , we get

The number of fruits = 13 + 9 = 22

Now , the proportion of apples to fruits A is

Ratio of the number of apples to the number of fruits in the fruit salad A = number of apples : number of fruits

Substituting the values in the equation , we get

Ratio of the number of apples to the number of fruits in the fruit salad

A = 9 / 22

A = 9 : 22

Therefore , the value of A is 9 : 22

Hence , the proportion is 9 : 22

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Select the relationship that does represent a function

Answers

the 4th one is a relationship that is a fuction I think

Answer:

4th image

Step-by-step explanation:

the others cannot be functions since one domain cannot be in two ranges

If the ratio of boys to girls at the school is 2:5 and there are 40 boys how many girls are there?

Answers

Answer:

100 girls

Step-by-step explanation:

The ratio of boys : girls is 2 : 5.

In other words, boys are 2 parts of the school while girls are 5 parts of the school.

Since there are 40 boys, 2 parts of the school is 40. Thus:

[tex]2p = 40\\p = 20[/tex]

1 part is 20.

Since there are 5 parts girls, there are

[tex]5p = 5*20 = 100[/tex]

100 girls.

Answer: 100 girls

The total number of students in school is 140 and number of girls at the school is equal to 100.

What do you mean by ratio ?

Ratio is the quantitative relationship between two values indicating how frequently one value contains or is contained within the other.

It is given that the ratio of boys to girls at the school is 2:5.

Let's assume the total number of students in school is x.

We now need to find the number of girls in the school but before that we must try to find the total number of students in the school.

Sum of ratios = 2 + 5 = 7

It is given that there are 40 boys in students.

2/7 of the total number of students are boys.

i.e., the expression can be written as :

2x / 7 = 40

2x = 40 × 7

2x = 280

x = 140

The total number of students in school is 140.

So , the number of girls in school is :

= 140 - 40

= 100

There are 100 girls in the school.

Therefore , the total number of students in school is 140 and number of girls at the school is equal to 100.

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33

56

Find the unknown side length, x. Write your answer in simplest radical form.

A 2047

B. 60

С.

5169

D. 65

Answers

Answer:

D. 65

Step-by-step explanation:

The question lacks the appropriate diagram. Find the diagram attached.

The triangle is a right angled triangle that is made of of three sides namely the opposite, the adjacent and the hypotenuse (the longest side). According to the diagram, the longest side is the side with length x. To get the side length x, we will use the Pythagoras theorem as shown;

hyp² = opp²+adj²

hyp² = 33²+56²

x² = 1089+3136

x² = 4225

take the square root of both sides

√x² = √4225

x = 65

Hence the unknown side length x is 65

Write the following set using roster notation. Do not include repeats.
A is the set of odd integers between 4 and 12.

Answers

Answer:

The Set of Natural Numbers: {1, 2, 3, 4, 5, . . .}

The Set of Whole Numbers: {0, 1, 2, 3, 4, 5, . . .}

The Set of Integers: {. . . , −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, . . .}

Step-by-step explanation:



The Pham family and the Morgan family each used their sprinklers last summer. The water output rate for the Pham family's sprinkler was 25L per hour. The water output rate for the Morgan family's sprinkler was 35L per hour. The families used their sprinklers for a combined 65total of hours, resulting in a total water output of 1975L . How long was each sprinkler used?

Answers

Answer:

Pham Family = 30 hours

Morgan Family = 35 hours

Step-by-step explanation:

Step 1 Deriving the equation

Let the duration in hours of Pham Family sprinkler = "x"

Let the duration in hours  of Morgan Family = "y"

Total combined duration = 65 hours provided.

That is:

x + y = 65                               Equation 1

Pham's sprinkler capacity = 25 litre per hour

Total water through this = 25 litre per hour for "x" hours = 25x

Morgan's sprinkler capacity = 35 litre per hour

Total water through this = 35 litre per hour for "y" hours = 35y

Now, provided

Total water output from both = 1,975 litre

That means

25x + 35y = 1,975                   Equation 2

Step 2 Solving the equation

Let us multiply equation 1 with 25

We have

25x + 25y = 65 [tex]\times[/tex] 25

25x + 25y = 1,625                       Revised Equation 1

Subtracting revised equation 1 from equation 2 we have:

(25x - 25x) + (35y - 25y) = (1,975 - 1,625)

0 + 10y = 350

y = 350/10 = 35

Since y = 35

Putting value of y in original equation 1 we have

x + 35 = 65

x = 65 - 35 = 30

Thus, Total Sprinkler hours of Pham = 30

Total Sprinkler hours of Morgan = 35

What are the graphs to these?

Answers

Answer:

The graph is in the image

Step-by-step explanation:

[tex]y = \frac{3}{5} x -3\\\\2x -y =-4\\\\y=-6,\:x=-5\\[/tex]

i already know the answer, its increasing by 4 but i dont know how to write the answer.​

Answers

Answer: m+3

Step-by-step explanation:

Since the jump from each number increases by 3, you would write m+3, since m is indicated in the pattern.

While riding her bike to the ocean and back home 6 times, Mandi timed herself at 52min, 54min, 53min, 51min, 53min, and 43min. She had set a goal of averaging 51 minutes for her rides. How many minutes will she need to spend on her seventh ride to attain her goal?

Answers

Answer:

306 min

Step-by-step explanation:

A lamppost casts a shadow of 18 ft when the angle of elevation of the Sun is 33.7 degrees. How high is the lamppost? Round to the nearest foot

Answers

Answer:

12 feet or 12 ft

Step-by-step explanation:

We solve for this question using Trigonometric function of Tangent

tan θ = Opposite/ Adjacent

θ = Angle of elevation = 33.7°

Opposite side = Height of the lamp = ??

Adjacent side = Shadow of the lamp = 18 feet

Hence,

tan 33.7° = Opposite/ 18

tan 33.7° × 18 = Opposite

Opposite = 12.004507735 feet

Approximately to the nearest foot = 12.0feet

The height of the lamppost with a shadow of 18 ft. is 12 feet.

Trigonometric ratio

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Let h represent the height of the lamppost, hence:

tan(33.7) = h/18

h = 12 feet

The height of the lamppost with a shadow of 18 ft. is 12 feet.

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What number belongs in the box to make the equation true? 2 7 3 5​

Answers

It would be 5, because 2 +3 =5 and 7-2=5

What are the coordinates of B if the midpoint of line segment AB is (2,-5) and the coordinates of point A is (4,4)?

Answers

Answer:

i think it will be 20 unit diatance .

There are 20 triangles and 4 squares. What is the simplest ratio of squares to total shapes

Answers

Answer:

1/6

Step-by-step explanation:

Given:

Number of squares = 4Number of triangles = 20

Total

Number of total shapes = 20 + 4 = 24

Ratio of squares to total shapes:

4/24 = 1/6

Answer:

1:6

Step-by-step explanation:

There are 20 triangles and four squares, so we know the first part of the ratio is 4. The total number of shapes is 24, so we get 4:24, and if we simplify, we then get 1:6.

Hope this helps!

Simplify the following:

1.4 : 0.21

best answer gets brainliest.

Answers

Answer:

1.4/0.21= 140/21= 20/3

Step-by-step explanation:

Answer:

20:3

Step-by-step explanation:

decimal points can't be ratios so we have to convert to whole numbers:

so 1.4:0.21 becomes:

140:21

after simplifying fully( i divided both sides by 7) we come to 20:3.

You are trying to estimate the average amount a family spends on food during a year. In the past the standard deviation of the amount a family has spent on food during a year has been approximately $900. If you want to be 99% sure that you have estimated average family food expenditures within $50, how many families do you need to survey? Round your answer up to the nearest whole number, if necessary.

Answers

Answer:

the number of families needed for the survey is 2,157

Step-by-step explanation:

The computation of the number of families needed for the survey is shown below:

Given that

The Standard deviation is $900

Service level = 99%

z value at 99% = 2.58

Expenditures = $50

Based on the above information

The number of families needed for the survey is

[tex]n = (\frac{zs}{E})^2\\\\= (\frac{2.58\times 900}{50})^2[/tex]

= 2,157

Hence, the number of families needed for the survey is 2,157

Find the LCM and HCF.
(a) p3 + 8 and p2 - 4​

Answers

Answer:

In bold below.

Step-by-step explanation:

p^2 - 4 = (p - 2)(p + 2)

Note that 8 = 2^3 so

p^3 + 8 = ( p + 2)(p^2 + 4 - 2p)

So The HCF is p + 2.

The LCM =  (p + 2)(p - 2)(p^2 + 4 - 2p)

−2(2x + 5) − 3 = −3(x − 1)

Answers

Answer:

x =-16

Step-by-step explanation:

[tex]-2(2x + 5) - 3 = -3(x -1)[/tex]

Expand

[tex]\mathrm{Expand\:}-2\left(2x+5\right)-3:\quad -4x-13\\\\\mathrm{Expand\:}-3\left(x-1\right):\quad -3x+3\\\\-4x-13=-3x+3[/tex]

Collect like terms and simplify

[tex]-4x+3x =3+13\\-x =16\\[/tex]

Divide both side by -1

[tex]\frac{-x}{-1}=\frac{16}{-1}\\\\x =-16[/tex]

What is the most appropriate measurement of the amount of liquid in Starpoint's pool?
A. ML.
B. KL.
C. CL.
D. Cg.

Answers

Answer: B. KL.

Step-by-step explanation:

A kiloliter (kl) is a unit which is derived from the metric SI (System International). This measurement is used when unit of volume with sides equal to one meter (1m) and as such, is equivalent to one cubic meter. One kiloliter (1kl) is which is same as one thousand liters (1000l). The kiloliter is used when volume of liquid is to be measured. This applies to a pool in the question.

The average cost of an item is defined as the total cost to produce divided by the number produced.A shoe company that pays $240,000 in rent and employee salaries per year figures it also must pay $3.50 in materials per shoe set it produces Write the equation needed to solve the problem. Use the equation to find the number of shoe sets the company would need to produce for the average cost of each set to be $7.50. Work out the problem, show all of your steps, and provide explanations.

Answers

Answer:

Step-by-step explanation:

Average cost = Total cost to produce / number of items produced

Fixed cost per year = $240,000

Variable cost = $3.50s

Where s = number of shoes produced

Total cost= fixed cost + variable cost

Total cost = $240,000 + $3.50s

When average cost = $7.50

Average cost = Total cost to produce / number of items produced

7.50 = $240,000 + $3.50s / s

Cross product

7.50s = $240,000 + $3.50s

Collect like terms

7.50s - 3.50s = 240,000

4s = 240,000

divide both sides by 4

s = 240,000 / 4

= 80,000

s = 80,000

5. The Robin's Nest Nursing Home had a fundraising goal of $9,500. By the
end of the fundraiser, they had exceeded their goal by $2,100. How much
did they raise?

Answers

They raised $11,600.

Proportional ratios are like equivalent fractions, but

Answers

Answer:

what is the question?

Step-by-step explanation:

Please answer the last conversion !! 531 ms to s

Answers

Answer:

0.531 s

Hope it helped u if yes mark me BRAINLIEST

0.531
Hope this help

Phone numbers in Italy are in the format AB-CDDD-XXXX and have the following conditions · A can be any number 3-9 · B can be any number 4-9 · C can be any number 5-9 · D can be any number 1-7 · X can be any number 0-9 How many total phone numbers can the Italians have? Question 4 options: 720,300,000 phone numbers 823,200,000 phone numbers 102,900,000 phone numbers 16,800,000 phone numbers

Answers

Answer:

Hey there!

A: 7

B: 6

C: 5

D: 7

X: 10

7x6x5x7x7x7x10x10x10=720,300,000

Let me know if this helps :)

n engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 5.4 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 9 engines and the mean pressure was 5.7 pounds/square inch with a variance of 0.81. A level of significance of 0.025 will be used. Assume the population distribution is approximately normal. Make the decision to reject or fail to reject the null hypothesis.

Answers

Answer:

The calculated t- value =  1.11 > 2.89 at 0.025 level of significance

Null hypothesis is rejected

The engineer designed the valve such that it would produce a mean pressure is not equal to  5.4

Step-by-step explanation:

Step(i):-

Given mean of the Population (μ) = 5.4

Given sample size 'n' = 9

Mean of the sample (x⁻) = 5.7

Standard deviation of the sample (s) = 0.81

Step(ii):-

Null Hypothesis: H₀:  The engineer designed the valve such that it would produce a mean pressure of 5.4

H₀: μ = 5.4

Alternative Hypothesis : H₁:  μ ≠ 5.4

Level of significance = 0.025

Test statistic

            [tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]

           [tex]t = \frac{5.7 -5.4}{\frac{0.81}{\sqrt{9} } }[/tex]

         t = 1.11

Degrees of freedom

ν = n-1 = 9-1 =8

t₀.₀₁₅ , ₈  = 2.89

The calculated t- value =  1.11 > 2.89 at 0.025 level of significance

Null hypothesis is rejected

The engineer designed the valve such that it would produce a mean pressure is not equal to  5.4

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please help asap!!! If you where going from Palo Duro Canyon to Caddo Lake, which direction would you travel? Suppose you have a credit card debt of $4,000. Last month the bank charged you $40 interest on the debt. The solution to the equation 40= 4000/12r represents the annual interest rate (r) on the credit card. Find the annual interest rate on the credit card. my favorite season is summer because I like sunny weather Please Help ASAP Will give the brainiest answer Describe new laws and ideas that rulers during the Enlightenment put in place in their empires that reflect Enlightenment ideas. pls Which of the following is not a possible effect of increasing carbon dioxide levels in the atmosphere?a.increase in water contamination and floodsb.ocean acidificationc.cutting down forestsd.reduction of cold-related deaths Please select the best answer from the choices providedABCD This is an excerpt from a press release on the opening of a new nature trail by the mayor of the small city of Bridgedale. Make a prediction about the experience the mayor will have when she visits the new trail. Use specific details from the text to support your answer. We will be working with Escherichia coli, a bacteria that requires oxygen for growth. Very briefly describe the conditions needed to grow 5ml of liquid culture of E.Coli in the laboratory? Choose all the answers that apply. What do all cells do? reproduce contain hereditary information have a nucleus break down food into energy have a cell membrane tristan wants to build a square garden in his backyard. if the garden is going to be 64 ft squared how many feet of material will he need for the perimeter of the garden? Varun said I have bought a new work into indirect speech Which of the following terms best describes the suburban area of Illinois where many residents commute to Chicago? Which of the following statements best describes how American Indians reacted to the policy of assimilation? if jeff had 10 cookies and sam ate 10 how many are left? 1. Cmo eres?2. De dnde eres?3. Cmo ests hoy?4. Dnde ests ahora?Copyright by McDougal Littell, a division of Houghton Mifflin ComparTu casa5. Cmo es tu casa?6. Dnde est tu casa?Tu clase de espaol7. Cmo es tu clase de espaol?8. A qu hora es tu clase de espaol? A club has 20 members, 12 boys and 8 girls. The club needs to select a president, vice-president and secretary. They decide to select randomly. What is the probability that: a) The officers are all female? b) The officers are all male? c) At least one member from each gender is an officer? When introduced in 1997, a DVD player sold for about $500. Five years later, the average price was $155. Find and interpret the average rate of change in price per year. What is the order for the set of daga What is the meaning of leaching During the Renaissance, this type of person provided financial backing for the arts.