G find the point on the plane x + 4y + 2z =14 closest to the point (1,1,1)

Answers

Answer 1

Answer:

(4/3, 7/3, 5/3)

Step-by-step explanation:

The line perpendicular to the plane through the point will be ...

... (x, y, z) = (1, 1, 1) +t(1, 4, 2)

Using this expression for (x, y, z), we can find the point on the line where it intersects the plane. That point is the one of interest.

... (1 +t) +4(1 +4t) +2(1 +2t) = 14 . . . . . substituting for (x, y, z) in the equation of the plane

... 7 +21t = 14 . . . . . collect terms

... 21t = 7 . . . . . . . . subtract 7

... t = 7/21 = 1/3 . . . divide by 21

The point of interest is ...

... (x, y, z) = (1, 1, 1) + (1/3)(1, 4, 2) = (1 1/3, 2 1/3, 1 2/3)

Related Questions

What is 32,020.20 rounded to the nearest square mile

Answers

it's 32,021

you have to round up the whole number in this situation because its asking for nearest mile

There are about 4200 college presidents in the United States, and they have annual incomes with a distribution that is skewed instead of being normal. Many different samples of 40 college presidents are randomly selected, and the mean annual income is computed for each sample. What is the approximate shape of the sample means?

Answers

Because a mean is an average, the means of each of the samples of 40 college presidents' incomes will have less of a skew than the actual income distribution in dollars of all of them. That is because outliers, like a president who is paid $2 million a year, will be averaged in with many others who are paid less. The shape of the curve of the means will depend upon how many different samples of 40 presidents are included, with the shape becoming more bell-like (normal distribution) the more random samples are included. Another consideration is how often the outliers are included and how big the income skew is that you start with. For example, if 2 college presidents are earning $2 million a year and the other 4,198 are earning $200,000 or less then the shape of your curve will depend greatly upon the number of times those two high earners are randomly selected and factored into the mean.

Final answer:

The distribution of sample means for college presidents' incomes, based on many different samples of size 40, will approximate a normal distribution due to the Central Limit Theorem.

Explanation:

The question regarding the distribution of sample means for college presidents' incomes pertains to a concept in statistics known as the Central Limit Theorem. When dealing with a population whose distribution is skewed, the distribution of sample means tends to become approximately normal if the sample size is large enough, which is usually considered to be over 30. As multiple samples of size 40 are taken in this case, the distribution of the sample means for the college presidents' annual incomes should approximate a normal distribution.

Write a user-defined function that determines the polar y coordinates of a point from the cartesian coordinates in a two-dimensional plane.

Answers

it really depends on what you are trying to find

What is the rate of change of y with respect to x for this function?
HELP FOR BRAINLYEST

Answers

First let's assume that the table contains points on a straight line. Then all we have to do is to determine the slope of that line.

Suppose we go from (0,3) to (7,-28.5).
-28.5-3 -31.5
Then the slope, m, is m = ------------- = ---------- = - 9/2, or - 4.5.
7-0 7

Let's check this result!

Suppose that y = mx + b governs the relationship between x and y.

Then y = -4.5x + b

suppose we find b by substituting the coordinates from the point (0,3):

3 = -4.5(0) + b

Then b = 3, and y = -4.5x + 3. Does the point (-2,12) satisfy this equation?

Does 12 = -4.5(-2) + 3? Does 12 = 9 + 3? YES.

So y = -4.5x + 3 is the equation from which these points came, and the rate of change of y with respect to x is the slope m = -4.5, or m = -9/2.

HELP PLEASE URGENT NEED TO PASS THIS CLASS

Answers

Hello!

Answer is y = 1/3x - 1

b = -1
m = rise/run = 1/4

y = 1/4 x + 1

Henry is making a corn grits recipe that calls for 14 cup of corn grits for every 12 cup of water. How much water will he need if he uses 112 cups of corn grits? Enter the number in the box

Answers

96 cups of water
To find this answer you have to first divide the 112 cups of corn grits by 14, your answer will be 8. Next you multiply 8 by the cups of water per 14 cups of corn grits which is 12 cups of water (8x12) which gives you your answer of 96 cups of water.

96 cups, 112 cups of corn grits divided by 14 cups, multiplied by 12

how many times more respondents chose silver than red round to the nearest tenth if necessary silver 0.2 red 0.09

Answers

well, 0.2 is the same as 0.20, and 0.20-0.09 is 0.11.

Answer: 2.2

Step-by-step explanation:

Given : Proportion of choosing silver = 0.2 =0.20.

Proportion of choosing red= 0.09

Clearly, 0.20> 0.09

Now, the number of times more respondents chose silver than red will be :-

[tex] n=\dfrac{0.20}{0.09}\\\\=\dfrac{20}{9}\\\\=2.22222\approx2.2\ \text{ Rounded to the nearest tenth}[/tex]

Hence, 2.2 times the respondents chose silver than red.

a rectangular flower garden has area of 32 square feet. if the width of the garden is 4 feet less than the length, what is the perimeter, in feet, of the garden?

Answers

let length be x feet
length= x
width=x-4
area = 32
length * width=32
x(x-4)=32
x^2 - 4 x -32=0
(x-8)(x+4)=0
x=8 feet
length=8 feet
width=4 feet
perimeter=2(len+wid)
=2(8+4)
2*12=24 feet

Final answer:

To find the perimeter of the rectangular flower garden, we first need to find its dimensions. Once we have the length and width, we can calculate the perimeter by using the formula: P = 2(length + width). Therefore, the perimeter of the garden is 4x - 8 feet.

Explanation:

To find the perimeter of the rectangular flower garden, we first need to find its dimensions. Let's use x to represent the length of the garden.

According to the problem, the width of the garden is 4 feet less than the length, so the width would be x - 4.

The area of the garden is 32 square feet, so we can set up the equation: x * (x - 4) = 32.

We can solve this equation by factoring or by using the quadratic formula to find the length.

Once we have the length and width, we can calculate the perimeter by using the formula: P = 2(length + width).

Substituting the values, we get P = 2(x + x - 4), which simplifies to P = 4x - 8.

Therefore, the perimeter of the garden is 4x - 8 feet.

For the number 4768.325, what is the sum of the tens digit and the tenths digit

Answers

tens digit = 60
the tenths digit = 0.3
sum = 60 + 0.3 = 60.3

answer
60.3

Which of the following numbers is the smallest?
4/9
0.44
3/7
400%

Answers

3/7 is the smallest.

A dealer dealt the following cards from a shuffled deck: 3 , 2 , 2 , A , K , Q , K , 5 , 2 , 6 4 , 5 , K , 2 , 7 , 6 , A , J , J , A What was the experimental probability of dealing a black card?

Answers

Answer:

Total number of cards in shuffled deck=3 , 2 , 2 , A , K , Q , K , 5 , 2 , 6, 4 , 5 , K , 2 , 7 , 6 , A , J , J , A .

Total number of cards in a deck of card = 52 cards, out of which 26 are black cards and 26 are red card.

As, it is not given that out of the 20 cards dealt by dealer is either red card or black card.

A=3=2B +1 R or 1 B + 2 R

2=4=2 R +2 B

3=1=1 R or 1 B

4=1=1R or 1 B

5=2=2 R or 2 B

6=2=2 R or 2 B

7=1=1 R or 1 B

8=0

9=0

10=0

J=2= 2 R or 2 B

K=3= 2 R + 1 B or 1 R +2 B

Q=1=1 R or 1 B

If you count total number of black cards among the number of cards dealt by dealer, the possibilities of black card drawn is either 15 or 16 from 20 cards drawn.

As, Experimental probability is the probability obtained through experiment which is different from theoretical Probability.

Total number of cards =52

So, Probability of dealing with black cards by dealer which is either 15 or 16 in number is given by

[tex]=\frac{\text{total favorable outcome}}{\text{total possible outcome}}\\\\\frac{15}{52} {\text{or}} \frac{16}{52}=\frac{4}{13}.[/tex]

Answer:

40%

Step-by-step explanation:

There are 20 cards in total.

8 are black: 3,2,K,5,6,4,A,J

12 are red: 2,A,K,Q,2,5,K,2,7,6,J,A

so that means 8 of the 20 are black or 8/20

and 8/20 is 40% which is your answer.

Harvey invested $6000 for 2 years in a savings account paying simple interest with a yearly interest rate of 5.5%. How much simple interest did he earn.

Answers

[tex]\bf \qquad \textit{Simple Interest Earned}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\to& \$6000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\to &0.055\\ t=years\to &2 \end{cases} \\\\\\ I=6000\cdot 0.055\cdot 2[/tex]

Harvey earned a simple interest of $660 over 2 years on his $6000 investment.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Since, We know that;

Simple interest is calculated using the formula:

I = P r t

Where: I = Interest earned P = Principal amount (amount invested) r = Annual interest rate t = Time period (in years)

Now, In this case,

Harvey invested $6000 for 2 years at an annual interest rate of 5.5%.

So, using the formula:

I = 6000 x 0.055 x 2

I = $660

Therefore, Harvey earned a simple interest of $660 over 2 years on his $6000 investment.

Learn more about the multiplication visit:

https://brainly.com/question/10873737

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Find the point p where the line x = 1 + t, y = 2t, z = -3t intersects the plane x + y - z = 3.

Answers

The given lines are
x = 1 + t
y = 2t
z = -3t

The plane is x + y - z = 3

If the lines intersect the plane at a point p, then the lines should satisfy the equation of the plane.
That is,
(1 + t) + (2t) - (-3t) = 3
1 + t + 2t + 3t = 3
1 + 6t = 3
6t = 2
t = 1/3

Therefore the coordinates of the point p are
x = 1 + 1/3 = 4/3
y = 2(1/3) = 2/3
z = -3(1/3) = -1

That is p (4/3, 2/3, -1)

Answer: The point p has coordinates (4/3, 2/3, -1)

Find the measures of two angles, one positive and one negative, that are coterminal with pi divided by five.

Answers

The given angle is π/5.

The coterminal angles differ from the given angle by 2π and -2π.
The lower coterminal angle is
[tex] \frac{ \pi }{5}-2 \pi = - \frac{9 \pi }{5} [/tex]
The higher coterminal angle is
[tex] \frac{ \pi }{5} +2 \pi = \frac{11 \pi }{5} [/tex]

Answer: [tex]- \frac{9 \pi }{5} . \, \frac{11 \pi }{5} [/tex]

Daniel ate 1/3 of the left over pizza. If there were 2 1/2 pizzas left, how much did Daniel eat?

Answers

I think I got this right 5/6 I think?

It takes 40 min for a bus to travel the 36 miles from Framingham to Worcester. A car traveling from Worcester to Framingham moves 1.5 times as fast as the bus. If the car and the bus start moving towards each other simultaneously, after how many minutes will they meet?

Answers

The velocity of the bus is:

velocity (bus) = 36 miles / 40 min

velocity (bus) = 0.9 miles / min

Since the car is 1.5 times faster, so the velocity of the car is:

velocity (car) = 1.5 * 0.9 miles / min

velocity (car) = 1.35 miles / min

At the meeting point, the sum of the distance is equal to 36 miles. Therefore:

1.35 t + 0.9 t = 36

2.25 t = 36

t = 16 min

So they will meet after 16 minutes.

Which of the following is a measurement of the space between two objects? A. Area B. Pounds C. Circumference D. Miles

Answers

D, miles. Pounds would be weight. Circumference is the distance around a circle. Area is the amount of square units in an area.

Final answer:

The space between two objects is measured as distance or length, with miles being the correct unit of measurement among the given options.

Explanation:

The measurement of the space between two objects is referred to as length or distance. If we look at the options provided: A. Area, B. Pounds, C. Circumference, D. Miles, it is clear that miles is a unit of measurement that describes distance. Area measures the size of a surface, pounds measure weight or mass, and circumference measures the distance around a circle. When considering distances, especially those that are long such as between two cities, miles is an appropriate unit to use. For example, the distance between your house and school would best be measured in kilometers or miles, rather than in smaller units like inches or centimeters, or in unrelated units like pounds or areas.

Given the function f(x) = −2x2 + 4x − 7, find f(−4). −55 −7 9 25

Answers

Answer:

Option (a) is correct.

The value of function [tex]f(x) = -2x^2 + 4x- 7[/tex] at x = -4 is -55

Step-by-step explanation:

Given : [tex]f(x) = -2x^2 + 4x- 7[/tex]

We have to find the value at f(-4) and choose the correct option from the given options.

Consider the given function [tex]f(x) = -2x^2 + 4x- 7[/tex]

Since, we have to find the value of f(-4) that is value of f(x) at x = -4

Substitute, value of x = -4 in given function, we have,

[tex]f(-4) = -2(-4)^2 + 4(-4)- 7[/tex]

Simplify, we have,

[tex]f(-4) = -55[/tex]

Thus, the value of function [tex]f(x) = -2x^2 + 4x- 7[/tex] at x = -4 is -55

Option (a) is correct.

Find the area of one segment formed by a square with sides of 6" inscribed in a circle.
(Hint: use the ratio of 1:1: to find the radius of the circle.)

Answers

check the picture below.

now, bear in mind that, we could simply get the area of the whole circle with that radius, and tease out a quarter, because the segment is just using up a quarter of the circle, because the angle made is 90°, and then subtract the triangle from that sector, and what's leftover is the segment.

[tex]\bf \stackrel{\textit{area of the circle}}{A=\pi r^2}\implies A=\pi (3\sqrt{2})^2\implies A=\pi 3^2\sqrt{2^2}\implies A=18\pi \\\\\\ \textit{now one-quart of that is }\cfrac{18\pi }{4}\implies \cfrac{9\pi }{2}\impliedby \textit{sector's area}[/tex]

[tex]\bf \stackrel{\textit{area of the triangle}}{A=\cfrac{1}{2}bh}\implies A=\cfrac{(3\sqrt{2})(3\sqrt{2})}{2}\implies A=\cfrac{3^2\sqrt{2^2}}{2}\\\\\\A=\cfrac{18}{2}\implies A=9\impliedby \textit{area of that triangle}\\\\ -------------------------------\\\\ \stackrel{sector's area}{\cfrac{9\pi }{2}}~~-~~\stackrel{\textit{area of the triangle}}{9}\implies \cfrac{9\pi -18}{2}\impliedby \textit{segment's area}[/tex]

or you can always just use the area of a segment, with the radius and angle given.

[tex]\bf \textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left[\cfrac{\theta \pi }{180}-sin(\theta ) \right] \\\\\\ \begin{cases} r=3\sqrt{2}\\ \theta =90 \end{cases}\implies A=\cfrac{(3\sqrt{2})^2}{2}\left[\cfrac{90 \pi }{180}-sin(90^o ) \right][/tex]

At the frozen yogurt shop, a machine fills cups with 4 ounces of frozen yogurt before adding the toppings. After the cups are filled, customers add as many toppings as they want without exceeding a total weight of 6 ounces. Which of the following represent the acceptable weights for the frozen yogurt options? Select all that apply.

Answers

Is this for algebra 1 if so I believe it's 4,5,6

In this question, every cups will be filled with 4 ounces yogurt. That mean, the lowest possible of the cups weight would be 4 ounces. After that the customer can the topping without exceeding 6 ounces of total weight. Since it total weight, that means from the 6 ounces there should be 4 ounces of yogurt. Then the maximum weight is 6 ounces
Minimum weight is 4 ounces and maximum weight is 6 ounces, so the answer would be 4,5,6 or any number between 4-6

How many boxes of carrots are left? 75 boxes − 68 boxes = 7 boxes

Answers

7
i dont know why you would ask thisquestion

The question pertains to a basic subtraction operation where the student is left with 7 boxes of carrots after subtracting 68 boxes from an initial count of 75 boxes.

The subject of the question is mathematics, specifically involving subtraction and the concept of determining the number of items remaining after a reduction. The mathematical operation presented in the question is 75 boxes - 68 boxes = 7 boxes, which indicates that when you start with 75 boxes of carrots and remove 68 boxes, you are left with 7 boxes of carrots.

This type of problem is common in elementary mathematics and does not involve complex concepts such as permutations, probability, or statistical distributions.

Which function has an inverse that is also a function? a {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} b {(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} c {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} d {(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}

Answers

an expression, that is a function, will have no x-repeats on the x,y pairs.

and expression that is a function, and has an inverse that is also a function, will have no x-repeats, and no y-repeats either, so the pairs will be unique for the set, let's do some checking then,

[tex]\bf a \qquad\{(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)\}\\\\ b \qquad\{(-1, 2), (0, \stackrel{\downarrow }{4}), (1, 5), (5, \stackrel{\downarrow }{4}), (7, 2)\}\impliedby \begin{array}{llll} \textit{notice the } y-rep eats\\ \textit{thus, no dice} \end{array}[/tex]

[tex]\bf c \qquad\{(-1, -2), (0, \stackrel{\downarrow }{4}), (1, 3), (5, 14), (7, \stackrel{\downarrow }{4})\}\impliedby \begin{array}{llll} \textit{notice the } y-rep eats\\ \textit{thus, no dice} \end{array}\\\\ d \qquad\{(-1, \stackrel{\downarrow }{4}), (0, \stackrel{\downarrow }{4}), (1, 2), (5, 3), (7, 1)\}\impliedby \begin{array}{llll} \textit{notice the } y-rep eats\\ \textit{thus, no dice} \end{array}[/tex]

Answer:

Step-by-step explanation:

It is called the inverse or reciprocal function of f to another function f − 1 that fulfills that:

If f (a) = b, then f − 1 (b) = a.

The inverse of a function when it exists is unique, so that neither "X" nor "Y" can be repeated.

If we analyze the possibilities, in the case of b, c, and d, the value 4 of the "Y" is repeated twice; in the case of a, that does not happen, therefore the answer is: a {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2) }

I need help someone explain?????

Answers

In 9, the error is that the 276 should be the numerator, not the denominator, because in the proportion Elisa made, the number of students is the numerator and the number of teachers is the denominator.

Monique Fournier deposited $12,500 into a savings account paying 6.5% annual interest compounded monthly. What amount will she have in her account after 3 years? How much compound interest will she have earned?

Answers

Explaining the calculation of the amount in the account after 3 years and the compound interest earned.

Amount in the account after 3 years:

Calculate the monthly interest rate: 6.5% annual interest divided by 12 (months) = 0.0054167

Calculate the total amount using the compound interest formula: $12,500 * (1 + 0.0054167)^36 = $15,183.41

Compound interest earned:

Subtract the initial deposit from the total amount: $15,183.41 - $12,500 = $2,683.41

A line has a slope of -1/2 and a y-intercept of –2.

what is the x-intercept of the line?

Answers

y = (slope)x + (y-intercept)

y = -1/2x - 2

x-intercepts occur when y = 0

0 = -1/2x - 2

2 = -1/2x

x = -4

Thus, the x-intercept is at (-4,0)

hannah and anthony are siblings who have ages that are consecutive odd integers. the sum of their ages is 92 . which equations could be used to find hannah's age,h, if she is the older sibling?

Answers

Let h = Hannah's age.

Hannah is older than her sibling, and their ages are consecutive odd integers. Therefore, h = an odd number and the sibling's age = h-2.

The sum of their ages is 92, therefore
h + (h-2) = 92
2h - 2 = 92

2h = 94
h = 47 years

Answer:
The equation to find Hannah's age is 2h - 2 = 92.
This yields Hannah's age as 47 years.

Answers matching "The combined average weight of an okapi and a llama is 450 kilograms. The average weight of 3 llamas is 190 kilograms more than the average weight of one okapi. On average, how much does an okapi weigh, and how much does a llama weigh?"

Answers

Let us say that:

x = weight of llamas

y = weight of okapi

From the problem, we can create the equations:

x + y = 450 --> 1

3 x = y + 190 --> 2

Rewriting equation 1:

x = 450 – y

From equation 2:

3 (450 – y) = y + 190

1350 – 3 y = y + 190

4 y = 1160

y = 290

From equation 1:

x = 450 – 290

x = 160

Therefore a llama weighs 160 kilograms while okapi weigh 290 kilograms on average.

at 1:00 pm you have 24 megabytes of a movie. at 1:15 pm you have 96 megabytes what is the download rate in megabytes per minute

Answers

in the 15 minutes that have passed a total of 96-14 = 82 Mbs have been downloaded.

82/15 = 5.47 Mbs/min

Carmen is making 5 parts strawberry juice to 3 parts water. Carmen would like to make 64 fluid ounces of the strawberry drink. How many fluid ounces of strawberry juice and water does Carmen need?

Answers

Ok so if she needs 64 floz, If u add 5+3 you get 8. 64/8 = 8

Now You multiply your parts of water and juice by 8.

5*8= 40 <---- Answer

3*8 =24 <----Answer

To check your answer you would add up the parts of each. 40+24= 64

WILL GIVE BRAINEST
Identify one characteristic of exponential decay.

Answers

A. This is true. If 0 < r < 1, then we have decay. For example, if r = 0.5 then we cut each term in half to get successive new terms (10, 5, 2.5, 1.25, etc etc)

B. False. Common differences apply to arithmetic sequences which are not exponential in nature.

C. False. Decay curves slope downward. As you read them from left to right, they will drop down.

D. False. If r > 1, then we have exponential growth. It is effectively the opposite of choice A.

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

So in summary, the final answer is choice A

Answer: A

Step-by-step explanation:

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