Find an equation of the plane that contains the point p(5,1,4) and the line x = 2−t, y = 3 + t, t = 3−3t.

Answers

Answer 1

The vector from the reference point on the line to the point is
.. (5-2, 1-3, 4-3) = (3, -2, 1)
The cross product of this with the line's direction vector (-1, 1, -3) is (5, 8, 1). The dot product of that with any of the points in the problem statement is 37. Your plane equation can be written as
.. 5x +8y +z = 37

_____
A suitable vector calculator is very handy for this. I used an HP-48 app on my phone.

Related Questions

If s = 1 over 2 unit and A = 12s2, what is the value of A, in square units? ____ square unit(s). (Input whole number only.)

Answers

Answer
3 square unit(s)

Explanation
The question is testing the concept of substitution.
A=12s^2
If s=1/2 , what is the value of A?
Substituting s with 1/2 we get;

A=12(1/2)^2
=12×1/4
=3
The answer is 3 unit squared. The is not fraction in the answer.

the answer is three square units

find x intercepts of y=-3^× + 2

Answers

to find the x-intercept, substitute in 0 for y and solve for x.

Clayton wants to make a cylindrical case that will fit a bass drum with a height of 14 inches and a diameter of 24 inches. With is the surface area of the case? Use 3.14 \pi[tex] \pi [/tex]

Answers

1. You can solve this problem and calculate the surface area of the case, by applying the formula for calculate the surface area of a cylinder, which is:

A=2πr²+2πrh

"A" is the surface area of the cylinder.
"r" is the radius.
"h" is the height of the cylinder (h=14 inches).

2. You need to calculate the radius. So, you have:

r=Diameter/2
r=24 inches/2
r=12 inches.

3. You already have the height and the radius, so you can substitute these values into the formula (A=2πr²+2πrh) for calculate the surface area of the case:

A=2πr²+2πrh
A=2(3.14)(12 inches)²+2(3.14)(12 inches)(14 inches)
A=904.32 inches²+1055.04 inches²
A=1959.36 inches²

Combine like terms to simplify the expression below 5y-8x-y+12x

Answers

There are like terms 5y and y. Since there is a subtraction sign in front of y, we would subtract that from 5y, which becomes 4y. 8x and 12x are also like terms (x). Since 12x has an addition sign in front, indicating it's positive, we would add it to -8x (which is negative b/c of the subtraction sign in front). 12x + -8x = 4x. The expression is 4y + 4x.

Hope this helps!

What would happen to a monthly payment if the interest rate increased

Answers

If the interest rate increases it is expected the monthly payment also increases.

What is the interest rate?

This is usually a low percentage of money paid to the bank or a similar institution for borrowing money. The interest rate is established when the loan is approved and it is proportional to the amount of money that needs to be paid.

What would happen if the interest rate increased?

As both the payment and the interest rate are directly related if the interest rate increases, the amount of money to be paid would also increase.

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Earth's diameter at the equator is 7,926 miles. Find the distance around Earth at it's equator to the nearest tenth.

Answers

(7926π) miles ≈ 24,900.3 miles

when derek planted a tree it was 36 inches tall. the tree grew 1 1/4 inches per year the tree is now 44 3/4 inches tall. how many years ago did derek lant the tree?

Answers

Derek would have planted the tree 7 years ago. You subtract 36 from 44.75 and get 8.75. This is how much the tree grew since he planted it. Then, you'll divide 8.75 by 1.25 (1 1/4) which tells you how many years it has been since he planted the tree. The final answer is 7 years. Hope this helps!

Lars deposited $50 into a savings account. According to the rule of 72, what interest rate will cause his money to double in approximately 29 years?

Answers

The rate that will double Lars deposit of $50 in 29 years will be calculated as follows:
Suppose the account used was using compound interest. Thus to determine his future value we shall use the formula:
FV=P(1+r)^n
where:
FV is future value
p=principle
r=rate
n=periods
from the information given
FV=$100
p=$50
n=29 years
we are required to find r
thus
100=50(1+r)^29
100/50=(1+r)^29
2=(1+r)^29
2^(1/29)=1+r
1.02419=1+r
hence:
r=0.02419~2.419%

Answer:

Step-by-step explanation:

The answer is 2.5%

How would the domain and range of the function y= 1/4x-6 be determined

Answers

Is there any suggestions to this question?

Answer: Create a table or a graph of the function. The domain represents all input values and the range represents all output values. The domain and range contain all real numbers

The president of the math club is conducting a survey to see where the twelfth-grade class wants to go on their field trip. Instead of asking the whole class, she surveys only the twelfth-grade members of the math club. She records their choices and plans to present the results to the school principal. What type of sampling did she use?

Answers

She used convenience sampling

Answer:

The answer is convenience sampling.

Step-by-step explanation:

As per the given scenario, the president of the math club is conducting a survey to see where the twelfth-grade class wants to go on their field trip and she surveys only the twelfth-grade members of the math club.

This is convenience sampling as here the samples are the closest people available. Convenience sampling is a method where the samples are taken who are close to hand.

Here also the math club president is asking the math club students only. This is why it is convenience sampling.

Simplify the sum 4/m+9+5/m^2-81
A. 9/(m-9)(m+9)
B. 4m+41/(m-9)(m+9)
C.9/m2+m-72
D.4m-31/(m-9)(m+9)

Answers

4/(m+9)+5/(m^2-81)=
4/ ( m+9) +5 / ( m-9)(m+9)=
4(m-9)/(m+9)(m-9)+ 5 / (m+9)(m-9)=
(4m-36+5)/(m+9)(m-9)=
4m-31/ (m+9)(m-9)

the answer is D

Answer:
D

Explanation:
1- The given expression is:
[tex] \frac{4}{m+9} [/tex] + [tex] \frac{5}{m^2 - 81} [/tex]

2- Factorize the denominator of the second term:
[tex] \frac{4}{m+9} [/tex] + [tex] \frac{5}{(m+9)(m-9)} [/tex]

3- Get the common denominator for both terms. In this case, the common denominator would be (m+9)(m-9):
[tex] \frac{4(m-9)}{(m-9)(m+9)} [/tex] + [tex] \frac{5}{(m-9)(m+9)} [/tex]

This will give:
[tex] \frac{4m-36}{(m+9)(m-9)} [/tex] + [tex] \frac{5}{(m-9)(m+9)} [/tex]

4- Add the numerators normally since the two terms have common denominator:
[tex] \frac{4m-36+5}{(m-9)(m+9)} [/tex] = [tex] \frac{4m-31}{(m-9)(m+9)} [/tex]

Comparing the calculated result with the given options, we will find that the correct option is the last one

Hope this helps :)

Carly bought a new house for $125,000. The value of the house appreciates approximately 3.5% each year. What will be the value of the house after 10 years

Answers

Multiply 125000 by 0.035= 4375. Then multiply that by 10. 43750 and add it to the house value 125000. 168750

A probability experiment consists of rolling a a 6 6-sided die. find the probability of the event below. rolling a number with exactly 2 not necessarily unique prime factors number with exactly 2 not necessarily unique prime factors

Answers

The probability of rolling a number with exactly two prime factors on a six-sided die is 1/3, as there are two outcomes (4 and 6) with exactly two prime factors and six possible outcomes in total.

The student is asking about the probability of an event in a probability experiment involving rolling a single six-sided die. The specific event of interest is rolling a number with exactly two, not necessarily unique, prime factors. On a standard six-sided die, the faces are labeled with the numbers 1 through 6. When considering the numbers on a die with two prime factors, we must first identify which of these numbers have exactly two prime factors. The numbers are:

4 has two prime factors: 2 and 2 (2 squared).6 has two prime factors: 2 and 3.

The other numbers (1, 2, 3, and 5) have fewer than two prime factors. Since 4 and 6 are the only outcomes with exactly two prime factors, we have two favorable outcomes out of six possible outcomes on a six-sided die.

Thus, the probability of rolling a number with exactly two prime factors is:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 2 / 6 = 1 / 3

Therefore, the probability of the event is 1/3, or approximately 0.3333 (repeating).

Keller boat travels 24mph. find the rate of the river if she can travel 6 mi upstream. in the same amount of time she can go 10 mi downstream.

Answers

Given that Kellen can travel upstream in the same amount of time she travels downstream, the rate of river will be found as follow:
time=(distance)/(speed)
time taken to travel upstream is:
(24+x)/10
Time taken to travel downstream is:
(24-x)/6
given that the time taken to travel upstream and downstream is the same then:
(24+x)/10=(24-x)/6
6(24+x)=10(24-x)
144+6x=240-10x
6x+10x=240-144
16x=96
x=96/16
x=6 mph

The correct answer is:

6 mph.

Explanation:

We will use the formula d = rt for this, where d is distance, r is rate, and t is time.

We know that the time for both distances is the same; this means we want to isolate t in our formula. To do this, we will cancel r by dividing both sides:
d/r = rt/r
d/r = t

We will write an expression for the time upstream, an expression for the time downstream, and set them equal.

For the time upstream, the distance is 6 and the rate is 24-x; this gives us

[tex]\frac{6}{24-x}[/tex]

For the time downstream, the distance is 10 and the rate is 24+x; this gives us

[tex]\frac{10}{24+x}[/tex]

Together, these give us the equation

[tex]\frac{6}{24-x}=\frac{10}{24+x}[/tex]

We cross-multiply to solve this:
6(24+x) = 10(24-x)

Using the distributive property, we have
6*24 + 6*x = 10*24 - 10*x
144+6x = 240-10x

Adding 10x to each side,
144+6x+10x = 240-10x+10x
144+16x = 240

Subtract 144 from each side:
144+16x-144 = 240-144
16x = 96

Divide both sides by 16:
16x/16 = 96/16
x = 6

Classify each pair of labeled angles as complementary, supplementary, or neither. Drag and drop the choices into the boxes to correctly complete the table. Each pair of angles may belong to more than one category. complementary supplementary neither Two angles, on the left a fifty three degree angle and on the right a one hundred twenty seven degree angleTwo angles, on the top a thirty four degree angle and on the bottom a fifty six degree angleTwo lines intersect with an angle on the top left labeled sixty seven degrees and on the bottom right sixty seven degrees

Answers

complementary angles have the sum of 90 degrees.
supplementary angles have the sum of 180 degrees
1-
[tex]53 + 127 = 180[/tex]
so its supplementary
2-
[tex]34 + 56 = 90[/tex]
it's complementary

3-
[tex]67 + 67 = 134[/tex]
it's none of them
hope it helps

Answer:

Step-by-step explanation:

Since it is given that when two lines intersect, the angle on the top left is 53° and 127°, thus they both form supplementary angles as the sum of both angles that is 53+127=180°.

Also, from the given information, the angle on the top is 34° and on the bottom is 56°, they both form a complementary angle pair, a sthe sum of both the two angles is 90° as 56+34=90°.

Also, the angle on the top left is =67° and the angle on the bottom right =67°, they both form vertical pair angles as both the angles are vertically opposite to each other.

square root of -72 written in terms of i

Answers

Given: √-72
Work:
√-72 --> √36 * √-2 (36 is the perfect square needed to solve this problem)
6√-2 ---> 6i√2
Answer: 6i√2

Hope this helps!

Find the radius and the circumference to the nearest hundredth when d ≈ 3.8 in. Use 3.14 for π.

Answers

d=3.8
radius r=d/2=1.9
C, circumference
C=2*3.14*r or C=d*3.14
C=3.08*3.14=11.932
C=11.93

The radius is approximately 1.9 in and the circumference is approximately 11.94 in, both rounded to the nearest hundredth.

We have,

If we let d be the diameter of a circle, then the radius of the circle, r, is half of the diameter.

Therefore, we can find the radius of the circle by dividing the diameter by 2:

r = d/2

In this problem,

d ≈ 3.8 in, so we have:

r = 3.8/2 = 1.9 in

To find the circumference of the circle, we can use the formula:

C = 2πr

where π is approximately equal to 3.14 and r is the radius we just found. Substituting in the values, we get:

C = 2 x 3.14 x 1.9 ≈ 11.94 in

Therefore,

The radius is approximately 1.9 in and the circumference is approximately 11.94 in, both rounded to the nearest hundredth.

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what is the discount on shirts if shirts cost $24 and there is a discount 25%

Answers

Step-by-step explanation:

25% × $24 = $6

Subtract the discount from the original

24 - 6 = $18.00

Find all the points where the tangent plane to this ellipsoid is parallel to the plane y-8x-4z = 0

Answers

i dont know i will tell you when i find out

A video game club has 42 members. The number of high school members is six less than twice the number of middle school members. Which expression represents the number of high school members in the club?

Answers

There are no expressions listed to choose from, but the expression should look something like the following:

x= # middle school members
2x-6= # high school members

Two times the number of middle school students is 2 times x. 6 less means to subtract 6 from 2x.

ANSWER: 2x-6 is an expression representing the number of high school members.

Hope this helps! :)

Answer:

2x-6

Step-by-step explanation:

The length of a side of a rectangle is 2 units less than a number, and the width is 4 units more than the length. Which of the following expressions represents the area of the rectangle, in square units?

Answers

Let's find the expressions for the length and width of the rectangle. The length (which we will call l) is 2 units less than some undefined number, thus we will use the variable x:
l = x - 2

The width is 4 more than this length:
w = l + 4 = (x - 2) + 4 = x + 2

Now, given that we have the length and width and are looking for the area, we need to multiply these expressions together.

One way to write this would simply be (x + 2)(x - 2). If we wanted to find a different way of writing the area, we could use FOIL to find all terms and get x^2 - 4.

Which of the points listed is the same distance from the x-axis as the point (7, 8.75)?

Answers

the complete question in the attached figure

we know that

The distance of the point (7, 8.75) to the x-axis (the horizontal line) is 8.75

then
case A) (-7, 5.25)---------> is not correct ( the distance to the x-axis is 5.25)
case B) (8.75, 6)---------> is not correct ( the distance to the x-axis is 6)
case C) (6, -8.75)---------> is correct ( the distance to the x-axis is 8.75)

the answer is the option C) (6, -8.75)

Answer:

(7,-3.25)

Step-by-step explanation:

Greg drew a pair of parallel lines and a line segment next to each other on a chalkboard. Which of these statements best compares the pair of parallel lines and the line segment? (1 point) Parallel lines and the line segment have no dimensions of measurement. The parallel lines and the line segment always meet at a common endpoint which is called the vertex. Parallel lines and a line segment cannot lie on the same plane at the same time because they do not overlap. The parallel lines extend infinitely in both directions, and the line segment has two endpoints.

Answers

The parallel lines extend infinitely in both directions, and the line segment has two endpoints.

Answer: If drew drew a pair of lines and draw the segment between them, in a way that the segment is delimited by both lines, then:

If two lines are parallel, then they will never overlap each other, and if you draw a segment between them, then the segment will have two endpoints (one at each intersection with the lines)

So the correct answer is that the parallel lines extend infinitely in both directions, and the line segment has two endpoints.

You buy a house for $130,000. It appreciate 1.6% per year. identify the initial amount, growth rate and growth factor for the situation above. Then great an equation that will model it.

Answers

[tex]\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\to &\$130000\\ r=rate\to 1.6\%\to \frac{1.6}{100}\to &0.016\\ growth~factor\to &1+0.016\\ t=\textit{elapsed time}\\ \end{cases} \\\\\\ A=\stackrel{P}{130000}(\stackrel{growth~factor}{1+\stackrel{r}{0.016}})^t[/tex]

Find the sum of each row in the table. Explain why these sums make sense.
Table:
Food | Rent | Transportation
1/4 6/10 3/20
25%. 60%. 15%
0.25 0.60 0.15

Answers

Food | Rent | Transportation l Sum
1/4 6/10 3/20 1
25%. 60%. 15% 100%
0.25 0.60 0.15 1

Answer:
The sum of each row in the table makes sense because we are writing the same amount in three different ways.
Therefore, the result is the same.

Final answer:

The sums of each row in the table represent allocations of a whole expressed in different formats (fractions, percentages, and decimals), and they all add up to 1 or 100%, signifying a full allocation of resources.

Explanation:

To find the sum of each row in the provided table, we add the numbers given within that row. Since the table is arranged with fractions, percentages, and decimals that all represent proportions of a whole, the sum of each row should theoretically be equal if converted into the same format. For instance, we should expect each row to total 1 or 100% if we are discussing a full allocation of resources like a budget.

For the first row, we need to add the fractions: 1/4 + 6/10 + 3/20. To do this, we'd need a common denominator, which is 20. So we get (5/20) + (12/20) + (3/20) = 20/20, which simplifies to 1.

The second row represents percentages and they need to total 100%: 25% + 60% + 15% = 100%

Finally, the third row lists decimals which should sum up to 1: 0.25 + 0.60 + 0.15 = 1.00

All three rows make sense because they represent different ways of expressing the whole, which is split into portions allocated to Food, Rent, and Transportation.

the product of nine and x is greater than six more than the product of three and x...?

Answers

9x > 6 + 3x
6x>6
It doesn't tell my to graph anything so I went ahead and just simplified.
Hope this helps!

Finley's pumpkin had a mass of 6.5 kilograms before he carved it. After carving it, the pumpkin had a mass of 3.9 k.g.
What was the percent decrease in the mass of the pumpkin?

Answers

I believe the answer is 20%

The answer to this question is 40%

inverse of f(x)=5x+4

Answers

Change f(x) to y
Switch x and y
Solve for y

-⅘ + x/5 =y → y = ⅕x - ⅘

If the graph of the function h defined by h(x)=-3x^2+3 is translated vertically upward by 3 units , it becomes the graph of a function g. Find the expression for g(x)

Answers

g(x) = h(x) +3 . . . . . h translated upward by 3 units

g(x) = (-3x² +3) +3
g(x) = -3x² +6 . . . . . . . . . the desired expression for g(x)

Ben has b dollars. Cam has 7 fewer dollars than Ben. How many dollars does Cam have? Write your answer as an expression.

Answers

b - 7
B is the number of dollars Ben has and Cam has 7 less so you just subtract 7 from b

Answer:

Cam has [tex]b-7[/tex] dollars.

Step-by-step explanation:

Here b represents the number of dollars Ben has,

Given,

Cam has 7 fewer dollars than Ben,

So, the number of dollars cam has = The number of Ben's dollar - 7

[tex]=b-7[/tex]

Hence, the expression that represents cam's dollar is,

[tex]' b-7 '[/tex]

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