Mathematics College

Which of the following is the proper notation used to express a point in the three-dimensional coordinate plane?
A. (x)
B. (x, y, z)
C. (x, y)
D. (w, x, y, z)

Answers

Answer 1
The answer is : B. (x, y, z)


Hope this helps ✌️
Answer 2

Answer:  Option 'B' is correct.

Step-by-step explanation:

Since we have given that

We need to express a point in the three-dimensional coordinate plane.

As we know that In 3- dimensional plane, there are 3 axes;

One for x-axis (say  length)

One for y- axis (say breadth)

One for z-axis (say height)

So, the proper notation would be (x,y,z).

Hence, Option 'B' is correct.

Related Questions

Which polygon has an interior angle sum of 1080°?

Answers

The polygon which has an interior angle sum of 1080° is an Octagon

Interior angles of a Polygon

From the question, we are to determine which polygon has an interior angle sum of 1080°

To find that, we will determine the number of sides the polygon has.

From the formula for sum of the interior angles in a polygon

Sum of interior angles = (n-2)180°

Where n is the number of sides

Then,

1080° = (n-2) 180°

1080° ÷ 180° = n-2

6 = n-2

n = 6 + 2

n = 8

A polygon with 8 sides is called an Octagon

Hence, the polygon which has an interior angle sum of 1080° is an Octagon

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An object is thrown from an initial height of 0 feet with an initial velocity of 160 feet per second. Solve for when it will return to the ground. Show your work and explain the steps used to solve.

Answers

Projectile motion is when the direction of an object follows the shape of an arc. The only force acting on the object is gravity. Also, the concept is that the motion of the horizontal and vertical directions are independent. Therefore, assuming no air resistance, the time for a rock thrown over the cliff at some angle to reach the ground will be the same time if you just simply free-fall the rock. 

Hence, we can solve this using rectilinear motion equations.

y = vt + 1/2*a*t^2, where
y is the vertical distance
v is the initial velocity
a is the acceleration due to gravity equal to -32.2 ft/s^2
t is the time of flight

However, it would be impossible to have 0 height. I think there is some typographical error right there. Let's just assume a height of 1000 ft. Substituting the values,

100 = 160*t + 1/2*-32.2*t^2
t = 9.3 seconds


What is the greatest angle measure in the diagram?
95˚
105˚
119˚
180˚

Answers

the answer should be 119

The solution is, The greatest angle measure is angle F which is 119°

What is an angle?

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

The sum of all the angles of a quadrilateral is 360°

(15x-10)°+(15x+14)°+(9x-4)°+(11x+10)° = 360°

Open up the brackets and rearrange the expression

15x-10°+15x+14°+9x-4°+11x+10°=360°

15x+15x+9x+11x-10°+14°-4°+10° = 360°

50x+10°=360°

Collect like terms

50x=360°-10°

50x=350°

Divide by the coefficient of x

x= 350/50

X=7°

Substitute the value of x into the various angles

15x-10°=(15×7)-10= 105-10=95°

15x+14°=(15×7)+14=105+14=119°

9x-4°=(9×7)-4=63-4=59°

11x+10°=(11×7)+10=77+10=87°

The greatest angle measure is angle F which is 119°

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Tim count his friends fingers by fives. he counts the fingers on six hands. what number does he say?

Answers

6*5= 30 fingers, so tim would say there are 30 fingers.

How do i simplify this?

Answers

[tex]\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^{ n}} \qquad \qquad \cfrac{1}{a^{ n}}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \cfrac{(xy^{-3})^{-5}}{(x^{-3}y)^{-6}}\impliedby \textit{first off, distribute the exponent} \\\\\\ \cfrac{x^{1\cdot -5}y^{-3\cdot -5}}{x^{-3\cdot -6}y^{1\cdot -6}}\implies \cfrac{x^{-5}y^{15}}{x^{18}y^{-6}}\implies \cfrac{y^{15}\cdot y^6}{x^{18}\cdot x^5}\implies \cfrac{y^{15+6}}{x^{18+5}}\implies \cfrac{y^{21}}{x^{23}}[/tex]

11.   Edgar Anderson earns $200 a week plus a 15% commission on all sales over $1,000. If Mr. Anderson's sales for one week are $2,500, what is his gross pay for that week?

Answers

well, for that one week, he made his salary, 200 bucks, plus 15% of his sales, because his sales were over $1000, to be exact, they were $2500, so he made 15% of 2500 extra on top of his salary.

so, what's 15% of 2500? well, is just (15/100) * 2500.

so, add that to his $200 salary, and that's his gross pay.

determine the heat energy received per kilogram of steam produced

Answers

According to steam tables, steam produced from liquid water at 100 deg. C and standard atmospheric pressure (101.3 kPa) is 2257.0 kJ/kg.K.

Note : this value varies greatly with pressure and temperature.

x+3menor que 8 qual o resultado

Answers

x+3<8

8-3 =5

 X<5

 any number less than 5 will work

Match each word from Column A with the correct definition from Column B. Column A Column B 1. impulse 2. muster 3. naught 4. renown 5. vacancy 6. thrifty A. the state of being empty or not filled B. nothing, nonexistence C. to stir up or bring to action D. a sudden stirring to do something E. fame F. careful with money

Answers

1. D
2. C
3. B
4. E
5. A
6. F

Answer:

The correct matches are:

1. impulse - a sudden stirring to do something

2. muster - to stir up or bring to action. Like to muster up the courage to speak against the wrong doer.

3. naught - nothing, nonexistence

4. renown - fame ; the condition when you are known or talked about by many people.

5. vacancy - the state of being empty or not filled. Like vacancy for new candidates for a job.

6. thrifty - careful with money . Like a person is thrifty about his own time.


A total of 

644

 tickets were sold for the school play. They were either adult tickets or student tickets. There were 

56

 fewer student tickets sold than adult tickets. How many adult tickets were sold?

Answers

a + s = 644
s = a - 56

a + (a - 56) = 644
2a - 56 = 644
2a = 644 + 56
2a = 700
a = 700/2
a = 350 <=== adult tickets

s = a - 56
s = 350 - 56
s = 294 ...student tickets

A company has a sales revenue of $10,000, cost of goods sold of $4500, and other operating expenses of $1500. what is this company's pre-tax income?

Answers

$10,000-$1500= $8,500- $4500=$4,000

martin brought 30 shares of microsoft at the close price of $24.53. In a few years, Martin sells all of his shares at $33.71. How much money did martin make?

Answers

Difference: 33.71 - 24.53 = 9.18

9.18*30 = 275.4

Of course, we can't take into account inflation, because nothing is said, I mean that the $24 a few years ago are not the same as today ...

Answer:

Money did martin make = 275.4 $

Step-by-step explanation:

Martin brought 30 shares of Microsoft at the close price of $24.53.

Number of shares = 30

Cost per share = 24.53 $

Total cost = 30 x 24.53 = 735.9 $

Martin sells all of his shares at $33.71

Selling price per share = 33.71 $

Total selling price = 30 x 33.71 = 1011.3 $

Gain for Martin = 1011.3 - 735.9 = 275.4 $

Money did martin make = 275.4 $

A carpenter is assigned a job of installing a spa into a pre-existing deck. The dimensions of the deck are (6x + 1) wide by (4x - 3) long. The dimensions of the spa are (4x + 5) wide by (x + 6) long.

Write the polynomial that represents the remaining area of the deck after the carpenter cut the hole out for the spa.

Answers

Area of the deck minus area of spa is equal to the area of the deck remaining...

A=(6x+1)(4x-3)-(4x+5)(x+6)

A=24x^2-18x+4x-3-4x^2-24x-5x-30

A=24x^2-14x-3-4x^2-29x-30

A=20x^2-43x-33  or if you factor...

A=20x^2+12x-55x-33   

A=4x(5x+3)-11(5x+3)

A=(4x-11)(5x+3)

If a person is randomly selected, find the probability that his or her birthday is in May. ignore leap years

Answers

May has 31 days

 there are 365 days in a year

31/365 probability someone has a birthday in May

The probability of the event A that represents that the man's birthday is in May is 0.084.

What is probability?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur. Mathematically -

P(A) = n(A)/n(S)

Given is a person who is randomely selected.

Assume that the Event A represents that the man's birthday is in may.

Total number of days in the month of may = n(A) = 31

Total number of days in a year = n(S) = 365

Therefore, the probability that the man's birthday is in may will be -

P(A) = n(A)/n(S)

P(A) = 31/365

P(A) = 0.084

Therefore, the probability of the event A that represents that the man's birthday is in May is 0.084.

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An experiment consist of drawing 1 card from a standard 52 -card deck. Let E be the event that card drawn is a 2. Find P(E').

Answers

The sum of the probabilities of an event E and its complement E' is  1, 

that is P(E)+P(E')=1, where E' is "not E".

The event E can happen in 4 ways, because there are four 2's that can be drawn.

P(E)=n(E)/52=4/52=0.08

P(E')=1-P(E)=1-0.08=0.92


Answer: 0.92

What percentage of muscle weight would you have if 60 pounds out of 140 pounds is muscle weight?

Answers

What percentage of muscle weight would you have if 60 pounds out of 140 pounds is muscle weight?
all you have to do is divide the muscle weight by the total weight which is...60/140=
ANSWER: about 42.86%
Percent literally means per one hundred...

p/100=60/140  multiply both sides by 100

p=6000/140  

p=300/7 %

p≈42.86%  (to nearest hundredth of a percent)

Outside diameter of a pipe is five and 7/32 inches the wall of the pipe or 5/32 inches thick find the inside diameter

Answers

5  7/32 = 167/32

5/32 + 5/32 (2 wall thicknesses of the pipe) =10/32

167/32 - 10/32 = 157/32

= 4 29/32

what is 795840000 in a scientific notation

Answers

795840000 in a scientific notation
=
7.9584 x 10^8
hope it helps
The answer would be 7.9584 * 10^8

To avoid distortion of extreme values, a good indicator would be the A. mean. B. weighted-mean. C. mode. D. median

Answers

To avoid distortion of extreme values, a good indicator would be the


B. median.


I agree the answer is 
median

a squared + b - c ÷ m , if a=6 , b= 8 ,c = 5 and m = 3. Is it 12 , 13, 14, or 15?

Answers

Hello there!

A^2 + B - C / M; A = 6, B = 8, C = 5, M = 3.
Plug in our numbers.

6^2 + 8 - 5 / 3
36 + 8 - 5 / 3
44 - 5 / 3
39 / 3
13.

Your answer is 13.

I hope this helps!

A recipe calls for 1/2 cup of ingredient A for every 1 2/5 cups of ingredient B. You use 4 cups of ingredient A. How many cups of ingredient B do you need?

Answers

Let x = number of cups of ingredient B if 2 cups of ingredient A are used. Set up a proportion:  (1/2)/(1 2/5) = (2)/x. Cross multiplying we get (1/2)x = (1 2/5)(2) 
 (1/2)x = 14/5, so x = 28/5 = 5 3/5 cups.
you use 1 2/5 of B for every 1/2 A and they use 4 of A so times 1 2/5 by 8 and you get 11.2 cups of B

Megumi earned a salary of $39,312 last year. How much did she earn per month

Answers

2 months in a year

39312/12 = 3276 per month

Answer:

She earned $ 3,276 per month.

Step-by-step explanation:

We know that,

1 year = 12 months,

Given,

Megumi earned a salary of $39,312 last year

⇒ His salary of one year = $ 39,312

⇒ Salary of 12 months = $ 39,312

[tex]\implies \text{salary of 1 month} = \frac{39312}{12}=\$ 3276[/tex]

Hence, she earned $ 3,276 per month.

Rita borrowed 8000 at a rate of 10.5% compounded monthly assuming she makes no payments how much willshe owe after8 years

Answers

[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$8000\\ r=rate\to 10.5\%\to \frac{10.5}{100}\to &0.105\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve times} \end{array}\to &12\\ t=years\to &8 \end{cases} \\\\\\ A=8000\left(1+\frac{0.105}{12}\right)^{12\cdot 8}[/tex]

PLEASE HELP
If AD is median in triangle ABC and BD=24, then CD is:

24.
12.
6.
None of the choices are correct.

Answers

 

To solve this problem, let us first define what a median is. A median is a line segment that connects a vertex and the midpoint of the side opposite to that vertex.

In this case, the vertex is point A while the opposing side is side CB. Since it connects to the midpoint of CB, therefore this means that the median AD equally divides side CB into 2 parts.  Since the length side CB is the sum of the lengths side CD and side BD. Therefore this means that:

length of CD = length of BD

length of CD = 24

 

Answer:

 24

Kholdy enterprises' outstanding bonds mature in 6 years, have a par value of $1,000, and make an annual coupon payment of $60. the market yield on the bond is currently 10%. what is the bond's price?

Answers

You are given Kholdy enterprises' outstanding bonds that mature in 6 years with a par value of $1,000. You are also given the an annual coupon payment of $60. You are also given the market yield on the bond that is currently 10%. The bond's price is $825.79. What it can infer from Kholdy enterprises' is that the $825.79 is a discount bond since its price is less than $1,000, its par value.

The ordered pair (a, b) gives the location of point P on the coordinate plane. The value of a is zero and the value of b is not zero. Where could point P be located on the coordinate plane?





Select one or more:
x-axis
Quadrant IV
y-axis
Quadrant I
Quadrant II
Quadrant III

Answers

Answer:

y axis and

Step-by-step explanation:

The point P(a, b) where the value of a is 0, hence point P is located on the y axis.

Coordinate plane

The coordinate plane is a two-dimensional surface formed by two lines known as the horizontal axis (x axis) and the vertical axis (y axis). The origin is the point of intersection of both axis and it serves as a reference point.

A point on the coordinate plane is located using the x and y coordinates.

Given the point P(a, b) where the value of a is 0, hence point P is located on the y axis.

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There are 65 people who want to go on a tea cups ride at an amusement park. There are 10 tea cups that each seat 4 people. How many people need to wait before they get to go on the ride?

Answers

25 people will wait for the next ride

The perimeter of a triangle is 240. Its sides are proportional to 3:4:5. The largest side of the triangle is ?

Answers

If the sides are proportional you can use the formula:

3x + 4x + 5x = 240 and solve for x.

which is:  12x = 240
x = 20

The longest side is 5x, so the longest side is 100.

Find the point on the line y = 3x + 2 that is closest to the origin.

Answers

1.
the slope of the line y=3x+2 is the coefficient of x, that is 3.

2.
the slope of any line perpendicular to the line y=3x+2, is m, such that:

[tex]3*m=-1[/tex]

so [tex]m= \frac{-1}{3} [/tex]

3. 
so any line with equation y=-1/3x+k is perpendicular to y=3x+2.

moreover, the line y=-1/3x (so k=0) is the line passing through the origin
(0, 0) and perpendicular to y=3x+2


4. This means that the closest point of y=3x+2 to the origin is the intersection point of lines y=3x+2 and y=-1/3x

5.
to find this point:

3x+2=(-1/3)x
x(3+1/3)=-2
x(9/3+1/3)=-2

x*10/3=-2

[tex]x= \frac{-2*3}{10} = \frac{-6}{10}=-0.6 [/tex]


thus y is :  (-1/3)(-6/10)=0.2



Answer: (-0.6, 0.2)

The point on the line [tex]y=3x+2[/tex] that is closest to the origin is [tex](-0.6, 0.2)[/tex].

Given,  [tex]y=3x+2[/tex], whose slope is [tex]3[/tex].

Let [tex]m[/tex] is the slope of the line perpendicular to the above line.

So,

[tex]3\times m=-1\\m=-1/3[/tex]

Then, the general equation of a line perpendicular line will be [tex]y=-1/3x+k[/tex].

So the equation line passing through the origin [tex](0,0)[/tex] and perpendicular to the line [tex]y=3x+2[/tex] is [tex]y=-1/3x[/tex] , [tex](k=0)[/tex].

Then the closest point will be the intersection point of these two lines, i.e.

[tex]3x+2=-1/3x\\9x+6=-x\\10x+6=0\\x=-0.6[/tex]

and

[tex]y=\dfrac{-0.6}{3} \\y=0.2[/tex]

Therefore, the point on the line [tex]y=3x+2[/tex] that is closest to the origin is [tex](-0.6, 0.2)[/tex].

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Suppose a and b are independent events. if p(a)=0.4 and p(b)=0.1, what is p(a u

b.?

Answers

Final answer:

To find the probability of the union of two independent events, use the formula P(A U B) = P(A) + P(B). In this case, P(A U B) = 0.4 + 0.1 = 0.5.

Explanation:

To find the probability of the union of two independent events, we can use the formula:

P(A U B) = P(A) + P(B) - P(A ∩ B)

Since the two events, A and B, are independent, the probability of their intersection, P(A ∩ B), is 0. This is because the occurrence of one event does not affect the occurrence of the other event. Therefore, we have:

P(A U B) = P(A) + P(B)

Substituting the given values, we get:

P(A U B) = 0.4 + 0.1

= 0.5

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