How many points are needed to define a plane?

Answer:

v . w= -13

Step-by-step explanation:

Evaluate the expression: v ⋅ w Given the vectors: r = <8, 1, -6>; v = <6, 7, -3>; w = <-7, 5, 2>

Solution

Given the vectors:

r = <8, 1, -6>

v = <6, 7, -3>

w = <-7, 5, 2>

If you're asking about the dot product.

The dot product is a scalar. It is the sum of the product of the corresponding components.

v.w = (6*-7) + (7*5) + (-3*2)

= -42+35-6

= -13.

Answer:

20100

Step-by-step explanation:

To find the sum of:

[tex]1 + 2 + 3+ 4+ ...... +200[/tex]

As per the trick of Gauss, let us divide the above terms in two halves.

[tex]1+2+3+4+\ldots+100[/tex] and

[tex]101+102+103+104+\ldots+200[/tex]

Let us re rewrite the above terms by reversing the second sequence of terms.

[tex]1+2+3+4+\ldots+100[/tex]  (it has 100 terms) and

[tex]200+199+198+197+\ldots+101[/tex] (It also has 100 terms)

Adding the corresponding terms (it will also contain 100 terms):

1 + 200 = 201

2 + 199 = 201

3 + 198 = 201

:

:

100 + 101 = 201

The number of terms in each sequence are 100.

So, we have to add 201 for 100 times to get the required sum.

Required sum = 201 + 201 + 201 + 201 + . . . + 201  (100 times)

Required sum = 100 [tex]\times[/tex] 201 = 20100

Answer:

(1,0)

Step-by-step explanation:

3x + 6y = 3

7x + 3y = 7

Multiply the second equation by -2

-2( 7x + 3y = 7)

-14x -6y = -14

Add this to the first equation to eliminate y

3x + 6y = 3

-14x -6y = -14

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

-11 x = -11

Divide by -11

x = 1

Now find y

3x + 6y = 3

3 +6y = 3

Subtract 3 from each side

6y = 0

y =0

Answer:

x = 1

y = 0

Step-by-step explanation:

3x + 6y = 3

7x  + 3y = 7

=> 3y = 7 - 7x

=> y = -7/3x + 7/3

3x + 6(-7/3x + 7/3) = 3

=> 3x - 14x + 14 = 3

=> -11x = -11

=> -x = -11/11

=> -x = -1

=> x = 1

So, 3(1) + 6y = 3

=> 3 + 6y = 3

=> 6y = 0

=> y = 0/6

=> y = 0

So, x = 1

      y = 0

Answer:

1). Algebraic expression - a letter or symbol used to represent an unknown.

2). Coefficient - a numerical value.

3). Constant - the constant preceding the variables in a product.

4). Expression - a mathematical expression containing one or more variables.

5). Variable - a mathematical phrase that cannot be determined true or false.

Hello, a car was purchased for $20,000.

This is the initial value.

The car depreciates by 22% of each year.

After 1 year, the value is the initial value 20,000 minus 22% of 20,000.

[tex]20000-20\%*20000=20000\cdot (1-20\%)=20000\cdot (1-0.20)=20000\cdot 0.8=16000[/tex]

After 2 years, the value is.

[tex]20000\cdot 0.8\cdot 0.8=20000\cdot0.8^2=12800[/tex]

Let's take n a positive integer, after n years, the value is.

[tex]\large \boxed{\sf \bf \ 20000\cdot0.8^n \ }[/tex]

a) After 12 years, the value is.

[tex]20000\cdot0.8^{12}=1374.389...[/tex]

This is rounded to $1,374

b) We need to find n such that

[tex]20000\cdot0.8^n=100\\\\ln(20000)+nln(0.8)=ln(100)\\\\n=\dfrac{ln(100)-ln(20000)}{ln(0.8)}=23.74...[/tex]

This is around 23.75 meaning 23 years and 75% of 1 year (meaning 9 months).

So to be worth less than $100, 23 years and 9 months are required.

Thank you

Hi there! :)

Answer:

[tex]\huge\boxed{C}[/tex]

To simplify the process, convert each given weight into standard notation:

Lion:

[tex]1 * 10^{5} = 1 * 100000 = 100,000 g[/tex]

Ant:

[tex]2 * 10^{-3} = 2* 0.001 = 0.002[/tex]

Divide the ant's weight from the lion's weight:

[tex]100000 / 0.002 = 50,000,000[/tex]

Convert to scientific notation: (use # of zeros to determine exponent)

[tex]50,000,000 = 5 * 10^{7}[/tex]

Therefore, the correct answer is C.

Answer:

Q = 6

Step-by-step explanation:

Step 1: Write equation

4 - Q = -2

Step 2: Subtract 4 on both sides (Subtraction Equality)

-Q = -6

Step 3: Divide -1 on both sides (Division Equality)

Q = 6

And we have our answer!

Answer:

Step-by-step explanation:

[tex] \mathrm{4 - Q = - 2}[/tex]

Move constant to R.H.S and change its sign

[tex] \mathrm{ - Q = - 2 - 4}[/tex]

Calculate

[tex] \mathrm{ - Q = - 6}[/tex]

Change the signs on both sides of the equation

[tex] \mathrm{Q = 6}[/tex]

Hope I helped!

Best regards!

Answer:

23 x 4

=> 23 x (2 + 2)

=> 23 x 2 + 23 x 2

23 x 21

=> 23 x (3 x 7)

=> (23 x 3) x (23 x 7)

23 + 23 + 23 + 23 = to get the answer of 92

23 x 2 + 23 x 2 =.92

Answer:

640

Step-by-step explanation:

800-160=640...............................

Answer:

$800-$160

=$640

Hope it helps.

Answer:

Initially 18,500 students

Every 1 year

increase by a factor 1.03

Step-by-step explanation:

The missing information is selected from the given options from the drop down menu. The correct answers are : Initially 18,500 students enroll at the university. Every 1 years the number of students who enroll at the university increases by a factor 1.03.

F(t) = 18,500 * (1.03)^t

Answer:

Step-by-step explanation:

16y = 80

You want to get y by itself so you divide 80 by 16

y = 80/16

y = 5

Hope I helped

The solution to the equation 16y = 80 is y = 5.

To solve the equation 16y = 80 for the variable y, you can follow these steps:

Step 1: Divide both sides of the equation by 16 to isolate the variable y:

(16y)/16 = 80/16

y = 5

Therefore, the solution to the equation is y = 5.

Learn more about Equation here:

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Answer:

2 added to cube of 5 times x

Step-by-step explanation:

Answer:

2 plus cube 5 times.

cube = (³).

times = (multiplying).

Answer:

Step-by-step explanation:

I'm going to walk through this analytically, so I will have to assign some variables to angles that are not marked. Pay close attention so you can follow the logic.

The angle at the top left next to and to the left of 40 will be "x", and the one to the right of 40 will be "y". Because that angle is a right angle, then we know that

x + y + 40 = 90 and

x + y = 50.

We also know that, by the Triangle Angle-Sum Theorem, the 2 triangles that contain alpha and beta will add up to equal 360, 180 apiece. So now we have:

x + 90 + α + y + 90 + β = 360.

Let's regroup a bit:

x + y + α + β + 90 + 90 = 360 and

(x + y) + α + β + 180 = 360.

But we know from above that x + y = 50, so

50 + α + β + 180 = 360 and

230 + α + β = 360 and

α + β = 130. There you go!

Answer:

α + β = 130

Step-by-step explanation:

∠ A = ∠ C = 90°

The sum of the 3 angles in a triangle = 180°

vertex angle at D inside the Δ = 180 - (90 + α ) ← Δ on left

vertex angle at D inside the Δ = 180 - (90 + β ) ← Δ on right

∠ ADC = 90° thus

180 - (90 + α) + 180 - (90 + β) + 40 = 90

180 - 90 - α + 180 - 90 - β + 40 = 90, that is

220 - α - β = 90 (add α and β to both sides )

220 = 90 + α + β (subtract 90 from both sides )

130 = α + β

Answer:

[tex]\Large \boxed{11.08}[/tex]

Step-by-step explanation:

The triangles are congruent, we can use ratios to solve.

AD/DC = BE/EC

Let the length of EC be x.

6/14 = 4.75/x

Solve for x.

Cross multiply.

6 × x = 14 × 4.75

6x = 66.5

Divide both sides by 6.

(6x)/6 = (66.5)/6

x = 11.083333...

Greetings from Brasil...

Here we can use similarities of triangles

AC/DC = BC/EC

20/14 = (4.75 + X)/X

X ≅ 11.1

see attachment

Answer:

$54.65 profit per seat

Step-by-step explanation:

150(185) + 35(185)(.8) = 27,750 + 5,180 = 32,930 - 22,000 = 10,930

10,930/200 = $54.65 profit per seat

Answer:

$54.65

Step-by-step explanation:

First, we find the total amount made. This is easy:

(150 x 185) + (35 x .8(185)) =

27750 + 5180 =

32930

We then subtract the $22000, so the company makes a profit of 10930. There are 200 seats, so the profit made per seat is $54.65

Answer:

y = 4.8

Step-by-step explanation:

Given that y is inversely proportional to x² then the equation relating them is

y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of proportion

To find k use the condition when x = 4, y = 7.5 , then

7.5 = [tex]\frac{k}{4^2}[/tex] = [tex]\frac{k}{16}[/tex] ( multiply both sides by 16 )

k = 16 × 7.5 = 120

y = [tex]\frac{120}{x^2}[/tex] ← equation of proportion

When x = 5 , then

y = [tex]\frac{120}{5^2}[/tex] = [tex]\frac{120}{25}[/tex] = 4.8

Answer:

a +d = a2

Step-by-step explanation:

-2 - (-9) =

-2+9=7

a + d = a2

Answer:

The cousins have 4 bags of white marbles and 4 bags of pink marbles.

Step-by-step explanation:

If x is the number of bags with white marbles and y is the number of bags with pink marbles, we can write the following system:

x + y = 8 -- Equation 1

5x + 7y = 48 -- Equation 2

5x + 5y = 40 -- Equation 3 (Multiply Equation 1 by 5)

2y = 8 -- (Subtract Equation 3 from 2)

y = 4 -- (Divide both sides by 2)

x + 4 = 8 -- (Substitute y = 4 into Equation 1)

x = 4 -- (Subtract 4 from both sides)

Answer:

Movies cost $2.50 and video games cost $5.50

Step-by-step explanation:

Let the rental cost of movies be x and the rental cost of video games y

12x + 2y = 41

3x + 5y = 35

Solve by substitution

Answer:

Movie price: $2.5

Video game price: $5.5

Step-by-step explanation:

First month

12 movies ([tex]m[/tex]);

2 video games ([tex]v[/tex]);

Cost: $41

Second month

3 movies ([tex]m[/tex]);

5 video games ([tex]v[/tex]);

Cost: $35

[tex]$\left \{ {{12m+2v=41} \atop {3m+5v=35}} \right.$[/tex]

[tex]$\left \{ {{12m+2v=41} \atop {3(-4)m+5(-4)v=(-4)35}} \right.$[/tex]

[tex]$\left \{ {{12m+2v=41} \atop {-12m+-20v=-140}} \right.$[/tex]

[tex]-18v=-99[/tex]

[tex]v=5.5[/tex]

[tex]12m+2(5.5)=41[/tex]

[tex]12m+11=41[/tex]

[tex]12m=30[/tex]

[tex]m=2.5[/tex]

Answer:

(8/5) Centimeyers

Step-by-step explanation:

From 1 PM to 6 PM there is a 5 Hour difference.

Mean (total/hours) = 8/5

Answer:

1.6 cm/hour.

Step-by-step explanation:

Yes it is the unit rate.

So mean horly snowfall = total snowfall / time

= 8 / (6 - 1)

= 8/5

= 1.6 cm/hour.

Answer:

A

Step-by-step explanation:

Khan academy

The equation for the g(x) is g(x) = -4|x| if function g can be thought of as a scaled version of f(x)=|x| option (B) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

Function g can be thought of as a scaled version of f(x)=|x|

The function f(x):

f(x) = |x|

The blue lines represent the function f(x)

First reflect the function f(x) around the x-axis

F(x) = -|x|

Multiply by the factor 4 to stretch the function:

g(x) = -4|x|

Thus, the equation for the g(x) is g(x) = -4|x| if function g can be thought of as a scaled version of f(x)=|x| option (B) is correct.

Learn more about the function here:

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Answer:

How many people like both drinks?

To find the overlap, we can do (104 + 74) - 140 = 38.

How many people like tea only?

To find this, we can do 74 - 38 = 36.

How many people like milk only?

To find this, we can do 104 - 38 = 66.

Answer:

Step-by-step explanation:

A = Number of people who likes tea

B = Number of people who likes milk

Total people = n(A U B) = 140

(i) n(AUB) = n(A) + n(B) - n(A ∩B)

n(A∩B) = n(A) + n(B) - n(A ∪B)

n(A∩B)  = 74 + 104 - 140

             = 178 - 140

n(A∩B)  = 38

Number of people who likes both tea and milk = 38

(ii)Number of people who likes tea only = n(A) - n(A∩B)

                                                                  = 74 - 38

                                                                 = 36

(iii) Number of people who likes milk only = n(B) -n(A∩B)

                                                                     = 104 - 38

                                                                     = 66

Answer:

Ok, this question seems incomplete, so i will answer it in a general way.

Suppose that regularly, Ken eats A calories during the day. (A is a positive number)

Now, Ken wants to reduce this number, but his nutritionist tells him to reduce no more than 7% (So the max reduction possible is a reduction of the 7%).

So after the reduction, Ken eats C calories per day.

First, the maximum reduction that Ken can do is when he reduces exactly 7% of the calories.

So if he regularly consumes A calories, the reduction will be of

(7%/100%)*A = 0.07*A

So after the reduction, the amount of calories that he consumes per day is:

C = A - 0.07*A = A*(1 - 0.07) = A*0.93

But this is the minimum amount of calories that he can consume, the actual range of possible options will be:

A < C ≤ A*0.97.

C is strictly smaller than A because we must have a reduction in the number of calories.

Those values of C is all the posible amounts of calories that Ken eats per day after the initial reduction in the number of calories per day.

Answer:

[tex]\huge\boxed{\sf Area\ of \ Semicircle = 56.55 \ units^2}[/tex]

Step-by-step explanation:

Diameter = 12

Radius = 12/2 = 6

[tex]\sf Area\ of \ Semicircle =\frac{\pi r^2}{2} \\Area\ of \ Semicircle =\frac{\pi (6)^2}{2} \\Area \ of \ Semicircle = \frac{\pi (36)}{2}\\ Area \ of \ Semicircle = 18 \ pi[/tex]

[tex]\sf Area\ of \ Semicircle = 56.55 \ units^2[/tex]

Answer:

18π units²

Step-by-step explanation:

(see attached for reference)

Recall that the area of a whole circle is given by:

A = (π/4) D²,

where D is the diameter of the circle.

We know that the area of a semi-circle is half the area of a whole circle.

Therefore,

Area of Semi Circle

= (1/2) x area of whole circle

= (1/2) x (π/4) D²     (Substitute D = 12 units)

= (1/2) x (π/4) (12)²  

= 18π units²

Answer:

  3.75 years

Step-by-step explanation:

If the debt is to be paid in 3 years, 9 months, then the term of the loan is ...

  3 9/12 = 3 3/4 = 3.75 . . . years

Answer:

I think D but im not sure

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]P(2,8) \: , B(1,3)\\x_1=2\\y_1=8\\x_2 =1\\y_2 =3\\\\d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\ d = \sqrt{(1-2)^2+(3-8)^2} \\\\d = \sqrt{(-1)^2+(-5)^2}\\\\ d = \sqrt{1+25}\\\\ d = \sqrt{26}[/tex]

Answer:

1) A. Add/subtract a quantity to/from only one side  

2) B. No

Step-by-step explanation:

Answer two questions about Equations A and B:  

1) How can we get Equation B from Equation A?

2) Based on the previous answer, are the equations equivalent? In other words, do they have the same solution?  

=================================

1) As we see left sides of the equations are different but right sides are same.

To make them equal we need to remove the difference.

We need to add 2 to the left side of equation A to get Equation B.

The answer choice for this case is:

2) Since the equations are not same, they will have different solutions.

Answer choice is:

Equivalent equations are equations that have the same value.

The equations are given as:

[tex]A:\ 5x-2+x = x-4[/tex]

[tex]B: 5x+x = x-4[/tex]

(a) How to get equation (B) from (A)

By comparing equations (A) and (B), we have the following observations

This means that, only the left-hand side of equation A will be altered to get equation B.

Hence, the solution is:

A. Add/subtract a quantity to/from only one side

(b) Are they equivalent?

No, they are not.

This is so, because only one side of equation A is altered to get equation B.

Read more about equivalent equations at:

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