PLEASE HELP WILL GIVE BRAINLIEST BE QUICK

Answer:

a) The nonzero vector orthogonal to the plane through the points P, Q and R is (0, 10, -10).

b) The area of the triangle PQR is [tex]5\sqrt{2}[/tex].

Step-by-step explanation:

The statement is incomplete. The complete question will be presented below:

Consider the points below: P(2, 0, 2),  Q(−2, 1, 3),  R(4, 2, 4)

(a) Find a nonzero vector orthogonal to the plane through the points

P, Q,  and R. (b) Find the area of the triangle PQR.

a) Let [tex]P(x,y,z) = (2,0,2)[/tex], [tex]Q(x,y,z) = (-2,1,3)[/tex] and [tex]R(x,y,z) = (4,2,4)[/tex]. First, we construct vectors PQ and PR by using the following formulas:

[tex]\overrightarrow{PQ} = Q(x,y,z) -P(x,y,z)[/tex] (1)

[tex]\overrightarrow{PQ} = (-2,1,3)-(2,0,2)[/tex]

[tex]\overrightarrow{PQ} = (-4,1,1)[/tex]

[tex]\overrightarrow{PR} = R(x,y,z) -P(x,y,z)[/tex] (2)

[tex]\overrightarrow{PR} = (4,2,4)-(2,0,2)[/tex]

[tex]\overrightarrow{PR} = (2,2,2)[/tex]

Then, we can find the nonzero vector orthogonal to the plane by means of the following cross product:

[tex]\vec S = \overrightarrow{PQ}\,\times\,\overrightarrow{PR}[/tex]

Which can be solved by the following determinant (Law of Sarrus):

[tex]\vec S = \left|\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\-4&1&1\\2&2&2\end{array} \right |[/tex]

[tex]\vec S = (2-2,2+8, -8-2)[/tex]

[tex]\vec S = (0, 10,-10)[/tex]

The nonzero vector orthogonal to the plane through the points P, Q and R is (0, 10, -10).

b) The area of the triangle is determined by the following formula:

[tex]A = \frac{1}{2}\cdot \|\overrightarrow{PQ}\,\times\,\overrightarrow{PR} \|[/tex]

[tex]A = \frac{1}{2}\cdot \|\vec S\|[/tex] (3)

[tex]A = \frac{1}{2}\cdot \sqrt{0^{2}+10^{2}+(-10)^{2}}[/tex]

[tex]A = 5\sqrt{2}[/tex]

The area of the triangle PQR is [tex]5\sqrt{2}[/tex].

Answer:

60

Step-by-step explanation:

75-15=60

Answer:

x = 10.6 units

Step-by-step explanation:

We can use sine to solve this since sine is opposite over hypotnuse.

sin(62) = x/12

.883 = x/12

x = .883 * 12

x = 10.6

Answer:

I just got this right...hopefully this helps :)

Step-by-step explanation:

Answer:

the third one

List 3

Step-by-step explanation:

1*100=100

2*50=100

4*25=100

5*20=100

10*10=100

Hey there!

the slope of the line is [tex]3[/tex]

Slope is [tex]\frac{rise}{run}[/tex], meaning that the slope is [tex]\frac{3}{1}[/tex] or [tex]3[/tex]

Hope it helps and have a great day!

Answer:

306. If you multiply 30 and 9 you will get 270, and if you add 4 * 9, which is 36, you will get 306.

Step-by-step explanation:

I hope that helped you out! :)

The Multiplication of 7 and 2 results to 14.

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

We have to multiply 9 x 34.

So, we can split the number 34 as (30 + 4) then

First, 9 x 30 = 270

and, 9 x 4 = 36

Now, add the values

9 x 34

= 270 + 36

= 306

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Answer:

dont really know this one sorry:)

Step-by-step explanation:

Answer:

The length of the rectangle is of 9 units.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

Area of a rectangle:

A rectangle has width [tex]w[/tex] and length [tex]l[/tex]. The area is the multiplication of these measures, that is:

[tex]A = wl[/tex]

The length of a rectangle is the sum of the width and one.

This means that [tex]l = w+1[/tex], or [tex]w = l - 1[/tex]

The area direct angle 72 units. What’s the length, in units, of the rectangle

We want to find the length. So

[tex]wl = 72[/tex]

[tex](l-1)l = 72[/tex]

[tex]l^2 - l - 72 = 0[/tex]

Quadratic equation with [tex]a = 1, b = -1, c = -72[/tex]. So

[tex]\bigtriangleup = (-1)^{2} - 4(1)(-72) = 289[/tex]

[tex]l_{1} = \frac{-(-1) + \sqrt{289}}{2*(1)} = 9[/tex]

[tex]l_{2} = \frac{-(-1) - \sqrt{289}}{2*(1)} = -8[/tex]

Since the length is a positive measure, the length of the rectangle is of 9 units.

Answer:

25% increase

Step-by-step explanation:

[tex]\frac{(v_{2}- v_{1}) }{|v_{1}| }x100[/tex]

[tex]\frac{25-20}{|20|}x100[/tex]

=[tex]\frac{5}{20}x100[/tex]

=0.25×100

=25% change

=25% increase

Answer:

11.7

Step-by-step explanation:

Answer:

What about the wink face?

Step-by-step explanation:

Answer:

he would need 11 quarters.

Step-by-step explanation:

you already have 3 dimes which is $0.30 and 11 quarters is $2.75.

Answer:

as a decimal = 0.45

Fraction= 9/20

Step-by-step explanation:

Answer:

1. y=-x-3 2.y=1/3x-4

Step-by-step explanation:

1. 3x+3y=-9

3y=-3x-9

y=-x-3

2. x-3y=12

-3y=-x+12

y=1/3x-4

Answer:D

Step-by-step explanation:its the same thing but the numbers are flipped, you get the same answer either way.

The statement that illustrates the commutative property of addition is

8i + 4 = 4 + 8i. The correct option is D.

The commutative property of addition:

Let a and b are numbers.

a + b =  b + a

The change in the position of two numbers in an addition operation does not change the sum.

The commutative property of addition:

Let a and b are numbers.

So, a + b =  b + a.

LHS = 8i + 4

= 2 (4i+2)

= 2(2 + 4i)

=  4 + 8i

That means,  8i + 4 = 4 + 8i holds the commutative property of addition.

Therefore, the equation is 8i + 4 = 4 + 8i.

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Answer:

32x^25

Step-by-step explanation:

4x^14*8x^11

Answer:

0 (b)

Step-by-step explanation:

So we're estimating in this one.

we can round -49/100 to -50/100 and 10/21 to 10/20

Then we can get a common denominator

10/20 will become 50/100

so

-50/100 + 50/100 = 0

So your answer is b.

Answer:

B. 0

Step-by-step explanation:

-49/100 + 10/21

They are both about half

Therefore, since one is negative and the other is a positive they would equal about .02 which the closest number out of the 4 answers would be B. 0

Answer:

A: 2x^3 + 3x - 5

Step-by-step explanation:

All of the others have fractions in places where they aren't allowed to.

Answer:

A: 2x^3 + 3x - 5

Step-by-step explanation:

Answer:

tito

Joshua

Caleb

Arthur

Answer:

q =90

Step-by-step explanation:

q/18=5

Multiply each side by 18

q/18  * 18=5* 18

q =90

Answer:

q = 90

Step-by-step explanation:

Multiply each side by 18:

q = 90

Answer:

[tex] 2y + 4y - 3 = 27 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 6y = 27 + 3 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 6y = 30 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = \frac{30}{6} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = 5[/tex]

Answer:

c is correct

Step-by-step explanation:

The equation that represents this fraction is 1 ÷ 6 =1/6. Therefore, option C is the correct answer.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Given that, a cake is cut into 6 equal-sized pieces. Each piece is one sixth of the whole.

The equation is 1 ÷ 6 =1/6

Therefore, option C is the correct answer.

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Answer:

go and watch a movie together

Answer:

i. 6 feet by 3 feet

ii. 7 feet by 2 feet

iii. 8 feet by 1 feet

Step-by-step explanation:

From the given question, we have;

length of the rectangular fence, l = 6 feet

perimeter of the rectangular fence = 18 feet

Let the width of the rectangular fence be represented by w.

So that,

Perimeter of a rectangle= 2(length + width)

18 = 2(6 + w)

18 = 12 + 2w

18 - 12 = 2w

6 = 2w

w = [tex]\frac{6}{2}[/tex]

w = 3

The width of the rectangular fence would be 3 feet when the length is 6 feet.

Thus, the possible dimensions of the rectangular fence are:

i. 6 feet by 3 feet

ii. 7 feet by 2 feet

iii. 8 feet by 1 feet

AnswerNot A. Or B.

Step-by-step explanation:

A-Half of the students watched fewer than two TV shows.

A- is wrong

B-More than half of the students watched three or more TV shows.

B- is wrong

It is either C. Or D.

Answer:

its D on the Edge Test

Step-by-step explanation:

Have an amazing day :)

Answer:

1. Subtract 18 from both sides to get the equation set to 0:

x2 + 7x - 18 = 0

Now factor. Given the negative sign in front of the 18, you will have (x + ) (x - ) as your factors, with the larger one being positive. Now, which factors of 18 can be combined to get a result of 7? I'll leave that for you.

2- 2.3 Solve : p-7 = 0

Add 7 to both sides of the equation :

p = 7

3-Final result :

(m - 1) • (m - 8)

4-Step by step solution :

STEP

1

:

Trying to factor by splitting the middle term

1.1 Factoring x2-16x+63

The first term is, x2 its coefficient is 1 .

The middle term is, -16x its coefficient is -16 .

The last term, "the constant", is +63

Step-1 : Multiply the coefficient of the first term by the constant 1 • 63 = 63

Step-2 : Find two factors of 63 whose sum equals the coefficient of the middle term, which is -16 .

-63 + -1 = -64

-21 + -3 = -24

-9 + -7 = -16 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and -7

x2 - 9x - 7x - 63

Answer:

The number of people going

Step-by-step explanation:

That is what can vary.

Answer:

that guy/girl is correct

Answer:

5. 40% of Sam's collection of 64 cars is new. How many cars are new?

Known: Number of cars.

Unknown: How many cars are new.

Equation: 64*0.4=x x=24.

6. 90 out of 20 students liked pizza. What percent of students did

not like pizza?

Known: number of students

Unknown: percent of students did not like pizza.

Equation: 90*20/20 = 90.

90>20 so 0% did not like pizza.