Find the least common multiple of 14 and 22.

The given line is orthogonal to the plane you want to find, so the tangent vector of this line can be used as the normal vector for the plane.

The tangent vector for the line is

d/dt (⟨0, 9, 6⟩ + ⟨7, -7, -6⟩t ) = ⟨7, -7, -6⟩

Then the plane that passes through the origin with this as its normal vector has equation

⟨x, y, z⟩ • ⟨7, -7, -6⟩ = 0

We want the plane to pass through the point (9, 6, 0), so we just translate every vector pointing to the plane itself by adding ⟨9, 6, 0⟩,

(⟨x, y, z⟩ - ⟨9, 6, 0⟩) • ⟨7, -7, -6⟩ = 0

Simplifying this expression and writing it standard form gives

⟨x - 9, y - 6, z⟩ • ⟨7, -7, -6⟩ = 0

7 (x - 9) - 7 (y - 6) - 6z = 0

7x - 63 - 7y + 42 - 6z = 0

7x - 7y - 6z = 21

so that

a = 7, b = -7, c = -6, and d = 21

An equation of the plane orthogonal to the line 7x - 7y - 6z = 21.

The given line is orthogonal to the plane you want to find,

So the tangent vector of this line can be used as

The normal vector for the plane.

The tangent vector for the line is,

A tangent vector is a vector that is tangent to a curve or surface at a given point.

d/dt (⟨0, 9, 6⟩ + ⟨7, -7, -6⟩t ) = ⟨7, -7, -6⟩

Then the plane that passes through the origin with this as its normal vector has the equation

⟨x, y, z⟩ • ⟨7, -7, -6⟩ = 0

We want the plane to pass through the point (9, 6, 0), so we just

translate every vector pointing to the plane itself by adding ⟨9, 6, 0⟩,

(⟨x, y, z⟩ - ⟨9, 6, 0⟩) • ⟨7, -7, -6⟩ = 0

Simplifying this expression and writing it in standard form gives

⟨x - 9, y - 6, z⟩ • ⟨7, -7, -6⟩ = 0

7 (x - 9) - 7 (y - 6) - 6z = 0

7x - 63 - 7y + 42 - 6z = 0

7x - 7y - 6z = 21

So that, a = 7, b = -7, c = -6, and d = 21.

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9514 1404 393

Answer:

  24

Step-by-step explanation:

The front face is an 8-sided star, so has 8 edges. We presume the back face is the same, so it also has 8 edges. Each of the front vertices is connected by an edge to each of the corresponding back vertices, so there are 8 more edges connecting front and back.

The total number of edges is 8 + 8 + 8 = 24.

y=x²-10x-7

a>0 so we will be looking for minimum

x=-b/2a=10/2=5

y=25-50-7=-32

Answer: (5;32)

Answer:

Question to number 6 is-3

Question to number 7 is 3

Question to number 8 is 2 to the second power

Step-by-step explanation:

please correct me if I’m wrong and for number 8 I am correct it’s just I didn’t know how to put the little 2 on top of the big one

Step-by-step explanation:

question 6 is - 3

question 7 is 3

question 8 is 4

Answer:

C. 1 and 2

Step-by-step explantation:

First, i would order them as U>T, T>R, R>Q, S>T

we can rewrite them as

U>T>R>Q,

now adding S, we get U>S>T>R>Q,

so U>S

We can also rewrite all of them as inequalities:

U-T>0

T-R>0

R-Q>0

S-T>0

Add R-Q and T-R

(R-Q)+(T-R)>0

-Q+T>0

T>Q, but because S>T we can say S>Q

Answer:

(1)-3/4, (2) 5/21, (3)4/43

Answer:

56

Step-by-step explanation:

A=(3*4)+(4*(4+3+4))=56

Answer:

that is n standard notation mah frand

8.9 × 10^3 being scientific notation of " 8900 "

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{8.9}\times\large\textsf{10}^\mathsf{3}\\\\\mathsf{10^3}\\\mathsf{= 10\times10\times10}\\\mathsf{= 100\times10}\\\mathsf{= \bf 1,000}\\\\\large\textsf{8.9}\times\large\textsf{1,000}\\\\\large\textsf{= \bf 8,900}\\\\\\\boxed{\boxed{\huge\text{Answer: \boxed{\underline{\underline{\bf 8,900}}}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\boxed{\huge\text{}\boxed{\frak{Amphitrite1040:)}}}[/tex]

Multiplying a matrix by a scalar results in every entry in a matrix get multiplied by that scalar, as defined,

[tex]a\begin{bmatrix}b&c\\d&e\\\end{bmatrix}=\begin{bmatrix}ab&ac\\ad&ae\\\end{bmatrix}[/tex]

So in our case, ([tex]0.2=\frac{1}{5}[/tex]

[tex]\frac{1}{5}\begin{bmatrix}50&10\\25&15\\\end{bmatrix}=\begin{bmatrix}\frac{50}{5}&\frac{10}{5}\\\frac{25}{5}&\frac{15}{5}\\\end{bmatrix}=\boxed{\begin{bmatrix}10&2\\5&3\\\end{bmatrix}}[/tex]

Hope this helps :)

9514 1404 393

Answer:

  118

Step-by-step explanation:

Oganesson is the heaviest element ever created. It is a "super-heavy" noble gas with a half-life less than 1 millisecond. Its atomic number is 118.

Answer:

[tex]y=\frac{3}{2}x-3.5[/tex] or, preferably, [tex]y=\frac{3}{2}x-\frac{7}{2}[/tex]

Step-by-step explanation:

First is to find the perpendicular slope. In this case, you swap the numerator and denominator and then multiply that fraction by -1.

In this case, -2/3's inverse slope is 3/2.

Now, the initial y=3/2 passes through 7.5,5

So, you must subtract 3.5 from that to make it pass through 4,5.

In this way, you get the answer in slope-intercept form.

Answer:

y = [tex]\frac{3}{2}[/tex] x - 1

Step-by-step explanation:

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{2}{3} }[/tex] = [tex]\frac{3}{2}[/tex] , then

y = [tex]\frac{3}{2}[/tex] + c ← partial equation in slope- intercept form

To find c substitute (4, 5) into the partial equation

5 = 6 + c ⇒ c = 5 - 6 = - 1

y = [tex]\frac{3}{2}[/tex] x - 1 ← equation of line

Answer:

Because it's a negative.

Step-by-step explanation:

The value of a positive number is still a positive number.

Answer:

the reasoning states that "all the numbers begin with a 7 or an 8"

however this is not accurate as they can be in different placements

which can make a big difference in the total estimate.

for example:

the number could've been an 8, or an 80

they both begin with an 8

however have totally different values and could have messed up the total estimated number.

hope this helps :D

Answer: x = 45

Step-by-step explanation:

Given

(2/3)x + 4 = (4/5)x - 2

Add 2 on both sides

(2/3)x + 4 + 2 = (4/5)x - 2 + 2

(2/3)x + 6 = (4/5)x

Subtract (2/3)x on both sides

(2/3)x + 6 - (2/3)x = (4/5)x - (2/3)x

6 = (12/15)x - (10/15)x

6 = (2/15)x

Divide 2/15 on both sides

6 / (2/15) = (2/15)x / (2/15)

[tex]\boxed{x=45}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

x = 45

Step-by-step explanation:

2/3 x + 4 = 4/5x - 2             Add 2 to both sides

2/3 x + 4 + 2 = 4/5x            Combine

2/3x + 6 = 4/5x                   Subtract 2/3 x from both sides.

6 = 4/5x - 2/3 x                  Multiply both sides by 15

6*15 = 4/5 x * 15 - 2/3x * 15

6*15 = 12x - 10x                   Combine the left and right

90 = 2x                               Divide by 2

x = 45

Let's see if it works.

LHS = 2/3 * 45 + 4

LHS = 2*15 + 4

LHS = 30 + 4

LHS = 34

RHS

Right hand side = 4/5 * 45 - 2

RHS = 36 - 2

RHS = 34 which is the same as the LHS

Answer:

Apply Hooke's Law to the integral application for work: W = int_a^b F dx , we get:

W = int_a^b kx dx

W = k * int_a^b x dx

Apply Power rule for integration: int x^n(dx) = x^(n+1)/(n+1)

W = k * x^(1+1)/(1+1)|_a^b

W = k * x^2/2|_a^b

From the given work: seven and one-half foot-pounds (7.5 ft-lbs) , note that the units has "ft" instead of inches.   To be consistent, apply the conversion factor: 12 inches = 1 foot then:

2 inches = 1/6 ft

1/2 or 0.5 inches =1/24 ft

To solve for k, we consider the initial condition of applying 7.5 ft-lbs to compress a spring  2 inches or 1/6 ft from its natural length. Compressing 1/6 ft of it natural length implies the boundary values: a=0 to b=1/6 ft.

Applying  W = k * x^2/2|_a^b , we get:

7.5= k * x^2/2|_0^(1/6)

Apply definite integral formula: F(x)|_a^b = F(b)-F(a) .

7.5 =k [(1/6)^2/2-(0)^2/2]

7.5 = k * [(1/36)/2 -0]

7.5= k *[1/72]

k =7.5*72

k =540

To solve for the work needed to compress the spring with additional 1/24 ft, we  plug-in: k =540 , a=1/6 , and b = 5/24 on W = k * x^2/2|_a^b .

Note that compressing "additional one-half inches" from its 2 inches compression is the same as to  compress a spring 2.5 inches or 5/24 ft from its natural length.

W= 540 * x^2/2|_((1/6))^((5/24))

W = 540 [ (5/24)^2/2-(1/6)^2/2 ]

W =540 [25/1152- 1/72 ]

W =540[1/128]

W=135/32 or 4.21875 ft-lbs

Step-by-step explanation:

Answer:

y=-4x-5

Step-by-step explanation:

The slope of the line is - 4, the equation of line is y=-4x-5

The position of the helicopter and the two VORs forms a triangle and the third angle formed by these three entities is 40 degrees

The diagram is not shown; however, the question can still be answered.

The given angles are:

[tex]\theta_1 = 74.0^o[/tex]

[tex]\theta_2 = 66.0^o[/tex]

Represent the third angle as [tex]\theta_3[/tex]

The helicopter and the 2 VORs form a triangle.

So, we make use of the following theorem to calculate the third angle

[tex]\theta_1 + \theta_2 + \theta_3= 180^o[/tex] ---- sum of angles in a triangle

Substitute known values

[tex]74.0^o + 66.0^o + \theta_3= 180^o[/tex]

[tex]140.0^o + \theta_3= 180^o[/tex]

Collect like terms

[tex]\theta_3= 180 -140.0^o[/tex]

[tex]\theta_3= 40^o[/tex]

Hence, the third angle is 40 degrees.

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Answer:

[tex](x,y) = (1,2)[/tex] -------- [tex]R_{y-axis}[/tex]

[tex](x,y)=(2,-1)[/tex] --------- [tex]R_{y=x}[/tex]

Step-by-step explanation:

Given

[tex](x,y) = (-1,2)[/tex]

Required

[tex]R_{y-axis}[/tex]

[tex]R_{y=x}[/tex]

[tex]R_{y-axis}[/tex] implies that:

[tex](x,y) = (-x,y)[/tex]

So, we have: (-1,2) becomes

[tex](x,y) = (1,2)[/tex]

[tex]R_{y=x}[/tex] implies that

[tex](x,y) = (y,x)[/tex]

So, we have: (-1,2) becomes

[tex](x,y)=(2,-1)[/tex]

Answer:

It's the last one.

Step-by-step explanation:

For example, if you have 0, the absolute valeu of 0 is 0. A postive number like 2, has an absolute value of 2. 0 is not greater than 0 and 2 is not greater than 2. Hope this helps!

Answer: Kayla is incorrect. The absolute value of 0 or a positive number is equal to the number.

Answer:

a) 6:8

Because you have 14 books total if you substract 14 - 6= 8, so now you have

14 Books total

6 New Books

8 Used Books.

So, the ratio of new books to used books is 6:8 or if you simplified is 3:4.

b) 8:14

Because you have 8 used books compare to 14 books total. If you simplified your fraction you'll have 4:7

Step-by-step explanation:

Answer:

arcsin0.616

Step-by-step explanation:

arcsino.616

Answer:

x = 34

Step-by-step explanation:

Pytago:

x[tex]30^{2} + 16^{2} = x^2\\x = \sqrt{30^2 + 16^2} \\x = 34[/tex]

Answer:

574

Step-by-step explanation:

To round a two-digit number to the nearest ten, simply increase it or decrease it to the nearest number that ends in 0: When a number ends in 1, 2, 3, or 4, bring it down; in other words, keep the tens digit the same and turn the ones digit into a 0

Hope this helps <3

Answer:

I doubt it is not going to be a great

The complete table is

x    y

0    0.75

3     3.75

9     9.75

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Substitution means putting numbers in place of letters to calculate the value of an expression or equation.

According to the given question.

We have values of x.

Also, one rule that y is 0.75 greater than x.

So, we have a equation for finding the value of y  i.e.

[tex]y = x + 0.75..(i)[/tex]

For finding the value of y

At x = 0, substitute x = 0 in equation (i)

[tex]y = 0 + 0.75\\\implies y = 0.75[/tex]

At x = 3, substitute x = 3 in equation (i)

[tex]y = 3+0.75\\\implies y = 3.75[/tex]

At x = 9, substitute x = 9 in equation (i)

[tex]y = 9+0.75\\\implies y = 9.75[/tex]

Hence, the complete table is

x    y

0    0.75

3     3.75

9     9.75

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Answer:

9.9 hours

Step-by-step explanation:

The formula to determine the time together is

1/a+1/b = 1/c  where a and b are the times alone and c is the time together

1/18 + 1/22 = 1/c

The least common multiply of the denominators is 198c

198c(1/18 + 1/22 = 1/c)

11c+ 9c = 198

20c = 198

Divide by 20

20c/20 =198/20

c =9.9

Answer:

B - 9.9 hrs

Step-by-step explanation:

took the test.

Answer:

[tex](f-g)(x)[/tex]

[tex]f(x)-g(x)[/tex]

[tex]x^{2} -6x-27-x+9[/tex]

[tex]x^{2} -7x-18[/tex]

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

[tex](f*g)(x)[/tex]

[tex]=f(x)g(x)[/tex]

[tex](x^{2} -6x-27)(x-9)[/tex]

[tex]=x^{3} -15x^{2}+27x+243[/tex]

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

[tex]\frac{f}{g} (x)[/tex]

[tex]\frac{x^{2} -6x-27}{x-9}[/tex]

[tex]\frac{(x-9)(x+3)}{x-9}[/tex]

[tex]x+3[/tex]

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

[tex](f+g)(x)[/tex]

[tex]f(x)+g(x)[/tex]

[tex]=x^{2} -6x-27+x-9[/tex]

[tex]=x^{2} -5x-36[/tex]

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

OAmalOHopeO

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

Answer:

.................

Step-by-step explanation:

............