Find the equation of the line

Answer:

They are not.

Step-by-step explanation:

Let's first calculate the vectors joining the first point to the second and the first to the third, they will be useful later.

[tex]\vec v_1_2 = \vec P_2 -\vec P_1 = <3; -7; -7>\\\vec v_1_3= \vec P_2 -\vec P_1 = <6; -14; -13>[/tex]

At this point we have at least three options:

Write down the line between P1 and P2 in vector form, and then see if we can fit the third point in there.

Calculate the cross product between the two, if it's non-zero the three point are not in a line.

Try to determine the plane passing for the 3 points: if we find one they are not in a line.

Option 1:

The vector form of the lne between the firs two points is [tex]<6+3t;9-7t;7-7t>[/tex]. Let's check the coordinates of the third point:

[tex]x_3:\ 6+3t= 12 \rightarrow t=2\\y_3:\ 9-7t = -5 \rightarrow t =2\\7z_3:\ 7-7t=-6 \rightarrow t = 13/7\ne 2[/tex]

So the three points are not in a line.

Option 2:

Let's calculate the cross product of the two vectors we found at the beginning.

[tex]\vec v_1_2 \times \vec v_1_3 = det \left[\begin{array}{ccc}\hat i&\hat j&\hat k\\3&-7&-7\\6&-14&-13\end{array}\right] = \hat i [-7(-13)-(-14)(-7)] - \hat j[3(-13)-6(-7)]+\hat k [3(-14)-6(-7)] = 7\hat i -3 \hat j + 0 \hat k \ne 0[/tex]

Since the result is not the null vector, the three points are not in a line.

Option 3:

Let's write the plane (in the [tex]z= ax+by+c[/tex] form that contain the three points. If the thre points are in a line, means that we can find only two of these parameters.

[tex]P1: 7= 6a+9b+c\\P2: 0= 9a+6b+c\\P3: -6= 12a-5b +c[/tex]

Since you can determine a, b and c ( I ended up with [tex]a=-\frac {10}3; b=-\frac18; c= \frac{123}8[/tex] but I probably messed something in there) the thre points are not in a line

The rate of growth will she need to achieve her goal is 2.8%

The formula for finding the compound amount is expressed as:

[tex]A =P(1+\frac{r}{n} )^{nt}[/tex]

P is the amount invested = $25000

t is the time in years = 25 years

A is the amount = $125000

r is the rate in %

Substitute the given parameters into the formula to have:

[tex]125000 =25000(1+r )^{25}\\5 =(1+r)^{25}\\log5=25log(1+r)\\log(1+r)=\frac{log5}{25} \\log(1+r)=0.02796\\1+r = e^{0.02795}\\1+r=1.0283\\r = 1.0283 -1\\r = 0.0283\\[/tex]

Hence the rate of growth will she need to achieve her goal is 2.8%

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[tex]\huge \bf༆ Answer ༄[/tex]

The translation can be can be expressed as : -

A translation

[tex]꧁  \:  \large \frak{Eternal \:  Being } \: ꧂[/tex]

Step-by-step explanation:

-4y + 8y = 4y

it is the same as -4 + 8 = 4

Answer:

4y is the answer.

Step-by-step explanation:

Since there is like variables, we can add -4y and 8y.

=> -4y + 8y = 4y.

Therefore, 4y is the answer. Hoped this helped.

Answer: point (60,0)

Step-by-step explanation: the x-intercept (60,0) shows that at 60 minuetes the balloon is 0 meter above the ground

The coordinates of the function of height and time are (210, 0) and (60, 10). The graph is attached below.

The function is a relationship between a set of potential outputs and a set of possible inputs, where each input has a single relationship with each output. This means that if an object x is present in the set of inputs (also known as the domain), then a function f will map that object to exactly one object f(x) in the set of potential outputs (called the co-domain).

Given:

r(t) = 210 - 15t

Calculate the height after 10 minutes as shown below,

The height = 210 - 15 × 10

The height = 210 - 150

The height = 60

At time 0 the height will be,

The height = 210 - 15 × 0

The height = 210 - 0

The height = 210 meters,

Thus, the coordinates will be (210, 0) and (60, 10)

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Answer:

[tex]\sf k + 6 > -37[/tex]

[tex]\sf k+6-6>-37-6[/tex]

[tex]\boxed{\sf k>-43}[/tex]

Answer:

Subtract 6 from both sides:

K +6 - 6 > - 37 - 6

Simplify the arithmetic:

k > - 37 - 6

Simplify the arithmetic

k > - 43

Answer:

The answer to " How much is a pen or pencil at the school store?" is $0.5

Step-by-step explanation:

3+5=8

-1.00 for erasers

total cost now =4

4/8= $0.5

total cost of everthing =5

Answer:

79.04 liters

Step-by-step explanation:

20.8 x 3.8 = 79.04

Answer:

[tex] \large\color{red}{ \tt{36n⁸}}[/tex]

Step-by-step explanation:

[tex] \large\color{lime}{ \tt{(3n×2n³)²}}[/tex]

[tex] \large\color{lime}{ \tt{(3n⁴ × 2)²}}[/tex]

[tex] \large\color{lime}{ \tt{(6n⁴)²}}[/tex]

[tex] \large\color{lime}{ \tt{6²(n⁴)²}}[/tex]

[tex] \large\color{lime}{ \tt{6²n⁸}}[/tex]

[tex] \large\color{lime}{ \tt{36n⁸}}[/tex]

Hope It's Help

Answer:

y=2x+9

Step-by-step explanation:

I got y-2x+9 because if you add 8-1 that equals 7 and if u do 7-5 that equals 2 so y2x and then 7 Plus 2 equals 9 so it all adds up to Y=2x+9?.

Answer:

24-8=t

Step-by-step explanation:

I cant really explain much...

but, Hope it helps

plz mark brainiest if it does

Answer:

The Awnser is 27 for both I did that I-ready before

Step-by-step explanation:

Answer:

27 for both blanks

Step-by-step explanation:

I just did it on iready and I got it correct

Answer:

D IS THE ANSWER

Step-by-step explanation:

HOPE IT HELPS

Answer:

They are equal, so =

Step-by-step explanation:

We know that one-half is .50.  3/2 is an improper fraction and when we solve to a decimal, we get 1.5.  

[tex]\\ \sf\longmapsto {\displaystyle{\lim_{x\to 1}}}\dfrac{x^2-1}{x-1}[/tex]

[tex]\\ \sf\longmapsto {\displaystyle{\lim_{x\to 1}}}\dfrac{x^2-1^2}{x-1}[/tex]

[tex]\\ \sf\longmapsto 2(1)^(2-1)[/tex]

[tex]\\ \sf\longmapsto 2(1)[/tex]

[tex]\\ \sf\longmapsto 1[/tex]

Step-by-step explanation:

[tex] \tt \lim \limits_{x \to1} \frac{ {x}^{2} - 1 }{x - 1} = ...[/tex]

[tex] = \tt \lim \limits_{x \to1} \frac{(x + 1) \cancel{(x - 1)}}{ \cancel{(x - 1)}} [/tex]

[tex] = \tt \lim \limits_{x \to1}(x + 1)[/tex]

[tex] = \tt1 + 1[/tex]

[tex] = \boxed{ \bold{ \blue{ \underline2}}}[/tex]

Answer:

2 ( 2y + 5 )

Step-by-step explanation:

→ Take out 2 as a factor

2 ( 2y + 5 )

Answer:

Step-by-step explanation:

The area equation is:

Given:

This can be factored as:

Let y = 3, then the dimensions are:

Answer:

all of the above

Step-by-step explanation:

Answer: 13 1/3 degrees per hour

Explanation: 10/3 x 4 = 40/3

40/3 = 13 1/3

Answer: i dont know if this will be correct but, the 2 goes on the bottom count 5 up so you will get the first one done, bottom 3 and count up 8, bottom 4 and count up to 13, its the same for all of them.

Step-by-step explanation:

Answer: [tex]h=\frac{-g}{g-2}[/tex]

Step-by-step explanation:

Let's solve for h.

[tex]3h+g=5h-hg[/tex]

Step 1: Add [tex]gh[/tex] to both sides.

[tex]g+3h+gh=-gh+5h+gh[/tex]

[tex]gh+g+3h=5h[/tex]

Step 2: Add [tex]-5h[/tex] to both sides.

[tex]gh+g+3h+-5h=5h+-5h[/tex]

[tex]gh+g-2h=0[/tex]

Step 3: Add [tex]-g[/tex] to both sides.

[tex]gh+g-2h+-g=0+-g[/tex]

[tex]gh-2h=-g[/tex]

Step 4: Factor out the variable [tex]h[/tex].

[tex]h(g-2)=-g[/tex]

Step 5: Divide both sides by [tex]g-2[/tex].

[tex]\frac{h(g-2)}{g-2} =\frac{-g}{g-2}[/tex]

[tex]h=\frac{-g}{g-2}[/tex]

Answer:

[tex]h=\frac{-g}{g-2}[/tex]

Answer:

Step-by-step explanation:

hmm

The graph of a quadratic function is always a parabola. The vertex of the parabola after transformation is (-1,-4).

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.

The graph of the two functions can be made as shown below. Therefore, the two functions are,

y=2x² → Drawn by the red line

y = 2(x + 1)² − 4 → Drawn by the blue line

Now, the vertex of a quadratic function or a parabola is the point at which the function or the parabola changes its slope, it's either the maximum of the function or the minimum of the function, depending on which side the parabola opens.

Hence, The vertex of the parabola after transformation is (-1,-4).

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Answer:

12.89

Step-by-step explanation:

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Answer:

100

Step-by-step explanation:

10,000 * 100 = 1,000,000

So there are 100 ten thousands in 1,000,000

There are no prime numbers are multiples of 8​. All the multiples of 8 are divided by 2.

Prime numbers are whole numbers larger than one with only one element the number itself. Prime numbers can only be divided by the number 1 or by themselves.

All the terms that come in the table of 8 are multiples of 8.

8, 16, 24, 32, 40, 48, 56, 64, 72, and 80 are the multiples of 8. There are no prime numbers are multiples of 8​.

Hence there is no prime numbers multiples of 8​.

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Answer:

9,687,600

Step-by-step explanation:

27P5

= 27!/(27-5)!

= 27!/22!

= 27*26*25*24*23

= 9,687,600

Answer:

X=5

y= -4+5(5+6)

y= -4+25+30

y= -4+55

y = 51

Answer:

x=120 y=60

Step-by-step explanation:

Interior angle of a hexagon = 120

Straight line = 180

180-120=60

Answer:

Circle

Step-by-step explanation:

The area of a circle is

[tex]\pi r^{2}[/tex]

A. circle

The area of a circle is 2[tex]\pi[/tex]r²

The Circle Formulas are expressed as,

The collection of all points equidistant from a fixed point in a plane is called a circle.

the circle is a closed 2-dimensional figure in which the set of all the points in the plane is equidistant from a given point called the “center”. Every line that passes through the circle forms the line of reflection symmetry.

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Answer:

12

Step-by-step explanation:

Hi there!

We are given the following equation:

1/2x + 6 = -x-3

And we want to find the value of -2x

First, let's solve for x, and then substitute the number found as x into -2x to find the value of -2x

Start by adding x to both sides to remove -x from the right side

1/2x + 6 = -x -3

+x            +x

_______________

3/2x+6=-3

Subtract 6 from both sides to remove it from the left side

3/2x=-9

Multiply both sides by 2/3 in order to clear the fraction

x=-6

Now substitute -6 as x into -2x

-2x

x=-6

-2(-6)=12

Hope this helps!