Which equation describes the same line as y-5=-2(x+4)

According to the given table the line of best fit is

f(x)=4.54x+77.84

The term "line of best fit" describes a line that passes across a scatter plot of data points and best captures their connection. Statisticians often utilise regression analysis software or manual computations to arrive at the geometric equation for the line using the least squares approach. A straightforward linear regression study of two or more independent variables will provide a straight line. 

Hence, as asked by the question we need to find the time at which the tempurature will become 100°C.

To find that let us put f(x)=100 and find out the value of x for which it is satisfied.

4.54x+77.84=100

⇒[tex]x=\frac{100-77.84}{4.54}=4.88[/tex]

⇒x≈5

Therefore the time at which the tempurature is 100°C is 5 minutes.

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The equation fourth represents the ellipse that has vertices at (1, 0) and (11, 0), and an eccentricity of 3/5 option fourth is correct.

An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called focus adds up to a constant. It is taken from the cone by cutting it at an angle.

We have:

The vertices of the ellipse = (1, 0) and (11, 0)

Eccentricity of ellipse = 3/5

We have equations:

[tex]\rm \dfrac{\left(x-6\right)^{2}}{100}+\dfrac{y^{2}}{64}=1[/tex]

[tex]\rm \dfrac{\left(x+6\right)^{2}}{64}+\dfrac{y^{2}}{100}=1[/tex]
[tex]\rm \dfrac{\left(x+6\right)^{2}}{16}+\dfrac{y^{2}}{25}=1[/tex]

[tex]\rm \dfrac{\left(x-6\right)^{2}}{25}+\dfrac{y^{2}}{16}=1[/tex]

From the fourth equation:

The vertices of the ellipse:

(1, 0) and (11, 0)

The eccentricity:

c²  = a² - b²

c² = 25-16

c = 3

e = c/a = 3/5

Thus, the equation fourth represents the ellipse that has vertices at (1, 0) and (11, 0), and an eccentricity of 3/5 option fourth is correct.

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Answer:

10π cm

Step-by-step explanation:

c = 2πr

c = (2*5) * π

c = 10π

Answer:

A exponential equation is usually of the form f(x)=a (1±r)ˣ.

Our limitation: Initial Vale is 500.

Let's look at our options:

#1- Initial Value of 1000  --- WRONG!

#2- Initial Value of 1000  --- WRONG!

#3- Initial Value of 500 ---- Maybe

#4- Initial Value of 500 ---- Maybe

Let's look at 3 and 4:

#3- Fits Our Form of f(x)=a (1±r)ˣ ---- CORRECT!

#4- Does not fit Our Form of f(x)=a (1±r)ˣ, It's to the 2nd power, not the x power! ---- WRONG!

Hence, #3 Is correct!

Step-by-step explanation:

Well, I hope you understood, and I'd gladly explain anything that didn't make sense. A brainliest would be appreciated, thank you!

-Zylynn Jade Ardenne

Answer:

[tex]a = 7[/tex]

Step-by-step explanation:

[tex]1. \: 7a - 70 = 13 - 4a - 6 \\ 2. \: 7a - 70 = - 4a + 7 \\ 3. \: 7a = - 4a + 7 + 70 \\ 4. \: 7a = - 4a + 77 \\ 5. \: 7a + 4a = 77 \\ 6. \: 11a = 77 \\ 7. \: a = \frac{77}{11} \\ 8. \: a = 7[/tex]

Answer:

0.462

Step-by-step explanation:

1km=1000m

so to get from metres to kilometres you divide by 1000

so 462÷1000=0.462

Answer:

y = -2

(first option listed)

Step-by-step explanation:

a y-intercept is a point where the line crosses over the y-axis, which happens when x = 0.

So, the y-intercept is actually pretty each to find.

this is the easier way to find it:    {plug directly into equation given}

2x - 3y = 6

(set x equal to 0)

[0] - 3y = 6

(divide both sides by -3)

y = -2

but you might have seen/ learned to solve the equation like this {to actually find the equation of the line and solve from that}

[this method is helpful to know/practice for when equations for functions get more complex]

  2x - 3y = 6

      + 3y      + 3y           {add 3y to both sides}

  2x = 3y + 6

   -6          -6                {subtract 6 from both sides}

  2x - 6 = 3y

    ÷3      ÷3            {divide both sides by 3 to isolate y}

  [tex]\frac{2}{3}x[/tex] [tex]- 2 = y[/tex]                [flip sides of the equation]

 [tex]y=\frac{2}{3}x-2[/tex]  

set x equal to 0 (x = 0)

y = [tex]\frac{2}{3} (0)[/tex] - 2

y = 0 - 2

y = -2

So, the y-intercept is -2.

Using the combination and the arrangements formula, it is found that the number of possible playlists is given by:

[tex]7.98 \times 10^8[/tex]

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, we have that:

Hence, without considering the order, the number of playlists is given by:

[tex]C_{7,7}C_{12,3} = \frac{7!}{7!0!} \times \frac{12!}{3!9!} = 220[/tex]

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

In this problem, the 10 musics are arranged, hence the number of playlists, considering the order, is given by:

[tex]n = 10! \times 220 = 798336000 = 7.98 \times 10^8[/tex]

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The height of the tree to the nearest tenth of a meter is 73.7m

The angle formed by the line of sight and the horizontal plane for an object above the horizontal.

Given:

base = 13 m

angle of elevation = 53

Using trigonometry

tan 53 = P/B

5.671 = P/ 13

P= 5.671 * 13

P= 73.723

Hence, the height of the tree is 73.7 m.

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Answer:

it's 5 degrees celsius I think you must have entered a 4-32 instead of a 41-32 is what threw you off

Step-by-step explanation:

Answer:

[tex]m \leqslant 10 \: or \: m > 4[/tex]

Step-by-step explanation:

[tex] \frac{m - 2}{3} \leqslant - 4 \\ \frac{m - 2}{3} \times 3 \leqslant - 4 \times 3 \\ m - 2 \leqslant - 12 \\ m - 2 + 2 \leqslant - 12 + 2 \\ m \leqslant 10[/tex]

OR

[tex]3m - 8 > 4 \\ 3m - 8 + 8 > 4 + 8 \\ 3m > 12 \\ \frac{3m}{3} > \frac{12}{3} \\ m > 4 [/tex]

Step-by-step explanation:

Answer:

see the attachment photo!

i hope this can help you! :)

Answer:

A (top left)

Step-by-step explanation:

Assuming that the dot is multiplying the numbers, we get the function:

[tex]f(x) = 8^{x}[/tex]

First, lets knock off the obviously wrong answers.

Substitute 0 into the x spot, as anything to the power of zero is one.

[tex]f(0) = 8^{0}=1[/tex]

Automatically, the two answers on the right are incorrect, as y is not equal to 1 when x is 0.

Next, lets substitute 1 into the x spot, as anything to the power of one is itself.

[tex]f(1) = 8^{1} = 8[/tex]

As a result, the top left graph is correct, as y is equal to 8 when x is 1, unlike the bottom left graph.

Answer:

34791112

Step-by-step explanation:

Please check the attached for the explanation.

The next number for given sequence is 34791112.

The given sequence is 2,2,5,12,62,749,46450,......

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same.

Each number in the sequence is of the form Number3 × Number2 + Number1 = Number4

5×2+2=12

12×5+2=62

62×12+5=749

749×62+12=46450

So, the required number is

46450×749+62=34791112

Therefore, the next number for given sequence is 34791112.

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Answer:

[tex]\frac{3}{7}.v[/tex]    option (C) is correct

Step-by-step explanation:

projection of vectors: The vector projection of one vector over another vector is the length of the shadow of the given vector over another vector.

projection of vector u on v is given by :

Given,

vector u = <5, 7, 1>

vector v = <2, -1, 3>

substituting these values in the above formula

thus the correct answer is option (C)

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Answer:

LM

Step-by-step explanation:

Perpendicular slope would be   - 1 / m   =   - 1/(-5/6)   = 6/5

slope m = rise / run       line   LM   rises 6    for a run of 5      

The result after rationalizing is [tex]\frac{9\sqrt{x+3} }{x+3}[/tex].

Rationalization can be considered as the process used to eliminate a radical or an imaginary number from the denominator of an algebraic fraction.

Here, given fraction

 [tex]\frac{9}{\sqrt{x+3} }[/tex]

Multiply and divide by [tex]\sqrt{x+3}[/tex], we get

[tex]\frac{9}{\sqrt{x+3} } \frac{\sqrt{x+3} }{\sqrt{x+3} }[/tex]  =  [tex]\frac{9\sqrt{x+3} }{x+3}[/tex]

Thus, the result after rationalizing is [tex]\frac{9\sqrt{x+3} }{x+3}[/tex].

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An axiom is a statement that is assumed to be true without proof.

In logic, a statement could be shown to be valid or true by the use of premises that lead to a sound conclusion.

The following terms can be used to describe the statements;

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Answer:

The answer is axiom, theorem, and then conjecture

Step-by-step explanation:

Answer:

is B

Step-by-step explanation:

this is the best possible answer

The statement about the sides must respect to represent a triangle is given as follows:

A. a + b > c.

In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.

The smaller sides for the triangle are given as follows:

a and b.

Hence the statement is:

a + b > c.

(as the sum of the lengths of the smaller sides a and b must be greater than the length of the larger side, which is of c).

Hence the correct statement is given by option A.

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If she puts 0 in the box she would have a direct variation.

Lydia writes the equation y = 5x - __ with a missing value.

She puts a value in the box and says that the equation represents a direct variation.

We have to choose the correct option from the given options that explain that the equation could represent a direct variation.

When two variables are such that one is a constant multiple of the other, we said they are in Direct variation.

In form of y = ax, where y and x are in direct variation.

Consider the given equation y = 5x  - __

For the equation to be in direct variation the value of the missing term has to be 0.

then the equation becomes,

y = 5x

Thus, If she puts 0 in the box she would have a direct variation.

Option (a) is correct.

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Answer:

a

Step-by-step explanation:

Answer:

radius ≈ 15.5

Step-by-step explanation:

the radius is RS

the angle between a tangent and the radius at the point of contact is 90°

then Δ RST is a right triangle

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , then

RS² + ST² = RT² ( substitute values )

RS² + 7² = 17²

RS² + 49 = 289 ( subtract 49 from both sides )

RS² = 240 ( take square root of both sides )

RS = [tex]\sqrt{240}[/tex] ≈ 15.5 ( to 1 dec. place )

Answer: 32x+4

Step-by-step explanation:

[tex]f(x) \cdot g(x)=(8x+1)(-5+9)=4(8x+1)=\boxed{32x+4}[/tex]

Answer:

(24 + 3√3) / 16.

Step-by-step explanation:

Tan 60° + Cos 30° sin 60° + Cot 30 /  csc 30 sec 30

= √3 + √3/2 * √3/2 + √3 /   2 * 2/√3

= 2√3 + 3/4 / 4/√3

= (8√3 + 3)/ 4 / √3

= 24 + 3√3 / 16

If Richards Corporation uses the FIFO method of process costing. The  equivalent units of materials is 294,000.

Using this formula

Equivalent unit of material (FIFO) =[(Beginning inventory×Percentage complete)+Units started and complete+ (Ending inventory× Percentage complete as to materials)]

Let plug in the formula

Equivalent unit of material (FIFO) = [80,000×40%+250,000+30,000×40%]

Equivalent unit of material (FIFO) = 32,000+250,000+12,000

Equivalent unit of material (FIFO) = 294,000

Therefore the equivalent units of materials is 294,000.

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It can be modeled by an exponential function, f(x) is divided by 3 each time x increases by 1.

This means that the base of the exponential function is 1/3, and since the value of f(x) when x=0 is 81, [tex]f(x)=81\left(\frac{1}{3} \right)^{x}[/tex]

After factorizing the given equation, we can find the three iterations by putting the consecutive values of x.

The given equation is 3∧x = 2∧(-x) + 4. We can modify it as shown below:

Take logarithm on both the sides

log(3∧x) = log[2∧(-x) + 4]

xlog3 = log[2∧(-x) + 4]

x = log[2∧(-x) + 4] / log3

For the first iteration, put x = 1

x = log[2∧(-1) + 4] / log3

x = log4.5 / log3

x = 0.477

For the second iteration, put x = 2

x = log[2∧(-2) + 4] / log3

x = log4.25 / log3

x = 0.477

For the third iteration, put x = 3

x = log[2∧(-3) + 4] / log3

x = log4.125 / log3

x = 0.477

So, this is how we can find three iterations.

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Solution: Below! ^^

Detailed explanation:

Hii! I'm sorry, I can't graph the line for you, but I'll try to give you the best possible explanation.

First, note that the question provides us with the info that the y intercept is -8. This is a very valuable piece of information!

This means that the line crosses the y axis (since it's the y intercept) at the point (0,-8). Plot it on the co-ordinate plane.

Next, this question also provides us with the fact that the slope of the line is 1/4. This is yet another valuable piece of information!

What this tells us is: from that point (0,-8), you need to go up 1 unit, then over 4, and so forth, until you obtain a line.

_________

Hope I helped, best wishes & happy studies!

Please reach out to me if any queries arise.

_________

Answer:

Image attached below

Step-by-step explanation:

The line should cross y axis as -8 and should have a point of (0,-8)

The line should have a gradient / slope of 1/4