there is a number that is eight less than the sum of 20 + 12. find the number let n = the number

The equation of the parabola is x² = 60y after applying the concept of the parabola.

It is defined as the graph of a quadratic function that has something bowl-shaped.

(x - h)² = 4a(y - k)

(h, k) is the vertex of the parabola:

a = √[(c-h)² + (d-k²]

(c, d) is the focus of the parabola:

It is given that:

Focus of (0, 15) and directrix y = –15.

Let (x, y) be on the parabola:

The distance between focus and (x, y):

The distance formula can be given as:

[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\rm d=\sqrt{(x-0)^2+(y-15)^2}[/tex]

[tex]\rm d=\sqrt{x^2+(y-15)^2}[/tex]

Directrix y = -15

y + 15 = 0

[tex]\rm \sqrt{x^2+(y-15)^2} = |y + 5|[/tex]

Squaring both sides:

x² + (y - 15)² =  (y + 15)²

x² + y² -30y + 225 =  y² + 30y + 225

x² -30y  = 30y

x² = 30y + 30y

x² = 60y

Thus, the equation of the parabola is x² = 60y after applying the concept of the parabola.

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We get that the function that models this situation is

where L is the liters the tank contains and m is the minutes that has passed. So we get:

so the tank has been drained for 2 minutes

In linear equation, x = 18 is the value of x in equation .

What is a linear equation example?

6x +4(x - 10) = 140.

6X + 4X - 40 = 140

10X = 140 + 40

10x = 180

  x = 180/10

  x = 18

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The simplified form of the expression, negative six sevenths times k minus 7 plus the expression 5 plus one half times k is negative 5 over 14 times k plus negative 2.

Hence, the correct option is option (B).

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given expression is,

negative six sevenths times k minus 7 plus the expression 5 plus one half times k.

The expression can be written in mathematical term,

(-6/7)k - 7 + 5 + 1/2(k)

Simplify the expression,

(-6/7)k + 1/2(k) - 7 + 5

((-12 + 7)/14) k - 2

(-5/14) k - 2.

-(5/14)k + (-2)

The simplified form is, negative 5 over 14 times k plus negative 2.

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The equation of the line in slope intercept form  perpendicular to 6x - 2y = 12 and has the same y-intercept is  y = - 1 / 3 x - 6

The equation in slope intercept form can be represented as follows:

y = mx + b

where

Therefore, the equation of the line is perpendicular to 6x - 2y = 12 and have the same y-intercept.

Hence, perpendicular lines follows the rule below:

m₁m₂ = -1

6x - 2y = 12

6x - 12 = 2y

y = 3x - 6

Hence,

3m₂ = -1

m₂ = - 1 / 3

Therefore, the slope of the line is - 1 / 3.

The y-intercept is -6

Therefore,

the equation of the line is y = - 1 / 3 x - 6

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We have the following:

simplify:

The answer are (2x - 1) or (4x + 15)

Answer

The most obvious conclusion from this is that

Adding 0 to any number gives that number itself.

This concept is known as the additive identity property of 0.

Hope this Helps!!!

Answer:

120 candles

Step-by-step explanation:

42/35 = x/100 and solve for x

x = 120

Answer:

120

Step-by-step explanation:

35%/100=42/x

ANSWER

N'(-2 , -4) Option C

EXPLANATION

Given:

A polygon KLMN with vertices at K(1, 5), L(1, 0), M(−1, −1), N(−4, 2).

Desired Outcome:

Image vertices of N′ if the preimage is rotated 90° counterclockwise

Answer: The correct answer is C

Step-by-step explanation:

I was correct on the quiz. WOWWWW

Given:

If two triangles are congruent, then their corresponding angles are congruent.

Contapositive statement:

If two triangles are not congruent , then their corresponding angles are not congruent.

Option C is the correct answer

currency-

exchange rate- c

extrinsic value - g

fiat monetary system- e

gold standard - a

intrinsic value

trade

The equation of the line will be y = 2x + 1.

So, the equation of the line:

Then, y = 2x + b

Now, substitute x = 1 and y = 3 in the above equation to find b:

So, the equation of the line will be: y = 2x + 1

Therefore, the equation of the line will be y = 2x + 1.

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Answer.

D.

Step by step explanation.

It's defined as the procedure of collecting, measuring, and analyzing accurate insights for research using standard validated techniques.

The most critical objective is ensuring that information rich and reliable data is collected dor statistical analysis so that data-driven decisions can be made for research

Step 1: Problem

Find the measure of

Step 2: Concept

Use trigonometry ratio to find the value of angle x.

Step 3: Method

Given data

Opposite = 3.2 side facing given angle

Adjacent = 5

Step 4: Final answer

The following functions have the following growth rates:

2/N < 37 <√N < N < N log log N < N log N < N log(N^2) < N . log^2 . N < N^1.5 < N^2 <N^2. log N < N^3 < 2^N/2 < 2^N

How can you determine a function's growth rate?

The present value is divided by the past value, multiplied to the 1/N power, and then one is subtracted to get the formula for the average growth rate over time approach.

How may the growth rates of two functions be compared?

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Here, we want to find the x and y intercepts of the given line

We start by writing the equation of the line in the standard form

The standard form is;

where m is the slope and b is the y-intercept

We have the equation re-written as;

As we can see, we have the y-intercept at the point y = -12/5

The coordinate form at this point is (0,-12/5)

To find the x-intercept, we simply set y to zero

This is;

The x-intercept is thus (6,0)

This equation of the ellipse can be modeled by

The major axis is the y-axis and minor axis is the x-axis.

So, the length of the minor axis of this ellipse is "2a".

First, let's find "a",

The length of the minor axis is >>>

The equation of the line that passes through point (8,-1) and perpendicular to 8y = x - 16 is f(x) = -8x + 63.

Given the data in the question;

First we determine the slope of the initial line using the slope intercept-form. y = mx + b

8y = x - 16

y = (1/8)x - 2

Compared with the slope intercept form,

Slope m = 1/8

Now, for the equation of line perpendicular to the initial line, its slope must be a negative reciprocal of the initial slope.

Hence, slope of the perpendicular line is;

Slope m = -1/1/8 = -8

To find the equation of the perpendicular line, we use the point slope formula.

y - y₁ = m( x - x₁ )

Plug in the slope m ( -8) and point (8,-1).

y - (-1) = (-8)( x - 8 )

y+1 = -8x + 64

y = -8x + 64 - 1

y = -8x + 63

Therefore, the equation of the perpendicular line is y = 8x + 63

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The correct range of definition is;

Here, we want to get the range of values of x for which the given expression is defined

The key here is that any value of x that will make us have a negative value inside the root will make the expression undefined as that would give us a non-real root

Now, let us take a look at the options;

a) if x is greater than 1, we will have a negative root on the right, making the expression undefined. This option is wrong

b) This is also wrong; if 5 is less than x, then x might be 6 , which would give a negative root value

c) If -5 is less than x, x could take values of -4, -3, -2 and the root on the right will never be negative. But in cases like this, we have the spectrum upto positive values of x such as 5 which would make the root on the right negative and undefined. This range here is the correct answer

d) Here, 5 is greater than x, so the root on the left can never be negative. For values less than -1, like -6, what we have on the left will be undefined

Answer: easy it's A -500

The slope of the function (x) is -500!! :D

The equation of the line that passes through the point (-4,2) and the parallel to the line y = 1/4x + 1 is y = (1/4)x+3

The equation of the line parallel to the line is

y = 1/4 x +1

The slope intercept form is

y = mx + b

Where m is the slope of the line and b is the y intercept

By comparing the given equation and slope intercept form of the line

The slope of the line is m = 1/4

Then the point slope form is

[tex](y-y_1)= m(x-x_1)[/tex]

The line is passing through the point (-4,2)

Substitute the values in the equation

(y-2) = 1/4(x-(-4))

y-2 = 1/4(x+4)

y-2 = (1/4)x+1

y = (1/4)x+3

Hence, the equation of the line that passes through the point (-4,2) and the parallel to the line y = 1/4x + 1 is y = (1/4)x+3

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The value of g(9) + h(-14) is 15.

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The given expression is

Let's replace x = 2, and z = 5.

Step-by-step explanation:

your teacher gave you the formula, the values, even did the tricky part by telling you that 63 months are 5.25 years.

all you need to do is put everything into the formula and calculate.

so, calm down, breathe and just use common sense :

1.

after 2 years (means t = 2) :

2000 × (1.025)^(2×2) = 2000 × (1.025)⁴ =

= 2000 × 1.103812890625 =

= $2,207.62578125 ≈ $2,207.63

as rounding to the nearest cent means rounding to 2 positions after the decimal point.

2.

after 63 months = 5.25 years (t = 5.25)

2000 × (1.025)^(2×5.25) = 2000 × (1.025)^10.5 =

= 2000 × 1.295986825... =

= $2,591.973651... ≈ $2,591.97

3.

$2,000

because, even t = 0 we have

2000 × (1.025)^(2×0) = 2000 × (1.025)⁰ = 2000 × 1 =

= $2,000

The least degree polynomial function with rational  coefficients and the given zeros, -1, 2 and 3i is f(x) =[tex]x^{2} -x -2(\sqrt{x} -9)[/tex]

What do we mean by polynomial function?

A polynomial function is one that involves only non-negative integer powers or positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, and so on.

For example, 2x+5 is a polynomial with an exponent of one.

So given zeroes are -1 , 2 and 3i

We have,

x = -1

x +1 =0

Similarly for 2

x = 2

x -2 = 0

Again, For 3i

We have, x = 3i

Rewrite as x =  [tex]\sqrt{-9}[/tex]

For easy calculation, squaring on both sides

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

[tex]x^{2} +9[/tex] =0

So, the polynomial has the function:

(x + 1)(x - 2) ([tex]\sqrt{x} -9[/tex])

[tex]x^{2} - 2x +x -2 (\sqrt{x} -9)\\x^{2} -x -2(\sqrt{x} -9)\\[/tex]

Therefore, the least degree polynomial function with rational  coefficients and the given zeros, -1, 2 and 3i is f(x) =[tex]x^{2} -x -2(\sqrt{x} -9)[/tex].

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Answer:

renting a movie for 2 dollars a day

Step-by-step explanation:

the y does not repeat

Coplanar lines are referred to as parallel lines because they may be extended indefinitely without ever intersecting. || is the sign meaning "parallel to." If two lines are drawn, they don't have to be parallel, and a third line runs across them as seen in the diagram below. We may obtain eight distinct angles by drawing two parallel lines, and then drawing a transverse line through them.

Four pairs of matching angles will be created from all eight angles. One of the pairings is represented by angles F and B in the preceding diagram. If the two lines are parallel, corresponding angles are congruent.

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We can express the area of a triangle as half the product of its base and height:

Then, we can express the base in function of the known variables (area and height) as:

We replace with the known values (A=432 sq in, h=48 in) and calculate the base b:

Answer: the base is 18 inches.

Answer:

y=2x

y=x+2

there's ur answer.