A parabola has an axis of symmetry at x = 5/12. The distance between its roots is 13/6. What is the equation of the parabola?

Answer:

[tex]y=-4x+5[/tex]

Step-by-step explanation:

The equation of a line with slope [tex]m[/tex] and [tex]y[/tex]-intercept [tex](0,b)[/tex] is [tex]y=mx+b[/tex].

Answer: the correct anserw is A.!

Step-by-step explanation:

The solution is

A) The vertical asymptote of the function f ( x ) is = -3

B) The holes in the graph of f ( x ) = ( 0 , 6 )

C) The horizontal asymptote of the function f ( x ) is = 6

What are Asymptotes?

An asymptote is a line that a curve approaches but never touches. A line where the graph of a function converges is known as an asymptote. When graphing functions, asymptotes are typically not required

There are 3 types of asymptotes

Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k. Horizontal Asymptote is when the function f(x) is tending to zero

Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k. Vertical asymptotes are defined when the denominator of a rational function tends to zero

Slanting asymptote (Oblique asymptote) - It is a slanting line and hence its equation is of the form y = mx + b

Given data ,

Let the function be f ( x ) = ( 6x² + 6x - 36 ) / ( x² + 3x )

A)

Now , to find the vertical asymptote

To find the vertical asymptote of a rational function, we simplify it first to lowest terms, set its denominator equal to zero, and then solve for x values

So , when x² + 3x = 0

x ( x + 3 ) = 0

So , x + 3 = 0

x = 0 is a hole in the graph

x = -3 is the vertical asymptote

B) The hole in the graph is ( 0 , 6 )

C)

Now , to find the horizontal asymptote

If both the polynomials have the same degree, divide the coefficients of the leading terms

So , 6x² and x² are the polynomials having the same degree

So , the coefficients are 6 and 1

y = (leading coefficient of numerator) / (leading coefficient of denominator)

y = 6 is the horizontal asymptote

Hence ,

A) The vertical asymptote of the function f ( x ) is = -3

B) The holes in the graph of f ( x ) = ( 0 , 6 )

C) The horizontal asymptote of the function f ( x ) is = 6

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Answer:

slope=3/2 y- intercept=9

Answer:

Slope: 3/2

y-intercept: 9

Step-by-step explanation:

Slope-Intercept Form is given in the form: [tex]y = mx+b[/tex], where [tex]m = \text{slope and }b=\text{y-intercept}[/tex].

So it's very convenient to have a linear equation in this form to identify the slope and y-intercept. To get into this form, we simply need to isolate the y-value.

We start with the initial equation:

[tex]-3x+2y=18[/tex]

The first step to isolating "y" is to move any terms on the same side as the "y" variable to the other side. So let's move the 3x term to the other side, by adding 3x to both sides.

[tex](-3x+3x)+2y=18+3x\implies 2y=18+3x[/tex]

From here, the only thing that is with the "y" variable is the coefficient. The [tex]2y[/tex] is the same thing as: [tex]2\ *\ y[/tex]. We want to get rid of the 2, which we do by dividing by 2, to cancel out the multiplication by 2.

[tex]\frac{2y}{2} = \frac{18 + 3x}{2} \implies y = \frac{18 + 3x}{2}[/tex]

Now from here we want to distribute the division by 2 as such:

[tex]y = \frac{18 + 3x}{2} \implies y = \frac{3}{2}x + \frac{18}{2} \implies y= \frac{3}{2}x + 9[/tex]

So now we have the equation:

[tex]y= \frac{3}{2}x + 9[/tex]

this is in the slope-intercept form:

[tex]y=mx+b[/tex]

in this form the coefficient of x is the slope, so 3/2 is the slope. The constant is the y-intercept, so 9 is the y-intercept.

Answer:

x= -3

Step-by-step explanation:

5x + 15 =0

5x= -15

x= -3

Answer:

x= -3

5x= -15

x = -15/3

x= -3

The answer to the Question based on Federal Income Tax return is Yes

What is Federal Income Tax Returm?

It is a kind of tax that people have to pay to government.

Federal Income tax has some of its special conditions also and so is suggested by its name

Solution:

As MJF husband is aged 66 and his Gross income is 25200$ and this amount of money is not very less but infact very high hence there is fixed percentage of tax decided by government per fixed amount of money and MJF husband has to pay that amount of tax to government

Hence answer to the Question is Yes

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The equations of the perpendicular lines are matched as follows:

y = 1/3x + 4 → y = -3x - 4.

y = 2/5x - 7 → y = -5/2x + 7.

y = -5/2x + 8 → y = 2/5x - 6.

y = -2x + 6 → y = 1/2x + 3.

y = 7/5x - 9 → y = -5/7x - 11.

If the equations of lines are written in slope-intercept form as y = mx + b, where the slope is the value of m, then the slope of lines that are perpendicular to each other will be negative reciprocal of each other.

For example, if the equation of a line is y = 1/2x + 5, the equation of a line that is perpendicular to it would have a slope of -2.

y = 1/3x + 4 has a slope of 1/3. The negative reciprocal of 1/3 is -3. Therefore, the line that is perpendicular to it would be, y = -3x - 4.

y = 2/5x - 7 has a slope of 2/5. The negative reciprocal of 2/5 is -5/2. Therefore, the line that is perpendicular to it would be, y = -5/2x + 7.

y = -5/2x + 8 has a slope of -5/2. The negative reciprocal of -5/2 is 2/5. Therefore, the line that is perpendicular to it would be, y = 2/5x - 6.

y = -2x + 6 has a slope of -2. The negative reciprocal of -2 is 1/2. Therefore, the line that is perpendicular to it would be, y = 1/2x + 3.

y = 7/5x - 9 has a slope of 7/5. The negative reciprocal of 7/5 is -5/7. Therefore, the line that is perpendicular to it would be, y = -5/7x - 11.

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Equivalent expression to the given expression [ ( 5/7)² ( 1/3)⁻³]⁻¹ is equal to

Option d. ( 7 /5)² ( 1/3)³.

As given in the question,

Given expression is equal to :

[ ( 5/7)² ( 1/3)⁻³]⁻¹

Apply law of exponent power to power we get,

( mᵃ nᵇ )ˣ =  (m)ᵃˣ × (n )ᵇˣ

( x /y)⁻ᵃ = ( y /x)ᵃ

Here m = 5/ 7, n = 1/3 , a = 2 , b = -3 and x = -1

Equivalent expression of the given expression is:

[ ( 5/7)² ( 1/3)⁻³]⁻¹

= ( 5 / 7 )^(2 × -1) ( 1 / 3)^(-3 × -1)

= ( 5 / 7 )⁻² ( 1 / 3)³

= ( 7 / 5 )²× ( 1 / 3)³

Therefore , equivalent expression of [ ( 5/7)² ( 1/3)⁻³]⁻¹  is equal to the

option d.( 7 /5)² ( 1/3)³.

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the slope of the line is zero, as change in y cordintae is 0.

What is the slope of line?

Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.

In the given line in the graph, the change in y coordinate is 0.

We know that slope = change in y / change in x

As the change in y coordinate is 0.

The slope of the line will be zero.

Hence, the slope of the line is zero.

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The domain of s = 13.5h is (0, 1, 2, 3, 4).

The range of s = 13.5h is (0, 13.5, 27, 40.5, 54).

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

s = 13.5h

For h = 0,

s = 0

For h = 1,

s = 13.5

For h = 2,

s = 27

For h = 3,

s = 40.5

For h = 4,

s = 54

Thus,

The domain is (0, 1, 2, 3, 4).

The range is (0, 13.5, 27, 40.5, 54).

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Y Intercept is the point where a line or curve crosses the y-axis of a graph or in other words where x=0.

Knowledge of the y-intercept can be used when graphing lines or when writing an equation in slope-intercept form.

Formula to calculate y-intercept.

We get the y-intercept by using the equation of a straight line which is;

y = mx + b

Where;

m is the gradient of the slope

b is the y-intercept.

We can use the following formula to calculate the y-intercept.

y – a = m ( x – b )

a and b being a point on a line.

Example:

Suppose you have a straight line whose gradient is 3 and a point 2,1, calculate its y-intercept.

Since the y-intercept is when x=0, therefore;

y – 2 = 3 ( x – 1 )

y – 2 = 3x – 1

y = 3x – 1

Therefore, the number that has replaced b is -1, which means that -1 is the y-intercept.

Answer:

Step-by-step explanation:

First question. Answer is

Answer:

[tex]\dfrac{2(x+4)}{x}[/tex]    or     [tex]2 + \dfrac{8}{x}[/tex]

Step-by-step explanation:

Rewrite the problem as a fraction.

[tex]\dfrac{6(x+4)^2}{3x(x+4)}[/tex]

Then, represent the squared term on the top as two values to make it easier to cancel.

[tex]\dfrac{6(x+4)(x+4)}{3x(x+4)}[/tex]

Now, cancel an x+4 from the top and bottom.

[tex]\dfrac{6(x+4)}{3x}[/tex]

Finally, divide the numerator and denominator by 3.

[tex]\dfrac{2(x+4)}{x}[/tex]     or     [tex]2 + \dfrac{8}{x}[/tex]

[tex]\bf{\dfrac{6(x+4)2}{3x(x+4)} \iff \ Eliminate \ (x+4).}\\ \\ \bf{That\:is, isolating\:the \ common \ factor \ \dfrac{\not{6}\times2 }{\not{3}x} \ \--\to\dfrac{2\times2}{x}=\dfrac{4}{x} } \\ \\ \boldsymbol{\sf{\dfrac{4}{x} }}\bf{\iff}\boxed{\boxed{\bf{Answer}}}[/tex]

Answer:

s = 9

Step-by-step explanation:

calculate the slope m through the 2 points using the slope formula and equate to - 5

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (7, 3 ) and (x₂, y₂ ) = (s, - 7 )

m = [tex]\frac{-7-3}{s-7}[/tex] = [tex]\frac{-10}{s-7}[/tex]

equate m to slope of - 5

[tex]\frac{-10}{s-7}[/tex] = - 5 ← multiply both sides by s - 7

- 10 = - 5(s - 7) ← divide both sides by - 5

2 = s - 7 ( add 7 to both sides )

9 = s

For the given expression -21 is not a irrational number.

What is irrational number?

In mathematics, all real numbers that are not rational are referred to as irrational numbers. Irrational numbers can't be expressed as the ratio of two integers, in other words.

Any real number that cannot be expressed as the ratio of two integers—that is, as p/q, where p and q are both integers—is an irrational number. For instance, there is no integer or fraction that equals the square root of 2.

Consider the given expression,

(-14) + (-7)

Solving this, we get

(-14) + (-7) = -14 - 7 = -21

Here 21 can be written in the form p/q.

⇒ -21 = -21/1

So, -21 is a rational number.

Hence, -21 is not a irrational number.

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Answer:

8

Step-by-step explanation:

72 ÷ 9 = 8

Answer:

8

Step-by-step explanation:

72 divided by 9 is 8

Answer:

A reflection over the x axis

Step-by-step explanation:

x is the horizontal line we are reflecting one across it to get the other

[tex]\int\limits\frac{4}{x^2+2} \, dx[/tex] =  [tex]2^{\frac{3}{2} }tan^{-1}(\frac{x}{\sqrt{2} })[/tex] + C where C is the integrating constant.

What do you mean by integration?

The summing of discrete data is indicated by the integration. To determine the functions that will characterise the area, displacement, and volume that result from a collection of little data that cannot be measured separately, the integral is calculated.

The idea of integration has evolved to address the following issues:

once the derivatives of the problem function have been determined.

to determine the region enclosed by a function's graph under specific restrictions.

Given function f(x) = [tex]\frac{4}{x^2+2}[/tex]

[tex]\int\limits\frac{4}{x^2+2} \, dx[/tex]

Substitute u = [tex]\frac{x}{\sqrt{2} }[/tex]

⇒ [tex]\frac{du}{dx} =\frac{1}{\sqrt{2} }[/tex]

⇒ dx = [tex]\sqrt{2}[/tex] du

= [tex]\frac{2^{\frac{5}{2}} }{2u^2+2}du[/tex]

On simplifying

= [tex]2^{\frac{3}{2} }[/tex][tex]\int\limits\frac{1}{u^2+1} \, du[/tex] .........(1)

Now  [tex]\int\limits\frac{1}{u^2+1} \, du[/tex] = [tex]tan^{-1} (u)[/tex]

Substitute this value in equation (1)

= [tex]2^{\frac{3}{2} }tan^{-1}(u)[/tex]

Substitute the value of u here

= [tex]2^{\frac{3}{2} }tan^{-1}(\frac{x}{\sqrt{2} })[/tex]

Therefore, [tex]\int\limits\frac{4}{x^2+2} \, dx[/tex] =  [tex]2^{\frac{3}{2} }tan^{-1}(\frac{x}{\sqrt{2} })[/tex] + C where C is the integrating constant.

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Answer: the slope of the line is 2 or 2/1

Step-by-step explanation:

Answer:

3 cats are orange and The other 1 is not

Because

Answer:

14 gallons

Step-by-step explanation:

456 - 28.5g = 5

28.5g =399

G=14

The age of Lance and Chad are 7 years and 20 years respectively.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let age of Lance's is  = L

Age of Chad's = C

Given that The sum of Lance's and Chad's ages is 27 years. Chad is 6 years younger than twice Lance's age.

The system of equations that represents this situation is;

L + c = 27

C - 6 = 2L

2L - c = -6------ (1)

Therefore,

⇒ ( 2L - c ) + (L + c) = 21

⇒ 3L = 21------- (2)

L = 7

C = 20

Therefore the age of each person;

7 years and 20 years

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The statement B is as x approaches positive infinity f(x) approaches positive infinity is true.

What is the definition of the limit?

A point or level beyond which something does not or may not extend or pass.

We have to check for continuity by evaluating 2ˣ and -x² - 4x + 1

at the breakpoint x = 0

2⁰ is 1 and -x² - 4x + 1 is also 1,

So these two functions approach the same value as x approaches 0.

Now do the same thing with

-x² - 4x + 1  and (1/2)x + 3 at x = 2;

The first comes out to -11 and the second to 4.  

Thus, this function is not continuous at x = 2.  

We must reject statement A.

for D we have as x increases without bound,

(1/2)x  + 3

also increases without bound.  

Therefore the statement D is true statement.

Statement C is  False,

because the quadratic has a maximum -x² - 4x + 1 has a maximum at

x = -b/[2a],

x = -(-4) / [-2],

x = -2

There are no limitations on the values of the input, x.

A is also a false negative number are in real numbers.

Therefore, the statement B is as x approaches positive infinity f(x) approaches positive infinity is true.

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Answer:

The Answer is B for Edmentum users

Step-by-step explanation:

Answer: i think it's 942,480

Step-by-step explanation:

i just multiplied all of the numbers but i'm probably wrong srry

Answer:

7986m^2

Step-by-step explanation:

140-102=38

area of triangle:

(38*66)/2=1254m^2

area of rectangle:

66*102=6732m^2

total area:

1254+6732=7986m^2

The predicted height for someone with a femur length of 55 cm is of:

175 cm.

The linear function in this problem is obtained using the point-slope format, which is given as follows:

y - y' = m(x - x').

In which:

From the image given at the end of the answer, two points on the line are given as follows:

(35, 139) and (40, 151).

Given two points the slope is calculated as the change in y divided by the change in x, hence:

m = (151 - 139)/(40 - 35) = 2.4.

Considering the first point, the definition of the line is given as follows:

y - 139 = 2.4(x - 40).

The predicted height for someone with a femur length of 55 cm is y when x = 55, hence:

y - 139 = 2.4(x - 40).

y - 139 = 2.4(55 - 40)

y = 175 cm.

The graph of the linear function is given by the image shown at the end of the answer.

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Jack spend $15 on sweets

Jack spend $35 on magazines

Jack saves $50

Given,

Jack spends 15 % of his pocket money on sweets and 35 % on magazines.

Jack save the rest ; 100 - (15 + 35) = 100 - 50 = 50%

Here,

If Jack has a pocket money of $100

The money he spends on sweets = 15% of 100 = $15

The money he spends on magazines = 35% of 100 = $35

Then,

The money he saves = 50% of 100 = $50

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Answer:

b=12

Step-by-step explanation:

1) The annual decay rate of the exponential function is given as follows: 12.94%.

2) The number of people who started the rumor is of 10.

3) The number of people who will have heard the rumor after 3 days is given as follows: 96 people.

For item 1, the format of the exponential function is given as follows:

A(t) = A(0)(1 - r)^t.

In which r represents the annual decay rate.

The half-life of Radium-228 is 5.75 years, hence:

A(5.75) = 0.5A(0).

Thus the annual decay rate of the exponential function is given as follows:

0.5A(0) = A(0)(1 - r)^5.

(1 - r)^5 = 0.5

Applying the fifth root to both sides:

1 - r = (0.5)^(1/5)

1 - r = 0.8706

r = 1 - 0.8706

r = 0.1294 = 12.94%.

Then for items 2 and 3 we just obtain the numeric values.

The number of people who started the rumor is N(0), hence:

N(0) = 600/(1 + 59e^(-0.7 x 0)) = 600/60 = 10 people.

The number of people who heart the rumor after three days is N(3), hence:

N(3) = 700/(1 + 69e^(-0.8 x 3)) = 96 people.

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