Please help with this geometry question!

Answer:

[tex]f(x) = 20x - 4 \\ substitute \: y \: for \: f(x) \\ y = 20x - 4 \\ interchange \: x \: and \: y \\ x = 20y - 4 \\ swap \: the \: sides \: of \: the \: equation \\ 20y - 4 = x \\ move \: the \: constant \: to \: the \: right \: hand \\ 20y = x + 4 \\ divide \: both \: sides \: by \: 20 \\ y = \frac{1}{20} x + \frac{1}{5} \\ substitute \: f {}^{ - 1} (x) \: for \: y \\ f {}^{ - 1} (x) = \frac{1}{20} x + \frac{1}{5} [/tex]

The domain of the inverse of a relation is the same as the range of the original relation. In other words, the y-values of the relation are the x-values of the inverse.

Thus, domain of f(x): x∈R = range of f¯¹(x)

and range of f(x): x∈R =domain of f¯¹(x)

Answer:

-2

Step-by-step explanation:

When x = 1, 3x² + 2x - 7 = -2.

The first car consumed 25 gallons of fuel while the second car consumed 30 gallons of fuel.

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

Let x represent the first car consumption and y represent the second car consumption, hence:

x + y = 55   (1)

Also:

15x + 20y = 975   (2)

From both equations:

x = 25, y = 30

The first car consumed 25 gallons of fuel while the second car consumed 30 gallons of fuel.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

I didn't got the question well

Answer:

122,599

Step-by-step explanation:

In words, what I am is asking is 17.7% of what number is 21,700.  I will need to change 17.7% to a decimal.  To do that, I move the decimal 2 places to the left.  Then solve.

.177 x w = 21700  Divide both sides by .177

w = 122,599

hi,

the function is given with it's canonic form.  

canonic form is  :  f(x) = a ( x-α)² + β

α  and β are the value of the coordonnates of the vertex.

so here we  have : ƒ(x) = 2(x−1)² +3

with α = 1  and β = 3

so vertex is  V (1;3)

So yes, answer is   A.

The given differential equation has characteristic equation

[tex]r^5 - 4r^4 + 4r^3 - r^2 + 4r - 4 = 0[/tex]

Solve for the roots [tex]r[/tex].

[tex]r^3 (r^2 - 4r + 4) - (r^2 - 4r + 4) = 0[/tex]

[tex](r^3 - 1) (r^2 - 4r + 4) = 0[/tex]

[tex](r^3 - 1) (r - 2)^2 = 0[/tex]

[tex]r^3 - 1 = 0 \text{ or } (r-2)^2=0[/tex]

The first case has the three cubic roots of 1 as its roots,

[tex]r^3 = 1 = 1e^{i0} \implies r = 1^{1/3} e^{i(0+2\pi k)/3} \text{ for } k\in\{0,1,2\} \\\\ \implies r = 1e^{i0} = 1 \text{ or } r = 1e^{i2\pi/3} = -\dfrac{1+i\sqrt3}2 \text{ or } r = 1e^{i4\pi/3} = -\dfrac{1-i\sqrt3}2[/tex]

while the other case has a repeated root of

[tex](r-2)^2 = 0 \implies r = 2[/tex]

Hence the characteristic solution to the ODE is

[tex]y_c = C_1 e^x + C_2 e^{-(1+i\sqrt3)/2\,x} + C_3 e^{-(1-i\sqrt3)/2\,x} + C_4e^{2x} + C_5xe^{2x}[/tex]

Using Euler's identity

[tex]e^{ix} = \cos(x) + i \sin(x)[/tex]

we can reduce the complex exponential terms to

[tex]e^{-(1\pm i\sqrt3)/2\,x} = e^{-x/2} \left(\cos\left(\dfrac{\sqrt3}2x\right) \pm i \sin\left(\dfrac{\sqrt3}2x\right)\right)[/tex]

and thus simplify [tex]y_c[/tex] to

[tex]y_c = C_1 e^x + C_2 e^{-x/2} \cos\left(\dfrac{\sqrt3}2x\right) + C_3 e^{-x/2} \sin\left(\dfrac{\sqrt3}2x\right) \\ ~~~~~~~~ + C_3 e^{-(1-i\sqrt3)/2\,x} + C_4e^{2x} + C_5xe^{2x}[/tex]

For the non-homogeneous ODE, consider the constant particular solution

[tex]y_p = A[/tex]

whose derivatives all vanish. Substituting this into the ODE gives

[tex]-4A = 69 \implies A = -\dfrac{69}4[/tex]

and so the general solution to the ODE is

[tex]y = -\dfrac{69}4 + C_1 e^x + C_2 e^{-x/2} \cos\left(\dfrac{\sqrt3}2x\right) + C_3 e^{-x/2} \sin\left(\dfrac{\sqrt3}2x\right) \\ ~~~~~~~~ + C_3 e^{-(1-i\sqrt3)/2\,x} + C_4e^{2x} + C_5xe^{2x}[/tex]

Applying the triangle sum theorem, we have:

First angle measure = 35°

Second angle = 70°

Third angle = 75°

According to the triangle sum theorem, all angles in a triangle will give a sum of 180 degrees.

First angle measure = x

Second angle = 2x

Third angle = (2x + x) - 30 = 3x - 30

x + 2x + 3x - 30 = 180 [triangle sum theorem]

6x - 30 = 180

6x = 180 + 30

6x = 210

x = 210/6

x = 35

First angle measure = x = 35°

Second angle = 2x = 2(35) = 70°

Third angle = 3x - 30 = 3(35) - 30 = 75°

Learn more about the triangle sum theorem on:

https://brainly.com/question/7696843

#SPJ1

The probability of all three events happening when the dies are rolled is; 0.0083

A) On the first die, it has 6 sides and 3 must come out, that is, 1 event out of 6 possible, therefore the probability is: 1/6

B) On the second die, it has 20 sides and if 19 or 20 can come out, that is 2 events out of 20 possible, so the probability is: 2/20 = 1/10

C) On the third die, which is 12 sides, an odd number can come out. The odd numbers would be 1, 3, 5, 7, 9, 11; i.e, 6 events out of 12 possible numbers.

Thus, the probability would be: 6/12 = 1/2

The final probability would be;

(1/6) * (1/10) * (1/2) = 0.0083

Read more about Probability of rolling a Die at; https://brainly.com/question/14192140

#SPJ1

Answer:

12u²

Step-by-step explanation:

area of a regular quadrilateral is always base x vertical height.

the base here is clearly 4 (just count the squares)

draw an imaginary line connecting the bottom right corner to the line before the top right corner (the line should be vertical)

count the squares here too and you get 3.

so the area = 3 x 4,

the area is 12u²

Answer: 4

Step-by-step explanation:

[tex]1102_{3}=2+0(3)+1(9)+1(27)=38\\\\212_{n}=2+1(n)+2(n^2)=2n^2 + n+2\\\\\implies 2n^2 + n+2=38\\\\2n^2 + n-36=0\\\\(n-4)(2n+9)=0\\\\n=-\frac{9}{2}, 4[/tex]

However, as the base must be positive, n=4.

Answer:

Step-by-step explanation:

∫(cos(1/x)/x² dx

[tex]put~\frac{1}{x} =t\\diff.\\\frac{-1}{x^2} dx=dt\\\int(- cos~t~)dt=-sin~t+c\\=-sin (\frac{1}{x} )+c[/tex]

Hence, the missing internal angle is [tex]15[/tex].

What is the angle?

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays.

Angles are also formed by the intersection of two planes. These are called dihedral angles.

Here given that,

[tex]Q = 87 + 40Q = 127X + 127 + 38 = 180X = 180 - 127 - 38X = 15[/tex]

Hence, the missing internal angle is [tex]15[/tex].

To know more about the angle

https://brainly.com/question/15277238

#SPJ2

The point that the graphs of f and g have in common are (1,0)

The given functions are:

f(x) = log₂x

and

g(x) = log₁₀x

We know that logarithm of 1 is always zero.

This means that irrespective of the base, the y-values of both functions will be equal to 0 at x=1

Therefore the point the graphs of f and g have in common is (1,0).

Learn more about graph on:

https://brainly.com/question/19040584

#SPJ1

Answer:

Its (1,0)

and the second one is A. F

Step-by-step explanation:

answer : 2 1/2

divide y by x

divide  2 1/2 by 1

its 2 1/2

10 divided by 4 is also

2 1/2

17 1/2 divided by 7 is also

2 1/2

Answer:

8by + 2ax - 4bx - 4ay

Step-by-step explanation:

I assume you mean expand so:

(a - 2b)(3x - 5y) + (2b - a)(x - y)

3ax - 5ay - 6bx + 10by + 2bx - 2by - ax + ay

Now collect like terms:

2ax - 4ay - 4bx + 8by

This is your answer but in a better order:

8by + 2ax - 4bx - 4ay

The amount that the insurance company will pay is $1800.

It should be noted that the insurance company will pay John for the expenses of his injuries and repair of the car.

For the injury, he will get:

= $500 + ($1400 - $100)

= $500 + $2300

= $1800

Therefore, the amount is $1800.

Learn more about insurance on:

brainly.com/question/2141892

#SPJ1

The five-number summary is: 41, 56, 65, 67, 69.

The box plot that represents the data is: option B.

Correct statement for the shape of the distribution is: B. the distribution is skewed to the left.

The five-number summary is a five data value that describes the distribution of a data set, which include: lower and upper quartiles, minimum and maximum values, and the median of the data.

The five-number summary is used to construct a box plot.

Given the data, 65, 56, 67, 68, 66, 66, 67, 69, 48, 57, 59, 68, 59, 41, 44, the five-number summary for the data is:

This means that the box plot that will represent this data will have a box that ranges between 56 and 67, and the data at both whiskers will be 41 and 69, while the data at the point where the vertical line divides the box would be 65.

Thus, the box plot that represents the data is: option B.

The median is closer to the right of the third quartile/upper quartile, therefore: B. the distribution is skewed to the left.

Learn more about five-number summary on:

https://brainly.com/question/24809873

#SPJ1

Answer:

Angle D & Angle E

Step-by-step explanation:

Angle C & Angle F are ALTERNATE EXTERIOR angles.

Angle B & Angle E are CONSECUTIVE angles.

Angle D & Angle G are CORRESPONDING angles.

The height of candle 4 is twice that of candle B after 2.4 hours.

For candle, A time is taken for 100% bearning=4hour.

For 1 hour, it burns for 25%(100/4)

After 1 hr.[tex]\frac{25}{100}[/tex]

After x hours, the amount burnt[tex]=\frac{x}{4}[/tex]

Amount left[tex]=1-\frac{x}{4} =\frac{4-x}{4}[/tex]

Let's not presume that candle B's height will be half that of candle A after x hours.

After x hours, part vemacing [tex]=1-\frac{x}{3} =\frac{3-x}{3}[/tex]

[tex]\frac{4-x}{4} =1\frac{3-x}{3}[/tex]

Height of candle A[tex]=2[/tex]×Height of candle B.

[tex]12-3x=24-8x[/tex]

   ⇒[tex]5x=12[/tex]

        [tex]x=\frac{12}{5}[/tex]

           [tex]=2.4[/tex]

The height of candle 4 is twice that of candle B after 2.4 hours.

To learn more about the candles of equal height, refer to:

https://brainly.com/question/15493665

#SPJ9

Answer:

0.375 second and 3.5 second

Step-by-step explanation:

The position can be modeled by a quadratic function [tex]\displaystyle{h=-16t^2+62t+6}[/tex]. We are tasked to find the time when a ball reaches a height of 27 feet. Therefore, let h = 27:

[tex]\displaystyle{27=-16t^2+62t+6}[/tex]

Solve for t:

[tex]\displaystyle{27-6=-16t^2+62t}\\\\\displaystyle{21=-16t^2+62t}\\\\\displaystyle{16t^2-62t+21=0}[/tex]

Since the equation is quite complicated and more time-consuming to solve, i'll skip the factoring or quadratic part:

[tex]\displaystyle{t=0.375, 3.5}[/tex]

After done solving the equation, you'll get t = 0.375 and 3.5 seconds. These solutions are valid since both are positive values and time can only be positive.

Hence, it'll take 0.375 and 3.5 seconds for a ball to reach 27 feet.

The equation of the line that is perpendicular to y = 1/6 is: B. x = -8.

Perpendicular lines have slope values that equals -1 when multiplied together, that is, they are negative reciprocals.

Given the equation, y = 1/6, the slope is 0. This means it is a vertical line, therefore, the line that is perpendicular to it would automatically be a vertical line with an undefined slope which passes through (,8, -2).

The line therefore, would intercept the x-axis at -8. The equation would be: x = -8.

Equation of the perpendicular line is therefore: B. x = -8.

Learn more about the equation of perpendicular lines on:

https://brainly.com/question/19044397

#SPJ1

The electricity that is used, on average, by a security system in 2 years is 4.3Kw.

The average power consumption of the security system given is 2.7 watt.

(a) Electricity consumption in 2 years

in KW-h = (24*365*2.7)/1000 = 4.304 KWh

(b) As per US data CO2 emissions = 0.99 pound per kilowatt-h.

Hence here CO2 emissions = 4.3 × 0.99 = 4.2610 pounds / KW-h.

= 4.3 pound / KW-h.

Learn more about electricity on:

https://brainly.com/question/776932

#SPJ1

Based on the angles of a + b and b + c, the value of b can be calculated to be 40°.

As this is a triangle, all the internal angles must add up to 180°.

This means that:

a + b + c = 180°

As we have the value of b + c, this becomes:

a + 100 = 180

a = 80°

b is therefore:

a + b = 120

80 + b = 120

b = 120 - 80

= 40 °

Full question is:

If in triangle abc, angle a + angle b= 120° and angle b + angle c = 100°, then find angle b.

Find out more on the internal degrees of a triangle at https://brainly.com/question/7888180.

#SPJ1

Answer:

Step-by-step explanation:

ascxne rdsjazs bcbnnnncccd

The solution set that represent the solution to the inequality is (16,+infinity)

The mathematical representation of the statement given is expressed as shown below;

4 1/2 x - 9 1/2 >62.5

Convert to improper fraction to have:

9/2 x - 19/2 > 62.5

Find the LCM

9x-19/2 > 62.5

9x-19 > 125

9x > 125 + 19

9x > 144

x > 16

Hence the solution set that represent the solution to the inequality is (16,+infinity)

Learn more on inequality here: https://brainly.com/question/11613554

#SPJ1

Answer: 23,5%

Step-by-step explanation:

[tex]23\frac{1}{2} %[/tex]% = [tex]\frac{47}{200}[/tex] = 0,235 = 23,5%

There are 238 passengers in the plane in 2010

The given parameters are:

Weight = 150 pounds and Passenger = 270 --- Year 2000

Weight = 170 pounds --- Year 2010

Represent the parameters using the following inverse proportion

Weight * Passenger= Fixed

So, we have:

150 * 270 = 170 * Passenger

Divide both sides by 170

150 * 270/170 = Passenger

Evaluate

238 = Passenger

Rewrite as

Passenger = 238

Hence, there are 238 passengers in the plane in 2010

Read more about variation at:

https://brainly.com/question/6499629

#SPJ1

Answer:

Second option

Step-by-step explanation:

The range is the set of output values a function can take. As shown in the table, as x is substituted in, y is the corresponding value.

The area of the desktop is 12. 5 feet square

The formula for area of a rectangle;

Area = length × width

Length = 2. 5 feet

Width = 5 feet

Area = 2. 5 × 5

Area = 12. 5 feet square

Thus, the area of the desktop is 12. 5 feet square

Learn more about area of a rectangle here:

https://brainly.com/question/14137384

#SPJ1