Find the inverse function.
f(x) =
f-¹(x) =
=
=
2x+5
4
4x + [?]
[

Slope of AB = 4/3, Slope of BC = -2/7, Slope of CD = 4/3, Slope of AD = -2/7 and Quadrilateral ABCD is a parallelogram because both pairs of opposite sides are parallel.

We are given the coordinates of the quadrilateral ABCD as;

A(−5, 1), B(−2, 5), C(5, 3), and D(2, −1).

Slope of AB = (5 - 1)/(-2 + 5) = 4/3

Slope of BC = (3 - 5)/(5 + 2) = -2/7

Slope of CD = (-1 - 3)/(2 - 5) = 4/3

Slope of AD = (-1 - 1)/(2 + 5) = -2/7

Thus we can see that both pairs of slope are equal which denotes that both pairs are parallel.

Read more about Slope of quadrilateral at; https://brainly.com/question/16691874

#SPJ1

The equation of the line passing through the points is y = x + 2

The points are (-1, 1) and (4, 6).

The slope is calculated using:

m= (y2 - y1)/(x2 - x1)

So, we have:

m = (6 - 1)/(4 + 1)

Evaluate

m = 1

The equation of the line is then calculated as:

y = m(x -x1) + y1

This gives

y = 1 *(x + 1)  + 1

Evaluate

y = x + 2

Hence, the equation of the line passing through the points is y = x + 2

Read more about linear equations at:

https://brainly.com/question/14323743

#SPJ1

[tex]\therefore \sf{ LHS = \dfrac{tan \theta}{1 – cot \theta } + \dfrac{cot \theta}{1 – tan \theta}}[/tex]

[tex]\\[/tex]

[tex]\therefore\sf{ LHS = \dfrac{tan \theta}{1 – \dfrac{1}{tan \theta}} + \dfrac{ \dfrac{1}{tan \theta}}{1 – tan \theta} }[/tex]

[tex]\\[/tex]

[tex]\therefore\sf{ LHS = \dfrac{ tan^{2} \theta }{tan \theta – 1} + \dfrac{1}{tan \theta (1–tan \theta) } }[/tex]

[tex]\\[/tex]

[tex] \therefore\sf{ LHS = \dfrac{tan^{2} \theta}{tan \theta–1} – \dfrac{1}{tan \theta(tan \theta – 1 )}}[/tex]

[tex]\\[/tex]

[tex]\therefore \sf{LHS = \dfrac{tan^{3}\theta–1}{tan \theta(tan \theta –1)}}[/tex]

[tex]\\[/tex]

[tex]\therefore\sf{LHS = \dfrac{tan^{3}\theta–(1)^{3}}{tan\theta(tan\theta–1)}}[/tex]

[tex]\\[/tex]

[tex] \therefore\sf{ LHS = \dfrac{ (tan \theta -1)(tan^{2}\theta+tan\theta .1 + (1)^{2})} {tan \theta (tan\theta(tan \theta –1 )}}[/tex]

[tex]\\[/tex]

[tex] \therefore\sf{ LHS = \dfrac{(tan^{2} \theta×tan\theta .1+1)}{tan \theta}}[/tex]

[tex]\\[/tex]

[tex] \therefore\sf{ LHS = \dfrac{(sec^{2}\theta+tan\theta)}{tan\theta}}[/tex]

[tex]\\[/tex]

[tex] \therefore\sf{ LHS = \dfrac{sec^{2}\theta}{tan\theta} + \dfrac{tan \theta}{tan\theta}}[/tex]

[tex]\\[/tex]

[tex] \therefore\sf{ LHS = sec^{2}\theta \times cot \theta + 1 }[/tex]

[tex]\\[/tex]

[tex] \therefore\sf{ LHS = \dfrac{1}{cos^{2}\theta} \times \dfrac{cos \theta }{sin\theta}+1}[/tex]

[tex]\\[/tex]

[tex] \therefore\sf{ LHS = \left( \dfrac{ 1}{cos \theta} \times \dfrac{1}{sin \theta} \right) + 1}[/tex]

We have proven that the trigonometric identity [(tan θ)/(1 - cot θ)] + [(cot θ)/(1 - tan θ)] equals 1 + (secθ * cosec θ)

We want to prove the trigonometric identity;

[(tan θ)/(1 - cot θ)] + [(cot θ)/(1 - tan θ)] = 1 + sec θ

The left hand side can be expressed as;

[(tan θ)/(1 - (1/tan θ)] + [(1/tan θ)/(1 - tan θ)]

⇒ [tan²θ/(tanθ - 1)] - [1/(tan θ(tanθ - 1)]

Taking the LCM and multiplying gives;

(tan³θ - 1)/(tanθ(tanθ - 1))

This can also be expressed as;

(tan³θ - 1³)/(tanθ(tanθ - 1))

By expansion of algebra this gives;

[(tanθ - 1)(tan²θ + tanθ.1 + 1²)]/[tanθ(tanθ(tanθ - 1))]

Solving Further gives;

(sec²θ + tanθ)/tanθ

⇒ sec²θ * cotθ + 1

⇒ (1/cos²θ * cos θ/sin θ) + 1

⇒ (1/cos θ * 1/sin θ) + 1

⇒ 1 + (secθ * cosec θ)

Read more about Trigonometric Identities at; https://brainly.com/question/7331447

#SPJ1

Similar triangles are those triangles whose corresponding sides are in the same ratio. The triangles that are similar to ΔABC are ΔDEF and ΔJKL.

Similar triangles are those triangles whose corresponding sides are in the same ratio. And the corresponding angles measure the same.

For two triangles to be similar there sides should be in the same ratio.

For ΔABC ~ ΔMNO,

AB/MN should be equal to BC/NO,

AB/MN = 15/35 = 0.4286

BC/NO = 8/12 = 0.66

Thus, there are not similar triangles.

For ΔABC ~ ΔDEF,

AB/MN should be equal to BC/NO,

AB/DE = 15/22.5 = 0.66

BC/EF = 8/12 = 0.66

Thus, there are similar triangles.

For ΔABC ~ ΔGHI,

AB/GH should be equal to BC/HI,

AB/MN = 15/77 = 0.1948

BC/NO = 8/36 = 0.222

Thus, there are not similar triangles.

For ΔABC ~ ΔJKL,

AB/MN should be equal to BC/NO,

AB/JK = 15/60 = 0.250.25

BC/KL = 8/32 = 0.66

Thus, there are similar triangles.

Hence, the triangles that are similar to ΔABC are ΔDEF and ΔJKL.

Learn more about Similar Triangles:

https://brainly.com/question/25882965

#SPJ1

The correct option regarding whether the triangles are similar is given by:

Inaccurate. The triangles are not similar because angle M is not congruent to angle H, and angle N is not congruent to angle G.

Similar triangles are triangles that have congruent angles, that is, angles with the same measure.

Considering that the sum of the internal angles of a triangle is of 180º, the third angle of triangle FGH is given as follows:

98.6 + 61.1 + x = 180

x = 180 - (98.6 + 61.1)

x = 20.3º.

The second triangle has an angle of 20.3º, hence they are not similar, and the correct option is given by:

Inaccurate. The triangles are not similar because angle M is not congruent to angle H, and angle N is not congruent to angle G.

More can be learned about similar triangles at https://brainly.com/question/305520

#SPJ1

The possible values is  θ = π/4 and 5π/4

The branch of mathematics concerned with specific functions of angles and their application to calculations.

Given:

sin θ = cos θ

The above condition satisfied for θ = π/4 and 5π/4

sin π/4 = cos π/4 = 1/√2

sin  5π/4 = cos 5π/4 = -1/√2

Learn more about trigonometry here:

https://brainly.com/question/26719838

#SPJ1

Answer:

110

Step-by-step explanation:

Sally takes $110 from her bank account if she spent $54.00 for a round-trip ticket.

It is defined as the money spends on the utility, the amount of money is required to buy something, in other words, it is the outflow of money from the sole earner's income or the money incurred by any organization.

We have:

Sally took money from her bank account to go out of town for an audition.

The expeses = (7.90 + 15.10) ÷ (1 - 1/2) = $46

Total money = 54 + 46

Total money = $110

Thus, Sally takes $110 from her bank account if she spent $54.00 on a round-trip ticket.

Learn more about the expenses here:

brainly.com/question/17136150

#SPJ5

By the converse of the basic proportionality theorem, we can say DE║AB.

We need to check whether DE is parallel to AB.

If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

In triangle ABC, we can see on side AC, D is midpoint (∵AD=DC) and on side BC, E is midpoint (∵BE=CE).

Therefore, by the converse of the basic proportionality theorem, we can say DE║AB.

To learn more about the parallel lines visit:

https://brainly.com/question/16701300.

#SPJ1

The proof is shown below:

The line segment joining the mid points of any two sides of a triangle is parallel to the third side.

△ABC in which D and E are the mid points of AB and AC,.

If D and E are the mid points of AB and AC,

then AD=DB and AE=EC.

Thus,

AD/DB = AE/ EC

​

by the converse of Thales theorem, DE∥BC.

As, by theorem we can say that DE∥BC.

So, there is no other side parallel to DE.

​

Learn more about mid point theorem here:

https://brainly.com/question/13677972

#SPJ1

The trigonometric function gives the ratio of different sides of a right-angle triangle. The given problems can be solved as given below.

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

1st.) x = 5 /Sin(30°)

x = 10

!) sin(45°) = 4/x

x = 4/sin(45°)

x = 4√2

I) Cos(45°) = √3 / x

x = √3 / Cos(45°)

x = √6

E) Tan(60°) = 3√3 / x

x = 3√3 / 3

W) For isosceles right-triangle, the angle made by the legs and the hypotenuse is always 45°.

x = 45°

N) x² + x² = (7√2)²

x = 7

V) Tan(60°) = 7 / x

x = 7√3/3

K) x² + x² = (9)²

x = 9/√2

Y) Sin(60°) = 7√3/x

x = 14

M) Sin(30°) = x/11

x = 11/2

T) Sin(45°) = x/√10

x = √5

A) x + 2x + 90° = 180°

x = 30°

O) Sin(45°) = √2 / x

x = 2

R) Tan(30°) = x / 4

x = 4/√3 = 4√3 / 3

S) Sin(60°) = x / (10/3)

x = 5√3 / 3

Learn more about Trigonometric functions:

https://brainly.com/question/6904750

#SPJ1

The ordered pair that is on g(x) is (2, -3/400)

determine the ordered pair:

The function is given as:

f(x)=3/4(10)∧-x

The rule of reflection across the x-axis is:

g(x) = -f(x)

So, we have:

g(x) = -3/4(10)∧-x

Set x = 2.

So, we have:

g(2) = -3/4(10)∧-2

Evaluate the exponent

g(2) = -3/4 * 1/100

Evaluate the product

g(2) = -3/400

This means that:

(x, y) = (2, -3/400)

Hence, the ordered pair that is on g(x) is (2, -3/400)

Ordered pairs are pairs of two numbers (or variables) that are enclosed in parentheses and separated by commas. For example, (1, 2) is an ordered pair. Coordinate geometry represents points, and set theory represents elements of relations / Cartesian products.

Ordered pairs are pairs of numbers in a particular order. For example, (1, 2) and (-4, 12) are ordered pairs. The order of the two numbers is important. (1, 2) is not equivalent to (2, 1)-(1, 2) ≠ (2, 1).

Learn more about the ordered pair here:https://brainly.com/question/1528681

#SPJ4

Answer:

-40

Step-by-step explanation:

First you have to look at the difference between 8 and 10. which is 80, then because it takes two steps to go from 8 to 10 you divide 80 by two, which is 40. And because the values are decreasing it is -40.

The computation shows that the total number of chocolate bars when there are 280 orange flavored bars will be

The total number of chocolate bars when there are 280 orange flavored bars will be:

= Coconut + Honeycomb + Coffee + Orange + Strawberry

= (4/6 × 280) + (5/6 × 280) + (1/6 × 280) + 280 + (4/6 × 280)

= 1033

The total number when there are 960 coconut bars will be:

= Coconut + Honeycomb + Coffee + Orange + Strawberry

= 960 + (5/4 × 960) + (1/6 × 960) + (6/4 × 960) + 960

= 960 + 1200 + 160 + 1440 + 960

= 4720

The mean of 7, 2, and 9 will be:

= (7 + 2 + 9)/3

= 6

The mean of 5, 6, 6, and 5 will be:

= (5 + 6 + 6 + 5)/4

= 22/4

= 5.5

The mean of 2, 1, 2, 3, 3, 1 will be:

= (2 + 1 + 2 + 3 + 3 + 1) / 6

= 15/6

= 2.5

Learn more about computations on:

brainly.com/question/4658834

#SPJ1

The volume of the rectangular prism is 1/10 cubic units

The formula for calculating the volume of a rectangular prism is expressed as;

V = Bh

B is the base area

h is the height

Given the following parameters

B = 3/20 units²

h = 2/3 units

Substitute

V = 3/20 * 2/3

V = 2/20

V = 1/10 cubic units

Hence the volume of the rectangular prism is V = 1/10 cubic units

Learn more on volume of prism here: https://brainly.com/question/23766958

#SPJ1

Answer:8 1/2^3

Step-by-step explanation:

Step-by-step explanation:

[tex]sin2x=sinx\\sin2x-sinx=0\\2*sinx*cosx-sinx=0\\sinx*(2*cosx-1)-0\\sinx=0 \\x=\pi n\ \ \ \ \ x\in[0;2\pi ]\ \ \ \ \Rightarrow\\x_1=0\ \ \ \ x_2=\pi .\\2*cosx-1=0\\2*cosx=1\ |:2\\cosx=\frac{1}{2} \\x=б\frac{\pi }{3} +2\pi n\ \ \ \ \ x\in[0;2\pi ]\ \ \ \ \Rightarrow\\x_3=\frac{\pi }{3} \ \ \ \ \ x_4=\frac{5\pi }{3}.\\[/tex]

[tex]Answer: x=0,\ \frac{\pi }{3} ,\ 1\pi ,\ \frac{5\pi }{3} .[/tex]

Answer:

I think it's 87.5 or 87½

Step-by-step explanation:

I hope it helps you.

Answer:

c. x=8

Step-by-step explanation:

make me a brain list.

The changes that transform C(t) to F(t) is that the function C(t) is stretched vertically to form the function F(t)

The Fahrenheit function

The Celsius  function is given as:

C(t) = -0.30 (t – 12)² + 40  

The conversion from Celsius to Fahrenheit is

F(t) = 9/5 * C(t)

Hence, the Fahrenheit function is F(t) = 9/5 * C(t)

Convert values from Celsius to Fahrenheit

The values are t = 0, 12 and 24.

So, we have:

F(0) = -0.54(0 - 12)² + 72 = -5.76

F(12) = -0.54(12 - 12)² + 72 = 72

F(24) = -0.54(24 - 12)² + 72 = -5.76

The new function F(t)

The conversion from Celsius to Fahrenheit is

F(t) = 9/5 * C(t)

So, we have:

F(t) = 9/5 * (-0.30 (t – 12)² + 40)

Expand

F(t) = -0.54(t – 12)² + 72

Hence, the new function is F(t) = -0.54(t – 12)² + 72

The graph of function F(t)

See attachment for the graph of function F(t)

The changes that transform C(t) to F(t)

We have:

C(t) = -0.30 (t – 12)² + 40  

F(t) = 9/5 * C(t)

The above implies that the function C(t) is stretched vertically to form the function F(t)

Read more about composite functions at:

https://brainly.com/question/20379727

#SPJ1

Answer: 28.40 cans of soda

Step-by-step explanation:

Volume of cylinder: pi * r^2 * h

Volume of the can of soda = pi * 3.25^2 * 12 = 126.75 pi

Volume of the cylindrical pitcher = pi * 10^2 * 36 = 3600 pi

3600/126.75: 28.40 cans of soda

Answer:

28 whole soda cans or 28.4 soda cans (rounding to nearest tenth)

Step-by-step explanation:

The soda cans and the pitcher can be modeled as cylinders.

Volume of a cylinder

  [tex]\sf Volume=\pi r^2h[/tex]

where:

Diameter of circle

[tex]\sf d= 2r[/tex]

[tex]\sf \implies r=\dfrac{1}{2}d[/tex]

Volume of Soda can

Given values:

[tex]\begin{aligned}\sf \implies Volume & = \sf \pi (3.25)^2 \cdot 12\\ & = \sf 126.75 \pi \:\:cm^3\end{aligned}[/tex]

Volume of Pitcher

Given values:

[tex]\begin{aligned}\sf \implies Volume & = \sf \pi (10)^2 \cdot 36\\ & = \sf 3600 \pi \:\:cm^3\end{aligned}[/tex]

To calculate how many cans of soda the pitcher will hold, divide the volume of the pitcher by the volume of one soda can:

[tex]\begin{aligned}\implies \textsf{Number of soda cans} & = \dfrac{\textsf{Volume of Pitcher}}{\textsf{Volume of one soda can}}\\\\&= \sf\dfrac{3600 \pi}{126.75 \pi}\\\\& = \sf 28.402366...\end{aligned}[/tex]

Therefore, the pitcher can hold 28 soda cans (nearest whole can), or 28.4 soda cans (nearest tenth).

Answer:

v = 2u

Step-by-step explanation:

note that

2u = 2 (5, - 2 ) ← multiply each component by 2

    = (10, - 4) = v , then

v = 2u

The system of equation is y = 300 + 3x and y = 250 + 5x and  the number of visits is 25

The given parameters are:

Jim's Gym

Sally's Salon

The equation is calculated as:

Total (y) = Initial * Charges * Number of visits (x)

So, the system of equation is

y = 300 + 3x

y = 250 + 5x

We have:

y = 300 + 3x

y = 250 + 5x

Substitute y = 300 + 3x in y = 250 + 5x

300 + 3x = 250 + 5x

Evaluate the like terms

-2x = -50

Divide by -2

x= 25

Hence, the number of visits is 25

Read more about system of equations at

https://brainly.com/question/12895249

#SPJ1

7

Step-by-step explanation:

p = 1, q = 72 =49, q = 7

ookrndodnepwkpqq

[tex]\huge\textbf{Hey there!}[/tex]

[tex]\mathbf{-3pq^2 + q^3}[/tex]

[tex]\mathbf{= -3(2.9)(-1.3)^2 + (-1.3)^3}[/tex]

[tex]\mathbf{= -3(2.9)(-1.3)^2 - 1.3^3}[/tex]

[tex]\mathbf{= -8.7(-1.3)^2 - 1.3^3}[/tex]

[tex]\mathbf{= -8.7(1.69) - 2.197}[/tex]

=[tex]\mathbf{ -14.703 -2.197}[/tex]

[tex]\mathbf{= -16.9}[/tex]

[tex]\huge\textbf{Thus, your answer should be: \boxed{\mathsf{-16.9}}}}\huge\checkmark[/tex]

[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]

The test static used for this procedure is Aspin Welch's t-test.

What is Aspin Welch's T-test?

A variation of the Student's t-test used to determine if two sample means are substantially different is known as the Aspin Welch's T - test for Unequal Variances (also known as Welch's t-test, Welch's adjusted T, or unequal variances t-test). The test's degrees of freedom have been changed, which generally boosts the test's power for samples with unequal variance.

Formula for Aspin Welch's T - test

The t-statistic in Aspin Welch's T-test is given as,

t = [tex]\frac{X' - X}{\sqrt{\frac{S1^{2} }{N1^{2} } -\frac{S2^{2} }{N2^{2} } } }[/tex]

Here, X' is the mean of the sample

X is the mean of the population

S1 and S2 are the respective standard deviations for the two samples

N1 and N2 are the respective strength of samples.

Calculating t-statistic for Aspin Welch's T-test

Given that,

X'-X = 1.33

[tex]\sqrt{\frac{S1^{2} }{N1^{2} } -\frac{S2^{2} }{N2^{2} } } = 2.90[/tex]

∴ t = 1.33/2.90

t=0.458

Learn more about Aspin Welch's T-test here:

https://brainly.com/question/15870238

#SPJ4

The probability of both events occurring is  4/15

The given parameters are:

P(A) = 4/5

P(B) = 1/3

Because the events are independent, we have:

p(A and B) = P(A) * P(B)

This gives

P(A and B) = 4/5 * 1/3

Evaluate

P(A and B) = 4/15

Hence, the probability of both events occurring is  4/15

Read more about probability at:

https://brainly.com/question/11234923

#SPJ1

yd=

yd=

16x2+12x+18=3x=2x2+6x+9=3x=

sorry i try

Answer:

D

Step-by-step explanation:

Answer:

4.09 seconds

Step-by-step explanation:

simplify miles per hour to feet per second how many feet is a mile and how many seconds are in an hour you end up with 88 fps from 60 mph

now simply a football field is 360 feet so 360/88 is 4.09090909 etc

Your eyes off the road for 4.09 seconds.

The rate of change of position of an object in any direction is called the speed.

Given that, Taking your eyes off the road for how many seconds at 60 miles per hour means you have travelled blindly for half the length of a football field,

Converting 60 mph into fps

60 mph = 88 fps

The length of a football field = 360 ft

Time = 350/88

= 4.09 seconds.

Hence, you travelled for 4.09 seconds.

For more references on speed, click;

https://brainly.com/question/28224010

#SPJ1

Answer:

26.6 cubic yards

Step-by-step explanation:

Remark

What you have is a rectangle prism. It has an easy enough formula.

Formula

V = L *w * h

Givens

L = 10 yards

w =  8 yards

h = 1/3 yards

Solution

V = L*w*h

V = 10 * 8 * 1/3

V = 26.66 yds^3

The answer choice which represents a solution to the system of equations is; (–2, 10).

The system of equations as given in the task content is;

-6x - (2/5)y = 8

(1/2)x +3y = 29

Hence, by making x subject in equation 1 and substitution; we have;

x = (-0.4y -8)/6

Hence; (0.4y -8)/12 + 3y = 29.

(0.4y -8) + 36y = 348

35.6y = 356

y = 10

and x = (-0.4(10) -8)/6 = -2.

Read more on solution to the system of equations;

https://brainly.com/question/13729904

#SPJ1

Answer:

415

Step-by-step explanation:

20x20=400+15= 415

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathbf{20^2 + 15^1}[/tex]

[tex]\huge\textbf{Solving:}[/tex]

[tex]\mathbf{20^2 + 15^1}[/tex]

[tex]\mathbf{= 20\times 20 + 15\times 1}[/tex]

[tex]\mathbf{= 400 + 15}[/tex]

[tex]\mathbf{= 415}[/tex]

[tex]\huge\textbf{Answer:}[/tex]

[tex]\huge\boxed{\mathsf{415}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]