Which ordered pair is a solution of the equation?

y-3=5(x-2) Choose 1 answer:

A

Only (2,3)

B

Only (3,2)

C

Both (2,3) (3,2)

D

Neither

Answer:

f^-1(y) =[ In(x-2) + 1] /3

Step-by-step explanation:

The inverse of this expression is to find x

Now taking In of both sides we have

y=2^3x-1

In y = In2^3x-1

In y = (3x- 1)In 2

(Iny / In2) + 1= 3x

x =[ (Iny / In2) + 1] /3

Therefore the inverse of y is

f^-1(y) =[ (Inx / In2) + 1] /3

f^-1(y) =[ In(x-2) + 1] /3

The equation of the inverse of the provided equation, which is equal to the reverse of the original equation, is y=(ln(x-2)+1)/3.

The inverse of an equation is the reverse of the original equation. The equation and the inverse of it has symmetry in each other.

To find the inverse of equation, we have to interchange the variable of equation to each other.

The given equation is,

[tex]y=2^{3x-1}[/tex]

Taking log both side of the equation,

[tex]\ln y = \ln 2^{3x-1}[/tex]

Use the log of power and simplify the equation further, as,

[tex]\ln y = \ln 2^{3x-1}\\\ln y = (3x-1)\ln 2\\\dfrac{\ln y}{\ln 2} = (3x-1)\\\ln (y-2)= (3x-1)\\\ln (y-2)+1= 3x\\x=\dfrac{\ln (y-2)+1}{3}[/tex]

Interchange the place of x and y,

[tex]y=\dfrac{\ln (x-2)+1}{3}[/tex]

This is the required inverse equation.

Thus, the equation of the inverse of the provided equation which is equal to the reverse of the original equation, is y=(ln(x-2)+1)/3.

Learn more about the inverse of an equation here;

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Answer:

Chord

Step-by-step explanation:

I believe the word you are looking for is a chord.

Answer:

32 pupils in a class

Step-by-step explanation:

You are going to divide 192 by 6 to figure out the average amount per class.

Step-by-step explanation:

4x2 + x3

Rearrange

x3 + 4x2

x2 (x + 4)

Answer:

It is 4 because length PO is also 4 and TR is across from it.

Step-by-step explanation:

Answer:

The answer is option B

Step-by-step explanation:

I cant exactly explain it cus i dont remember but i know i got it right lol

but here goes

after she proves that AD is congruent to the other sides, all she has left to prove is ∠A≅∠B and AB≅BC.

'Tis how you get thine answer

(╯°□°）╯

Answer:

Option 1

Step-by-step explanation:

ABCD is a parallelogram, Julie wants to prove that ABCD is also a square.

Remember that a parallelogram has opposite sides equal.

So,

AB ≅ CD

AD ≅ BC

The 4 triangles are congruent. The bases of the triangles are vertically opposite to each other and are congruent. We can use the definition of a parallelogram to prove AB ≅ BC.

Answer:

Step-by-step explanation:

a. The explanatory variables in this case is the mothers BMI on which the child's BMI is determined.

The response variable is the child's BMI which is also the outcome variable that exists if a child has an obese parent.

Other lurking variables may include the diets and exercise plan of either of these two variables.

b. No, this study cannot be used to conclude that maternal obesity causes obesity in daughters if the lurking variables are not dealt with.

Answer:

h = 76

Step-by-step explanation:

2 + h - 48 = 30

h + 2 - 48 = 30

h - 46 = 30

h - 46 + 46 = 30 + 46

h = 76

Answer:

2+h-48=30

2-48+h=30

-46+h=30

h=30+46

∴h=76

Answer:

D

Step-by-step explanation:

f(x ) = [tex]x^{2} - 1\\[/tex]

inverse ----> f(x) = y = x

x = [tex]y^{2}[/tex] - 1

[tex]y^{2} = x + 1[/tex]

y = ± [tex]\sqrt{x + 1}[/tex]

Answer:

84

Step-by-step explanation:

This is in the form

ax^2 + bx +c

3x^2 +12x +5

a =3  b = 12  c =5

The discriminant is

b^2 - 4ac

12^2 - 4 * 3 *5

144 - 60

84

Answer:

F-1(x)=7/(x+9)

Step-by-step explanation:

Change F(x) to y so    y=7/x -9

Swap variables x=7/y -9

Solve x+9=7/y

7/(x+9)=y

Then change y to F inverse

F-1(x)=7/(x+9)

Thats ur inverse!!!

Answer:

(x+9)/7

Step-by-step explanation:

Let f(x) = y;

y =7/x - 9

y + 9 = 7x

x = (y + 9)/7

Substitute x for y and X = f^{-1}(x)

f^{-1}(x) =(x+9)/7 this is the inverse of f(x)

Complete Question

The complete question is shown on the first uploaded image  

Answer:

it is convergent and  the solution is  [tex]= \frac{33 \pi }{2}[/tex]

Step-by-step explanation:

From the question we are given  

        [tex]\int\limits^1_0 {\frac{33}{\sqrt{1-x^2} } } \, dx[/tex]

When integrated

         [tex]= 33 sin^{-1} x \left | \ 1} \atop {0}} \right.[/tex]

        [tex]= 33[ \frac{\pi }{2} - 0][/tex]

        [tex]= \frac{33 \pi }{2}[/tex]

This implies that the integral converges

Answer:

85 + 35=120

Step-by-step explanation:

85 + 35= 120

85 - 35= 50

the difference is fifty

Answer:

The composite figure is made up of a rectangular prism and  square pyramid

Step-by-step explanation:

The figure on top is square pyramid since the base is a square and the 4 sides are triangles.  The bottom is a rectangular prism since the figure is made up of side rectangular faces

Answer:

square pyramid

also the figure has 896 cm2

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is:

Health issues are a concern of managers, especially as they evaluate the cost of medical insurance. A recent survey of 150 executives at Elvers Industries, a large insurance and financial firm located in the Southwest, reported the number of pounds by which the executives were overweight. Compute the mean and the standard deviation.

Pounds Overweight Frequency

0 up to 6 14

6 up to 12 42

12 up to 18 58

18 up to 24. 28

24 up to 30. 8

Solution:

This is grouped data. We would determine the midpoint or class mark, x of each class by taking their averages.

The table would become

Class. x f fx

0 up to 6 (0+6)/2 = 3 14 42

6 up to 12 (6+12)/2 = 9 42 378

12 up to 18 (12+18)/2 = 15 58 870

18 up to 24 (18+24)/2= 21 28 588

24 up to 30 (24+30)/2 = 27 8 216

Summation f = 14 + 42 + 58 + 28 + 8 = 150

Summation fx = 42 + 378 + 870 + 588 + 216 = 2094

Mean = Summation fx/Summation f

Mean, m = 2094/150 = 13.96

Standard deviation = √summation of f(x - m)²)/(n - 1)

We would create another column on the table

f x x - m f(x - m)²

14 3 - 10.96 1681.7024

42 9 - 4.96 1033.2672

58 15 1.04 62.7328

28 21 7.04 1387.7248

8 27 12.04 1159.6928

Total = 5325.12

Standard deviation = √5325.12/150 - 1)

Standard deviation = 5.98

Answer:

20 pi (sign)

Step-by-step explanation:

khan answer trust me bro

Answer:

33.0220147 % reduction

Step-by-step explanation:

Take the original price and subtract the new price

14.99-10.04 = 4.95

Divide by the original price

4.95/14.99 =.330220147

Change to percent form

33.0220147 %

Answer:

G1 : 0.3(2000) = 600

G2: 0.2(2000) = 400

G3: 0.15(2000) = 300

G4: 2000/15=150

Answer:

[tex] f(x) = x^2 -8x -20[/tex]

We know that one factor is (x-10). We know that we need to find two values that added we got -8 and multiplied we got -20. So then we can set the following options:

[tex] a(10) = -20[/tex]

[tex] a-10= -8[/tex]

And solving for a we got:

[tex] a = -8+10=-2[/tex]

And we got:

[tex] a = -2[/tex]

So then the other factor would [tex] x +2[/tex]

Step-by-step explanation:

For this case we have the following expression:

[tex] f(x) = x^2 -8x -20[/tex]

We know that one factor is (x-10). We know that we need to find two values that added we got -8 and multiplied we got -20. So then we can set the following options:

[tex] a(10) = -20[/tex]

[tex] a-10= -8[/tex]

And solving for a we got:

[tex] a = -8+10=-2[/tex]

And we got:

[tex] a = -2[/tex]

So then the other factor would [tex] x +2[/tex]

Answer:

Step-by-step explanation:

Answer:

x = 10/√2 ≈ 7.07

Step-by-step explanation:

Comenzaremos por dividir el triángulo en dos partes y definir H, como en la figura adjunta.

Aplicando el teorema de Tales, sabemos que:

[tex]\dfrac{l/2}{H}=\dfrac{x/2}{h}\\\\\\\dfrac{l}{H}=\dfrac{x}{h}[/tex]

También sabemos que, dado que el tirángulo menor es la mitad que el triángulo mayor, la relación entre áreas es:

[tex]\dfrac{A}{A_x}=\dfrac{lH/2}{xh/2}=\dfrac{lH}{xh}=2[/tex]

Dado que formamos dos triángulos rectángulos, podemos despejar el valor de H como:

[tex](l/2)^2+H^2=l^2\\\\H^2=l^2-(l/2)^2=10^2-5^2=100-25=75\\\\H^2=\sqrt{75}[/tex]

Podemos entonces despejar x de la siguiente manera:

[tex]h=\dfrac{H}{l}\cdot x=\dfrac{lH}{2x}\\\\\\2x^2\dfrac{H}{l}=lH\\\\\\2x^2=l^2\\\\\\x=\dfrac{l}{\sqrt{2}}=\dfrac{10}{\sqrt{2}}\approx7.07[/tex]

Answer:

11

Step-by-step explanation:

absolute value is always a positive number so

3|-5| -2|-2| =

3 * 5 -2*2

follow PEMDAS

15 -4 = 11

Answer:

12r-32

Step-by-step explanation:

Distribute the 4 between the different numbers.

3r * 4 = 12r and 8 * 4 = 32

So...you end up with 12r-32

Hi! I hope you're enjoying your day!

Let's recall that the Distributive Property states that

a(b+c)=ab+ac

Where

a, b, and c can be either constants (numbers like 4) or variables (letters like d)

Simplify:

4(3r-8)

4 times 3r is equal to 12r

12r- (4*8)

[tex]\boxed{\boxed{\bold{12r-32}}}[/tex]

Hope everything is clear.

If you have any questions, please comment.

#LearningIsFun

Answer:

The correct option is

(A). When given two names for the same quantity, you can use algebra to solve the equations.

Step-by-step explanation:

I had thesame quiz, lucky you...next time put the options :)

Answer:

x = 40

Step-by-step explanation:

Given 2 secants to a circle from an external point, then

The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant, that is

8(8 + x) = 12(12 + 20) ← distribute parenthesis on both sides

64 + 8x = 12 × 32 = 384 ( subtract 64 from both sides )

8x = 320 ( divide both sides by 8 )

x = 40

Answer:

The standard deviation of the population is 4.5 minutes.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation of the population [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

In this question:

[tex]s = 0.5, n = 81[/tex]

So

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.5 = \frac{\sigma}{\sqrt{81}}[/tex]

[tex]\sigma = 9*0.5 = 4.5[/tex]

The standard deviation of the population is 4.5 minutes.

Answer: Around a circular table, ten people can be seated 362880 ways.

We establish the conditions of the exercise:

It is a Combination so we use the formula:

    [tex]\boldsymbol{\sf{_{n}C_{r}=\cfrac{n!}{n\cdot (n-r)!} }}[/tex]

          [tex]\boldsymbol{\sf{n=10\; \; \; \; \; r=10}}[/tex]

We substitute and solve:

  [tex]\boldsymbol{\sf{_{10}C_{10}=\cfrac{10!}{10\cdot (10-10)!}=9!=9\cdot8\cdot7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1=362880}}[/tex]

Answer:

Step-by-step explanation:3x-y=18

y=27

Therefore 3x-(27)=18

3x=18+27..Nb when the 27 is now being added instead of subtracted.

3x=45

3x/3=45/3 Nb the 3 is now being divided instead of being multiplied.

Therefore X=15

Answer:

The answer is B.

Step-by-step explanation:

Given that the total angle in a triangle is 180°. So in order to find x, you have to subatract 95° and 57° from 180°

[tex]x + 95 + 57 = 180[/tex]

[tex]x = 180 - 95 - 57[/tex]

[tex]x = 28[/tex]

Answer:

-30

Step-by-step explanation:

(3-5)4(2) – 16+ 2= -2*8-14= -16-14= -30