hey can you please help me posted picture of question

Hey Can You Please Help Me Posted Picture Of Question

Answers

Answer 1
Answer:
f⁻¹(x) = [tex] \frac{7x-3}{4} [/tex]

Explanation:
To get the inverse of a function, we have to follow these steps:
1- replace f(x) with y
2- swap the x and y variables
3- solve for y
4- replace y with f⁻¹(x)

Applying this to the given as follows:
f(x) = [tex] \frac{4x-3}{7} [/tex]

Step 1: replace f(x) with y:
y = [tex] \frac{4x-3}{7} [/tex]

Step 2: swap the x and y variables:
x = [tex] \frac{4y-3}{7} [/tex]

Step 3: solve for y:
7x = 4y - 3
4y = 7x - 3
y = [tex] \frac{7x-3}{4} [/tex]

Step 4: replace y with f⁻¹(x):
f⁻¹(x) = [tex] \frac{7x-3}{4} [/tex]

Hope this helps :)

Related Questions

The table shows the number of boys and girls that have black, blonde, brown, or red hair color. What is the probability that a student is a boy with red hair? (round to nearest hundredth)

Hair Color Boys Girls
Black 4 5
Blonde 4 6
Brown 10 8
Red 2 1

Answers

2 of the 40 students are boys with red hair. If one is chosen at random, ...
  the probability that the student is a boy with red hair is 2/40 = 0.05.

Answer:

0.05

Step-by-step explanation:

Given :

Hair Color Boys Girls

Black          4                 5

Blonde          4                  6

Brown          10                 8

Red                  2                   1

Solution :

Since ware required to find the probability that a student is a boy with red hair.

Total no. of boys with red hair = 2

Total no. of students = 4+4+10+2+5+6+8+1=40

Thus the probability  that a student is a boy with red hair = [tex]\frac{\text{No. of boys with red hair }}{\text{total no. of students }}[/tex]

⇒[tex]\frac{2}{40}[/tex]

⇒[tex]\frac{1}{20}[/tex]

⇒[tex]0.05[/tex]

Hence the probability that a student is a boy with red hair is 0.05

Which ordered pair is the vertex of y = [x - 3]+ 2?

A.(2, –3)

B.(–3, 2)

C.(3, 2)

D.(2, 3)

Answers

An absolute value function without transformations, [tex]y = |x|[/tex], has a vertex at (0, 0).  The transformations here are to shift the function right 3 and up 2.  The vertex would then be at (3, 2).  Your answer should be C.

Evaluate: 18.4 ÷ 2.3 × 3.4 + 13.812 =

Answers

The answer would be 41.012

kaelyn has 14 coins that have a vaule of $ 1.20. she only has dimes and nickles. how many nickles does kaely have

Answers

Kaelyn has 14 coins made of dimes and nickels valued at $1.20. By setting up a system of equations and solving for the number of nickels, we determine that she has 4 nickels.

The student is asking a mathematical question involving coin values and combinations. When working with combinations of coins, we typically use a system of equations or algebraic expressions. Kaelyn has 14 coins consisting of dimes and nickels with a total value of $1.20. To systematize, let's let D be the number of dimes and N be the number of nickels. The following equations represent the relationships between the coins:

D + N = 14 (since there are 14 coins in total)0.10D + 0.05N = 1.20 (representing the total value of the coins in dollars)

Multiply the second equation by 100 to deal with whole numbers:

10D + 5N = 120

From the first equation, we can express D as:

D = 14 - N

Substitute this into the second equation:

10(14 - N) + 5N = 120140 - 10N + 5N = 120-5N = -20N = 4

So, Kaelyn has 4 nickels and the rest are dimes.

If you have 2500 to invest at 6 interest compounded quarterly. For how many years will the money need to be invested for that amount to triple?

Answers

For this case we have the following equation:
 P (t) = P * (1 + r / n) ^ (n * t)
 Where,
 P: initial investment
 r: interest rate
 n: periods
 Substituting values:
 3 * 2500 = 2500 * (1 + 0.06 / 4) ^ (4 * t)
 Rewriting:
 3 = (1,015) ^ (4 * t)
 Clearing t:
 log1.015 (3) = log1.015 ((1.015) ^ (4 * t))
 4 * t = log1.015 (3)
 t = (1/4) * log1.015 (3)
 t = 18.45 years
 Answer:
 
the money will need to be invested 18.45 years for that amount to triple

Chloe puts 4 soaps and two bottles of lotion in each gift basket. She has 127 soaps and 85 bottles of lotion. How many gift baskets can Chloe complete?

Answers

127/4 = 31.75 = 31
85/2 = 42.5 = 43

She can only make 31 full gift baskets with the amount of soap she has.

Therefore, Chloe can make 31 gift baskets.

On Sunday, 370 people bought tickets to the county fair. Tickets cost $7 for adults and $3 for children. The total revenue from ticket sales on Sunday was $1750. The system of equations below represents the number of people and total sales for the county fair on Sunday, where x represents the number of child tickets and y represents the number of adult tickets.

Answers

Number of child tickets: x
Number of adult tickets: y

1) x+y=370
2) 3x+7y=1750

Using the method of substitution
a) Isolating y in the first equation:
1) x+y=370→x+y-x=370-x→y=370-x

b) Replacing y=370-x in the second equation:
2) 3x+7y=1750→3x+7(370-x)=1750

c) Solving for x: Distributive property:
3x+7(370)-7x=1750
3x+2590-7x=1750

Adding similar terms:
-4x+2590=1750

-4x+2590-2590=1750-2590
-4x=-840

Dividing both sides of the equation by -4:
-4x/(-4)=-840/(-4)
x=210

Replacing x=210 in the first equation:
1) y=370-x→y=370-210→y=160

Answer:
The number of child tickets was 210 and
the number of adult tickets was 160

A die is tossed. find the odds against rolling a number greater than 11.

Answers

0% The # can be no greater than 6

BRAINLIEST!!!

Which statement about a dilation with a scale factor of 3 is true?

Answers

The picture shows a scale factor of 3/2, not 3. The only equation that makes any sense is the first one:
  3/2 = 6/4

_____
The others are just plain false.
Answer:

The statement which is true about the dilation is:

                        [tex]\dfrac{3}{2}=\dfrac{6}{4}[/tex]    

Step-by-step explanation:

We know that the dilation transformation changes the size of the original figure but the shape is preserved.

The dilation transformation either reduces the size of the original figure i.e. the scale factor is less than 1 or enlarges the size of the original figure i.e. the scale factor is greater than 1.

The ratio of the corresponding sides of the two figure are equal.

i.e.

                 [tex]\dfrac{3}{2}=\dfrac{6}{4}[/tex]

Unsaved If you are studying the effects of UV rays on eyesight and you group 10 people together and make them wear sunglasses for 10 weeks and see if their eyesight is affected and then take another group and do not give them sunglasses and test their vision after 10 weeks, what is the treatment ? note this is not an ethical study.

sunglasses.
10 weeks.
eyesight.
vision test.

Answers

In a statistical experiment, a treatment is the factor or the independent variable which is under the control of experimenter. Experimenter can change the conditions of this factor according to his will and according to needs of experiment.

In the given example, the experimenter make 10 people wear sunglasses and check their eyesight after 10 weeks. To another group he does not give sunglasses and check their eyesight after 10 weeks.

So, sunglasses are such a factor which are under the control of experimenter. So the treatment in this case is sunglasses.

Hence 1st option is the correct answer.

Answer:

Sunglasses

Step-by-step explanation:

The period if a function is 4pi
How many cycles of the function occur in a horizontal length of 12pi?
(answer was 3)
QUESTION: Which type of transformation of the parent function would be shown by the graph?

Answers

The answer is horizontal stretch

Answer:

She's right the answer is a horizontal stretch.

Which of the following functions are their own inverses? Select all that apply.
a. t(p) = p
b. y(j) = -1/j
c. w(y) = -2/y
d. d(p) = 1/x^2

Answers

A function is its own inverse if it is symmetrical about the line y=x. This is the case for functions t, y, w. Function d(x) = 1/x^2 is symmetrical about the line x=0, but is not symmetrical about the line y=x.

The appropriate choices are ...
  a. t(p) = p
  b. y(j) = -1/j
  c. w(y) = -2/y

Answer:

a,b and c.

Step-by-step explanation:

We have to find the the functions that are their own inverses.

a.t(p)=p

Then the inverse function of given function is

[tex]p=t^{-1}(p)[/tex]

Therefore, the given function is inverse function of itself.

Hence, option a is true.

b.y(j)=[tex]-\frac{1}{j}

Let y(j)=y then we get

[tex]y=-\frac{1}{j}[/tex]

[tex]j=-\frac{1}{y}[/tex]

[tex]j=-\frac{1}{y(j)}[/tex]

[tex]j=-\frac{1}{\frac{-1}{j}}[/tex]

[tex]j=j[/tex]

Hence, the function is inverse of itself.Therefore, option b is true.

c.[tex]w(y)=-\frac{2}{y}[/tex]

Suppose that w(y)=w

Then [tex]w=-\frac{2}{y}[/tex]

[tex]y=-\frac{2}{w}[/tex]

[tex]w(y)=-\frac{2}{-\frac{2}{w}}[/tex]

[tex]w(y)=w[/tex]

[tex]w(y)=-\frac{2}{y}[/tex]

Hence, the function is inverse function of itself.Therefore, option c is true.

d.[tex]d(p)=\frac{1}{x^2}[/tex]

Let d(p)=d

If we replace [tex]\frac{1}{x^2}by p then we get

[tex]d=\frac{1}{x^2}[/tex]

[tex]x^2=\frac{1}{d}[/tex]

[tex]x=\sqrt{\frac{1}{d}}[/tex]

[tex]x=\sqrt{\frac{1}{d(p)}[/tex]

Hence, the function is not self inverse function.Therefore, option d is false.

HELP
______________________

Answers

The answer is the third one, since it goes up between the two by 50.
x*50 = y

Answer:

The answer is the third option/choice.




Write an equation of the line with the given​ slope, m, and​ y-intercept (0,b) m=-3/5 b=7/10

Answers

y=-3/5x+7/10 is the correct answer. y=mx+b
Final answer:

The equation of the line with a slope of -3/5 and a y-intercept of 7/10 is y = (-3/5)x + (7/10).

Explanation:

To write an equation of a line with a given slope (m) and y-intercept (0,b), we use the slope-intercept form of a linear equation which is y = mx + b. In this case, the slope is -3/5 and the y-intercept is 7/10.

Substituting these values into the slope-intercept formula, the equation of the line is y = (-3/5)x + (7/10).

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Yanis fires pottery in a kiln. He decides to measure the rate of change of temperature of the pottery over time. What would be an appropriate unit for Yanis's purpose?

Answers

degrees celcius/ hour

Answer with explanation:

Pottery is on a Kiln.

Unit of temperature can be Kelvin(°K) or Degree Celsius(°C) or Fahrenheit(°F).

Unit of time is second, minute and hour.

Rate of change of temperature of the pottery over time can be written as

     [tex]1.=\frac{\text{Degree Celsius}}{\text{Second}}\\\\2.=\frac{\text{Degree Celsius}}{\text{Minute}}[/tex]

Internationally , Kelvin is used as S.I unit of Temperature.

So,Yanin can use

  [tex]1.=\frac{\text{Kelvin}}{\text{Second}}\\\\2.=\frac{\text{Kelvin}}{\text{Minute}}[/tex]

 as Rate of change of temperature of the pottery over time.

hey can you please help me posted picture of question

Answers

The correct answer is D. Graph D

Find the Vertex of   y = 3x2+7x+2

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 3 , is positive (greater than zero). 

 Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions. 

 Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex. 

 For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is  -1.1667  

 Plugging into the parabola formula  -1.1667  for  x  we can calculate the  y -coordinate : 
  y = 3.0 * -1.17 * -1.17 + 7.0 * -1.17 + 2.0 
or   y = -2.083
Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = 3x2+7x+2
Axis of Symmetry (dashed)  {x}={-1.17} 
Vertex at  {x,y} = {-1.17,-2.08}  
 x -Intercepts (Roots) :
Root 1 at  {x,y} = {-2.00, 0.00} 
Root 2 at  {x,y} = {-0.33, 0.00} 

We can find the roots of the given equation to determine its graph.

3x²+7x+2=0

Solving using factorization.

3x²+6x+x+2=0

3x(x+2)+1(x+2)=0

(3x+1)(x+2)=0

This means the roots of the equation are x = -2 and x = -1/3

Now from the graphs determine which one has the roots at  these two points. We can observe that Graph D has the roots at x=-2 and x=-1/3

So the answer to this question is option D

A cirlce with a radius of 8 cm rotates 30 degrees in one second. Determine the angle of rotation in radians.
Angle:___ w:___ v:___

Answers

same as before, since 180° is π, how much is 30° in radians?

[tex]\bf \begin{array}{ccll} de grees&radians\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 180&\pi \\\\ 30&x \end{array}\implies \cfrac{180}{30}=\cfrac{\pi }{x}\implies x=\cfrac{30\pi }{180}\implies x=\cfrac{\pi }{6}\\\\ -------------------------------\\\\ \stackrel{angular~velocity}{w}=\cfrac{\stackrel{central~angle}{\frac{\pi }{6}}}{\stackrel{time}{1~s}}\implies w=\cfrac{\pi }{6}~\frac{radians}{seconds}[/tex]

[tex]\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ ------\\ r=8\\ \theta =\frac{\pi }{6} \end{cases}\implies s=8\cdot \cfrac{\pi }{6}\implies s=\cfrac{4\pi }{3} \\\\\\ \stackrel{linear~velocity}{v}=\cfrac{\stackrel{arc's~length}{\frac{4\pi }{3}}}{\stackrel{time}{1~s}}\implies v=\cfrac{4\pi }{3}~\frac{cm}{seconds}[/tex]

A right triangle has one side, s, and a hypotenuse of 12 meters. Find the area of the triangle as a function of s.
A) A(s) = 2s
144 - s2
B) A(s) = s
144 - s2
C) A(s) = 2s
12 - s2
D) A(s) = 12s
144 - s2

10)
The base of a ladder is placed 5 feet away from a 13 foot tall wall. What is the minimum length ladder needed to reach the top of the wall (rounded to the nearest foot)?
A) 12 ft
B) 13 ft
C) 14 ft
D) 15 ft

Answers

A(s) equals 1/2 s square root of 144 minus s squared.. As s and r are the sides and the area of the triangle are 1/2(s)(r)

Answer: A(s) = [tex]\frac{s\sqrt{144-s^{2} } }{2}[/tex] ; 10) c) 14ft

Step-by-step explanation:  Area of a triangle is: A = [tex]\frac{b.h}{2}[/tex]

where:

b is base of a triangle

h is height of a triangle

For this right triangle, it is known one side, s, and hypotenuse, 12. To determine the other side, we use Pythagoras Theorem:

hypotenuse² = side² + side²

[tex]12^{2} = s^{2} + x^{2}[/tex]

[tex]x^{2} = 12^{2} - s^{2}[/tex]

[tex]x^{2} = 144 - s^{2}[/tex]

x = [tex]\sqrt{144 - s^{2} }[/tex]

To determine the Area of the right triangle as function of s:

A = [tex]\frac{b.h}{2}[/tex]

A = [tex]\frac{1}{2}[/tex](s.x)

A = [tex]\frac{1}{2}[/tex] . (s.[tex]\sqrt{144 - s^{2} }[/tex])

Therefore, the area of the right triangle is:

A = [tex]\frac{1}{2}[/tex] . (s.[tex]\sqrt{144 - s^{2} }[/tex])

The ladder and the wall form a right triangle. The height of it is 13 ft, the base is 5ft and the hypotenuse is the length of the ladder. So, to find the minimum length, use Pythagoras Theorem:

hypotenuse² = side² + side²

h² = 13² + 5²

h² = 169 + 25

h = [tex]\sqrt{194}[/tex]

h = 14

The minimum length the ladder has to have to reach the top is 14 ft.

The exponential function y = 2(3)x grows by a factor of 9 between x = 1 and x = 3. What factor does it grow by between x = 5 and x = 7?

Answers

Given the function y=2(3)^x
the growth factor between x=1 and x=3 is given by:
[2(3)^3]/[2(3)^1]
=54/6
=9
thus the growth factor between x=5 and x=7 will be as follows:
[2(3)^7]/[2(3)^5]
simplifying the above we get:
=[3^7]/[3^5]
=3^(7-5)
=3^2
=9

Answer:

9

Step-by-step explanation:

Help ASAP PLEASE!!! match the term with the appropriate definition.

Answers

1) x-1>5→x-1+1>5+1→x>6: Option F. x>6, open dot at 6 and shaded to the right

2) 5x+1>=11→5x+1-1>=11-1→5x>=10→5x/5>=10/5→x>=2: Option J. x>=2, closed dot at 2 and shaded to the right

3) x-7>-4→x-7+7>-4+7→x>3: Option H. x>3, open dot at 3 and shaded to the right

4) -2x<6→(-1/2)(-2x<6)→(-1/2)(-2x)>(-1/2)(6)→x>-3: Option G. x>-3, open dot at -3 and shaded to the right

5) 4<-4x→(-1/4)(4<-4x)→(-1/4)(4)>(-1/4)(-4x)→-1>x→x<-1: Option B. x<-1, open dot at -1 and shaded to the left

6) -2x+3<-7→-2x+3-3<-7-3→-2x<-10→(-1/2)(-2x<-10)→
(-1/2)(-2x)>(-1/2)(-10)→x>5: Option A. x>5, open dot at 5 and shaded to the right

7) 2x<=6→2x/2<=6/2→x<=3: Option I. x<=3, closed dot at 3 and shaded to the left

8) 3(x+4)>8x-6→3x+12>8x-6→3x+12-3x+6>8x-6-3x+6→18>5x→
18/5>5x/5→18/5>x→x<18/5: Option E. x<18/5, open dot at 18/5 and shaded to the left

9) -3x+4<-x+2→-3x+4+3x-2<-x+2+3x-2→2<2x→2x>2→2x/2>2/2→x>1: Option C. x>1, open dot at 1 and shaded to the right

10) -2(x-4)>5-(x+2)→-2x+8>5-x-2→-2x+8>3-x→-2x+8+2x-3>3-x+2x-3→
5>x→x<5: Option D. x<5, open dot at 5 and shaded to the left

help me out with this

Answers

The process is similar to (and easier* than) adding three 4-digit numbers. Add the numbers in each column.

The sum is ...
  (2+1-3)x³ +(-4+6+2)x² +(6-8-4)x +(-3+12-7)
  = 0x³ +4x² -6x +2

The sum is 4x² -6x +2


_____
* The process is easier because there are no "carry" operations from one column to another as there may be when adding multi-digit numbers.

What is the null hypothesis if we want to test the hypothesis that the mean score on campus 1 is higher than on campus 2? h0: µ1 = 0?

Answers

μ1 <= μ2
____________

No, the null hypothesis will be, there is no difference between the mean scores of campus 1 and campus 2.

Therefore, the null hypothesis would be:

H₀: µ₁ - µ₂ = 0

where µ₁ is the population mean score of campus 1 and µ₂ is the population mean score of campus 2.

What is mean by Subtraction?

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Now, We test this null hypothesis against the alternative hypothesis that the mean score on campus 1 is higher than on campus 2:

Hₐ: µ₁ > µ₂

Hence, if there is sufficient evidence to reject the null hypothesis and conclude that there is a significant difference between the mean scores of campus 1 and campus 2.

Thus, No, the null hypothesis will be, there is no difference between the mean scores of campus 1 and campus 2.

Therefore, the null hypothesis would be:

H₀: µ₁ - µ₂ = 0

where µ₁ is the population mean score of campus 1 and µ₂ is the population mean score of campus 2.

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Ben buys a car for $50,000. The value of the car decreases at a rate of 4% per year. How much will the car be worth in 3 years? A. $48,000 B. $44,237 C. $45,082 D. $43,270

Answers

Given that the value of $50000 car decreases by 4%  per year, the value after 3 years will be given by exponential form:
y=abˣ
where:
a=initial value
b=decreasing rate
x=time in years
from the information:
a=50000, b=0.96, x=3
thus
y=50000(0.96)³
simplifying we get:
y=$44, 236.8
~$44237

Answer:
B. $44,237

Solve the equation 3x+5y=4
for y

Answers

Answer:

y = (4 -3x)/5

Step-by-step explanation:

Find the terms containing y. If they are all on one side of the equation (it is), then identify the terms not containing y. Subtract those. Then, divide by the coefficient of y.

3x +5y = 4

5y = 4 - 3x . . . . . non-y term subtracted

y = (4 -3x)/5 . . . . divide by the coefficient of y

_____

If you like, you can rearrange this to slope-intercept form:

... y = -3/5x +4/5

what is the product of r and t if R equals 5.33 and T equals 0.5

Answers

product is multiplication so product of r and t would be r x t

replace the letters with the numbers you have 5.33 x 0.5 = 2.665

Mr. Morris left work at 5:53 P.M. and drove 47 minutes to his home. What time did he arrive?

Answers

Hi there!

First, we know that the remaining time until 6 PM is 7 minutes. So, we can subtract 7 minutes from 47 and now we have 40 minutes left to add and it is 6 PM. Next, since 40 is not more than 60 minutes, we'll add 40 minutes to 6 PM. This leaves us with the time 6:40.

ANSWER:
He arrived at 6:40


Hope this helps!! :)
If there's anything else that I can help you with, please let me know!

Answer:

6:40

Step-by-step explanation:

What is the area of sector GPH?

Answers

The area of the entire circle = pi r^2
The area of the shaded area = (40/360) * pi r^2
r = 9 cm

Area of the shaded area = 1/9 * 3.14 * 9^2
Area of the shaded area = 3.14 * 9
Area of the shaded area = 28.26

Notice one of the 9s disappeared. Where did it go?
You could begin the problem by writing out 9^2
Area = 1/9 * 3.14 * 9 * 9 Notice that 1/9 will cancel out 1 of the nines.

28.26 yds = Shaded area. 

The area of sector GPH is [tex]\(\frac{1}{4}\pi r^2\).[/tex]

To find the area of sector GPH, we use the formula for the area of a sector of a circle, which is given by [tex]\(\frac{\theta}{360^\circ} \times \pi r^2\)[/tex], where [tex]\(\theta\)[/tex] is the central angle of the sector in degrees, and [tex]\(r\)[/tex] is the radius of the circle.

Given that the central angle of sector GPH is [tex]\(90^\circ\) (or \(\frac{\pi}{2}\)[/tex] radians, since[tex]\(180^\circ\) is \(\pi\) radians)[/tex], and the radius [tex]\(r\)[/tex] is unspecified, we can express the area of the sector in terms of [tex]\(r\).[/tex]

 Using the formula for the area of a sector:

[tex]\[ \text{Area of sector GPH} = \frac{\theta}{360^\circ} \times \pi r^2 \][/tex]

Substituting [tex]\(\theta = 90^\circ\):[/tex]

[tex]\[ \text{Area of sector GPH} = \frac{90^\circ}{360^\circ} \times \pi r^2 \][/tex]

Simplifying the fraction:

[tex]\[ \text{Area of sector GPH} = \frac{1}{4} \times \pi r^2 \][/tex]

 So, the area of sector GPH is [tex]\(\frac{1}{4}\pi r^2\)[/tex], which is one-fourth of the area of the entire circle. This makes sense because the sector represents a quarter of the circle's area due to its [tex]\(90^\circ\)[/tex] central angle.

ln(x+2)-ln(4x+3)=ln(1/2*x)

Answers

ln(x+2)-ln(4x+3)=ln(1/2*x)

Using properties of  logarithms

[tex] \frac{ln(x+2)}{ln(4x+3)} = ln \frac{x}{2} \\ \\ \frac{x+2}{4x+3} = \frac{x}{2} \\ \\2(x+2)=x(4x+3) 2x+4=4x^2+3x \\ \\ 4 x^{2} +x-4=0 \\ \\ x= \frac{-b+/- \sqrt{b^{2}-4ac} }{2a} \\ \\ x= \frac{ -1+/-\sqrt{1+64} }{8} \\ \\ x_{1} = \frac{-1+ \sqrt{65} }{8} \\ \\ x_{2} = \frac{-1- \sqrt{65} }{8} Check: When you substitute x_{2} into \\ \\ ln(4x+3)=ln(4* \frac{-1- \sqrt{65} }{8} ) =ln( \frac{-1- \sqrt{65} }{2} ) you will get negative number under ln, that is impossible , [/tex]

so x2 is not a solution of this logarithmic equation.

Only x1 is a solution.


Amy has 5 yards of border to put around a garden. She uses all the border to make four sections that are the same length. Which expession does not equal the length of one these sections in yards?

Answers

I added a screenshot of the question along with the given choices

Answer:
F. 4 ÷ 5

Explanation:
We know that Amy has 5 yards of boarders and that she will use them to make 4 equal borders.
This means that:
she will divide 5 yards by 4 to know the length of each border

Among the given choices, choices G, H and J show the division of 5 by 4 which is correct representation of the length
On the other hand. choice F shows the division of 4 by 5 which is an incorrect representation of the length.

Hope this helps :)

Answer:

4 ÷ 5

Step-by-step explanation: becuz i said so

Two events are independent when the following is true:

a. the outcome of one event determines the outcome of the other event

b. there is no correlation between the two events

c. the outcome of one event does NOT determine the outcome of the other event

d. The outcome of the event is determined by the theoretical probability of the event

Answers

Solution:

Independent Events:

Consider an experiment of Rolling a die, then getting an even number and multiple of 3.

Total favorable outcome = {1,2,3,4,5,6}=6

A=Even number = {2,4,6}

B=Multiple of 3 = {3,6}

A ∩ B={6}

P(A)=[tex]\frac{3}{6}=\frac{1}{2}[/tex], P(B)= [tex]\frac{2}{6}=\frac{1}{3}[/tex]

P(A ∩ B)=[tex]\frac{1}{6}[/tex]

So, P(A)× P( B)=[tex]\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}[/tex]=P(A ∩ B)

Hence two events A and B are independent.

Option (c). the outcome of one event does NOT determine the outcome of the other event



Answer:

C on edge or the outcome of one event does NOT determine the outcome of the other event

Step-by-step explanation:

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