Which value, to the nearest tenth, is the smallest solution of f(x) = g(x) if f(x) = ln(x + 5) – 1 and g(x) = x3 – 2x + 1?

Answers

Answer 1

Answer:

There are two possibilities of determine which solution is the smallest one:

(i) The smallest solution is the value of [tex]x[/tex] has the smallest distance with respect to origin: [tex](x_{2},y_{2}) = (0.18,0)[/tex]

(ii) The smallest solution is the most negative value: [tex](x_{1},y_{1}) = (-1.577,0)[/tex]

Step-by-step explanation:

Let [tex]f(x) = g(x)[/tex], [tex]f(x) = \ln (x+5)-1[/tex] and [tex]g(x) = x^{3}-2\cdot x + 1[/tex], then we have the following implicit equation:

[tex]\ln (x+5)-x^{3}+2\cdot x -2 = 0[/tex] (1)

This equation cannot be solved by analytical means. There are two different strategies to solve this expression: (i) Numerical methods, (ii) Graphical methods. We decide to use the second method:

Let suppose that we use this function [tex]h(x) = \ln (x+5) -x^{3}+2\cdot x - 2[/tex]. By the help of a graphing tool, we find the smallest solution such that [tex]h(x) = 0[/tex]. There are three possible solutions: [tex](x_{1},y_{1}) = (-1.577,0)[/tex], [tex](x_{2},y_{2}) = (0.18,0)[/tex], [tex](x_{3}, y_{3}) = (1.376, 0)[/tex]

There are two possibilities of determine which solution is the smallest one:

(i) The smallest solution is the value of [tex]x[/tex] has the smallest distance with respect to origin: [tex](x_{2},y_{2}) = (0.18,0)[/tex]

(ii) The smallest solution is the most negative value: [tex](x_{1},y_{1}) = (-1.577,0)[/tex]

Which Value, To The Nearest Tenth, Is The Smallest Solution Of F(x) = G(x) If F(x) = Ln(x + 5) 1 And
Answer 2

The smallest smallest solution of f(x) = g(x) will be [tex]\rm \left(-1.577,0.223\right)[/tex]

What exactly is a function?

A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.

Given functions;

f(x) = ln(x + 5) – 1

g(x) = x³ – 2x + 1

After graphing both the function, we get the three solutions of the given equation,

[tex]\rm \left(-1.577,0.223\right)[/tex]

[tex]\left(0.18,0.645\right)[/tex]

[tex]\left(1.376,0.853\right)[/tex]

Hence,the smallest smallest solution of f(x) = g(x) will be [tex]\rm \left(-1.577,0.223\right)[/tex]

To learn more about the function, refer to:

https://brainly.com/question/5245372

#SPJ5

Which Value, To The Nearest Tenth, Is The Smallest Solution Of F(x) = G(x) If F(x) = Ln(x + 5) 1 And

Related Questions


At work, Mr. Grinnell receives 20 phone calls every 60 minutes. How many calls should he expect to receive in 180 minutes?
60
80
100
40

Answers

Answer:

Use a ratio.

20/60 = x/180

180/60 = 3, so 20*3 is 60.

The answer is 60.

Answer:

60

Step-by-step explanation:

Find out how many phone calls Mr. Grinnell receives in 1 minute.

60 mins = 20

1 min = 20 ÷ 60 = 0.333

180 mins = 0.333 x 180 = 59.94

59.94 rounded to the nearest whole number = 60

The exponential function h, whose graph is given below, can be written as h(x) = a•b^x


Complete the equation for h(x).


Answers

Answer:

1,6

Step-by-step explanation:

1,6 thats how

I AM BEGGING, PLEASE HELP ME. CAN SOMEONE PLEASE HELP ME!

I NEED IT QUICK:
WHAT IS THE VALUE OF X - YOU DONT HAVE TO EXPLAIN YOUR ANSWER I JUST NEED THE VALUE OF X

Answers

Answer:

37.5

Step-by-step explanation:

180-75 = 105

180 is the sum of all the angle in a triangle

180-105 = 75

75/2 = x becuz the triangle is icoceles

=37/5

Hope this helps :) Giving me brainiest would help a lot :))

How many times will a circle's diameter fit around that circle?​

Answers

3 times

Step-by-step explanation:

NEED HELP ASAP! TY IN ADVANCE <3 DO THE TABLE OF VALUES AS WELL!

Answers

Answer:

Domain {-2, 0, 1, 6}

Range {13, 5, 7, 77}

Step-by-step explanation:

table of values

Domain {-2, 0, 1, 6}

Range {13, 5, 7, 77}

Answer:

Step-by-step explanation:

[tex]y_{1}[/tex] = 2( - 2 )² + 5 = 2(4) + 5 = 13

[tex]y_{2}[/tex] = 2( 0 )² + 5 = 5

[tex]y_{3}[/tex] = 2( 1 )² + 5 = 7

[tex]y_{4}[/tex] = 2( 6 )² + 5 = 77

Range: { 5, 7, 13, 77 }

Jack correctly wrote another expression, 100−2t 100 - 2 t , to find the number of tickets Kate has now. Use the drop-down menus to explain what each part of Kate's and Jack's expressions mean.

Answers

Complete question :

Kate had 50 tickets to use for rides at the fair. She lost some of them. Her dad doubled the tickets she had left. Kate wrote the expression 2(50−t) to find the number of tickets she has now, where t t is the number of tickets she lost. Jack correctly wrote another expression, 100−2t, to find the number of tickets Kate has now. Use the drop-down menus to explain what each part of Kate's and Jack's expressions mean.

Answer:

50 means Kate's initial number of tickets

t = number of tickets she lost

2 = multiple by which her dad gave ; two times the number of her remaining tickets.

100 = double the number of initial tickets

2t = two times the number of tickets lost

Step-by-step explanation:

Kate's expression :

2(50 - t)

50 means Kate's initial number of tickets

t = number of tickets she lost

2 = multiple by which her dad gave ; two times the number of her remaining tickets.

Jack's expression:

100 - 2t

Jack's expression is an expanded for of Kate's equation

100 = double the number of initial tickets

2t = two times the number of tickets lost

2(50 - t) :

(2 * 50) - (2 * t)

100 - 2t

PLEASE HELP ME THANK YOU IF U DO

Answers

Answer: Acceleration

Step-by-step explanation:

Ahmad went on a bicycle tour. In the first two hours , he averaged 12 km/h; but in the next three hours he averaged 8 km/h;. A)Calculate the total distance covered b) , calculate his average speed for the whole journey

Answers

Answer: See explanation

Step-by-step explanation:

We are informed that Ahmad averaged 12 km/h in the first 2 hours. Total distance for the first 2 hours = 12km × 2 = 24km.

In the next three hours he averaged 8 km/h. The total distance for the next 3 hours = 8km × 3 = 24 km

A) Calculate the total distance covered.

This will be the distance covered for the 5 hours. This will be:

= 24km + 24km

B. Calculate his average speed for the whole journey.

This will be:

= Total distance covered / Total time taken

= 48km / 5

= 9.6 km/hour

somebody help me fast pleaseee 5 rate

Answers

Answer:

(7m+4m+8m)×219m×2=38m

What is the best measure of center for this data set?
{101, 2, 108, 104, 102, 107, 109, 102}

A.mean because there is an outlier

B.median because there is an outlier

C.mean or median because there is no outlier

D.mode because there is an outlier

Answers

Answer:

it is B the median hope this helps :)

Step-by-step explanation:

Answer:

A. Mean

Step-by-step explanation:

When there is an outlier, the mean is the best way to figure out the average. Median doesn't work because it determines the exact middle, and the outlier (that 2) would affect it greatly, and the mode doesnt work, because it is the value that apears most in the data set, but just because it appears most doesnt mean its the average. In this case the mode is 102, but that is not the average. I hope this helps :)

HURRY I NEED HELPPPPP !!!!
Write each expression as a single power of 10 .

A. 10^(−3) ⋅ 10^(−2)

B. 10^4 ⋅ 10^(−1)

C. 10^5/10^7

D. (10^(−4))^5

E. 10^(−3) ⋅ 10^2

F. 10^y / 10^5

Answers

Answer:

A. 10^(−3) ⋅ 10^(−2) = 10^-5

B. 10^4 ⋅ 10^(−1) = 10^3

C. 10^5/10^7  = 10^-2

D. (10^(−4))^5 = 10^-20

E. 10^(−3) ⋅ 10^2 = 10^-1

F. 10^y / 10^5 = 10^(y-5)

find the nth term - 8,14,20,26

Answers

The ninth term is 20

Zach wants to buy a skateboard that costs $85. He currently has $15 saved. Zach plans to save d, dollars to have enough to buy the skateboard. Which equation represents the amount of money Zach still needs to buy the skateboard? *

Answers

Answer:

85 = 15 + d

d = 70

Step-by-step explanation:

Cost of a skateboard = $85

Zach savings = $15

Amount needed more to save = $d

Which equation represents the amount of money Zach still needs to buy the skateboard?

Total cost = available savings + more savings

85 = 15 + d

85 - 15 = d

70 = d

d = 70

Henry's height is 3 inches more than one-half of Charlie's height. If Henry is 24 inches tall, how tall is Charlie?

Answers

Answer:

Charlie is 20.5 inches tall

Step-by-step explanation:

Henry: 24 inches

            3 and 1/2 inches taller than Charlie

Charlie: 24 - 3.5 inches

            20.5 inches

Answer:

9 inches

Step-by-step explanation:

henry = 3 inches more than 1/2 of charlie

24=henry

24/2= 12-3=9 inches hope this helps

In a certain country the heights of adult men are normally distributed with a mean of 69 inches and a standard deviation of 2.2 inches. The country's military requires that men have heights between 64.6 inches and 73.4 inches.

Answers

Complete Question

In a certain country the heights of adult men are normally distributed with a mean of 69 inches and a standard deviation of 2.2 inches. The country's military requires that men have heights between 64.6 inches and 73.4 inches.

What percentage of this country's men are eligible for the military based on height?

Answer:

95.45 %

Step-by-step explanation:

We solve using z score formula

z-score iis z = (x-μ)/σ, where

x is the raw score

μ is the population mean = 69

σ is the population standard deviation = 2.2

For x= 64.6 inches

z = 64.6 - 69/2.2

z = -2

Probability value from Z-Table:

P(x = 64.6) = 0.02275

For x= 73.4 inches

z = 73.4 - 69/2.2

z = 2

Probability value from Z-Table:

P(x<73.4) = 0.97725

The probability of this country's men are eligible for the military based on height is calculated as:

p(x = 73.4) - p( x = 64.6)

0.97725 - 0.02275

= 0.9545

Converting to Percentage is

= 0.9545 × 100

= 95.45 %

Jonas wants to paint the walls of his bedroom and the
ceiling. The dimensions of his room are 7 feet by 12 feet
by 8 feet
What statements about calculating the surface area of
the walls to be painted are correct? Select all that
apply.
Include the areas of all six faces.
Include the areas of five faces.
7 ft
Include the areas of four faces.
The surface area that will be painted is 376 ft?.
The surface area that will be painted is 472 ft2.
8 ft
12 ft

Answers

Answer:

Include the areas of five faces.

The surface area that will be painted is 376 ft2.

Step-by-step explanation:

Answer:

Include the areas of five faces

The surface area that will be painted is 376 ft2.

2 and 4

Find The Volume (nearest integer):*

Answers

Answer:

3053.63 or to the nearest integer 3054

Step-by-step explanation:

Volume formula of a sphere

[tex]V=4/3\pi r^3\\V=4/3*\pi *9^3\\V= 3053.63 \\[/tex]

Rounded off = 3054

(x^7 + 3x^6 - x^2 + 4) + (3x^7 - x^4 + 3x^2 - 9) add

Answers

4x^7 + 3x^6 - x^4 + 3x^2 - 5

Answer:

4x^7 + 3x^6 - x^4 + 2x^2 - 5

The slope of the line below is-2. Which of the following is the point-slope
form of the line?
10-
10
10
(4-8)
10-
A. y + 8 = -2(x-4)
B. y - 8 = -2(x + 4)
c. y - 4 = -2(x+8)
a
D. y+ 4 = -2(x-8)

Answers

Answer:

A

Step-by-step explanation:

y-y1 = m(x-x1)

Expand (- 3a - 5x) (- 2b - 4y).​

Answers

Answer:  −3a(−2b−4y).−5x(−2b−4y). to this  

6ab+12ay+10bx+20xy

Step-by-step explanation: hope this helps :)

Answer:

( −3a − 5x ) ( −2b − 4y )

= ( −3a + − 5x ) ( −2b + −4y )

=( −3a ) ( −2b ) + ( −3a ) ( −4y ) + ( −5x ) ( − 2b ) + ( − 5x ) ( − 4y )

= 6ab + 12ay + 10bx + 20xy

Hope it helps

Please mark me as the brainliest

Thank you

1
Which is an equation of the line with slope 2 that contains the point (6,4)?
a.y= 22 - 8
1
y =
+1
b.
х
1
2
2 +4
C С.
1
y =
2
Question 2
Which is the equation of a line that passes through the point (5, 6) and has a slope of O?
a.y = 5
b.y=6
X cx=5
d. x = 6
Okoo

Answers

Answer:

Step-by-step explanation:

1. y - 4 = 2(x - 6)

y - 4 = 2x - 12

y = 2x - 8

2. y - 6 = 0(x - 5)

   y - 6 = 0

   y = 6

answer is b

The slope of the tangent to a curve at any point (x, y) on the curve is negative x divided by y . Find the equation of the curve if the point (2, -2) is on the curve.

x + y = 0
x^2 - y^2 = -2
x^2 + y^2 = 16
x^2 + y^2 = 8

Answers

Answer:

.

Step-by-step explanation:

.

Answer:

i belive its x^2 + y^2 = 8

Step-by-step explanation:

Given: m∠B = 46°; m∠C = 45°; m∠R = 46°;
m∠T = 89°

Prove: △ABC ~ △TRS

Triangles A B C and T R S are shown. Angles A B C and T R S are 46 degrees. Angle B C A is 45 degrees. Angle R T S is 89 degrees.

Melissa believes that the AA similarity theorem can prove that the triangles are similar. Which fact would be necessary in the proof?

△ABC is an acute triangle.
△TRS is larger than △ABC.
The sum of the measures of the interior angles of a triangle is 180°.
The sum of the side lengths of two sides of a triangle is greater than the third side length

Answers

Answer:

85

Step-by-step explanation: multiply

Answer:

B: Triangle R S P is similar to triangle Z X Y

C: Triangle S R P is similar to triangle X Z Y

E: Triangle R P S is similar to triangle Z Y X

Step-by-step explanation:

what is the positive solution to this equation?
4x²+12x=135

Answers

4x^2 + 12x - 135 =0
Using calculator mode 3 3 or formula
X= 9/2 or x = -15/2

Answer:

x = 4.5

Step-by-step explanation:

Solve for x by using the quadratic formula

x = -12 + or - [tex]\sqrt{144+2160}[/tex] / 8

so (-12 + 48) / 8 or (-12 - 48) / 8

so 36/8 or -60/8, they just want the positive solution so x = 4.5

Order the steps to solve the equation log(x2 - 15) = log(2x) form 1 to 5.
x² – 2x - 15=0
Potential solutions are -3 and 5
x² – 15 = 2x
X-5 = 0 or x + 3 = 0
(x - 5)(x + 3) = 0

Answers

step 1: x²-15=2x
step 2: x²-2x-15=0
step 3: (x-5)(x+3)=0
step 4: x-5=0 or x+3=0
step 5: x=5 of x=-3

Answer:

Took L for my gang   keep working hard

Step-by-step explanation:

Expand to write an equivalent expression: −14(8x+12y)
Factor to write an equivalent expression: 36a−6
Pls solve these quick

Answers

Answer:

-112x-168y, 6(6a-1).

Step-by-step explanation:

-14(8x+12y)

-112x-168y

-----------------

36a-6

6(6a-1)

Answer:

Step-by-step explanation:

yassssssss

Lin opened a lemonade stand during the summer. She
noticed that she sold more lemonade on warmer days.
For each day she sold lemonade, she plotted the point
(t,c), where t represents high temperature and c
represents cups of lemonade sold.
b. A computer program found that the line c= 2t - 89
is a good fit for the data. Use this equation to predict
how many cups of lemonade Lin might sell on a day
when the high temperature is 74 degrees.
Use the sketch pad to show or explain your thinking.

Answers

Answer:

3

Step-by-step explanation:

One angle of an isosceles triangle measures 48°. Which other angles could be in that isosceles triangle? Choose all that apply.

Answers

Answer:

70° and 62° could be the other angles in that isosceles triangle

PLEASE SHOW WORK AND EXPLAIN IM AM VERY CONFUSED ASAP WILL GIVE BRAINLIEST 10 MINUTES TILL ITS DUE

Answers

Answer:

b

Step-by-step explanation:

let y = f(x) and rearrange making x the subject , that is

y = 4x + 3 (subtract 3 from both sides )

y - 3 = 4x ( divide both sides by 4 )

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

Change y back into terms of x with x = [tex]f^{-1}[/tex] (x) , then

[tex]f^{-1}[/tex] (x) = [tex]\frac{x-3}{4}[/tex] → b

b) Select all expressions that can be used to find 85% of 280.
A. O
8.5
10
280
B.
0.85
100
280
c. O
85
100
• 280

Answers

Answer:

238

Step-by-step explanation:

85%of 280 is 238 ok.......

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