PLEASE HELP ASAP!!!!!!!!!!!!!!!!!

PLEASE HELP ASAP!!!!!!!!!!!!!!!!!

Answers

Answer 1

Answer:

Twelve tickets cost $30 --> True

Thirty tickets cost $12 --> False

Each additional costs $2.50 --> True

The table is a partial rep --> True

ordered pairs --> False

Step-by-step explanation:

Twelve tickets cost $30 --> True, you can literally see that in the table

Thirty tickets cost $12 --> False, 30 is not in the table so you don't have that information. Besides, $12 is an unlikely low value for so many tickets.

Each additional costs $2.50 --> True, you can see the difference in the TotalCost column to be consistently 2.50.

The table is a partial rep --> True, values below 11 are not shown for example.

ordered pairs --> False --> Then the x value should be first, e.g., (11, 27.50), since the cost y is a function of the number x.


Related Questions

Find the mode. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. The​ mode(s) is(are) nothing. ​(Type an integer or a decimal. Do not round. Use a comma to separate answers as​ needed.) B. There is no mode.

Answers

Answer:

The question is not complete, but I found a possible match:

Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question. Listed below are the jersey numbers of 11 players randomly selected from the roster of a championship sports team. What do the results tell us?

86 4 85 83 9 51 24 34 28 43

Find the mode. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A. The​ mode(s) is(are) nothing. ​(Type an integer or a decimal. Do not round. Use a comma to separate answers as​ needed.)

B. There is no mode.

Answer:

The correct answer is:

There is no mode (B.)

Step-by-step explanation:

b. The mode of data is the number that repeats the most number of times. The number that occurs most frequently. on the list of the distribution, 86 4 8 5 83 9 51 24 34 28 43, every number occurs just once, hence, there is no mode for the distribution.

a. To calculate the Mean

[tex]Mean: \frac{Sum\ of\ terms}{number\ of\ players}\\ Mean = \frac{86\ +\ 4\ +\ 8\ +\ 5\ +\ 83\ +\ 9\ +\ 51\ +\ 24\ +\ 34\ +\ 28\ +\ 43}{11}\\Mean= 34.09[/tex]

c. To calculate the median:

Median is  the mid-way term of the distribution, but first, we have to arrange the terms in ascending order (descending order can also be used)

4, 5, 8, 9, 24, 28, 34, 43, 51, 63, 86

To find the median, count the numbers equally from the left- and right-hand sides to the middle, the remaining number becomes the median. In this case, the median = 28

d. Midrange:

The midrange is the number mid-way between the greatest and smallest number in a data set. To find the midrange, we will add the smallest (4) and largest number (86), and divide by 2:

Midrange = (4 + 86) ÷ 2

Midrange = 90 ÷ 2 = 45

e. what do the results tell us:

Since only 11 of the jersey numbers were in the sample, the statistics cannot give any meaningful results

A die is thrown. Describe the following events: (i) A: a number less than 7 (ii) B: a number greater than 7 (iii) C: a multiple of 3 (iv) D: a number less than 4. (v) E: an even number greater than 4 (vi) F: a number not less than 3 (vii) find A× (B∩ E), A ∩B, B ∪ C, E ∩ F∩ D. Answer this if u want to be marked as the brainliest!

Answers

A: The probability of a number rolling less than 7 is 100% or 1 because a dice only has numbers 1,2,3,4,5, and 6. 1,2,3,4,5, and 6 are all less than 7 so you are guaranteed to roll a number less than 7.

B: The probability of a number rolling more than 7 is 0% or 0 because a dice only has numbers 1,2,3,4,5, and 6. 1,2,3,4,5, and 6 are all less than 7 so it's not possible to roll a number more than 7.

C: The probability of a number rolling to be a multiple of three is 33.33(repeating)% or 1/3. Out of 1,2,3,4,5, and 6, the multiples of 3 are, 3 and 6. 3 and 6 is two numbers out of six numbers. 2 out of 6 simplifies to 1 out of 3.

D: The probability of a number rolling to be less than 4 is 50% of 1/2. Out of the numbers, 1,2,3,4,5, and 6, only 1,2, and 3 are less than 4. 1,2, and 3 is three numbers out of six numbers. 3 out of 6 simplifies to 1 out of 2.

E: The probability of a number rolling to be an even number greater than 4 is 0.166(repeating) or 1/6. Out of the numbers, 1,2,3,4,5, and 6, 2,4, and 6 are even numbers. Out of 2,4, and 6, only 6 is greater than 4. 4 is one number out of 1,2,3,4,5, and 6 (six numbers).

F: The probability of a number rolling to be a number not less than 3 is 50% or 1/2. "Not less than" actually means greater than. In the numbers, 1,2,3,4,5, and 6, only 4,5, and 6 are greater than 3. 4,5, and 6 are three numbers. 3 out of 6 simplifies to 1 out of 2.

I don't really know the answer to the last question but anyways I hope this helped! ♡

❀ Have a good day! ❀

HURRY! QUICK! SHOW WORK THANKS Write the simplified polynomials that represent the perimeter and area for the rectangle.

Length: (x-5) ft

Width: (3x-10) ft

Perimeter =

Area =

Answers

P = 2(x - 5) + 2(3x - 10)
P = 2x - 10 + 6x - 20
P = 8x - 30

A = (x - 5)(3x - 10)
A = 3x^2 - 10x - 15x + 50
A = 3x^2 - 25x + 50

Answer:

Perimeter = (8x-30)

Area=(X-5)(3x-10)

Step-by-step explanation:

Perimeter equation for solving is this

2(X-5+3x-10)=p

it is length plus width twice which will equal the perimeter

solving this out

2(4x-15)=p

8x-30=p

area equation for solving this is

(x-5)(3x-10)=a

I don’t know how to solve this one out but i hope the setup helps!

Welcome to Gboard clipboard, any text you copy will be saved here.

Answers

Yes the internet is left to to clipboard

how to solve this question

Answers

Step-by-step explanation:

A + B + C = 360

[2/3]A + B + [4/3]C = 360

[2/3]A + [4/3]B + C = 360

A + B + C = 360

We could extract from all of this that Cans A, B, C must have equal amount of paint inside in order to attain those conditions slated. Thus we could tell that the amount of paint in each can is 60L.

Answer:

A)60l

B)60l

Step-by-step explanation:

Complete each equation with a number that makes it true. 8⋅______=40 8+______=40 21÷______=7 21−______=7 21⋅______=7

Answers

Answer:

8.5 =40

8+32=40

21÷3=7

21-14=7

21÷7=3

Step-by-step explanation:

The missing values are 5, 32, 3, 14, and 3 after using the arithmetic operation.

What is an arithmetic operation?

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

It is given that:

8⋅______=40

8+______=40

21÷______=7

21−______=7

21⋅______=7

We can use the arithmetic operation to find the unknown values:

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56 etc. are the numbers.

8x5  = 40

8 + 32 = 40

21 ÷ 3 = 7

21 - 14 = 7

21 ÷ 3 = 7

Thus, the missing values are 5, 32, 3, 14, and 3 after using the arithmetic operation.

Learn more about the arithmetic operation here:

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Which point is a solution to this system of inequalities?
y < 1/2x – 3
y + 2x > 6

Answers

Answer:   C. (5, -2)

Step-by-step explanation:

Graph each equation:

Equation 1: y < (1/2)x - 3 -->  m = (1/2)  b = -3,   dashed line,   shaded below

Equation 2: y > -2x + 6 -->  m = -2  b = 6,   dashed line,   shaded above

or  plug the values into the equations.  It must be TRUE for both equations:

               y < (1/2)x - 3         y > -2x + 6

(7, -8)            True                   False

(2, -3)            True                   False

(5, -2)            True                   True           <-- This works!

(4, 1)             False                  True

Inequalities help us to compare two unequal expressions. The correct option is C.

What are inequalities?

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

For a point to be the solution of the system of inequalities, the point when substituted in the inequalities must satisfy both the given inequalities.

A. (7, -8)

y < 1/2x – 3

-8 < (1/2)7 - 3

-8 < 0.5

y + 2x > 6

-8 + 2(7) > 6

-8 + 14 > 6

6 > 6

Since the second inequality is not satisfied, therefore, the given point is not the solution.

B. (2, -3)

y < 1/2x – 3

-3 < (1/2)2 - 3

-3 < -2

y + 2x > 6

-3 + 2(2) > 6

-3 + 4 > 6

1 > 6

Since the second inequality is not satisfied, therefore, the given point is not the solution.

C. (5, -2)

y < 1/2x – 3

-2 < (1/2)5 - 3

-3 < -2

y + 2x > 6

-2 + 2(5) > 6

-2 + 10 > 6

8 > 6

Since both the inequality are satisfied, therefore, the given point is the solution.

D. (4, 1)

y < 1/2x – 3

1 < (1/2)4 - 3

1 < -1

Since the first inequality is not satisfied, therefore, the given point is not the solution.

Learn more about Inequality:

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When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation
PV^1.4=C
where C is a constant. Suppose that at a certain instant the volume is 610 cubic centimeters and the pressure is 89 kPa and is decreasing at a rate of 10 kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant?

Answers

Answer:

48.96 cm³/min

Step-by-step explanation:

We are given;

Relationship between pressure P and volume V; PV^(1.4) = C

Volume;V = 610 m³

Pressure; P = 89 KPa

Rate of decreasing pressure; dP/dt = -10 kPa/minute.

We want to find the rate at which the volume is increasing at that instance, thus, its means we need to find dV/dt

So, we will differentiate the relationship equation of P and V given.

Thus, we have;

[V^(1.4)(dP/dt)] + d(V^(1.4))/dt = dC/dt

Differentiating this gives us;

[(dP/dt) × (V^(1.4))] + [1.4 × P × V^(0.4) × (dV/dt)] = 0

Plugging in the relevant values, we have;

(-10 × 610^(1.4)) + (1.4 × 89 × 610^(0.4) × (dV/dt)) = 0

This gives;

-79334.44155 + 1620.5035(dV/dt) = 0

Rearranging, we have;

1620.5035(dV/dt) = 79334.44155

Divide both sides by 1620.5035 to give;

dV/dt = 79334.44155/1620.5035

dV/dt = 48.96 cm³/min

PLEASE HURRY add n to the product of 7 and 5

Answers

Answer:

[See Below]

Step-by-step explanation:

Multiply 7 by 5.

*35

Now add n to it.

*35 + n

Solve the equation V2 + 4 + 12 = 3-
a.
330
-733
d. 753
b. -776
Please select the best answer from the choices provided

Answers

Answer:

d

Step-by-step explanation:

trust

Answer:

x = -733

Step-by-step explanation:

[tex]\sqrt[3]{x+4}[/tex] + 12 = 3

[tex]\sqrt[3]{x+4}[/tex]  = -9 (cube both sides)

x + 4 = -729

x = -733

Write the decimal as a fraction or a mixed number. Write your answer in simplest form. 0.2

Answers

Answer:

[tex] \frac{1}{5} [/tex]

Step-by-step explanation:

[tex]0.2 \times \frac{10}{10} = \frac{2}{10} = \frac{1}{5} [/tex]

This number can't be written as a mixed number since it is proper fraction.

It's numerator is less than it's denominator.

Hope this helps ;) ❤❤❤

Which of the following is not a 3-D shape? A. quadrilateral B. cube C. sphere D. prism

Answers

Answer:

A.

Step-by-step explanation:

A quadrilateral is simply a shape with 4 sides, therefore it does not HAVE to be 3-D.

Answer:

Quadrilateral.

Step-by-step explanation:

A quadrilateral is a 2d shape not 3d.

all the factors of 6

Answers

Answer:

1, 2, 3 and 6.

Step-by-step explanation:

Factors of 6 are 1, 2, 3 and 6.

what is the angle of the triangle below?

Answers

It is 45 degrees with us the last one

What's the answer to this question I need help I don't understand it

Answers

Greetings from Brasil...

Making the division

(X⁵ + 2X⁴ - 7X² - 19X + 15) ÷ (X² + 2X + 5)

we get

X³ - 5X + 3

Answer:

x³ − 5x + 3

Step-by-step explanation:

To solve with long division:

Start by dividing the highest terms:

x⁵ / x² = x³

This becomes the first term of the quotient.  Multiply by the divisor:

x³ (x² + 2x + 5) = x⁵ + 2x⁴ + 5x³

Subtract from the first three terms of dividend:

(x⁵ + 2x⁴ + 0x³) − (x⁵ + 2x⁴ + 5x³) = -5x³

Drop down the next two terms and repeat the process.

To use the "box" method:

Each square in the box is the product of the term at the top of the column and the term at the end of the row.  Also, squares diagonal of each other must add up to the term outside the box.

Look at the first diagonal.  There is only one square, so that must be x⁵.  Knowing this, we can say that x³ must be at the top of the column.  We can fill in the rest of the column (2x⁴ and 5x³).

Repeat this process until all squares are filled in.

What is the slope of the line in the graph?

Answers

Answer:

i believe it is 1

Step-by-step explanation:

Answer:

the slope is 1

Step-by-step explanation:

rise/run

1/1 = 1

Can someone please explain this to me? I’m really confused on how to find the limit with the piecewise function.

Answers

Answer:   2

Step-by-step explanation:

You only need to evaluate at the limit point.

f(x) = 4 - x  ; x ≠ 2

Consider the solution if x = 2 (because the limit is x → 2)

                                          f(2) = 4 - (2)

                                                =   2

We know that f(x) = 0  ; x = 2

                                         f(2) = 0

but we are looking for the y- value it approaches - not the y-value it is.

Look at the graph.  You will see that as x gets closer and closer to 2, the y-value gets closer and closer to 2.  This is the limit.

In a recent year, 32.3% of all registered doctors were female. If there were 46,300 female registered doctors that year, what was the total number of
registered doctors?
Round your answer to the nearest whole number.

Answers

Answer:

  143,344

Step-by-step explanation:

Let d represent the total number of registered doctors. The given relation is ...

  0.323d = 46,300

Dividing by the coefficient of d, we get ...

  d = 46,300/0.323 ≈ 143,343.7

The total number of registered doctors was about 143,344.

The sum of two numbers, x and y, is 12. The difference of four times the larger number and two
times the smaller number is 18. Whích system of equations should you use to find the two
numbers?
O
A X-y=12
4x - 2y = 18
O B x + y = 12
X-y= 18
C x+y=12
2x - 4y = 18
D x + y = 12
4% - 2y = 18

Answers

Answer:

D

Step-by-step explanation:

"Sum" indicates that we add the two variables so we can eliminate option A because that has x - y = 12 not x + y = 12. We can eliminate option B because the second equation should be 4x - 2y = 18, not x - y = 18. For that same reason, we can eliminate C because the coefficients are swapped. I will assume that in option D, the second equation is 4x - 2y = 18. Since we have eliminated everything else, the answer is D.

Determine the equation of the tangent line to the given path at the specified value of t. (Enter your answer as a comma-separated list of equations in (x, y, z) coordinates.) (sin(3t), cos(3t), 2t7/2); t=1

Answers

Answer:

k(t) =  (sin3, cos3, 2) + [(t - 1)(cos3, -3sin3, 7)]

Step-by-step explanation:

For a path r(t), the general equation k(t) of its tangent line at a specified point r(t₀) is given by;

k(t) = r(t₀) + r'(t₀) [t - t₀]            -----------------(i)

Where

r'(t) is the first derivative of the path r(t) at a given value of t.

From the question:

r(t) =  (sin3t, cos3t, 2[tex]t^{7/2}[/tex]) and t₀ = 1

=> r(1) = (sin3, cos3, 2) at t₀ = 1

Find the first derivative component-wise of r(t) to get r'(t)

∴ r'(t) = (cos3t, -3sin3t, 7[tex]t^{5/2}[/tex])

=>r'(1) = (cos3, -3sin3, 7)

Now, at t₀ = 1, equation (i) becomes;

k(t) = r(1) + [ r'(1) (t-1)]    [substitute the necessary values]

k(t) =  (sin3, cos3, 2) + [(t - 1)(cos3, -3sin3, 7)]

The net of a square pyramid is shown below. What is the surface area of the pyramid?

Answers

Answer:

D. [tex] 192 cm^2 [/tex]

Step-by-step explanation:

The net of the pyramid is made up of 1 square base and 4 triangles

Surface area of the pyramid = area of square + 4(area of square)

[tex] S.A = (s^2)+ 4(\frac{1}{2}bh) [/tex]

Where,

s = 8

b = 8

h = 8

[tex] S.A = (8^2)+ 4(\frac{1}{2}*8*8) [/tex]

[tex] S.A = 64+ 4(32) [/tex]

[tex] S.A = 64+ 128 [/tex]

[tex] S.A = 192 cm^2 [/tex]

192 cm^2

Step-by-step explanation:

base = 8 x 8 = 64

1 triangle = 1/2 x 8 x 8 = 32

32 x 4 = 128

128+64 = 192 cm^2

16y — 13= —157 solve for y

Answers

the answer is y= -24
y= 9

-16y-13=-157
You first want to get the y by itself on one side
So you do:
-16y= -157+13
(since you moved -13 to the other side it becomes positive) then you do
-16y= -144 (when you do -157+13 you get -144)
Then divide -144 by -16
y= -144/-16
So finally, you get:
y= 9


Use the coordinate plane to plot the points (6, 0) and (0, 5). Which statement is true? (0, 5) is located on the x-axis. (0, 5) is located at the origin. (6, 0) is located on the x-axis. (6, 0) is located at the origin.

Answers

Answer:

(6, 0) is located on the x-axis

Explanation:

For a point to be on the x-axis, its y-value must equal 0. (6, 0) has an x-value of 6 and a y-value of 0.

"(0, 5) is located at the origin" is not true because the origin is at (0, 0).

"(0, 5) is located on the x-axis" is not true because its y-value is 5, not 0.

"(6, 0) is located at the origin" is not true because the origin is at (0, 0).

The (6, 0) is located on the x-axis option (C) is correct because the y-coordinate is zero on the x-axis.

What is an ordered double?

It is defined as a representation of coordinates in a two-dimensional coordinate plane. It has a list of two elements in it, such as (x, y).

[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]

It is given that:

The points are (6, 0) and (0, 5).

After plotting on the coordinate plane,

For a point to be on the x-axis, its y-value must equal 0. (6, 0) has an x-value of 6 and a y-value of 0.

"(6, 0) is located at the origin" is not true because the origin is at (0, 0).

Thus, the (6, 0) is located on the x-axis option (C) is correct because the y-coordinate is zero on the x-axis.

Learn more about the order double here:

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If (x+12y)/x=19 find (144x^2 +24xy + y^2) /y^2

Answers

Answer:

81

Step-by-step explanation:

Given:

(x+12y)/x=19

Simplifying:

x+ 12y = 19x  12y=18x x/y = 2/3

Finding the value of:

(144x^2 +24xy + y^2) /y^2 = 144 (x/y)^2 + 24 (x/y) + 1 =

Substituting x/y with 2/3:

144 (2/3)^2 + 24 (2/3) + 1 = 144 (4/9) + 16 + 1 = 64 + 16 + 1 = 81

Answer is 81

Find the absolute minimum and absolute maximum values of f on the given interval. f(t) = t 25 − t2 , [−1, 5]

Answers

Answer: Absolute minimum: f(-1) = -2[tex]\sqrt{6}[/tex]

              Absolute maximum: f([tex]\sqrt{12.5}[/tex]) = 12.5

Step-by-step explanation: To determine minimum and maximum values in a function, take the first derivative of it and then calculate the points this new function equals 0:

f(t) = [tex]t\sqrt{25-t^{2}}[/tex]

f'(t) = [tex]1.\sqrt{25-t^{2}}+\frac{t}{2}.(25-t^{2})^{-1/2}(-2t)[/tex]

f'(t) = [tex]\sqrt{25-t^{2}} -\frac{t^{2}}{\sqrt{25-t^{2}} }[/tex]

f'(t) = [tex]\frac{25-2t^{2}}{\sqrt{25-t^{2}} }[/tex] = 0

For this function to be zero, only denominator must be zero:

[tex]25-2t^{2} = 0[/tex]

t = ±[tex]\sqrt{2.5}[/tex]

[tex]\sqrt{25-t^{2}}[/tex] ≠ 0

t = ± 5

Now, evaluate critical points in the given interval.

t = [tex]-\sqrt{2.5}[/tex] and t = - 5 don't exist in the given interval, so their f(x) don't count.

f(t) = [tex]t\sqrt{25-t^{2}}[/tex]

f(-1) = [tex]-1\sqrt{25-(-1)^{2}}[/tex]

f(-1) = [tex]-\sqrt{24}[/tex]

f(-1) = [tex]-2\sqrt{6}[/tex]

f([tex]\sqrt{12.5}[/tex]) = [tex]\sqrt{12.5} \sqrt{25-(\sqrt{12.5} )^{2}}[/tex]

f([tex]\sqrt{12.5}[/tex]) = 12.5

f(5) = [tex]5\sqrt{25-5^{2}}[/tex]

f(5) = 0

Therefore, absolute maximum is f([tex]\sqrt{12.5}[/tex]) = 12.5 and absolute minimum is

f(-1) = [tex]-2\sqrt{6}[/tex].

Eddie treated his sister to lunch while visiting her in Manchester, Their lunch cost $20, and the
sales tax in Manchester is 15%, If Eddie left a 15% tip on the $20, how much in total did he pay?
Sul

Answers

Answer:

Eddie spent $26 total

Step-by-step explanation:

15% of 20 is 3

He paid 15% tax which is $3

He also tipped 15% of the $20 which he paid for lunch so another $3

3+3+20= $26

What is the range of the function f(x) = -|3x + 3|?

Answers

Answer:

The range of the function [tex]f(x) = -|3\cdot x+3|[/tex] is every positive real numbers plus zero.

Step-by-step explanation:

According to definition of the absolute value, the range of absolute value covers positive real numbers or zero. A linear function is a continuous function, which means the existence of an image for every element from domain. The negative sign transforms the original range to all negative real numbers plus zero.

Hence, the range of the function [tex]f(x) = -|3\cdot x+3|[/tex] is every positive real numbers plus zero.

Identify the type of conic section given by the polar equation below. Also give the equation of its directrix (in rectangular coordinates is fine.)
r = 8/4+ cos θ.

Answers

Answer:

x = ±8

Step-by-step explanation:

A conic section with a focus at the origin, a directrix of x = ±p where p is a positive real number and positive eccentricity (e) has a polar equation:

[tex]r=\frac{ep}{1 \pm e*cos\theta}\\ \\[/tex]

From the question, the polar equation of the circle is:

[tex]r=\frac{8}{4+cos\theta}[/tex]

We have to make the equation to be in the form of [tex]r=\frac{ep}{1 \pm e*cos\theta}\\ \\[/tex]. Therefore:

[tex]r=\frac{8}{4+cos\theta}\\\\Multiply \ through\ numerator\ and\ denminator\ by\ \frac{1}{4}\\\\ r=\frac{8*\frac{1}{4} }{(4+cos\theta)*\frac{1}{4} }\\\\r=\frac{2}{4*\frac{1}{4} +cos\theta*\frac{1}{4}}\\ \\r=\frac{\frac{1}{4}*8}{1+\frac{1}{4}cos\theta}[/tex]

This means that the eccentricity (e) = 1/4 and the equation of the directrix is x = ±8

Use​ Newton's method to find an approximate solution of ln(x)=10-x. Start with x_0 =9 and find x_2 .

Answers

Answer:

x₂ = 7.9156

Step-by-step explanation:

Given the function  ln(x)=10-x with initial value x₀ = 9, we are to find the second approximation value x₂ using the Newton's method. According to Newtons method xₙ₊₁ = xₙ -  f(xₙ)/f'(xₙ)

If f(x) = ln(x)+x-10

f'(x) = 1/x + 1

f(9) = ln9+9-10

f(9) = ln9- 1

f(9) = 2.1972 - 1

f(9) = 1.1972

f'(9) = 1/9 + 1

f'(9) = 10/9

f'(9) = 1.1111

x₁ = x₀ -  f(x₀)/f'(x₀)

x₁ = 9 -  1.1972/1.1111

x₁  = 9 - 1.0775

x₁  = 7.9225

x₂ = x₁ -  f(x₁)/f'(x₁)

x₂ = 7.9225 -  f(7.9225)/f'(7.9225)

f(7.9225) = ln7.9225 + 7.9225 -10

f(7.9225) = 2.0697 + 7.9225 -10

f(7.9225) = 0.0078

f'(7.9225) = 1/7.9225 + 1

f'(7.9225) = 0.1262+1

f'(7.9225) = 1.1262

x₂ = 7.9225 - 0.0078/1.1262

x₂ = 7.9225 - 0.006926

x₂ = 7.9156

Hence the approximate value of x₂ is 7.9156

Solve for the largest value of $x$ such that $5(9x^2+9x+10) = x(9x-40).$ Express your answer as a simplified common fraction.

Answers

Hello, please consider the following.

[tex]\begin{aligned}5(9x^2+9x+10) &= x(9x-40)\\&=9x^2-40x\end{aligned}\\\\<=> 45x^2+45x+50=9x^2-40x\\\\<=> (45-9)x^2+(45+40)x+50=0\\\\<=> 36x^2+85x+50=0[/tex]

We can estimate the discriminant, and then, the solutions and we take the largest one.

[tex]\Delta=b^2-4ac=85^2-4*36*50=25=5^2\\\\x_1=\dfrac{-85-5}{2*36}=\dfrac{-18*5}{18*4}=\dfrac{-5}{4}\\\\x_2=\dfrac{-85+5}{2*36}=\dfrac{-80}{72}=\dfrac{-8*10}{8*9}=\boxed{\dfrac{-10}{9}}[/tex]

Thank you

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