2. Expand each of the following functions in ascending powers of x up to the term in
x³. In each case state the values of x for which the expansion is valid.

The value of x is −61.5 . option B

An algebraic expression is simply seen as one with terms, factors, variables, coefficients, constants.

These expressions may also consist of arithmetic operations, some of which includes;

Based on the information given, we have;

−0.28x − 15.3 = 1.92

To determine the value of the variable 'x' we need to take the following steps;

collect like terms from the equation

-0. 28x = 1. 92 + 15. 3

Add like terms

-0. 28x = 17.22

Divide both side by the coefficient of x

x = 17. 22/-0.28

x = - 61. 5

Hence, the value is - 61. 5

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Answer: 116 degrees

Step-by-step explanation: add JKM and MKL together to get JKL

The original price of the dishes is $80

The sale price is $72

10% was off from the original price to get the sale price

The original price can be calculated as follows

100-10

= 90%

Let y represent the original price

72 ÷ 90/100

= 72 ÷ 0.9

= 80

Hence the original price of the dishes before 10% was taken off is $80

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Solution:

The slope of a line that passes through two given points A and B, is expressed as

Given that the line passes through the points (-8, 4) and (-8, -9), this implies that

By substituting these values into the slope formula, we have

Hence, the slope of the line that passes through the points (-8, 4) and (-8. - 9) is evaluated to be

at infinity.

After solving : 100!/12^50, we get 1.025513e+104

Here, 100 factorial or 100!

The result of multiplying an integer by each natural number below it is the factorial of that number.

A factorial can be symbolically denoted by the sign "!"

The first n natural integers are added together to form "n factorial," which is represented by the number n.

100! = 100 × 99 × 98 × .... × 3 × 2 × 1 = 9.332621544 E+157.

This product is too big to calculate manually and hence a calculator is used.

Now, 9.332621544 E+157 / 12 ^ 50 = 1.025513e+104

Hence, after solving 100!/12^50, we get 1.025513e+104

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Please find attached the dilated image of triangle ΔXYZ obtained by using a scale factor of 1.5, with the center of dilation at (0, 0), giving the coordinates of the vertices at the points X'(-6, 3), Y'(9, 0) and Z'(-3, -6).

A dilation transformation is one in which the lengths of a figure are scaled up or down.

From a similar question online, we have:

The vertices of the triangle ΔXYZ are: X(-4, 2), Y(6, 0), and Z(-2, -4)

The given center of dilation is (0, 0)

The scale factor of the dilation is 1.5

The coordinates of the points on the image following a dilation of the point (x, y) by a scale factor of k about the origin is given by the formula:

(x, y) [tex]\underrightarrow{R_k}[/tex] (k·x, k·y)

Therefore, the coordinates of the vertices of the image of the triangle ΔXYZ following a dilation by a scale factor of 1.5 are:

X(-4, 2) [tex]\underrightarrow{R_k}[/tex] X'(1.5×(-4), 1.5×2) = X'(-6, 3)

Y(6, 0) [tex]\underrightarrow{R_k}[/tex] Y'(1.5×6, 1.5×0) = Y'(9, 0)

Z(-2, -4) [tex]\underrightarrow{R_k}[/tex] (1.5×(-2), 1.5×(-4)) = (-3, -6)

The vertices of the dilated image of ΔXYZ, which is ΔX'Y'Z' are; X'(-6, 3), Y'(9, 0), Z'(-3, -6)

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Answer:

Answer down below!

Step-by-step explanation:

Let's write out the equation!

2x + 8 = -4

To solve this, you have to subtract the 8 and bring it over to -4

That would look something like:

2x -(+8) = -4 -8

That leaves you with 2x = -12

Now you divide 2 and -12 which will give you

-6

Answer:X= - 6

Step-by-step explanation:

MOVE +8 to the right which would make it negative so -8-4.You would add both numbers which would be -12 and then u divide -12 with 2 so

-12/2 is -6

From the given function, it is found that:

a. A reasonable domain for the function is of 0 ≤ d ≤ 11.

b. The y-intercept of the graph represents that the initial radius of the algae is of 7 mm.

c. The average rate of change between the 4th and the 11th day of the function means that the radius of the algae grew by an average of 0.64 mm a day.

The function is modeled according to the following rule:

f(d) = 7(1.06)^d

In which:

When the biologist concluded her study, the radius of the algae was approximately 13.29 mm, hence the upper bound of the domain is found as follows:

[tex]13.29 = 7(1.06)^d[/tex]

[tex](1.06)^d = \frac{13.29}{7}[/tex]

[tex]\log{(1.06)^d} = \log{\left(\frac{13.29}{7}\right)}[/tex]

[tex]d\log{1.06} = \log{\left(\frac{13.29}{7}\right)}[/tex]

[tex]d = \frac{\log{\left(\frac{13.29}{7}\right)}}{\log{1.06}}[/tex]

d = 11.

The smallest possible number of days is of 11, hence a reasonable domain for the function is:

0 ≤ d ≤ 11.

The y-intercept of the graph represents that the initial radius of the algae, as it is calculated when d = 0, hence it's value is given by:

[tex]f(0) = 7(1.06)^0 = 7[/tex]

The average rate of change of a function is given by the change in the output divided by change in the input, hence:

r = (13.29 - 8.84)/(11 - 4) = 0.64 mm a day.

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Answer:

I am 99% certain that the answer is c. because it has defiantly been reflected. and if you look at the points in order for them to be moved like that it would have had to have been rotated first.

hope this helped!

The surface and of the cone is

The volume of the cone is

What is a cone?

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.

We are given that radius of the cone as 5yd and slant height as 13yd

We first find the height using pythagoras theorem

Let height be h

by Pythagoras theorem we have

[tex]r^{2}+h^{2}=13^2\\ 5^2+h^2=169\\ h^2=144\\h=12[/tex]

Height of the cone is 12yds

Now volume of the cone is given by

[tex]V=[/tex]π[tex]r^{2}\frac{h}{3}[/tex]

Substituting the values in the equation we get

[tex]V=100[/tex]π yd^3

Now we find the surface area

The formula for surface area is

[tex]A=r(r+\sqrt{r^2+h^2} )[/tex]π

Substituting the values in the equation we get

[tex]A=90[/tex]π yd^2

Hence the surface area of the cone is 90π yd^2

And the volume of the cone is 100π yd^3

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Int the place of F(x) PLUG IN 4X+6 AND THEN SIMPLIFY THE EXPRESSION.BELOW IS THE RESPONSE:

[tex]g(x) = \frac{1}{2} \times (4x + 6) \\ g(x) = \frac{1}{2} \times 2(2x + 3) \\ g(x) = 2x + 3[/tex]

g(x)=2x+3

IT MEANS IN THE BLANKS YOU WILL INSERT 2 IN THE FIRST BLANK AND IN THE SECOND BLANK INSERT 3

HOPE THIS HELPS

In 12 cups of flour,we are going to have 2 cups of flour in six(6) places.

Thus, for 12 cups of flour, Mrs Smith will use:

Answer: (y-(-43))=-7(x-6) and y=-7x-1

Step-by-step explanation:

1) Pick two points. I'll choose (3,-22) and (6,-43)

2) Next set it up in a rise-over-run function

-43 - (-22)

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

6    -  3

3) Solve

-21/3

-7

The slope is -7

4) Find the starting value.

You can do this by substituting two points in a slope-intercept equation(y=mx+b)

y=-7x+b

-22=-7(3)+b

-22= -21+b

-1=b

The starting value is -1.

5) Slope intercept form

We can put all the info together to find that the slope-intercept is:

y=-7x-1

6) Point-slope form:

Point slope form equation is this: y-y1=m(x-x1)

y1 and x1 are one of the points while keeping x and y as variables

So our final equation is (y-(-43))=-7(x-6)

Lets first look at the cost per round with the 25 round pass

Take the total cost and divide by the number of rounds

$84 / 25 rounds

$ 3.36 per round

OR

They can pay 3.25 per round with the single pay

$3.25 is less than 3.36 so it is cheaper ( less per round) to pay the single round price

Option 2 $3.25 is cheaper

Answer:

Remember, a positive and a negative while being added is always a negative outcome, so when you add -29.03 + 26.5, you get -2.53

When dividing 4 by 280.8, the answer gotten is 0.014245.

It should be noted that decimal numbers are numbers that have whole numbers as well as fractional parts. One of the number types in algebra that has a whole integer and a fractional portion separated by a decimal point is a decimal. The decimal point is the dot that appears between the parts of a whole number and a fraction. An example of a decimal number is 34.5. Examples are 2.4 and 9.34.

To divide a decimal by a whole number, follow these steps.

In this case, Dividing 4 by 280.8 will give a value of 0.014245.

Therefore the value is 0.014245.

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Dividing 4 by 280.8  gives

given data

4 ÷ 280.8

4 ÷ 280.8 = 4 / 280.8

= 4 / 280.8

= [tex]\frac{4}{\frac{2808}{10} }[/tex]

= 4/1 * 10 /2808

= 40 / 2808

= 20 / 1404

= 10 / 702

= 5 / 351

5//351 is the lowest form of the fraction and in decimal it is solved as

= 5 / 351

= 0.01424501425

= 0.0142 ( to 4 decimal place )

Decimals refers to number types which are displayed using points. The points used here is called decimal points.

Numbers appearing after the decimal point is not a whole number. If the set of number bearing decimal point has zero as the first and only number, then the whole number is not up to a whole number.

This is synonymous to the case of the solved problem. The number 0.0142 does not have a whole number part. Hence the number is less than 1

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The results of the operation of multiplication between two functions are, respectively:

According to function theory, there are five operations between two functions to create resulting functions:

In this problem we must use the operation of multiplication between two functions.

Case 1

(f · g)(x) = (2 · x + 4) · (x² + 4 · x + 4)

(f · g)(x) = (2 · x + 4) · x² + 4 · (2 · x + 4) · x + 4 · (2 · x + 4)

(f · g)(x) = 2 · x³ + 4 · x² + 8 · x² + 16 · x + 8 · x + 16

(f · g)(x) = 2 · x³ + 12 · x² + 24 · x + 16

Case 2

(h · g)(x) = (x² - 4) · (x² + 4 · x + 4)

(h · g)(x) = (x² - 4) · x² + (x² - 4) · (4 · x) + (x² - 4) · 4

(h · g)(x) = x⁴ - 4 · x² + 4 · x³ - 16 · x + 4 · x² - 16

(h · g)(x) = x⁴ + 4 · x³ - 16 · x - 16

Case 3

(f · h)(x) = (2 · x + 4) · (x² - 4)

(f · h)(x) = 2 · x³ - 8 · x + 4 · x² - 16

(f · h)(x) = 2 · x³ - 4 · x² - 8 · x - 16

(f · h)(2) = 2 · 2³ - 4 · 2² - 8 · 2 - 16

(f · h)(2) = - 32

Case 4

(g · f)(x) = (x² + 4 · x + 4) · (2 · x + 4)

(g · f)(x) = 2 · x³ + 12 · x² + 24 · x + 16

Case 5

(g · h)(x) = (x² + 4 · x + 4) · (x² - 4)

(g · h)(x) = x⁴ + 4 · x³ - 16 · x - 16

Case 6

(f · h)(x) = (2 · x + 4) · (x² - 4)

(f · h)(x) = 2 · x³ - 4 · x² - 8 · x - 16

Case 7

(h · g)(x) = (x² - 4) · (x² + 4 · x + 4)

(h · g)(x) = x⁴ + 4 · x³ - 16 · x - 16

(h · g)(1) = 1⁴ + 4 · 1³ - 16 · 1 - 16

(h · g)(1) = - 27

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The bottom is moving at a rate of [tex]4\sqrt{3}[/tex] ft/s along the ground when the botton of the ladder is at a distance of 6 ft from the wall.

Here we have been mentioned that a 12 feet ladder is leaning against the wall which is represened by AC in the below given triangle.

We have AB = y = distance of top of the ladder from the wall

BC = x = distance of bottom of the ladder from the wall

AC = z = height of the ladder = 12 ft (given)

The top of the ladder AB is sliding down at a rate of 4 [tex]ft/s[/tex]

∴ [tex]\frac{dy}{dt}[/tex] = - 4 ft/s (negative sign indicates that the top is sliding downwards)

Let the rate at which the bottom of the ladder is sliding be [tex]\frac{dx}{dt}[/tex]

Now in the right angled triangle [tex]ABC[/tex] by using Pythagoras theorem we have,

[tex]AB^{2} + BC^{2} =[/tex][tex]AC^{2}[/tex]

[tex]y^{2} +x^{2} = z^{2}[/tex]    (equation 1)

When x = 6ft and z = 12 ft,

[tex]y^{2} +6^{2} = 12^{2}[/tex]

⇒ [tex]y^{2} = 144 - 36[/tex]

⇒ [tex]y^{2} = 108[/tex]

⇒ y = √108

⇒ y = 6 √3 ft

Differentiating equation 1 with respect to [tex]time[/tex] we get,

[tex]\frac{d}{dt} (y^{2} +x^{2} ) = \frac{d}{dt} (z^{2})[/tex]

⇒ 2y[tex]\frac{dy}{dt}[/tex] + 2x[tex]\frac{dx}{dt}[/tex] = 2z[tex]\frac{dz}{dt}[/tex]

Putting the values of dz/dt = 0 (as the height is constant) , dy/dt = - 4 ft/s , y = 6 √3 ft, x = 6ft and z = 12ft we have,

∴ 2(6√3) (-4) + 2(6)[tex]\frac{dx}{dt}[/tex] = 2(12)(0)

⇒ -48√3 + 12[tex]\frac{dx}{dt}[/tex] = 0

⇒ 12[tex]\frac{dx}{dt}[/tex] = 48√3

⇒ [tex]\frac{dx}{dt} = \frac{48\sqrt{3} }{12}[/tex]

⇒ [tex]\frac{dx}{dt} = 4\sqrt{3}[/tex] ft/s

Hence the rate at which the bottom of the ladder is sliding is [tex]\frac{dx}{dt} = 4\sqrt{3}[/tex] ft\s

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Based on the mathematical statement, the unit rate is 3/4 books per hour

The mathematical statement is given as

"rewrite 1/4 book 1/3hour as a unit rate"

The above means that

Book = 1/4

Time = 1/3 hour

The unit rate is then calculated as

Unit rate = Book/Time

Substitute the known values in the above equation

So, we have the following equation

Unit rate = (1/4)/(1/3)

Evaluate

Unit rate = 3/4

Hence, the solution is 3/4 books per hour

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The variance of the sample mean is 12/35 = 0.3429.. This is a result of uniform distribution.

The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive.

According to the question, we have

Sample size (n) = 36; uniform continuous distribution has a maximum of 14 and a minimum of 2.

The notation for the uniform distribution is

X U(a,b), where  a=  the lowest value of x  and  b=  the highest value of x. The probability density function is f(x) = 1/(ba ) fo axb .

b = 14 and a = 2.

Variance in uniform distribution = (b-a)² / 12.

Put the value of a and b, 

Variance = ( 14-2)²/12 = 12

Sample variance is used to calculate the variability of sample sets.

The variance of the sample means = variance / (sample size- 1) 9= (b-a)²/ (n-1)

= 12/35= 0.342

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Answer: Here you go

Step-by-step explanation:

Answer:ok

Step-by-step explanation: good job

The output of the program code block given will be two.

Python is a high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation.

Given is the following code structure -

x = 6 % 2

if x == 1:

  print("ONE")

else:

  print("TWO")

If we dry run the program, we can write -

x = 6 % 2

x = 0

Now, x is not equal to 1, therefore, it will print two.

Therefore, the output of the program code block given above will be two.

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Answer:

a = 3 , b = - 18

Step-by-step explanation:

2 - [tex]\frac{x+1}{x-2}[/tex] - [tex]\frac{x-4}{x+2}[/tex]

express as a fraction with common denominator (x - 2)(x + 2)

= [tex]\frac{2(x-2)(x+2)-(x+1)(x+2)-(x-4)(x-2)}{(x-2)(x+2)}[/tex]

= [tex]\frac{2(x^2-4)-(x^2+3x+2)-(x^2-6x+8)}{x^2-4}[/tex]

= [tex]\frac{2x^2-8-x^2-3x-2-x^2+6x-8}{x^2-4}[/tex]

= [tex]\frac{3x-18}{x^2-4}[/tex]

compare to [tex]\frac{ax+b}{x^2-4}[/tex]

with a = 3 and b = - 18

Answer:

1a. 4/6

1b. 6/9

1c. 8/12

2. [tex] \frac{6}{12} [/tex]

3. 8/16

Step-by-step explanation:

1a. Multiply top and bottom value by 2

1b.multiply top and bottom value by 3

1c. multiply top and bottom value by 4

2.To get your denominator to twelve you multiply it by 2. and if you multiply by two at the bottom you also multiply by two on top.

3.to get your denominator to 16 multiply the denominator by 8. If you multiply the bottom you should multiply the top with the same value as well.

If  the probability that the florist shop will get at most 4 phone orders in a 30 minute period using the Poisson distribution, the average number of phone orders per 30 minutes is 5.

Given data:

Average 18 phone order in 2 hour

4 phone orders in a 30 minute

Let x  represent the average number of phone orders in 30 minutes.

Hence

then x30=18/120

Solving  for x

x =18(30)/120

x = 540 / 120

x = 4.5

x = 5 (Approximately)

Therefore we can conclude that 5 is the average number of phone that was order.

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