how to explain distributive property to show equivalent expression for 54 and 42

The fourth degree Taylor polynomial of f(x) centered at 2 the \(T_4(2.4) = 11.0225\).

What is Taylor polynomial?

The Taylor series or Taylor expansion of a function in mathematics is the infinite sum of terms expressed in terms of the function's derivatives at one particular point. The function and the sum of its Taylor series are roughly equal for the majority of common functions at this point.

Given:

\(f(x) = e^x\)  centered at 2.

\(f(2) = e^2\)

\(f'(x) = \frac{d}{dx}e^x = e^x , f'(2) = e^2\\f"(x) = \frac{d^2}{dx}(e^x) = e^x, f"(2) = e^2\\ f^3(x) = \frac{d^3}{dx}(e^x) = e^x, f^3(2) = e^2\\ f^4(x) = \frac{d^4}{dx}(e^x) = e^x, f^4(2) = e^2\)

Therefore,

\(T_4(x) = f(2) + \frac{f'(2)(x-2)}{1!} + \frac{f"(2)(x-2)^2}{2!} + \frac{f^3(2)(x-2)^3}{3!} + \frac{f^4(2)(x-2)^4}{4!} \\T_4(x) = e^2 [1 + (x - 2) + \frac{(x-2)^2}{2}+\frac{(x-2)^3}{6}+ \frac{(x-2)^4}{24} \\ T_4(2.4) = e^2[1 + (2.4-2) + \frac{(2.4-2)^2}{2}+ \frac{(2.4-2)^3}{6}+\frac{(2.4-2)^4}{24}]\\ T_4(2.4) = 11.0225\)

Hence, the fourth degree Taylor polynomial of f(x) centered at 2 the \(T_4(2.4) = 11.0225\).

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Yes, Jalen is correct because the rectangle has a perimeter of 20 inches with the smaller side measuring 3 inches and the longer side of the rectangle had to be 7 inches.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(3 + 7)

20 = 2(10)

20 = 20 (True).

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Answer:

The solution to \(3x\:-\:1\ge 12\) is \(x\ge \frac{13}{3}\).

Step-by-step explanation:

An inequality is a mathematical relationship between two expressions and is represented using one of the following symbols: inequalities involving "<", "≠" or ">" are referred to as "strict inequalities", while inequalities involving "≤" or "≥" are not.

Solving an inequality means finding all of its solutions. A solution of an inequality is a number which when substituted for the variable makes the inequality a true statement.

To find the solution to \(3x\:-\:1\ge 12\)

\(\mathrm{Add\:}1\mathrm{\:to\:both\:sides}\\\\3x-1+1\ge \:12+1\\\\\mathrm{Simplify}\\\\3x\ge \:13\\\\\mathrm{Divide\:both\:sides\:by\:}3\\\\\frac{3x}{3}\ge \frac{13}{3}\\\\\mathrm{Simplify}\\\\x\ge \frac{13}{3}\)

Answer:

B. Pentagon

Step-by-step explanation:

A Pentagon is a polygon with 5 sides like this one.

Hope that helps!

Answer:

9=-1=?

Step-by-step explanation:

What is the question. Do you want us to evaluate it?

The probability that the sum of the pips selected that is at least 11 would be = 1/12.

To determine the probability of the selected events, the formula for problem should be used which is given below;

Probability = possible outcome/sample space

Possible outcome = at least 11 = (5,6),(6,5),(6,6)

= 3

Sample space = 36

Probability = 3/36 = 1/12

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Answer:

The answer is option D

Step-by-step explanation:

Volume of a sphere is given by

\(V = \frac{4}{3} \pi {r}^{3} \)

where r is the radius

From the question to calculate the radius we use the formula

radius = diameter / 2

diameter =70mm

radius = 70/2 = 35 mm

So the volume of the sphere is

\(V = \frac{4}{3} \pi \times {35}^{3} \)

\(V = \frac{171500\pi}{3} \)

We have the final answer as

Hope this helps you

Answer:

B

Step-by-step explanation:

6x -8y = - 16y

6x = -8y

8y = 17x + 4

-8y = -17x - 4

6x = -17x - 4

23x = -4

x = -4/23

If the value of sin x = 0.2, then the values for sin(π - x) is 0.2.

Given that,

the value of sin x = 0.2

We have to find the value of sin(π - x).

We know the trigonometric rule that,

sin(π - x) = sin (x)

for any value of x.

So here whatever the value of x, the value of  sin(π - x) is sin (x) itself.

So here sin x = 0.2.

So, by the rule,

sin(π - x) = sin (x) = 0.2

Hence the value is 0.2.

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A mathematically indication example would be to solve the equation 3x + 2 = 14 for the value of x. The solution would be 4.

Looking for a mathematically indication example, we can consider a simple mathematical equation with one variable and solve it.

The equation would be 3 x + 2 = 14.

So we can solve for the equation to be :

3x + 2 - 2 = 14 - 2

3x = 12

3 x / 3 = 12 / 3

x = 4

In conclusion, the mathematically indication example would be 3x + 2 = 14 and the value of x would be 4.

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1. The x - intercepts of the parabola are

2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex of the parabola is at (5, 80).

A parabola is a curved shape

1. Given the parabola above, to find the x - intercepts, we proceed as follows.

The x-intercepts are the points at which the graph cuts the x-axis.

They are

2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.

The plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex is the maximum point on the graph.

So, we see that the vertex is at x = 5 s and y = 80 ft

So, the vertex is at (5, 80).

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Answer:

178,200 ways

Step-by-step explanation:

Given that :

Here,

Lerenzo can choose ;

4 appetizers from 12 = 12C4

2 entrees from 9 = 9C2

3 side dishes from 5 = 5C3

Recall :

nCr = n! / (n-r)! r!

Number of ways = 12C4 * 9C2 * 5C3

12C4 = 12! / (12 - 4)!4! = 12! / 8!4! = 495

9C2 = 9! / (9 - 2)!2! = 9! / 7!2! = 36

5C3 = 5! / (5 - 3)!3! = 5! / 2!3! = 10

Number of ways = 495 * 36 * 10 = 178,200

Answer:

Using vector concepts, it is found that:

1. The horizontal component of the vector is 5.

2. The magnitude is of 14.87.

3. The vertical component of the vector is 2.

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

A vector (x,y) has x as horizontal component and y as vertical component.

The magnitude is  

Given two points, a vector is formed by the subtraction of the endpoint by the start point.

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

Item 1:

The horizontal component of the start is -3.

The horizontal component of the end is 2.

Thus, the horizontal component of the vector is  

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

Item 2:

Starts at (1,9), ends at (6,-5), thus, the coordinates are:

The magnitude is:

The magnitude is of 14.87.

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

Item 3:

The vertical component of the start is -10.

The vertical component of the end is -8.

Thus, the vertical component of the vector is

Step-by-step explanation:

Answer: a, b, d

Step-by-step explanation: don’t count me on it

Answer:

B, D

Step-by-step explanation:

just find the common denominator and see if it works

9514 1404 393

Answer:

  16 square units

Step-by-step explanation:

The figure is a square with side lengths 4.

The area is 4×4 = 16 square units.

Answer:

Can you please format this? it's hard to understand right now

well, keeping in mind that to draw a line all we need is two points, now, the one drawn already has many points let's pick two off of it, hmmm (-1,4) and (-6,-2).

Now, let's recall that for inverse functions, the domain of the original is the range of the inverse and the range of the original is the domain of the inverse, what does that mean? heheh, well, it simple means that for any point on the original that is say (a , b), the inverse will have a point at the flipped version of it of (b , a).  So if the orginal has the points aforementioned above, then the inverse will surely have the points of (4 , -1) and (-2 , -6), and we can just draw a line through those.  Check the picture below.

According to the Empirical Rule, 99.7% of the measures fall within 3 standard deviations of the mean in the normal distribution.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

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The perimeter of a polygon is expressed as; the sum of all sides. In this case it is: 48cm.

It is to be noted that the image in this case is not supplied hence a supplementary image is used. See the attached. Based on this information,

To find the perimeter of the polygon, we need to find the lengths of the AB, BC, CD and DA

Since,  and to find the length, from circle theorem, "Two tangents from an external point to a circle are always equal in length".

From this statement we shall conclude,

Thus, the perimeter of the polygon is

AB + BC + CD + DA

= 11 +  13 + 13 + 11

= 48cm

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Answer: -5x^2 + 2

Step-by-step explanation:

"A school sports team sold candy bars to raise money for new uniforms.", The team sold the same amount of candy bars at

Week 3. 17/51 or 0.33 Option C.

This is further explained below.

Generally,  to give up something of worth in exchange for money or another commodity of value My brother bought the bicycle from him so that he could put it up for sale. The shop is a retailer of footwear. to be marketed or given a price The new product is doing quite well in the marketplace. Each one of them retails for one dollar.

In conclusion, The week with the highest percentage of sales is week three as

17/51>>8/25>>32%

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The value of the investment in 5 years is $5805.9

Interest is the amount earned over years for the amount invested.

It is given that

Principal = $5000

Rate = 3%

Compounded Quarterly

Time = 5 years

Amount = ?

The Amount is given by the formula

Amount = P( 1 + (r/n))ⁿˣ

Here n = t = time period for which the investment has been done.

Amount = 5000( 1+(3/4 * 100)⁴ˣ⁵

Amount = 5000 (1.16)

Amount = $ 5805.9

Therefore , The value of the investment in 5 years is $5805.9

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Answer:

4 cups=2 pint

3 cups=1.5 pint

5 cups=2.5 pints

Step-by-step explanation:

Because there are 2 cups in each pint, we can divide the number of cups by two to get the number of pints.

4/2=2

3/2=1.5

5/2=2.5

Let me know if you have any questions!

Answer:

A. 40 degree+ 90 degree = x

The sum of the angles = 130 degree

Step-by-step explanation:

\(Given:\:\:\angle RSV = 40\degree,\:\:\angle VST = 90\degree\\\because \angle RSV + \angle VST = \angle RST\\\therefore 40\degree + 90\degree = x\)

x = 130 degree

Answer:

6.7

Step-by-step explanation:

24.90 (saw) + 18.40 (hammer) = 43.3

43.3 - 50 = 6.7