Differentiate. y = (x2 - 2x + 6) et O (2x - 2) ex (x2 + 4x + 4) ex O (x2 + 4) ex + 4x + 6​

Answer:

13

Step-by-step explanation:

5x + 25 = 7x - 1

-7x. -7x

-2x + 25 = -1

-25. -25

-2x = -26

-2. -2

x = 13

Answer:

I believe [tex]\lim_{x \to a} f(x)[/tex] also equals 0.

Step-by-step explanation:

We know that g(x) has to be greater than or equal to 0. That means f(x) has to be smaller than g(x) or equal to 0.

If we plug in any value of x, f(x) will be positive because of the absolute value. The only way we are going to get f(x) smaller than g(x) or equal to g(x) is to have very small fractions.

Therefore, if [tex]\lim_{x \to a} g(x)=0[/tex], then [tex]\lim_{x \to a} f(x)=0[/tex] because f(x) must be smaller or equal to 0 as well.

Answer:

[tex]\displaystyle{ \lim_{x\to a}f(x)=0[/tex]

Step-by-step explanation:

The other user posted a great answer, but I would like to show you a more mathematical way!

We have [tex]|f(x)|\leq g(x)[/tex].

By the definition of absolute value, this is the same as saying:

[tex]f(x)\leq g(x)\text{ and } -f(x)\leq g(x)[/tex]

For the right, we can divide both sides by -1 to acquire:

[tex]f(x)\leq g(x)\text{ and } f(x)\geq- g(x)[/tex]

We can now combine them. This yields:

[tex]-g(x)\leq f(x)\leq g(x)[/tex]

Now, we can use the Squeeze Theorem (a.k.a. Pinch or Sandwich Theorem). The Squeeze Theorem posits that if we have:

[tex]g(x)\leq f(x)\leq h(x)[/tex]

And:

[tex]\displaystyle{ \lim_{x \to c} g(x)= \lim_{x \to c} h(x)=L}[/tex]

Then the following must be true:

[tex]\displaystyle{ \lim_{x \to c} f(x)=L[/tex]

We have:

[tex]-g(x)\leq f(x)\leq g(x)[/tex]

And we know that:

[tex]\displaystyle{ \lim_{x \to a} g(x)=0[/tex]

Then it follows that:

[tex]\displaystyle{ \lim_{x \to a} -g(x)=- \lim_{x \to a} g(x)=0[/tex]

Therefore, by using the Squeeze Theorem, we can conclude that:

[tex]\displaystyle{ \lim_{x\to a}f(x)=0[/tex]

And we're done!

Answer:

C and E

Step-by-step explanation:

the b value of an exponential function needs to be greater than one to be exponential growth

[tex] \sqrt{2} [/tex]

and 1.1 are the only 2 that are greater than one

The possible values for b are those that are greater than 1. The correct answers are square root of  and 1.1, the correct options are C and E.

Consider the function:

[tex]y = a(1\pm r)^m[/tex]

where m is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.

If there is plus sign, then there is exponential growth happening by r fraction or 100r %

If there is negative sign, then there is exponential decay happening by r fraction or 100r %

We are given that;

f(x)=ab^x

Now,

An exponential growth function is a function that increases as x increases. For the function f(x) = ab^x, this means that the base b must be greater than 1, so that the exponent x makes the function larger.

Therefore, by the exponential growth and decay the answer will be square root of 2 and 1.1

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Answer:

the slope is m= [tex]\frac{1}{4}[/tex] and the y-intercept is: (0, -5)

Step-by-step explanation:

hope this helps! <3

Answer:

here we go.....

Step-by-step explanation:

9+5 equals14 5 +2 equals 7

14 divided by 7 equals 2

hope you get it correct

Answer:

78.5

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

c because

Answer:

for the first question

solve for t:t= square root of 2da/a (2da over a)

Solve for a : a= 2d/t squared

Solver for d: d=t squared /2(over 2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

(1-2*1) (3*2+4*-1*1- 1*2)

=-1 (6+4-1-2)

-1*7

-7

Answer:

A. X = 6.

Step-by-step explanation:

First, combine like-terms. Combine 3X and 2X to get 5X.

Next, add five to both sides to get rid of the five on the other side. This should get you 30.

Finally, divide by 5, you should get X = 6.

Answer:

3.99

Step-by-step explanation:

2.19x2=3.99

20.34-4.39=15.96

15.96 divided by 4 =3.99

Answer:

44 hours

Step-by-step explanation:

just do 22 x 2

Answer: If 2 log x + 3 log y = 0, find y in terms of x.

sorry for my messy handwriting!!!

Step-by-step explanation:

Answer: A. -1.8

Step-by-step explanation: Hi there!

First, we have to see the constant rate of change in the x and y values.

For x: 2

For y: -3.6

If the slope is m=y/x

then we can do

-3.6/2

that simplifies to

-1.8/1

which is

-1.8

Hope this answer helps you!

Answer:  (0,0)

Step-by-step explanation:

The only integer"s" that both add and subtract to the same value are 0 "and" 0.  Properly stated, the only integer that can be added to itself and subtracted from itself with the same outcome is 0.

Of course, k will also be 0

So this system of equation works out to be

0 + 0 = 0

0 - 0 = 0

Step-by-step explanation:

What is the probability there are 2000 or fewer downloads of Amazon Alexa in a day (to 4 decimals)?

First, find the z-score.

z = (x − μ) / σ

z = (2000 − 2800) / 860

z = -0.930

Use a chart or calculator to find the probability.

P(Z < -0.930) = 0.1761

What is the probability there are between 1500 and 2500 downloads of Amazon Alexa in a day (to 4 decimals)?

Find both z-scores.

z = (x − μ) / σ

z₁ = (1500 − 2800) / 860

z₁ = -1.512

z₂ = (2500 − 2800) / 860

z₂ = -0.349

Use a chart or calculator to find the probability.

P(-1.512 < Z < -0.349) = P(Z < -0.349) − P(Z < -1.512)

P(-1.512 < Z < -0.349) = 0.3636 − 0.0653

P(-1.512 < Z < -0.349) = 0.2983

What is the probability there are more than 3000 downloads of Amazon Alexa in a day (to 4 decimals)?

Find the z-score.

z = (x − μ) / σ

z = (3000 − 2800) / 860

z = 0.233

Use a chart or calculator to find the probability.

P(Z > 0.233) = 1 − P(Z < 0.233)

P(Z > 0.233) = 1 − 0.5919

P(Z > 0.233) = 0.4081

Assume that Google has designed its servers so there is probability 0.01 that the number of Amazon Alexa app downloads in a day exceeds the servers' capacity and more servers have to be brought online. How many Amazon Alexa app downloads per day are Google's servers designed to handle (to the nearest whole number)?

Use a chart or calculator to find the z-score given the probability.

P(Z > z) = 0.01

P(Z < z) = 0.99

z = 2.3263

Now find the corresponding number for that z-score.

z = (x − μ) / σ

2.3263 = (x − 2800) / 860

x = 4801

Using the binomial probability principle, the probability values for the number of downloads are :

Given the Parameters :

The Zscore formula ::

1.) Probability of 2000 or fewer downloads :

P(X ≤ 2000) = P(Z ≤ (2000 - 2800)/860)) = -0.930

Using a normal distribution table :

P(Z ≤ - 0.930) = 0.1762

2.) Probability of between 1500 and 2000 downloads :

P(1500 ≤ X ≤ 2500) = P(Z ≤ (2500 - 2800)/860) - P(Z ≤ (1500 - 2800)/860)

P(1500 ≤ X ≤ 2500) = P(Z ≤ - 0.349) - P(Z ≤ - 1.511)

P(1500 ≤ X ≤ 2500) = 0.3635 - 0.0654

P(1500 ≤ X ≤ 2500) = 0.2981

3.) Probability of more than 3000 downloads :

P(X > 3000) = P(Z > (3000 - 2800) / 860)) = 0.2325

P(Z > 0.2325) = 1 - P(Z < 0.2325)

Using a normal distribution table :

P(Z > 0.2325) = 1 - 0.5919 = 0.4081

4.) Number of downloads given a probability of 0.01

P(X > 0.01) ;

Using a normal distribution table :

The Z score corresponding to P(Z > 0.01) is 2.326

Using the Zscore formula to calculate the number of downloads, X ;

Zscore = (X - μ) / σ

2.326 = (X - 2800) / 860

2.326 × 860 = X - 2800

2000.36 = X - 2800

X = 2000.36 + 2800

X = 4800.36

Therefore, maximum daily download system is designed to handle 4800.

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Answer:

Read the explanation

Step-by-step explanation:

Go to desmos (website) and open the Graphic Calculator (or you can use any graphic calculator) . Then in one of the text boxes on the side write A(-6,2) and it'll plot it. Or make a paper graph (Make sure the lines are spaced out correctly) and go to -6 on the x axis and 2 on the y axis, the point in which those 2 intecept is the plotted dot. Or print a graph and plot it there, both work.

Answer:

p = 15/40

Step-by-step explanation:

Since the total number of marbles is 40, that is our size of the sample. there are 16 red ones on that sample, so the probability of extracting a red marble from the box is given by the ratio of successes divided the total number of marbles:

p = 15/40

Answer:

$44

Step-by-step explanation:

So this original price is 110 dollars, with a 40% discount.

1) You want to change 40% to a decimal to be able to multiply. this is 40/100=0.4

2) With that in mind you can then do 110x0.4=44

That means the new discounted price is $44.

Answer: y= -2x + 3

Step-by-step explanation:

Answer:

A' (4,4), B' (5,7), C' (9,7)

Step-by-step explanation:

Answer:

your answer is A

Step-by-step explanation:

Answer:

do multiply

Step-by-step explanation:

and take line in right side

The solution of the inequality 2x - (3 – x) > x + 1 is the values greater than 2. Therefore, option D is the correct answer.

The given inequality is 2x - (3 – x) > x + 1.

A solution for an inequality in x is a number such that when we substitute that number for x we have a true statement.

Now, 2x - (3 – x) > x + 1 can be solved as follows:

2x -3+x>x+1 (Simplify the bracket)

⇒3x-3>x+1

Subtract x on both the sides of the inequality.

That is, 3x-3-x>x+1-x

⇒2x-3>1

Add 3 on both the sides of the inequality.

That is, 2x>4

Divide 2 on both the sides of the inequality.

That is, 2x÷2>4÷2

⇒ x > 2

The solution of the inequality 2x - (3 – x) > x + 1 is the values greater than 2. Therefore, option D is the correct answer.

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Answer:

5.5

Step-by-step explanation:

The y-intercept of the line graph shown above is the value of the point where the line cuts the y-axis. The y-intercept of this graph is between 5 and 6. However, we can get an accurate value by calculation. This can be done by generating an equation of the line.

Recall the slope-intercept equation, [tex] y = mx + b [/tex], where m = slope of the line, b = y-intercept.

To generate the equation of the line, first find slope using the points (-2, 7) and (6, 1):

[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 7}{6 -(-2)} = \frac{-6}{8} = -\frac{3}{4} [/tex].

Substitute m = ¾ and the coordinates (6, 1) into the slope-intercept equation to find the y-intercept (b):

[tex] y = mx + b [/tex]

[tex] 1 = -\frac{3}{4}(6) + b [/tex]

[tex] 1 = -\frac{18}{4} + b [/tex]

[tex] 1 = -4.5 + b + 4.5 [/tex]

[tex] 1 + 4.5 = -4.5 + b + 4.5 [/tex]

[tex] 5.5 = b [/tex]

Therefore, b = y-intercept = 5.5.

To generate the equation of the line, plug in the values of m and b, we would have:

y = ¾x + 5.5

The y-intercept of the line of the graph is 5.5.

6y^2 + 6y + 2y + 2 = 6y^2 + 8y + 2

The way you do this is basically multiplying the values in the brackets with 6y, and then adding that to the same values multiplied by 2.

Answer:

78 people were on the boat to begin with.

Step-by-step explanation:

Moving backwards is the way to solve this question.

74 - 22 = 52

52 + 26 = 78

And to prove the answer is correct.....

78 - 26 = 52

52 + 22 = 74

All of the aforementioned represent the same function except: C. {(0, 1), (2, 3), (4, 5), (7, 8)}.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables.

In Mathematics, there are different types of function and these include the following;

From the first mapping, we can logically deduce the following:

when x = 1, y = 0

y = x - 1

0 = 1 - 1

when x = 3, y = 2

y = x - 1

2 = 3 - 1

when x = 5, y = 4

y = x - 1

4 = 5 - 1

when x = 8, y = 7

y = x - 1

7 = 8 - 1

For the ordered pair, we have:

when x = 0, y = 1

y = x + 1

1 = 0 + 1

when x = 2, y = 3

y = x + 1

3 = 2 + 1

when x = 4, y = 5

y = x + 1

5 = 4 + 1

Therefore, the function for these ordered pairs is equal to y = x + 1.

For the table of value, we have:

when x = 1, y = 0

y = x - 1

0 = 1 - 1

In this context, we can reasonably infer and logically deduce that all of the aforementioned represent the same function except {(0, 1), (2, 3), (4, 5), (7, 8)}.

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