Explain how you can prove the difference of two cubes identity. a3 – b3 = (a – b)(a2 + ab + b2)

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:

The sum is positive.

Step-by-step explanation:

The 20 is a far greater value than -8, so no matter what, when you add them the sum will be positive. Though this would not be the same were the -8 greater than -20.

Hope this helps!

Answer:

13

Step-by-step explanation:

5x + 25 = 7x - 1

-7x. -7x

-2x + 25 = -1

-25. -25

-2x = -26

-2. -2

x = 13

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.

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:

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

Answer:

the answer is B

Step-by-step explanation:

Answer:

B, y = (x+2)^2+3

Step-by-step explanation:

Hi adenpetkowski, well to solve this problem we need to find the equation, so since a vertical parabola have equation of y = a(x-h)^(2)+k, where (h, k) is the vertex, we can use this formula to find the equation for the parabola, so since the vertex is (-2, 3) assuming it's lattice points, the formula now is y = a(x+2)^2+3, next, we can find a by taking a point from the parabola, say, (-1, 4). We then substitute the y and x to find that 4=a(1)^2+3, and we can find that a = 1. so the Formula is y=(x+2)^2+3. B

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

sorry for my messy handwriting!!!

Step-by-step explanation:

At age 77, Eastman suffered from chronic pain due to a spinal condition. On March 14, 1932, after a reportedly jovial meeting with friends, he excused himself to write a brief letter before he 4535

Answer:

Three consecutive even integers are x, x+2, x+4.

Step-by-step explanation:

Their sum is x+x+2+x+4 = 3x+6.

Hope this helped! <3

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:

9, 36, and 45

Step-by-step explanation:

The order is 9, 36, and 45 because as we have to divide 90 into 1:4:5, 1+4+5=10 total parts. Then 90 divided by 10 equals to 9. The first number has 1 part, so 9x1=9 for the first number. For 4 parts, 9x4=36 for the second number. For 5 parts, 9x5=45 for the third number. The order is 9, 36, and 45. Hope it helps!

When we divide 90 in 1:4:5 ratio so it comes 9,36, and 45.

Given that,

Based on the above information, the calculation is as follows:

x + 4x + 5x = 90

10x = 90

x = 9

Now multiply each ratio with 9 to get each value.

So, the values should be 9,36, and 45.

Therefore we can conclude that when we divide 90 in 1:4:5 ratio so it comes 9,36, and 45.

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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.

the quotient is that best of luck

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:

The set of all points that are 10 units from the origin is the circle centered at (0,0) with radius 10, which has equation  

x2 + y2 = 100.

So, if the y-coordinate is -6, then x2 + 36 = 100.

 x2 = 64

 x = ±8

The points are (8,-6) and (-8,-6).

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:  (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

Answer:

c

Step-by-step explanation:

c because

Answer:

Step-by-step explanation:

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

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

-1*7

-7

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:

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:

your answer is A

Step-by-step explanation:

Answer: y= -2x + 3

Step-by-step explanation:

Step-by-step explanation:

f(x)=|x|+8

f(-3)=|-3|+8 =3+8 =11