Write the equation of line of the line that passes through the point (5, 6) and a slope of 2

Let \(\(a\)\) and \(\(b\)\) be integers such that \(\(ab = 4\)\). We want to prove that \(\((a - b)^3 - 9(a - b) = 0\).\)

Starting with the left side of the equation, we have:

\(\((a - b)^3 - 9(a - b)\)\)

Using the identity \(\((x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3\)\), we can expand the cube of the binomial \((a - b)\):

\(\(a^3 - 3a^2b + 3ab^2 - b^3 - 9(a - b)\)\)

Rearranging the terms, we have:

\(\(a^3 - b^3 - 3a^2b + 3ab^2 - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\(a^3 - b^3 - 3a^2(4) + 3a(4^2) - 9a + 9b\)\)

Simplifying further, we get:

\(\(a^3 - b^3 - 12a^2 + 48a - 9a + 9b\)\)

Now, notice that \(\(a^3 - b^3\)\) can be factored as \(\((a - b)(a^2 + ab + b^2)\):\)

\(\((a - b)(a^2 + ab + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Simplifying further, we get:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\)

Now, we can observe that \(\(a^2 + 4 + b^2\)\) is always greater than or equal to \(\(0\)\) since it involves the sum of squares, which is non-negative.

Therefore, \(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\) will be equal to \(\(0\)\) if and only if \(\(a - b = 0\)\) since the expression \(\((a - b)(a^2 + 4 + b^2)\)\) will be equal to \(\(0\)\) only when \(\(a - b = 0\).\)

Hence, we have proved that if \(\(ab = 4\)\), then \(\((a - b)^3 - 9(a - b) = 0\).\)

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Answer: Baggy clothes, a new phone, art supplies, jewelry, posters(marvel, Billie Eilish, and just some random posters that I love) and room decorations.

Step-by-step explanation:

:D

To compare the values \(\(\frac{1}{3}\), \(\ln 1.5\)\), and \(\(\frac{5}{12}\)\), we can use the concept of areas. However, the provided sequence, 64, 112, 196, 343, does not give enough information to determine the common ratio.

(a) To compare the values \(\(\frac{1}{3}\), \(\ln 1.5\), and \(\frac{5}{12}\)\), we can utilize the concept of areas. We start by considering the area under the curve of the function \(\(y = \frac{1}{x}\) between \(x = 1\) and \(x = 1.5\)\). The area of this region represents \(\ln 1.5\). Similarly, we divide the area under the curve of \(\(y = \frac{1}{x}\) between \(x = 1\) and \(x = 2\)\) into three equal regions. The middle region represents \(\frac{1}{3}\), and the rightmost region represents \(\(\frac{5}{12}\)\). By comparing the areas visually or using calculus, we can confirm that \(\(\frac{1}{3} \ < \ \ln 1.5 \ < \ \frac{5}{12}\)\).

However, the second part of the question, regarding finding the common ratio in the sequence 64, 112, 196, 343, cannot be answered with the given information. A geometric sequence follows the pattern where each term is obtained by multiplying the previous term by a constant value called the common ratio. Without knowing the pattern or additional terms of the sequence, we cannot determine the common ratio. Therefore, we cannot provide a value rounded to the nearest hundredth for the common ratio in this sequence.

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Answer:

B) Reflect triangle ABC across line BC

and the 2nd one is also B

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer: -4.2

Step-by-step explanation:

=1-6+0.8

=-4.2

Answer:

18

Step-by-step explanation:

X= -6 which is x≤2

So,

f(-6) = -2(-6)+6

= 18

Answer: -2 1/16

if you add it all together it  should be 2 1/16

hoped this helped let me know if it did

Answer: 3.75

Step-by-step explanation:

3 is a whole number and 3/4 is 75% of 100 so this is why the answer is 3.75.

Hope this helps :)

Answer:3.75

Step-by-step explanation:

The midpoint of the line segment with the endpoints (5, 6) and (-5, -2) is (0, 2).Hence, the answer is: Midpoint = (0, 2).

The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is calculated using the formula:M = [(x1 + x2) / 2, (y1 + y2) / 2]where M is the midpoint.In the given problem, the endpoints are (5, 6) and (-5, -2).

So, we can find the midpoint by applying the formula mentioned above.Midpoint = [(5 + (-5)) / 2, (6 + (-2)) / 2]= [0/2, 4/2]= [0, 2]

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Answer:

your answer is 4+3

Step-by-step explanation:

Answer:

The answer to the question is (-5, -9)

The first step is to calculate the total area of 600 bricks.

Area of one brick = 12 inches x 18 inches = 216 square inches

Area of 600 bricks = 600 x 216 = 129,600 square inches

Next, we need to convert the height of the wall from feet to inches since the area of the bricks is in square inches.

10 feet = 120 inches

Now, we can divide the total area of the bricks by the height of the wall to find the length of the wall.

Length of the wall = Area of 600 bricks / Height of the wall
Length of the wall = 129,600 square inches / 120 inches
Length of the wall = 1080 inches

Finally, we can convert the length of the wall back to feet by dividing by 12 since there are 12 inches in a foot.

Length of the wall = 1080 inches / 12 inches/foot
Length of the wall = 90 feet

Therefore, the length of the wall is 90 feet.

To solve this problem, we need to use the formula for calculating area which is length x width. We also need to convert units from feet to inches and vice versa as necessary to ensure we are working with the same units throughout the problem.

The length of the wall is 90 feet.

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We are increasing every professor's salary by 4000, let this new salary be Yi for every professor then mean of new salary Y will be

Y = 1/n∑Yi

Y  = 1/n∑(Xi + 4000)

Y  = 1/n(∑Xi + ∑4000/n)

Y  = X + 4000

Median Xm is the middle most value of the Professor's old salary, since new salary is

            Yi = Xi + 4000

then new median salary Ym will be

            Ym = Xm + 4000

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Answer:

Step-by-step explanation:The mean and Median salary would increase by $4,000.

Let sum of the salaries be n1+n2+n3+.......... +n30

   Mean = sum of observation / no. of observation

Thus,

   Initial mean, M1 = n1+n2+n3+.......... +n30 / 30

When $4,000 is added to every salary 4000 is added 30 times to the sum.

Thus,

  New mean, M2 = n1+n2+n3+.......... +n30 +( 4000 * 30)

                                                30

                           = M1 + ( 4000 * 30)

                                              30

  Thus,         M2 = M1+ 4000

Therefore, The mean salary increase by $4,000.

We know Median of even number of observation =  [(n/2)th term + ((n/2) + 1)th term]/2

Here n/2th term is n15 and (n/2 +1)th term is n16

Thus,

    Initial Median, Median 1 = n15 + n16  

                                                     2

When $4,000 is increased in each salary

    New Median, Median 2 = n15 + 4000 + n16 + 4000

                                                                 2

                                         = Median 1 + 2 * 4000

                                                                    2

Thus,                  Median 2= Median 1 + 4000

Therefore, The median salary increases by $4,000

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Area of region A is equal to the sum of area of region B and area of region C when a right-angled triangle is formed by the diameters of three semi-circular regions A, B, and C.

Let the diameters of semicircle A, B and C be a, b and c respectively.

We know area of a semi-circular region of diameter d is

A = (1/2)(πd²/4)

A = πd²/8

Thus,

area of region A is πa²/8

area of region B is πb²/8

area of region C is πc²/8

The triangle formed is a right angled triangle, with hypotenuse a and legs b and c. By Pythagoras theorem

a² = b² + c²

Multiplying both sides by π/8

(π/8)a² = (π/8)(b² + c²)

πa²/8 = πb²/8 + πc²/8

Area of region A = Area of region B + Area of region C

Hence proved.

--The question is incomplete, answering to the question below--

"A right-angled triangle is formed by the diameters of three semi-circular regions A, B, and C as shown in the diagram. Show that area of region A = area of region B + area of region C."

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Answer:

x=30

Step-by-step explanation:

2x=x+30

x=30

Yes, they can use the walkie-talkies to talk to each other.

The distance between them is given as 28.2 meters.

The horizontal and vertical distances should be considered when calculating the distance between their apartments using the three-dimensional form of the Pythagorean theorem.

This comes out as \(\sqrt((18^2 + 19^2 + 7^2))\), which equals \(\sqrt(798)\) square root meters, or, to the nearest tenth, 28.2 meters.

Since this distance is less than the 35-meter range of the walkie-talkies, communication should be possible between the two apartments.

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Answer:

-18

Step-by-step explanation:

If you're looking for the y-intercept for this equation this means that x = 0.

So substitute x as 0 in the equation and you'll get the following.

y + 3 = 5 (0 - 3)

y + 3 = -15

y = -18

To compute the 99% confidence interval for the population mean, you need to determine the appropriate sample size to ensure that the sample mean does not deviate from the population mean by more than 1.3. The key terms involved in this process are the confidence interval, sample size, population mean, and sample mean.

The confidence interval represents the range within which the population parameter (in this case, the population mean) is likely to fall, given a certain level of confidence. A 99% confidence interval means that you are 99% confident that the true population mean falls within the specified range.

To calculate the required sample size, you will need to use the formula for the margin of error (E), which is E = (Zα/2 * σ) / √n, where Zα/2 is the critical value associated with the desired level of confidence (99%), σ is the population standard deviation, and n is the sample size.

Since you want the sample mean to not deviate from the population mean by more than 1.3, you will need to set E = 1.3 and solve for n. After finding the critical value for a 99% confidence interval (which is approximately 2.576) and assuming you know the population standard deviation, you can plug these values into the formula and solve for n.

By doing this, you will be able to determine the appropriate sample size to ensure that the 99% confidence interval for the population mean is within 1.3 units of the sample mean.

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As per the unitary method, most responsible for the increase is more packing.

The term unitary method in math refers the process of finding the value of a single unit, and based on this value.

Here we have given that One study indicates that each individual in the United States produces about 2 kg of solid waste per day. That figure is up from about 1.2 kg in 1960.

And we need to find most responsible for the increase.

While we looking into the given question, we have identified that in 1960 the solid waste per day is 1.2 kg.

And the current solid waste per day is 2 kg.

Then the the difference between these two is calculated as,

=> 2 - 1.2

=> 0.8kg.

So, there is 800 gram of waste is increased and while looking into the given option, the resulting one is option (a).

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Answer:

y=5x-2

Step-by-step explanation:

Answer:

y (x² + 1) (x² - 5)

Step-by-step explanation:

   Take 'y' from each term.

x⁴y - 4x²y - 5y = y[x⁴ - 4x² - 5]

Now factorize x⁴ - 4x² - 5.

            Sum = -4

        Product = -5

        Factors =  -5 , 1  

When we add (-5) + 1, it gives (-4) and when we multiply (-5)*1, gives (-5).

x⁴ - 4x² - 5 = x⁴ + x² - 5x² - 5

                 = x²(x² + 1)  -5(x² + 1)

                 = (x²+ 1) (x² - 5)

x⁴y - 4x²y - 5y = y (x² + 1) (x² - 5)

After considering all the given data we conclude that the current measured temperature in degree Fahrenheit is 91°F, under the condition that the midday temperature in Palm Beach was 86 °F and the given expression is 86 -|-2-3| which represents current temperature.

To evaluate the temperature let us first consider the expression 86 -|-2-3| which represents the current temperature after 3 hours of temperature change of 2°F per hour from an initial temperature of 86°F.

The given expression can be again simplified as

86 -|-2-3| = 86 -|-5|

= 86 - (-5)

= 91°F

Hence, after evaluating we finally measured the current temperature as 91°F.

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Answer:

-720

Step-by-step explanation:

We are given the expression:

\(10x^3y^2\)

and asked to evaluate when x= -2 and y= -3.

Therefore, we must substitute -2 for x and -3 for y.

\(10(-2)^3*(-3)^2\)

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Evaluate the first exponent.

⇒ (-2)³ = -2 * -2 * -2= 4*-2= -8

\(10(-8)*(-3)^2\)

Evaluate the second exponent.

⇒ (-3)²= -3 * -3= 9

\(10(-8)*9\)

Multiply 10 and -8.

\(-80*9\)

Multiply -80 and 9.

\(-720\)

The value of 10x³y² at x= -2 and y= -3 is -720

Answer:

Closed circle

Step-by-step explanation:

If the sign is less than or equal too/greater than or equal too the circle will be closed

Answer:

closed

Step-by-step explanation:

use an open circle for "less than" or "greater than", and a closed circle for "less than or equal to" or "greater than or equal to".

Answer:

7.45

Step-by-step explanation:

We are given a right triangle with one side length known and an angle know so we can use some trigonometry.

You need to find the hypotenuse so you are going to use either sine or cosine.

Since the adjacent from the angle is given (SOH-CAH-TOA) we can use cosine so,

cos(20) = 7/h

=>h = 7/cos(20)

=> 7.44924

=> 7.45

Answer:

48cm³

Step-by-step explanation:

volume = (7 X 6 X 1) + (3 X 2 X 1)

= (42 + 6)

= 48cm³

Answer:

66% or 2/3

Step-by-step explanation:

add all the games up and you get 24 games played total then divide 16 by 24 and you get .66 or 2/3 because 16 is 2/3 of 24 and they are both a multiple of 8

John and his three passengers travel a total of 20.25 miles on the toll lane.

To solve this problem, we can use the fact that each person pays about $0.81, which includes their contribution to the toll lane entry fee. This means that the total amount of money paid by John and his three passengers is 4 times $0.81, or $3.24.

We can then use this information to find the cost per mile of the toll lane. If they traveled a total of x miles on the toll lane, then the cost per mile would be:

$3.24 / x

We can set this equal to the given cost of 16 cents per mile:

$0.16 = $3.24 / x

Multiplying both sides by x, we get:

x * $0.16 = $3.24

Dividing both sides by $0.16, we get:

x = $3.24 / $0.16

x = 20.25 miles

In summary, to find the distance they traveled on the toll lane, we used the fact that they split the cost of the toll, and that each person paid about $0.81. We then set the cost per mile equal to the given cost of 16 cents per mile, and solved for the distance traveled on the toll lane, which turned out to be 20.25 miles.

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Answer:

\(f(x) = \frac{ {x}^{2} + x - 6 }{x + 2} = \frac{(x + 3)(x - 2)}{x + 2} \)

There are no holes in this function.

As x-->negative infinity, f(x)-->negative infinity.

As x-->infinity, f(x)-->infinity.