Directions: Simplify by multiplying the expressions.
1. (X + 8) (x-8)
2. (y + 10) (Y-10)
3. (m-4)(m + 4)
4. (n - 9) (n + 9)
5. (3x + 1)(3x - 1)
6. (5c+4)(5c - 4)
7. (11z-7)(11z + 7)
8. (20x + 9) (20x-9)
9. (8x + 3y)(8x - 3y)

Using the US customary system, 1 tablespoon is equivalent to 0.5 fluid ounces. A tablespoon is equivalent to 0.5 fluid ounces. According to the Imperial system, 1 imperial tablespoon is equal to 0.625 imperial ounces.

By multiplying the quantity of US tablespoons by 0.5—0.5 is a conversion factor—you can convert US tablespoons to fluid ounces:

the tablespoon times 0.5.

Multiply the amount of tablespoons by 0.625, where 0.625 is a conversion factor, to convert imperial tablespoons to imperial ounces:

by 0.625 times the tablespoon.

Consider an illustration. The US measurement system is applied to all computations below.

How many ounces are in two tablespoons?

2 tablespoons multiplied by 0.5 equals 1 fluid ounce, thus

two teaspoons make up one fluid ounce.

This table translates a quantity in teaspoons (tbsp) into fluid ounces (fl oz).

Tablespoons Ounces Tablespoons Ounces

8 tbsp of 1/2 teaspoon 0.25 fluid ounces

2 tbsp 1 fl ounce 10 tbsp 5 fl oz, 1 tbsp 0.5 fl oz, 9 tbs 4.5 fl oz, and 2 tbs 1 fl oz

3 tbsp 1.5 fl oz, 12 tbsp 6 fl oz

4 tbsp./2 fl. oz.

14 tbsp 7 fl oz, 5 tbsp 2,5 fl oz, and 16 tbsp 8 fl oz, along with 6 tbsp 3 fl ounce

17 tablespoons, 9 fluid ounces, 7 tablespoons, and 20 tablespoons

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A stick has a length of 5 units and the stick is then broken at two points, chosen at random, then the probability that all three resulting pieces are shorter than 3 units is 16%.

Total length of the stick = 5 units

The stick is broken into pieces = 3

The equal length of the stick = 5/3

The equal length of the stick = 1.67

The probability that all three resulting pieces are shorter than 3 units = 2/5 × 2/5

The probability that all three resulting pieces are shorter than 3 units = 4/25

The probability that all three resulting pieces are shorter than 3 units = 0.16

The probability that all three resulting pieces are shorter than 3 units = 16%

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The selling price for the jacket is $36.

To determine the selling price of the jacket, we need to calculate the markup percentage on the original price of $20. A markup percentage is the increase in price over the original cost. In this case, the markup percentage is 80%, which means the selling price is $20 + ($20 * 0.8) = $20 + $16 = $36.

Here is the breakdown of the calculation:

Original cost of the jacket: $20

Markup percentage: 80%

Markup amount: $20 * 0.8 = $16

Selling price: $20 + $16 = $36

Therefore, The selling price for the jacket is $36.

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Answer:

it is B

Step-by-step explanation:

It is B the answer is B you can make sure by using distance formula.

The intersection of events A and B is the event of exactly two tails. This is because event A is defined as exactly two tails and event B is defined as at least two tails.

Since two tails is both exactly two tails and at least two tails, the intersection of the two events is exactly two tails.

The intersection of two sets is the set of all elements that are common to both sets. This is also known as the intersection of two conjunctions. To find the intersection of two sets, you take the elements from both sets and keep only the elements that are found in both sets. For example, given the sets A = {1, 2, 3} and B = {2, 3, 4}, the intersection of A and B would be {2, 3}.

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It takes the runner distance 15.625 seconds to get to the flagpole because 125m/8m/s equals 15.625s.

1. Determine the distance: 125 metres

2. Determine the velocity: 8 m/s

3. Calculate the time as follows: 125 m/ 8 m/s = 15.625 s

We must know the distance the runner must cover and their pace in order to determine how long it will take them to get to the flagpole. This time, the runner begins 125 metres west of the flagpole and moves east at a speed of 8.0 metres per second. The formula distance (in meters)/speed (in metres per second) = time can be used to determine how long it takes the runner to get to the flagpole (in s).  Given that the speed is 8 m/s and the distance is 125 m, the calculation is 125 m/ 8 m/s = 15.625 s. It follows that the runner needs 15.625 seconds to get to the flagpole. This formula can be used to determine how long it will take any object to go a specific distance at a specific speed. It is crucial to remember that in order to obtain the duration in s, the speed must be expressed in m/s and the distance must be expressed in m.

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Answer:

see below

Step-by-step explanation:

z+66+z+69+43z=180

so 45z=180-66-69 = 45

so z=1

so angle U= 43 its opposite side length ST is the smallest

same logic for the other 2.

66+1=67

69+1=70

so ST<US <TU

Answer:

B

Step-by-step explanation:

Linear equations are straight lines and exponential equations are curves. Since this is a curve, we can get rid of A and C

Looks like the graph is a downwards line, so decreasing

Tthe required simplified solution of the given expression is -3.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Given expression
=  -3(9)⁰
= -3(1)     [a⁰ = 1]
= -3

Thus, the required simplified solution of the given expression is -3.

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Answer:

11 units

Step-by-step explanation:

-5 to zero is 5 units

zero to 6 is 6 units.

The solution of the inequality 3x + 4y ≤ 5 is (2, -1)

In mathematics, Inequality is a mathematical statement that gives unequal comparisons between algebraic terms or algebraic equations using the signs like less than, greater than, etc. The solution to an inequality is a value that satisfies the given inequality.    

Here we have

The inequality 3x + 4y ≤ 5  

To be the solution to given inequality, the ordered pair must satisfy the given equation  

So to find the correct solution check which of the following will satisfy the given inequality.    

At A. (7, 2)  

=>  3x + 4y ≤ 5  

=>  3(7) + 4(2) ≤ 5    

=>  29 ≤ 5   [ which is not true ]  

∴ A. (7, 2) is not a solution to the given inequality  

At B. (2, -1)

=> 3(2) + 4(-1) ≤ 5    

=> 6 - 4 ≤ 5  

=> 2 ≤ 5     [ which is true ]

∴ B. (2, -1) will be a solution to the given inequality  

C. (6, 1)

=> 3(6) + 4(1) ≤ 5    

=> 18 + 4 ≤ 5    

=> 22 ≤ 5    [ which is not true ]

∴ C. (6, 1) is not a solution to the given inequality

D. (5, -1)​  

=> 3(5) + 4(-1) ≤ 5  

=> 15 - 4 ≤ 5  

=> 11 ≤ 5   [ which is not true ]

∴ D. (5, -1)​ is not a solution to the given inequality

Therefore,

The solution of the inequality 3x + 4y ≤ 5 is (2, -1)

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The probability that both quartz and tourmaline will be found, but not aquamarine is P(A intersection B) = P(A)*P(B) = 0.80 * 0.36 = 0.29.

The Venn diagram for this situation is as follows:

A: Quartz specimens are found  _____

B: Tourmaline specimens are found  ____

C: Aquamarine specimens are found ____

The probability that both quartz and tourmaline will be found, but not aquamarine is P(A intersection B) = P(A)*P(B) = 0.80 * 0.36 = 0.29.

The probability that quartz will be found, but not tourmaline or aquamarine is P(A) – P(A intersection B) – P(A intersection C) = 0.80 - 0.29 - 0.24 = 0.27.

The probability that none of these types of specimens will be found is 1 – P(A) – P(B) – P(C) + P(A intersection B) + P(A intersection C) + P(B intersection C) = 1 - 0.80 - 0.36 - 0.28 + 0.29 + 0.24 + 0.16 = 0.17.

The probability of A intersection (B union C) is P(A)*P(B union C) = P(A)*(P(B) + P(C) – P(B intersection C)) = 0.80 * (0.36 + 0.28 – 0.16) = 0.41.

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A rectangle with sodes of lengrh 84 and 45 has the same perimeter asa hexagon. If the sides of the hexagon all have the same length then what is the length of a side of the hexagon

(A) 41

(B) 46

(C) 43

(D) 45

(E)Other

A square has an area of 25. Two opposite side of the square each have their length tripled what is the perimeter of the new figure

(A) 40

(B) 25

(C) 60

(D) 35

(E)Other

A rectangle measures 6 centimeters by 25 centimeters the probability that a point randomly chosen inside the rectangle is closer to a side of length 25 than a side of length 6 is p/q are relatively prime positive whole numbers what is the sum of p and q

(A) 5

(B) 19

(C) 37

(D) 47

(E)Other

The three values of x that are solutions to X^3 + mx = 37x^2 +n are positive whole numbers that form a geometric sequence what is the sum of the possible values of the common ration of the geometric sequence

(A) 25/12

(B) 9/4

(C) 7/4

(D) 2

(E)Other

Answer: 10/12

Step-by-step explanation:

Make 1/4 have the same denominator as 7/12. 1/4=3/12. 7/12+3/12 = 10/12

Matrix A belongs to the permutation and Markov classes.

This is the case for matrix A, as it has one 1 in each row and column and 0s everywhere else. Matrix A is also a Markov matrix, which means that all the entries are non-negative and the sum of each row is equal to 1. This can be seen by summing each row, which yields 1+0+0 = 1, 0+1+0 = 1, and 1+0+0 = 1.

Matrix B belongs to the orthogonal, projection, and diagonalizable classes. Matrix B is orthogonal, which means that it is a square matrix whose columns and rows are orthonormal unit vectors (i.e. the dot product of any two columns or rows is 0). This is the case for matrix B, as the dot product of any two columns or rows yields 0. Matrix B is also a projection matrix, which means that it is a square matrix whose columns are all of unit length (i.e. the dot product of any two columns or rows is 1). This can be seen by taking the dot product of any two columns or rows, which yields 1. Finally, matrix B is diagonalizable, which means that it can be transformed into a diagonal matrix using a similarity transformation. This can be seen by calculating the eigenvalues and eigenvectors of matrix B, which yields the same diagonal matrix.

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The time complexity average of this problem is O(n³). It involves three nested loops, each loop iterating n times. Therefore, the time complexity is O(n³).

The time complexity of this problem is O(n³). This problem involves three nested loops, each loop iterating n times. This means that the problem requires at least O(n³) time to complete. In the outer loop, which is the first loop, the value of i is initialized to 1 and then the loop iterates n times, meaning that the outer loop requires O(n) time. In the second loop, which is the nested loop, the value of j is initialized to 1 and then the loop iterates n times, meaning that the second loop requires O(n) time. In the third loop, which is the innermost loop, the value of k is initialized to 1 and then the loop iterates n times, meaning that the third loop requires O(n) time. Since the three loops are nested, the total time complexity of this problem is the product of the time complexities of the three loops, which is O(n³). Therefore, the time complexity of this problem is O(n³).

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Answer:

D. 64x4964, x, 49

Step-by-step explanation:

The expression [4x4(2x3)]2 means to square the result of the expression inside the brackets.

4x4 = 16x4

2x3 = 6x3

So, [4x4(2x3)] = [16x4(6x3)] = 96x7.

Squaring this result, we get

[4x4(2x3)]2 = 96x7 * 96x7 = (96 * 96)x(7 * 7) = 9216x49 = 9216x^49.

Therefore, the expression [4x4(2x3)]2 is equivalent to 64x49, x, 49.

The length of the rectangular pool is x + 7.

Area of a two dimensional shape is the total region which is bounded by the object's shape.

Area of a rectangular shape = Length × Width

Given that,

Area = x² + 15x + 56

Width = x + 8

Substituting,

x² + 15x + 56 = Length (x + 8)

Length = (x² + 15x + 56) / (x + 8)

Factorize x² + 15x + 56.

x² + 15x + 56 = (x + 7) (x + 8)

So length = x + 7

Hence the length of the pool can be represented as x + 7.

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The negation of the statement ∀x∃y(2 < x ≤y) is ∃x∀y(x ≤2 ∨ y < x) and the negation of the statement ∀y∃x(y > 0 →x ≤0) is ∃y∀x(y ≤0 ∨ 0 < x).

(a) ∃x∀y(x ≤ 2 ∨ y < x)

This statement can be read as: There exists an x such that for all y, x is less than or equal to 2 or y is less than x.  To calculate this, we can look at the inequalities in both directions. We know that x is greater than 2, so we can use this to determine the lower bound for y. To prove this, we can examine the case when x = 2 and y = 3. Since 3 is greater than 2, the statement is true.

(b) ∃y∀x(y ≤ 0 ∨ x > 0)

This statement can be read as: There exists a y such that for all x, y is less than or equal to 0 or x is greater than 0.

This statement states that there exists a y such that for all x, either y is less than or equal to 0 or x is greater than 0. To calculate this, we can look at the inequalities in both directionsTo prove this, we can examine the case when y = -1 and x = 1. Since 1 is greater than 0, the statement is true.

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The formula that shows how to find C, circumference, when d, diameter is given is C = πd.

Circumference is the line that bounds a circle or other two-dimensional (2D) figure.

Diameter is any straight line between two points on the circumference of a circle that passes through the centre/center of the circle.

The diameter can be used to find the radius of a circle using the following formula;

D = 2r

Circumference of a circle = 2πr

Substituting D in the equation for circumference......

Circumference of a circle = 2πd/2

Circumference of a circle = πd

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The number of pounds in 32 kg would be 70.5479.

A pound is an imperial unit used to measure bulk or weight. A kilogram is a metric measuring unit. The letters lb and lbm stand for pounds. Kilo or kg are used to denote kilograms. 0.4535 kilograms make up one pound.

In both the British imperial system and the United States' customary system, weight is measured in pounds. Measuring a person's weight is one common application of pounds.

The weight of a kilogram is 2.2046 pounds. We convert kilograms (kg) to pounds (lb) using the formula 1 kg = 2.2 lb. By multiplying by 2.2, we may convert a kilogram to a pound. We divide by 2.2 to change a pound into a kilogram.

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The probability that she will select a chicken would be =7/23.

Probability is defined as the expression that represents that possible outcome of an event.

The amount of pigs in the farm = 6

The amount of chicken in the farm = 7

The amount of cows in the farm = 10

The total animals in the farm = 10+7+6 = 23

The probability of selecting a chicken out from the whole farm = 7/23.

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Complete question:

Giovanna owns a farm. She is going to randomly select one animal to present at the state fair. She has 6 pigs, 7 chickens, and 10 cows. What is P (chicken) ?

one-sided limits of a function f(x) at x = 1 is  lim x → 2[f(x) - f(2)]/(x - 2) = 20

Since  function f(x) = 5(x² - 1) and we want to find its derivative, we can proceed thus.

Let x = h + 2

So,  

f(x) = 5(x² - 1)

f(2) = 5[(2)² - 1]

= 5[4 - 1]

= 5(3)

= 15

f(2 + h) = 5[(2 + h)² - 1)

= 5(4 + 4h + h² - 1)

= 5(3 + 4h + h²)

= 15 + 20h + 5h²

So, f(2 + h) - f(2) = 15 + 20h + 5h² - 15

= 20h + 5h²

So, we have that

[f(2 + h) - f(2)]/h = (20h + 5h²)/h

= 20 + 5h

Now, taking the limit as h → 0, we have

= 20 + 5(0)

= 20 + 0

= 20

So,  lim h → 0[f(2 + h) - f(x)]/h = lim x → 2[f(x) - f(2)]/(x - 2) = 20

So,  lim x → 2[f(x) - f(2)]/(x - 2) = 20

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1. Considering the equation [tex]z^{16}[/tex] = −1−i.The value of z which satisfies this equation and which has the second smallest positive argument θ, 0<θ<2π as z=r[tex]e^{i\theta}[/tex] where r = [tex]\underline{2^{1/32}}[/tex] and θ = 13π/64.

2. Considering the equation [tex]z^{13}=(-1+\sqrt{3i})[/tex]. The value of z which satisfies this equation and which has the second smallest positive argument θ,0<θ<2π as z=r[tex]e^{i\theta}[/tex] where r = [tex]\underline{2^{1/13}}[/tex] and θ = 8π/39.

1. The equation is z^{16} = -1 - i.

We have express our answer in the form of

[tex]\; z = re^{i\theta }[/tex]

When we enter it into the first equation, we obtain,

[tex]r^{16}e^{16i\theta }=-1-i\; \; \; \; \; \; \; \; \; \; \; \;[/tex]--(2)

Using the modulus of both sides, we obtain,

[tex]\left |r^{16} \right |\: \: \left | e^{16i\theta } \right |=\sqrt{\left ( -1 \right )^{2}+\left ( -1 \right )^{2}}[/tex]

Simplifying

[tex]\; \; \; \; \; r^{16}=\sqrt{2}[/tex]

Taking root of 16 on both side, we get

[tex]r=2^{1/32}[/tex]

Plugging this value of 'r' back in equation (2), we get,

[tex]\sqrt{2}\; \; e^{16i\theta }=-1-i[/tex]

Divide by √2 on both side, we get

[tex]e^{16i\theta }=-\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}}i[/tex]

We can write [tex]e^{16i\theta }[/tex] as

[tex]\; \; \; \;cos16\theta +isin16\theta =-\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}}i[/tex]

On comparing, we get

[tex]\; \; \; \;cos16\theta=-\frac{1}{\sqrt{2}}\;, \; \; \; \; \; \; \; sin16\theta =-\frac{1}{\sqrt{2}}[/tex]

Angle must therefore be in the third quadrant.

[tex]16\theta=\pi +\frac{\pi }{4}=\frac{5\pi }{4}\; \; \; \; \; \; \; \; ,\; \; \; \; \; \; \; \;16\theta=\frac{5\pi }{4}+2\pi =\frac{13\pi }{4}[/tex]

[tex]\theta=\frac{5\pi }{64}\; \; \; \; \; \; \; \; ,\; \; \; \; \; \; \; \;\theta=\frac{13\pi }{64}[/tex]

So, second smallest positive argument = 13π/64.

2) The equation is [tex]z^{13} = -1 +\sqrt{3i}[/tex].

We have express our answer in the form of

[tex]\; z = re^{i\theta }[/tex]

When we enter it into the first equation, we obtain,

[tex]r^{13}e^{13i\theta }=-1+\sqrt{3}i\; \; \; \; \; \; \; \; \; \; \; \;[/tex]

Using the modulus of both sides, we obtain,

[tex]\left |r^{13} \right |\: \: \left | e^{13i\theta } \right |=\sqrt{\left ( -1 \right )^{2}+\left ( \sqrt{3} \right )^{2}}[/tex]

Simplifying

[tex]r^{13}=2[/tex]

Taking root of 13 on both side, we get

[tex]r=2^{1/13}[/tex]

Reintroducing this 'r' value into the equation from [tex]r^{13}e^{13i\theta }=-1+\sqrt{3}[/tex], we get,

[tex]2e^{13i\theta }=-1+\sqrt{3}i[/tex]

Divide 2 on both side, we get

[tex]e^{13i\theta }=-\frac{1}{2}+\frac{\sqrt{3}}{2}i[/tex]

We can write [tex]e^{13i\theta }[/tex] as

[tex]\; \; \; \;cos13\theta +isin13\theta =-\frac{1}{2}+\frac{\sqrt{3}}{2}i[/tex]

[tex]\; \; \; \;cos13\theta=-\frac{1}{2}\;, \; \; \; \; \; \; \; sin13\theta =\frac{\sqrt{3}}{2}[/tex]

Angle must therefore be in the second quadrant.

[tex]13\theta=\pi -\frac{\pi }{3}=\frac{2\pi }{3}\; \; \; \; \; \; \; \; ,\; \; \; \; \; \; \; \;13\theta=\frac{2\pi }{3}+2\pi =\frac{8\pi }{3}[/tex]

[tex]\theta=\frac{2\pi }{39}\; \; \; \; \; \; \; \; ,\; \; \; \; \; \; \; \;\theta=\frac{8\pi }{39}[/tex]

So, second smallest positive argument = 8π/39.

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The length of the line segment ML is 15 cm.

An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.

A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.

The altitude is the measurement of the angle perpendicular to the parallel sides.

The area of a trapezoid is (1/2)×(sum of the two parallel sides)×height.

From the given information,

m∠LJ = m∠LM = 90°.

So, m∠LJ + m∠LM = 180°.

Line segment ML is parallel to JK.

Therefore, NP is the midline of the trapezoid.

ML + JK = 2NP.

JK = 2NP - ML.

9 = 24 - ML.

ML = 15 cm.

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Answer:

1/2

Step-by-step explanation:

So the point of this question is to compare all of the answers and see which one fits best.  To do this, first change the denominator to match 5/8.  To convert 1/2 into eighths, multiply 2 by 4 so you get eight.  Since you did that, you have to do the same to the numerator.  Therefore:  

1/2 = 4/8

Is 4/8 less than 5/8?  Yes.  Is it greater than 1/9?  Yes, but how?  Do the same thing but instead convert 1/2 into ninths.  Multiple 2 by 4.5 to get 9 and 1 by 4.5 to get 4.5.  

1/2 =  4.5/9

4.5/9 is greater than 1/9, so you answer would be 1/2.  

Normally you would test every answer, but to save time I'll just stop there because the first option was correct.  I hope you understand.  :)

Answer:

1/2

Step-by-step explanation:

1/2 = 4/8 which is less than 5/8.

1/9 = 2/18

1/2 = 9/18 which is greater than 2/18 (same as 1/9)

A graph of the equality that models the number of pizzas they can make is shown in the image attached below.

The three (3) possible solutions include the following:

In order to write an equation that model this situation, we would assign variables to the small pizza shop and the large pizza shop respectively, and then translate the word problem into algebraic equation as follows:

Next, we would translate the word problem into an algebraic equation based on the fact that the small pizza makes use of 12 ounces and a large pizza uses 18 ounces of dough as follows;

12x + 18y = 4800

Next, we would use an online graphing calculator to plot the above algebraic equation as shown in the graph attached below

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The amount of RNA transcribed from promoter gene, which can consequently influence the amount of protein made from this gene. So the option c is correct.

A gene's DNA sequence is duplicated during transcription in order to create an RNA molecule.

The primary transcribed enzyme is called RNA polymerase.

RNA polymerase connects to a promoter sequence close to the start of a gene to start transcription (directly or through helper proteins).

A new, complementary RNA molecule is created by RNA polymerase using a template from one of the DNA strands (the template strand).

Termination is the procedure that brings transcription to a conclusion. The RNA sequences that indicate that the transcript is done are what determine when a process is terminated.

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The complete question is:

How frequently RNA polymerase binds to DNA sequence

a. length of RNA transcribed from the gene

b. precise sequence of RNA transcribed from this gene

c. amount of RNA transcribed from promoter gene, which can consequently influence the amount of protein made from this gene

The coordinate of the point P that lies on the line segment AB will be (-1, -1).

Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have

x = (mx₂ + nx₁) / (m + n)

y = (my₂ + ny₁) / (m + n)

Given the points A(-4, 1) and B(8, -7). AP to PB is in the ratio of 1 to 3. Then the coordinate of the point P is given as,

x = (1 × 8 + 3 × (-4)) / (1 + 3)

x = (8 - 12) / 4

x = -4 / 4

x = -1

y = (1 × (-7) + 3 × 1) / (1 + 3)

y = (- 7 + 3) / 4

y = -4 / 4

y = -1

The coordinate of the point P that lies on the line segment AB will be (-1, -1).

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