identify the greatest common factor of 6s³t⁴ + 12s⁴t² - 15s²t³, then factor the expression. ​

The coordinates of the rotation are

Problem 5:

(4, 0), (0, -2), and (0, 0)  

Problem 6:

(0, -4), (-2, 0), and (0, 0)  

Describing each rotation

1. 90 degrees counterclockwise rotation about the origin

2. 90 degrees clockwise rotation about the origin

Problem 5: The transformation rule for 90 degrees clockwise rotation about the origin is

(x, y) becomes (y, -x)

preimage coordinates           image coordinates

(0, 4)                becomes        (4, 0)

(2, 0)                becomes        (0, -2)

(0, 0)                becomes        (0, 0)

The image is plotted and attached

Problem 6: The transformation rule for 180 degrees counterclockwise rotation about the origin is

(x, y) becomes (-x, -y)

preimage coordinates           image coordinates

(0, 4)                becomes        (0, -4)

(2, 0)                becomes        (-2, 0)

(0, 0)                becomes        (0, 0)

The image is plotted and attached

Describing each rotation

1. 90 degrees counterclockwise rotation about the origin

This can be likened to the rotation as in problem 6, the polygon moves in the counterclockwise direction and this is according to the rule:

(x, y) becomes (-y, x)

2. 90 degrees clockwise rotation about the origin

This is similar to the rotation as in problem 5, the polygon moves in the clockwise direction and this is according to the rule:

(x, y) becomes (y, -x)

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All real numbers make up the domain of a linear function, hence the domain of  [tex]f(x)=-5x+20x-7[/tex] is  [tex](-\infty , \infty )[/tex]  . The range of a linear function is also the set of all real numbers, hence   [tex]f(x)=-5x+20x-7[/tex] has a range of (-[tex]\infty[/tex], [tex]\infty[/tex]).

For the formula, [tex]y = 4x2 + 24x + 13[/tex]

All real numbers make up the domain of a polynomial function, hence the domain of y=4x2+24x+13 is [tex](-\infty , \infty )[/tex]

We can use calculus or the square root method to determine the function's range. At x=-3, where y=1, the function's minimal value is found. As a result, the function's range is  [tex][1, \infty )[/tex].

Using the formula [tex]f(x)=-5x+20x-7:[/tex]

Using related words together, we obtain [tex]f(x)=15x-7.[/tex]

Therefore, All real numbers make up the domain of a linear function, hence the domain of  [tex]f(x)=-5x+20x-7[/tex] is  [tex](-\infty , \infty )[/tex]  . The range of a linear function is also the set of all real numbers, hence   [tex]f(x)=-5x+20x-7[/tex] has a range of (-[tex]\infty[/tex], [tex]\infty[/tex]).

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Answer:

y = 5

Step-by-step explanation:

3(3y-8)=21

expand:

9y - 24 = 21

+24 to both sides to get 9y on its own.

9y = 45

divide both sides by 9 to get y on its own.

therefore

y = 5

hope this makes sense!

Answer: Solve for

y

by simplifying both sides of the equation, then isolating the variable.    

y≈−1.21698677,2.94165923

Step-by-step explanation:

The answer of the given question based on the triangle is the value of angle G or x  is approximately 52.6° degrees (rounded to the nearest tenth of a degree).

Trigonometric functions are mathematical functions that relate the angles and sides of a right triangle. The most commonly used trigonometric functions are sine (sin), cosine (cos), and tangent (tan). Trigonometric functions can be used to solve problems involving angles and sides of right triangles, as well as to model periodic phenomena such as waves and oscillations.

To find angle G, we need to use the trigonometric function tangent since we know the opposite and adjacent sides of angle G in the right triangle EFG.

Recall that the tangent of an angle is defined as the ratio of the opposite side to the adjacent side, i.e.,

tan(G) = opposite/adjacent = FG/EF

Substituting the given values, we get:

tan(G) = 3.4/2.6 = 1.3076

Using a calculator, we can find the inverse tangent of 1.3076, which gives us:

G ≈ [tex]tan^{-1}[/tex](1.3077) ≈ 52.6° degrees

Therefore, the value of angle G is approximately 52.6° degrees (rounded to the nearest tenth of a degree).

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The false statement is 3)sin30=cos40.

This is because the sine of 30 degrees is 0.5, whereas the cosine of 40 degrees is approximately 0.766. These two values are not equal to each other.

The following claims, however, are accurate:

Therefore, the false statement is 3)sin30=cos40.

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Answer:

Step-by-step explanation:

10x+y=10y+x-18 multiply the tens digit by 10 and leave the one's digit alone

9x=9y-18 divide by 9

x=y-2

x-y=-2

x+y=10

add above two equations

2x=8 divide by 2

x=4

y=10-4=6

numbers are 46 and 64

64=46+18 4+6=10

In the proportion, Gear A makes 120 turns when Gear B makes 90 turns.

What is Proportion?

A proportion is a statement that two ratios or fractions are equal. It shows the relationship between two or more quantities that are proportional to each other.

The gears have a fixed ratio of rotations, which is determined by the number of teeth on each gear.

To find out how many turns Gear A makes when Gear B makes 90 turns, we can set up a proportion:

=> [tex]\frac{36}{27} =\frac{ x}{90}[/tex]

where x is the number of turns Gear A makes.

To solve for x, we can cross-multiply:

=> 36 × 90 = 27 × x

=> 3240 = 27x

=> x = 120

Therefore, Gear A makes 120 turns when Gear B makes 90 turns.

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Answer:

Rounding down to a whole number, we get:

6,666 people

Step-by-step explanation:

First, we need to calculate the total area of the beach:

1000 ft x 200 ft = 200,000 sq ft

Next, we divide the total area by the desired area per person:

200,000 sq ft ÷ 30 sq ft per person = 6,666.67 people

5. The value of angle LNM in the given circle is 54 degrees. 7. The value of angle ABC is 51 degrees.

A circle is a two-dimensional shape made up of a collection of points that are spaced uniformly apart from one another (called the radius) on a plane. The fixed point is referred to as the circle's origin or centre, and the fixed distance between each point and the origin is referred to as the radius. The centre, the radius, and the diameter of a circle may be seen in the following illustration.

5. The angle subtended by the two chords is half the measure of the angle at the center.

Thus,

angle LNM = 1/2 (angle LPM)

Substitute the value of angle LPM = 108, thus:

angle LNM = 1/2(108) = 54 degrees.

Hence, the value of angle LNM in the given circle is 54 degrees.

7. For measure angle ABC we have:

16x-26 = 2(5x+11)

16x-10x = 22+26

6x=48

x = 8

Substituting the value of x we have:

5(8) + 11 = 40 + 11 = 51

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x^2-16÷ (x-16 )(x+4)

= (x^2)-(4^2)÷ (x-16)(x+4)

= (x+4)(x-4)÷ (x-16) (x+4)

=(x-4)÷(x-16)

The only number that could m is 480 as it is both divisible by 4 and 6. Thus, option J is correct.

A whole number that can be either positive, negative, or zero is known as an integer. It is a number without a decimal or fractional component. Integer examples include: -3, -2, -1, 0, 1, 2, 3, etc

Lets check if 4 and 6 are divisible by both a and b and is a positive integer,

F. 124:

124/4 = 31, is a positive integer

124/6 = 20.6 is a not positive integer

Thus, 124 is not m.

G. 222:

222/4 = 55.5, is a not positive integer

Thus, 222 is not m.

H. 310:

310/4 = 77.5, is a not positive integer

Thus, 310 is not m.

J. 480:

480/4 = 120, is a positive integer

480/6 = 80 is a positive integer

Thus, 480 is m.

K. 544:

544/4 = 136, is a positive integer

544/6 = 90.6 is not  a positive integer

Thus, 544 is not  m.

Thus, The only number that could m is 480 as it is both divisible by 4 and 6. Thus, option J is correct.

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Complete question:

Answer:

(4x+7)(4x-7)

Step-by-step explanation:

Use DoS (x+y)(x-y)=x^2-y^2

Answer:

54 =)

Step-by-step explanation:

m^2+7m-6
5^2+7(5)-6
25+35-6
Answer is 54

The value of a given arithmetic expression is 1.

We have given that an arithmetic expression -

22-(1×5)-4 to the seccond

So we can write it -

22-(1×5)-4²

we shall solve it with the help of the BODMASS rule

BODMAS Rule: The BODMAS Rule is a crucial mathematical tool for resolving issues. It is a technique for using an arithmetic expression to resolve mathematical problems. The abbreviation BODMAS stands for brackets, order of powers or roots, division, and multiplication. S indicates for subtraction, whereas A stands for addition.

according to BODMASS

first, solve the brackets and square,

=22-(5)-16

now subtract all

=22-21

=1

The complete question is

Solve the given arithmetic expression -

22-(1×5)-4 to the seccond

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Answer:

Step-by-step explanation:

Sorry, i can't "add up to five attachments" because i say only answer.

1.(−24,8)

2.[−3,1]

3.[−3,4]

4. (−3,5)

5 and 6 no answer (check my attachments)

7. (−∞,−8)v(4,+∞)

8 (−∞,1)v(7,+∞)

9. (−∞,−3]v[6,+∞)

10. (−∞,−3]v[2,+∞)

11. (−∞,∞)

12. (−∞,∞)

13. (−∞,−[tex]\frac{21}{4}[/tex]]v[[tex]\frac{15}{4}[/tex],+∞)

14.[-[tex]\frac{4}{5}[/tex],[tex]\frac{8}{5}[/tex]]

15. (-[tex]\frac{17}{3}[/tex];5)

16. (−∞,−14]v[22,+∞)

17. no answer (how 5 and 6)

18. (−∞,∞)

19. (−2,[tex]\frac{2}{3}[/tex])

20. (−∞,−4)v(−[tex]\frac{2}{3}[/tex],+∞)

Since it is less than 5, we do not round up, and our final answer is 2.00.

Decimal rounding is a process of changing a number to a certain number of decimal places, based on a specified rounding rule. In decimal rounding, the digits to the right of the specified decimal place are examined to determine whether rounding is necessary. If the digit immediately to the right of the specified decimal place is 5 or greater, the number is rounded up by adding 1 to the last digit of the specified decimal place. If the digit is less than 5, the number is rounded down by simply dropping the digits to the right of the specified decimal place.

(a).   To round 1 to 1 significant figure, we only keep the leftmost digit, which is 1. Therefore, 1 rounded to 1 significant figure is 1.

(b) . To write 2 as a decimal rounded to 3 significant figures, we start by identifying the leftmost significant digit. In this case, it is the digit 2. We then count two more digits to the right, which gives us 2.00. Finally, we look at the next digit, which is 0. Since it is less than 5, we do not round up, and our final answer is 2.00.

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The area of a rectangle is represented by an irrational number because the product of the two side lengths is an irrational number. This is because the product between an integer and an irrational number leads to another irrational number, which is the right answer.

A rectangle is a four-sided flat geometric form with right angles on all four sides. It is a quadrilateral, which implies that it has four sides. A rectangle's opposite sides are parallel and equal in length, whereas its adjacent sides are perpendicular to one other. A rectangle's area is computed by multiplying its length by its width, and its perimeter is computed by summing the lengths of all four sides.

According to this question, we know the lengths of the two sides of the rectangle, the length of a side is an positive integer and the length of the other one is an positive irrational number. The area of the rectangle is the product of the two sides lengths mentioned above.

By algebra, we know that the product between an integer and an irrational number leads to other irrational number. Therefore, the area of the rectangle is represented by an irrational number.

A = 3 x [tex]\sqrt{5}[/tex]

A = 3[tex]\sqrt{5}[/tex]

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The complete question is: A rectangle has side lengths of 3 inches and 5–√ inches. Which statement must be true about the area of the rectangle?

The value of x is approximately equals to 30.4 and the value of r is approximately 9.24.

What is circle ?

In geometry, a circle is a two-dimensional shape consisting of all points that are a fixed distance (called the radius) from a given point (called the center). A circle is a set of points that are equidistant from the center.

Is DE tangent to circle C?

Yes, DE is tangent to circle C. This is because a tangent to a circle is a line that intersects the circle at exactly one point, and in this case, DE intersects circle C at point E and only touches the circle at that point.

ST is tangent to circle Q. Find the value of r.

Since ST is tangent to circle Q at point T, the radius of the circle Q is perpendicular to ST at T. Therefore, triangle SRT is a right triangle, where RS is the hypotenuse and ST is the adjacent side to the angle at S. We can use the Pythagorean theorem to find the length of the hypotenuse:

We know that ST = 10 and RT = r, so we can substitute these values to get:

[tex]RS^{2}[/tex] = 100+ [tex]r^{2}[/tex]

We also know that RS = 2r, so we can substitute this value to get:

4[tex]r^{2}[/tex]= 100 + [tex]r^{2}[/tex]

3[tex]r^{2}[/tex] = 100

[tex]r^{2}[/tex] = 100/3

r ≈ 9.24

Therefore, the value of r is approximately 9.24.

Find the value(s) of x.

Since AB is a diameter of circle C, triangle ABC is a right triangle with right angle at B. Therefore, we can use the Pythagorean theorem to find the length of BC:

We know that AB = 26 and AC = x + 8, so we can substitute these values to get:

[tex](x + 8)^{2}[/tex]= 676 + [tex]BC^{2}[/tex]

We also know that BC = x - 2, so we can substitute this value to get:

[tex](x + 8)^{2}[/tex]= 676 + [tex](x - 2)^{2}[/tex]

[tex]x^{2}[/tex]+ 16x + 64 = 676 + [tex]x^{2}[/tex]- 4x + 4

20x = 608

x = 30.4

Therefore, the value of x is 30.4.

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An addition of the quantity negative 8 minus one fourth times p end quantity plus the quantity five eighths times p minus 7 end quantity is: C. 3 over 8 times p minus 15.

In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).

Based on the information provided above, we have the following mathematical expressions:

Expression = -8 - 1/4(p)

Expression = 5/8(p) - 7

By adding the two expressions, we have:

Addition = -8 - 1/4(p) + 5/8(p) - 7

Addition = -8 - p/4 + 5p/8 - 7

Addition = -15 +(-p/4 + 5p/8)

Addition = -15 +(-2p + 5p)/8

Addition = -15 + (3p)/8

Addition = 3p/8 - 15

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The area of the dish, a, can be represented by the product of its length and width. Thus, we can write:

a = (279/10) cm x (178/10) cm

Simplifying this expression, we get:

a = 4953/100 cm^2

So, the correct equations are:

B) 178/10 x 279/10 = a

and

D) a ÷ 178/10 = 279/10

Answer:

B. $365

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let A represent "The children are sick."

Let B represent "The doctors are not here."

Argument: A and ¬B

Rule(s) used to prove or disprove: Conjunction (AND)

Answer: i'm going to assume, this needs to be a full answer

meaning this would be

43.9823 inches (or 44 if fully rounded)

basically, to find arc length, you take the given degrees shown (210) and divide it over the full length of the circle (360)

dividing this gives us 58.333333 (repeated forever) or 7/12

then we need to find the circumference, which is c=pid (or c=pi times diameter)

so we would do 24 multiplied by 3.14159 (this is standard amount of numbers for naturally calculating pi in equations) and we get 75.39816

finally, we need to multiply 75.39816 to 7/12, and we will get 43.98226

which when rounded to the 4th digit will give us 43.9823

Answer with step-by-step explanation:

The formula to find the arc length of a circle is:

[tex]\sf \red {Arc\: length = \frac{\theta}{360} *2 \pi r}[/tex]

PQ major arc length

[tex]\sf Arc\: length = \frac{\theta}{360} *2 \pi r\\\\\sf Arc\: length = \frac{210}{360} *2 \pi*12\\\\\sf Arc\: length = \frac{15825.6}{360} \\\\\sf Arc\: length = 43.96\: in[/tex]

PQ minor arc length

[tex]\sf Arc\: length = \frac{\theta}{360} *2 \pi r\\\\\sf Arc\: length = \frac{150}{360} *2 \pi*12\\\\\sf Arc\: length = \frac{11304}{360} \\\\\sf Arc\: length = 31.4\: in[/tex]

The profit region is empty and cannot be shaded in blue. Which means that the business will not be profitable for any values of x greater than [tex]150[/tex] .

To determine which graph corresponds to the given situation, we need to understand the relationship between cost, profit, and revenue.

The revenue (R) of a small business is given by the product of the price per unit (p) and the number of units sold (x):

[tex]R = px[/tex]

The profit (P) of a small business is the difference between its revenue and cost (C):

[tex]P = R - C = px - (3000 + 12x) = (p - 12)x - 3000[/tex]

The profit will be positive when P > 0, which means that the revenue is greater than the cost:

[tex](p - 12)x > 3000[/tex]

[tex]x > 3000/(p - 12)[/tex]

This inequality tells us that the business will be profitable for all values of x greater than [tex]3000/(p - 12).[/tex]

Graph A: This graph shows a linear revenue function (R = 20x) and a linear cost function [tex](C = 3000 + 10x).[/tex] The profit function [tex](P = R - C)[/tex] is also linear.

To find the profit region, we need to shade the area above the profit function  [tex](P > 0)[/tex]. However, we cannot determine if this corresponds to the given situation without knowing the price per unit.

Graph B: This graph shows a linear revenue function  [tex](R = 25x)[/tex] and a quadratic cost function  [tex](C = 3000 + 15x + 0.5x^2).[/tex] The profit function [tex](P = R - C)[/tex]  is also quadratic. To find the profit region, we need to shade the area above the profit function [tex](P > 0)[/tex] .

We can solve for the roots of the quadratic equation [tex]P = 25x - (3000 + 15x + 0.5x^2) = -0.5x^2 + 10x - 3000[/tex] and find the interval of x-values for which [tex]P > 0.[/tex]

This corresponds to the range of x-values for which the graph of P is above the x-axis. We can see that this region is shaded in blue, so Graph B corresponds to the given situation.

Graph C: This graph shows a linear revenue function [tex](R = 15x)[/tex] and a linear cost function  [tex](C = 3000 + 20x).[/tex]The profit function  [tex](P = R - C)[/tex]  is also linear.

To find the profit region, we need to shade the area above the profit function  [tex](P > 0)[/tex]. However, we can see that the profit function intersects the x-axis at [tex]x = 150.[/tex]

Therefore, the profit region is empty and cannot be shaded in blue. Which means that the business will not be profitable for any values of x greater than [tex]150[/tex].

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The differentiation of the trigonometric function gives:

dy/dx = sin(x) - cos(x)

Here we want to find dy/dx for:

y = sec⁻¹(x) + csc⁻¹(x)

Remember that these two are the inverses of the sine and cosine function, then we can write that just as:

y = cos(x) + sin(x)

Now the differentiation is part by part, we know that:

d(cos(x))/dx = -sin(x)

d(sin(x))/dx = cos(x)

Then:

dy/dx = sin(x) - cos(x)

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The number "0.0505505550..." is an irrational number. The reason for it is that the number can't be expressed as the quotient of two integers. SInce it has the ellipsis (...) at the end, it indicates that the number isn't showing all its significant figures, therefore, can't be represented as the ratio of two integers. Thus, it is irrational.

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Answer:

No, it's not

Step-by-step explanation:

A rational number can be written in the form [tex]\sf{\dfrac{p}{q}}[/tex], where q ≠ 0.

While an irrational number cannot  be written in such a form.

Well, not only can't we express 0.0505505550... as [tex]\sf{\dfrac{p}{q}}[/tex], we also see three dots in the end that indicate that the number goes on forever.

It's impossible to express a number that goes on for ever, as a fraction.

Therefore the number is irrational.

The probability that a freshman is selected is 0.39. the probability that an art major is chosen is 0.36. the probability that a freshman math major or a sophomore biology major is chosen is 0.23.

(a) To find the probability that a freshman is selected, we need to add up the probabilities of selecting any of the three types of majors among the freshman group. Thus:

Probability of selecting a freshman = Probability of selecting a freshman math major + Probability of selecting a freshman art major + Probability of selecting a freshman biology major

Probability of selecting a freshman = 0.12 + 0.09 + 0.18

Probability of selecting a freshman = 0.39

(b) To find the probability that an art major is chosen, we need to add up the probabilities of selecting an art major from both the freshman and sophomore groups. Thus:

Probability of selecting an art major = Probability of selecting a freshman art major + Probability of selecting a sophomore art major

Probability of selecting an art major = 0.09 + 0.27

Probability of selecting an art major = 0.36

(c) To find the probability that a freshman math major or a sophomore biology major is chosen, we need to add up the probabilities of selecting a freshman math major and a sophomore biology major. Thus:

Probability of selecting a freshman math major or a sophomore biology major = Probability of selecting a freshman math major + Probability of selecting a sophomore biology major

Probability of selecting a freshman math major or a sophomore biology major = 0.12 + 0.11

Probability of selecting a freshman math major or a sophomore biology major = 0.23

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the probability that the mean per capita daily water consumption for a given sample is between 80 and 82 liters per person is approximately 0.1271 or 12.71%.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a numerical value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probability theory is a branch of mathematics that deals with the study of random events and their probabilities

In the given question,

We are given that the population mean per capita daily water consumption is 83 liters and the standard deviation is 11.9 liters. We are also given that random samples of size 50 are drawn from this population and the mean of each sample is determined.

We can use the central limit theorem to approximate the distribution of the sample means. According to the central limit theorem, the distribution of the sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

So, for a sample size of 50, the standard deviation of the sample mean is:

standard deviation of sample mean = 11.9 / √(50) = 1.68

To find the probability that the mean per capita daily water consumption for a given sample is between 80 and 82 liters per person, we need to find the z-scores corresponding to these values and use the standard normal distribution table or calculator to find the probability.

The z-score for 80 liters per person is:

z = (80 - 83) / 1.68 = -1.79

The z-score for 82 liters per person is:

z = (82 - 83) / 1.68 = -0.60

Using the standard normal distribution table or calculator, we can find that the probability of getting a z-score between -1.79 and -0.60 is 0.1271.

Therefore, the probability that the mean per capita daily water consumption for a given sample is between 80 and 82 liters per person is approximately 0.1271 or 12.71%

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Answer: (n - 2) + 20

Step-by-step explanation:

     We will create a mathematical expression using the statement given. 'Less' implies subtraction, let n be a number.

     'than a number' ➜ n

     'Two less' ➜ - 2

     'plus twenty.' ➜ + 20

'Two less than a number plus twenty.' ➜ (n - 2) + 20