Simplify (3x^2y^5)^3

We found the value of K is 5 and the root of equation is x = -1/2 and x = -5/2

An equation of second order polynomial having one variable is called quadratic equation. Second order means the highest power used with variable is 2.

We are given, 4x²+ 12x +k =0, k =Z and x = R

the quadratic equation is 4x²+12x+k =0

we know the roots of a quadratic equation is x = - b ± √ (b² - 4ac) / 2a

when the quadratic equation is ax²+bx+ c= 0

Hence, roots of the equation given in question will be,

 x = - 12 ±√ (12² - 4×4×k) / 2×4

x = - 12 ± √(144-16k) / 8

as per the condition given in question, one root of this equation is 5 times the other root.

hence, - 12 -12 √(144-16k) / 8 = [- 12 + √(144-16k) / 8] × 5

multiplying both sides by 8

- 12 - √(144-16k) = [-12 + √(144-16k)] ×5

- 12 - √(144-16k) = - 60 + 5√(144-16k)

- 12 + 60 = 6√(144-16k)

48 = 6√(144-16k)

8 = √(144-16k)

64 = 144 -16k

16k = 80

k = 5

the value of k =5

by putting the value of k =5

x = -12 ± √ (144 - 80) / 8 = (-12 ± 8) /8

x = -1/2 and x = -5/2

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Answer:

point A

Step-by-step explanation:

The value of y is 16 when x = 32 for equation y = (1/4)x divided by 2.

Mathematical expressions with two algebraic expressions on either side of the equals (=) sign are called equations. It displays how the expressions on the left and right sides are equally related. We have LHS = RHS in any mathematical equation. Equations can be solved to get the value of an unknown variable that represents an unknown quantity. If there is no "equal to" symbol, a statement is not an equation.

The given equation is

y = 1/4 x divided by 2

So,

y = ((1/4)x)/ 2

y = (2/4) × x

Put x = 32

y = 2/4 ×32

y = 2 × 8

y = 16

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The division expression is equivalent to the given expression is (13/ 3)/ (-5/6)

What is expression ?

expression can be defined as with the minimum of two variables or numbers and at least one math operation.

Given expression,

= 4 1/3 / (-5/6 )

= (13/3 )/ (-5/6)

= 13*6 / -15

= -26/5

By evaluating the other expressions to find its equivalent,

(13 / 3) / (-5/6)

= 13 * 6 / -15

= -26/5

Hence , the expression 4 1/3 / (-5/6 ) is equivalent to (13 / 3) / (-5/6) .

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The division expression is equivalent to the given expression is (13/ 3)/ (-5/6)

expression can be defined as with the minimum of two variables or numbers and at least one math operation.

Division is one of the four basic mathematical operations of arithmetic, along with addition, subtraction, and multiplication. The division operation is represented by the symbol ÷ or /, and it is the inverse operation of multiplication.

Given expression,

= 4 1/3 / (-5/6 )

= (13/3 )/ (-5/6)

= 13*6 / -15

= -26/5

By evaluating the other expressions to find its equivalent,

(13 / 3) / (-5/6)

= 13 * 6 / -15

= -26/5

Hence , the expression 4 1/3 / (-5/6 ) is equivalent to (13 / 3) / (-5/6) .

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4x - 2y = 6

2y = 4x - 6

y = (4x - 6)/2

y = 2x - 3

Answer: The conditions for inference are met in this scenario.

In order to use inference to determine if the true proportion of American adults who work more than one job differs from 12%, the following conditions must be met:

The sample must be randomly selected from the population.

The sample size must be large enough (usually at least 30).

The sample must be representative of the population.

In this case, it is stated that a random sample of 100 American adults was selected, which meets the first condition.

The sample size of 100 is also large enough, which meets the second condition.

There is no information given about whether the sample is representative of the population, but this is not necessary for the conditions for inference to be met.

Therefore, the conditions for inference are met in this scenario.

Step-by-step explanation:

Hello there!

Answer:

14

Step-by-step explanation:

Let the smaller side is x. Then the largest side is x * 7/5.

Perimeter is equal to 2 * (x + 7/5 * x) or 48.

2 * (x + 7/5 * x) = 48

5/5 * x + 7/5 * x = 24

12/5 * x = 24

12/5 * 5/12 * x = 24 * 5/12

x = 10.

Tha larger side is 10 * 7/5 = 14.

Step-by-step explanation:

Given ,

To Find : Which side is longer

We know the formula to find the perimeter of a parallelogram is,

[tex]P = 2(a+b)[/tex]

We take 'x' to find out which side is longer

[tex]48 = 2(7x+5x)\\48 = 2(12x)\\48 = 24x\\\frac{48}{24} = x[/tex]

[tex]2 = x[/tex]

Side a = 7x = 7 x 2 = 14

Side b = 5x = 5 x 2 = 10

Side a [tex]\geq[/tex] Side b

Hence,  side a is longer

The  value of the given polynomial equation would be: [tex]6(1)^2 + 3(1) - 1 = 6 + 3 - 1 = 8.[/tex]

In contrast to the vertex form of a quadratic equation, which is y = a (x h) 2 + k, the normal quadratic form is written as an x 2 + b x + c = y. The constant that indicates whether the parabola is facing up (+ a) or down ( a) is called a. It is represented in both forms by the letters y, x, and a.

In the equation we are given the value of y as: 1

[tex]6y2 + 3y - 1 4 \\\\6(1)^2 + 3(1) - 1 = 6 + 3 - 1 = 8.[/tex]

Therefore, we can say that the value of the given polynomial is: 8

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Complete question is: Find 6y2 + 3y - 1 4 for y = 1

Answer:

3 feet

Step-by-step explanation:

To solve this problem, we can use the Pythagorean theorem. Let's call the distance from the tent pole to the rope x. We can set up the following equation:

x^2 + 12^2 = 15^2

Solving for x, we get:

x = sqrt(15^2 - 12^2)

x = sqrt(9)

x = 3

Therefore, the distance from the tent pole to the rope is 3 feet.

Answer: 3/-2

Step-by-step explanation:

3/-2 and -3/2 mean the same thing and give same result if we divide the numerator by denominator.

hope that helps...

The value of the car will be £2,621 after 5 years.

Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time.

Given that, The value of a second-hand car is £8,000. Each year it loses 20% of its value, we are asked to find its value after 5 years.

This is a situation of exponential decay.

Hence, using the exponential decay formula =

A = P(1-r)ⁿ

Where A is final value, P is principal value, r is rate of decrease and n is the number of years.

Here, we will find A, and we have,

P = £8,000.

r = 20% = 0.20

t = 5

Therefore,

A = 8000(1-0.20)⁵

A = 8000(0.80)⁵

A = 8000(0.32768)

A ≈ 2,621

Hence, the value of the car will be £2,621 after 5 years.

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Answer:

2.66

Step-by-step explanation:

Answer:

2.66

Step-by-step explanation:

look at first at tenths for the biggest no .if there is a tie proceed to hundredths for biggest no and so on

4.8

Divide 250 by 2 which is 125 then do 600 divided by 125. Then your answer should be 4.8.

The inequality to represent the number of stamps Keshia can buy with $10.00, considering that each stamp costs 49 cents, can be written as:

0.49x + 7.65 <= 10.00

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

The inequality to represent the number of stamps Keshia can buy with $10.00, considering that each stamp costs 49 cents, can be written as:

0.49x + 7.65 <= 10.00

This inequality can be read as "the cost of x number of stamps plus the cost of the package is less than or equal to Keshia's budget of $10.00."

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Answer: 12x^3 y^3 (x − 4y)

(GCF is: 12x^3 y^3)

Step-by-step explanation:

This is the best I can do, sorry that I don't have an explanation.

The time required for Latisha to walk around the rim at a rate of 2 mph is 0.235 hours.

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

here,
Ubehebe crater in Death Valley has a diameter of a little more than 1/2 a mile.
Circumference of the rim,
= πD

= 3.14 × 1/2
= 1.57 mile

Time = Distance/speed
Time = 1.57 / 2
Time = 0.785 hours

Thus, the time required for Latisha to walk around the rim at a rate of 2 mph is 0.235 hours.

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The graph in the question is a parabola that opens downwards.

A function is a block of organized, reusable code that is used to perform a single, related action. Functions provide better modularity for your application and a high degree of code reusing. As you already know, Python gives you many built-in functions like print(), etc. but you can also create your own functions. These functions are called user-defined functions.

This means that the range of the function is all real numbers less than or equal to the y-intercept of the parabola, which is 0 in this case. Therefore, the range of the function is all real numbers less than or equal to 0.

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Answer:

x = 32

Step-by-step explanation:

• any lower base angle is supplementary to any upper base angle.

here base angle = 2(x - 10) and upper base angle = 4x + 8

supplementary angles sum to 180°

sum the base and upper base angles and equate to 180

2(x - 10) + 4x + 8 = 180

2x - 20 + 4x + 8 = 180

6x - 12 = 180 ( add 12 to both sides )

6x = 192 ( divide both sides by 6 )

x = 32

Each of the questions should be correctly classified as statistical or not statistical as follows:

In Mathematics, a statistical question can be defined as a type of question in which the resulting answer is in the form of an average, percentage, or a range such as "How many TV shows did each student in my class watch yesterday?"

A non-statistical question simply refers to a question that is not non-statistical and it can be defined as a type of question which has an exact or fixed answer such as "How many students in my class can swim?"

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A number between 47 and 53 such that the prime factors are not repeated is:

3*17 = 51

Remember that any number can be written as a product of prime factors.

If we want to find a number between 47 and 53, such that there are no repeated factors, we just need to take different primes and multiply them.

For example:

2*3*5*7 = 210

There are no repeated factors, but the number is not in the desired range.

2*5*7 = 70

Still not in the range.

You can try some times until you get for example:

3*17 = 51

This a number in the desired range, such that their prime factors are not repeated.

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The value of side GH as shown in the parallelogram is 2 units

Parallelogram is a polygon that has four sides (quadrilateral) and opposite sides are always equal and parallel to each other

Two shapes are said to be similar if they have the same shape and the ratio of their corresponding sides are proportional. Also, their corresponding angles are equal to each other.

Parallelogram abcd is similar to parallelogram efgh, hence:

FG/BC = GH / CD

substituting:

7/21 = GH / 6

GH = 6 * 7/21 = 2

GH is 2 in

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As a result, we take the square root of the both sides since if two expressions are equal, then so are their square roots.

By multiplying the square root of a positive integer by oneself, the number is obtained. As an illustration, 5 is the square root of 25, since 5 × 5 equals 25. Since (5) (5) = 25, 5 is also the square root of 25 as you can see. The symbol, which is, is always used to indicate the square root of a number of a variable x.

Here,

In this case, we're using the square to solve a quadratic equation.

Never forget to use both the negative and positive roots of the equation and to square the values of both sides.

We can accomplish this because to the rule that states that if two expressions are comparable, then their square roots are also equivalent.

As a result, we take the square root of both sides since if two expressions are equal, then so are their square roots.

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Answer:

-------------------------------

The height h of the tree is opposite to 49° angle of a right triangle with the other leg:

Use tangent to find the value of h:

The height of the tree is 40 feet to the nearest foot.

How can the height of the tree be found?

It can be found using similar triangles.

Let's call the height of the tree "x".

Since the angle of elevation to the sun is 49°, we have two similar triangles:

Triangle 1: Sun - Naomi - Ground (illustration attached)

Triangle 2: Sun - Tree - Ground

The height of Naomi, 5 feet, is one of the corresponding sides in the two triangles, and the height of the tree, x feet, is the other. We know the ratio of their heights is 8:1, so:

x ÷ 5 = 8

Solving for x, we find that:

x = 40

So the height of the tree is 40 feet to the nearest foot.

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The perimeter of the isosceles triangle with altitude 30 inches and base 10 inches is calculated to be 70.82 inches

Perimeter of a triangle refers to the surface dimensions, this is calculated by the formula

Perimeter, P = a + b + c

where

a, b, c are sides of the triangle

The third side of the triangle will be calculated using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

The right triangle consist 1/2 the isosceles triangle base = 5 inches and the altitude = 30 inches

plugging the values as in the problem

let x be the required distance

x² = 30² + 5²

x² = 900 + 25

x² =  925

x = √925

x = 30.41 inches

Perimeter of the isosceles triangle

= 30.41 + 30.41 + 10

= 70.82 inches

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The values of the [tex]\bar x[/tex] (x-bar) (the mean) and the median of the dataset in the question are;

[tex]\bar {x}[/tex] ≈ 13.05

Median = 13.60

The mean and the median are descriptive statistical values that provides a description of the data that can be found in the dataset.

The mean is the average value of the data in the dataset, and the median is the middle value of the set of data arranged in an order of increasing values.

The mean is the average value of the set of data which is obtained by dividing the sum of the data points by the number of the datapoints, we get;

The number of data points = 28

The sum of the data is;  (4.7 + 12.6 + 3.6 + 16.1 + 2.3 + 28.2 + 2.2 + 16.9 + 10.7 + 19.5 + 11.4 + 27.9 + 11 + 15 + 4.2 + 15.8 + 15.9 + 17.3 + 24.9 + 10.8 + 16.4 + 7.3 + 3.2 + 14.6 + 2.6 + 8.4 + 21.2 + 20.8) = 365.5

The average is the mean is therefore; [tex]\bar x[/tex] = 365.5 ÷ 28 ≈ 13.05

The median is the value of the number in the middle when the numbers are arranged in increasing order as follows;

2.2, 2.3, 2.6, 3.2, 3.6, 4.2, 4.7, 7.3, 8.4, 10.7, 10.8, 11, 11.4, 12.6, 14.6, 15, 15.8, 15.9, 16.1, 16.4, 16.9, 17.3, 19.5, 20.8, 21.2, 24.9, 27.9, 28.2

The numbers at the middle of the set of numbers are 14th and 15th numbers, which are 12.6 and 14.6, which indicates that the median is the average of the two numbers, which is therefore;

Median = (12.6 + 14.6)/2 = 13.60

The median is 13.60

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Sales Tax = $3.00

The total amount paid by the group was $48.15

The amount of the sales tax can be calculated by multiplying the pre-tax bill of $37.50 by the sales tax rate of 8%:

Sales tax = $37.50 * 8% = $3.00

The total amount paid including tax and tip can be calculated by adding the amount of the sales tax to the pre-tax bill and then calculating the tip on the new total:

Total = $37.50 + $3.00 + ($37.50 + $3.00) * 18% = $37.50 + $3.00 + $7.65 = $48.15

So the total amount paid by the group was $48.15.

The truth value of "If 3 + 4 = 12, then 3 + 2 = 6", is true.

Truth value is defined as whether the given proposition is either true or false, not both.

Here the proposition is of the form if p, then q.

Here p is the statement 3 + 4 = 12 and q is the statement 3 + 2 = 6.

Here, both of the propositions are false.

The truth value of 'if p, then q' is false only when p is true and q is false. In all other cases the truth value is true.

Here, since both of the statements are false, the truth value is true.

Hence the truth value of the given proposition is true.

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