||
2. Complete the steps for factoring 2x3 - 36x² + 162x by writing words, numbers,
or expressions in the blanks.
2x336x2 + 162x=
(x2-18x+81)
_2x [x²-2(____)x+ (__________)²]
=
11
(x-.
_)(x-____
_2=(x-_9_) ²
Factor out
Rewrite the trinomial.
Use the
pattern.
Simplify.

The measure of both angles is 45.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Right triangle:

One angle = 90

Other angles:

One = 2x - 45

Another = x

Now,

The sum of the three angles = 180

90 + x + 2x - 45 = 180

Add like terms.

90 + 3x - 45 = 180

Add 45 on both sides.

90 + 3x = 180 + 45

Subtract 90 on both sides.

3x = 225 - 90

3x = 135

Divide 3 into both sides.

x = 45

Now,

Other angles:

One = 2 x 45 - 45 = 45

Another = 45

Thus,

Both angles are 45.

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Answer:

min -1 max 3

Step-by-step explanation:

min: when x= -10 so f(x) = ∛-1 = -1

max: when x= 18 so f(x) = ∛27= 3

The value of x based on the information about the triangle is 3.

It should be noted that the total sum of angles in a triangle is 180°. Based on the information given, this will be illustrated as:

180 - (180 - 140) - (180 - 99)

= 180 - 40 - 81

= 59

Therefore, 41x - 2 + 59 = 180

41x = 180 + 2 - 59

41x = 123

Divide

x = 123 / 41.

x = 3.

The value of x is 3.

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The required simplified form of the given monomial is 11x²y + 6xy².

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

The monomial is given in the question, as follows

16x²y - 4xy²- 5x²y + 10xy²

Rearrange the like terms in the above expression,

16x²y - 5x²y - 4xy² + 10xy²

Add similar elements,

11x²y - 4xy² + 10xy²

Subtract similar elements, and we get

11x²y + 6xy²

Thus, the required simplified form is 11x²y + 6xy².

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The total time taken by Carmen in climbing the rocks will be 2¹/₄ hours.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Carmen went rock climbing at the climbing gym for 1¹/₂ hours on Thursday. On Saturday, she went to Castle Rock State Park and climbed for  1¹/₂ times as long.

The total time of climbing will be calculated as:-

Time = 1¹/₂ x 1¹/₂

Time = ( 3 / 2 ) x ( 3 / 2 )

Time = 9 / 4

Time = 2¹/₄ hours.

Hence, the climbing time would be 2¹/₄ hours.

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The solution is Option C.

The equation of line is y = 2x - 2 , where the slope m = 2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

2x - y = 2   be equation (1)

On simplifying the equation , we get

Adding y on both sides of the equation , we get

y + 2 = 2x

Subtracting 2 on both sides of the equation , we get

y = 2x - 2

Therefore , the value of A is y = 2x - 2

Hence , the equation of line is y = 2x - 2 and the graph is plotted

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The solution for the given inequalities is x≥15 or x≤1. Therefore, option A is the correct answer.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequalities are 3x + 7 ≤ 4x-8 or-2x + 3≥1.

Here, 3x + 7 ≤ 4x-8

Subtract 3x on both the sides of an inequality, we get

7 ≤ x-8

Add 8 on both the sides of an inequality, we get

15≤ x

x≥15

Here, -2x + 3≥1

Subtract 3 on both the sides of an inequality, we get

-2x≥-2

Divide -2 on both the sides of an inequality, we get

x≤1

So, x≥15 or x≤1

Therefore, option A is the correct answer.

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The stem-leaf representation of the data is,

0|7 9 9

1|0 1 3 4 4 4 4 5 5 7 7

2|0 5 7

3|5.

The values of the data are divided into a stem and a leaf in a stem-leaf plot.

The initial digit or digits will be put in the stem position, and the final digit will be written in the leaf position.

Let us first rearrange the data in ascending order,

78, 95, 96, 103, 112, 134, 141, 145, 147, 148, 153, 158, 172, 172, 200, 255, 271, 359.

The data is down with the truncated leaf unit of 10, 1|4 represents a number in the 140s.

0|7 9 9

1|0 1 3 4 4 4 4 5 5 7 7

2|0 5 7

3|5.

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The solution to the system of equations shown in the graph is (6, -2)

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

The standard form of a linear equation is:

Ax + By = C

Where A, B and C are constants

The slope intercept form of a linear equation is:

y = mx + b

Where m is the slope and b is the y intercept

The solution to a system of linear equations is the point where the two lines meet.

The lines meet at where the x value is 6 and the y value is -2, hence the solution is (6, -2)

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Answer:

negative one and one-fourth, negative one-half

Step-by-step explanation:

it seems to be the only possible answer because the y value is negative one half

Answer: negative one and one-fourth, negative one-half

The position of each point on the membrane for t>0 is given by u(x,y,t) = x(x-1)y(y-1) + (14+u) c2t.

The position of each point on the membrane can be determined by solving the equation u xx + u yy = c2u, where u is the displacement of the membrane from its equilibrium position and c is the speed of the wave propagation. Since we are given f(x,y) = x(x-1)y(y-1), we can solve this equation to find u. Differentiating f(x,y) twice with respect to x and y gives us the corresponding derivatives of u. Plugging these derivatives into the equation gives us u xx + u yy = (14+u) c2. Solving this equation yields the displacement of each point on the membrane for t>0. Thus, the position of each point on the membrane for t>0 is given by u(x,y,t) = x(x-1)y(y-1) + (14+u) c2t.

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Both lines A and line B have the same slope, hence they are parallel

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

The standard form of a linear equation is:

Ax + By = C

Where A, B and C are constants

The slope intercept form of a linear equation is:

y = mx + b

Where m is the slope and b is the y intercept

The slope of the line passing through points (x₁, y₁) and (x₂, y₂) is:

m = (y₂ - y₁) / (x₂ - x₁)

Two lines are parallel to each other if they have the same slope.

Line A passes through the points (0,4) and (4, 0)

Slope = (0 - 4) / (4 - 0) = -1

Line B passes through the points (0,7) and (7, 0)

Slope = (0 - 7) / (7 - 0) = -1

Since both lines have the same slope, they are parallel

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If Cesar had a bill of $82 for renting an LCD projector, he kept the projector for 4 days, based on the linear equation.

To determine the number of days the projector, we deploy linear equation, which is in the form of y = mx + b, where m is the slope, x and y are variables, and b is the y-intercept.

The flat fee for administrative costs = $10

The variable cost per day = $18

The total bill for renting the projector = $82

The number of days = x

10 + 18x = 82

18x = 72

x = 4

Check:

10 + 18x = 82

10 + 18(4) = 82

10 + 72 = 82

82 = 82

Thus, setting a linear equation, we can determine the number of days the projector was rented as 4 days.

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in order to calculate the descriptive statistics for the points scored by the team at home in 2013-2015, the mean, median, variance and standard deviation must be calculated using the appropriate formulas.

Descriptive Statistics

Mean: This is a measure of the center of the distribution, calculated as the sum of all values divided by the number of values. In this case, it is the average number of points scored by the team at home in 2013-2015. Formula: Mean = (Sum of all values)/(Number of values).

Median: This is the middle value of the data set after it is sorted in numerical order. It is the value that separates the upper half of the data set from the lower half. In this case, it is the middle value of the points scored by the team at home in 2013-2015. Formula: Median = (Sum of the lower and upper halves of the data set)/2.

Variance: This is a measure of how spread out the data set is, calculated as the sum of the squared differences between each value and the mean, divided by the number of values. In this case, it is the variance of the points scored by the team at home in 2013-2015. Formula: Variance = (Sum of the squared differences between each value and the mean)/(Number of values).

Standard Deviation: This is a measure of how spread out the data set is, calculated as the square root of the variance. In this case, it is the standard deviation of the points scored by the team at home in 2013-2015. Formula: Standard Deviation = Square Root of Variance.

Therefore, in order to calculate the descriptive statistics for the points scored by the team at home in 2013-2015, the mean, median, variance and standard deviation must be calculated using the appropriate formulas.

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We went to Vietnam on a holiday and spent a week in the north of the country. 2. I've got a rabbit and a dog. The rabbit's called Snowy and the dog's called Eric.

A brief, monosyllabic word called an article is used to indicate whether a noun is specific or not. Normally, articles come before nouns, and because they are employed to describe the noun, they can be thought of as adjectives.

1. We went to Vietnam on a holiday and spent a week in the north of the country.

2. I've got a rabbit and a dog. The rabbit's called Snowy and the dog's called Eric.

school photo, Kim is standing on the right and Harry is standing in the

middle next to the Headmaster.

4. I live in a flat in the centre of London, very close to the Big Ben and

Houses of Parliament.

5. Loch Ness is a Monster.

most famous lake in the Scotland because of the Loch Ness

6. David has a job working for the United Nations in a far away from his office. It takes him an hour to get to work.

7. They found the Titanic at the bottom of the Atlantic Ocean.

8. In the USA, most people go to work by clinic because he had

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The percent of the time you would expect the mean of the sample size of 25 to fall between 66 and 74 is 68.27%, to be less than 70 is 50%, and to be greater than 68 is 84.13%.

a. If a population has a mean of 100 and a standard deviation of 20, then the mean of the sampling distribution of a sample size of n=252 will be 100. This is because the sample means of a sampling distribution will always be equal to the population mean.

b. The standard deviation of the sampling distribution of a sample size of n=25 is 4. This is calculated using the formula: σx = σ/√n, where σ is the population standard deviation (20) and n is the sample size (25).

c. The percentage of the time you would expect the mean of the sample size to fall between 66 and 74 is 68.27%. This is calculated using the Z-score formula, which is (x-μ)/σ, where x is the upper limit (74), μ is the population mean (70), and σ is the population standard deviation (10). The Z-score for the upper limit is (74-70)/10=0.4. We then use the standard normal table to find the area between -∞ and 0.4, which is 0.6827.

d. The percentage of the time you would expect the mean of the sample size to be less than 70 is 50%. This is because the Z-score for a mean of 70 is 0, and the area below 0 is 0.5 or 50%.

e. The percentage of the time you would expect the mean of the sample size to be greater than 68 is 84.13%. This is calculated using the Z-score formula, which is (x-μ)/σ, where x is the lower limit (68), μ is the population mean (70), and σ is the population standard deviation (10). The Z-score for the lower limit is (68-70)/10=-0.2. We then use the standard normal table to find the area between -∞ and -0.2, which is 0.8413.

The percent of the time you would expect the mean of the sample size of 25 to fall between 66 and 74 is 68.27%, to be less than 70 is 50%, and to be greater than 68 is 84.13%.

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Shaded region is between the lines corresponding to both inequalities.

Point that satisfy both inequalities is (-6/7 , 19/7)

Inequalities are the mathematical expressions in which both sides are not-equal. In inequality, unlike in equations, we compare two values.

Given inequalities

y<(-5/6)x+2

equation of the line becomes

y = (-5/6)x + 2           ------(1)

y>(1/3)x+3

equation of the line becomes

y = (1/3)x + 3               --------(2)

By the inequalities

(1/3)x + 3 < y < (-5/6)x + 2

shaded region should be between the lines.

Solving equation 1 and 2

(-5/6)x + 2 = (1/3)x + 3

(-5/6)x - (1/3)x = 3 - 2

(-5 - 2)x/6 = 1

-7x = 6

x = -6/7

Putting value of x in equation 2

y = (1/3)(-6/7) + 3

y = -2/7 + 3

y = (-2 + 21)/7

y = 19/7

Point is (-6/7 , 19/7)

Hence, point that satisfy both inequalities is (-6/7 , 19/7),

shaded region is between both lines corresponding to the inequalities.

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Answer:

  see attached

Step-by-step explanation:

You want instructions for drawing a triangle with side lengths 6 cm, 7 cm, and 9 cm.

It works reasonably well to ...

The point where the arcs cross is the third vertex of the triangle.

The man should seek a payment of $725.08

The amount of money he wants to receive can be calculated using the formula for compound interest:

A = P * (1 + r/n)^(nt)

where A = $2400 ---- final amount

P = principal

r = 6%, -- interest rate

n = 12 --- number of times the interest is compounded

t = 20, number of years (20).

So, we have

2400 = P * (1 + 6%/12)^(12 * 20)

This gives

P = 2400/3.310

Evaluate

P = 725.08

So, the man should seek a payment of $725.08

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Answer:

A = 3 * B + 4

Step-by-step explanation:

A - 4=3 * B (given)

A = 3 * B + 4

Answer:

Step-by-step explanation:

The answer is A have a nice day :)

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{f(x) = 2x^2 - x - 12}[/tex]

[tex]\mathsf{f(x) = 2(8)^2 - 8 - 12}[/tex]

[tex]\mathsf{f(x) = 2(8^2) - 8 - 12}[/tex]

[tex]\mathsf{f(x) = 2(8 \times 8) - 8 - 12}[/tex]

[tex]\mathsf{f(x) = 2(64) - 8 - 12}[/tex]

[tex]\mathsf{f(x) = 128 - 8 - 12}[/tex]

[tex]\mathsf{f(x) = 120 - 12}[/tex]

[tex]\mathsf{f(x) = 108}[/tex]

[tex]\huge\text{Therefore your answer should be: }[/tex]

[tex]\huge\boxed{\mathsf{f(x) = 108}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

I think the answer is six i just searched it  or it could be 12

Step-by-step explanation:

The greatest common factor (GCF) of 48 and 6 is 6, so:

48 - 6 = 42.

this isn't college level *laugh*

Answer:

Step-by-step explanation:

C= 2pi

15= diameter. Radius= 13/2. R= 7.5

C= 2 times pi times 7.2

C=13 pi

C= 47.1

A series is given by 131+232+333+434+535+.... francine correctly applies the ratio test, the statement that reflects francine's conclusion is From the ratio test, r=1/3. The series converges.

We must calculate the ratio between two successive phrases in order to perform the ratio test:

The nth term is n / 3n.

The (n + 1)th term is (n + 1) / 3n + 1.

The ratio test:  lim |   [ (n + 1) / 3n + 1 ]  /  [  n / 3n ]   |

               =    lim |    [ (n + 1) / n ]  ·  [ 3n  / 3n + 1 ]   |

               =    lim |    [ (n + 1) / n ]  ·  [  1/3  ]   |

               =   (1/3) · lim |  (n + 1) / n  |

               =   (1/3) · lim |  ( n/n ) + (1/n)  |

               =   (1/3) · lim |  1 + (1/n)  |

               =   (1/3) · [ lim | 1 | + lim | 1/n |

               =   (1/3) · [ 1 + 0 |

According to the ratio test, the series converges if this ratio is between -1 and 1 (excluded). This sequence thus comes together.

               =   (1/3)   <---  converges

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Answer:

From the ratio test, r=13. The series converges.

Step-by-step explanation:

I took the Test

Therefore , the solution of the given problem of area comes out to be  Area of circle  85π cm2.

Its surface area provides a good estimate of its overall size. When computing a right triangle's squared, the surroundings are taken into consideration. The surface area of everything determines its overall size. The sum of the volumes on each of the six horizontal sides makes up the volume of water inside a cuboid. Utilize the following formula to get the box's dimensions: In 2lh, 2lw, and 2hw, the region is the same (SA). The flexible shape's total area serves as a representation of the area.

Here,

Given:

Points :P(-7; -2), Q(-1; 9) and R(5; -3).

The area of the circumscribed circle of the triangle.

is:

=> PQ = √(-7 - (-1))² + (-2 - (-9))²

=> PQ = √85

The radius is √85

=> Area of circle = π(√85)²

=>  Area of circle = 85π cm2

Therefore , the solution of the given problem of area comes out to be  Area of circle : 85π cm2.

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In a case whereby Grandma Gertrude gave 13 pieces of jewelry and Grandma Fien gave y pieces of jewelry to the Carlson sisters to divide evenly among themselves the number of pieces of jewelry that each sister receive can be expreesed as (13 + y)/5.

The concept that will be used here is simplification. The pieces of jewelry by Grandma Gertrude is 13 pieces

Then the pieces of jewelry by Grandma Fien can be seen as " y ".

Since 5 Carlson sisters available . The number of pieces of jewelry each sister receive. can be calculated as:

Total jewlry= (13 + y) which is needed by  5 sisters, the each of the sisters will have = [(13 + y)/5]

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complete quesion:

Grandma Gertrude gave 13 pieces of jewelry and Grandma Fien gave y pieces of jewelry to the Carlson sisters to divide evenly among themselves. There are 5 Carlson sisters.

How many pieces of jewelry did each sister receive?

Answer:

The equation that represents "triple the input, then subtract 5" will be written as y = 3x - 5.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The output is less than 5 to 3 times the input.

Let 'x' be the input and 'y' be the output. Then the equation is given as,

y = 3x - 5

The equation that represents "triple the input, then subtract 5" will be written as y = 3x - 5.

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The rate of acceleration of an object with a mass of 3 kilograms that is pulled by the same force is given as follows:

18 m/s².

According to Newton's Second Law, the force is given by the multiplication of the mass and of the acceleration, as follows:

F = ma.

The force is obtained as follows, considering a mass of 27 kg and an acceleration of 2 m/s².

F = 27 x 2

F = 54N.

Then the acceleration of an object of 3 kilograms with the same force is given as follows:

3a = 54

a = 54/3

a = 18 m/s².

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