n is an integer greater than 1

Prove algebraically that 10 + [tex]n^{2}[/tex] - (n-2)[tex]^{2}[/tex] is always an even number.

Your final line must have, "always even" as part of the line.

Answer:

x=2/11 + (1/11) (√15) or 2/11 - (1/11) (√15)

Step-by-step explanation:

Plug it into the quadratic formula

The values of x are 9/11 and -5/11.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

To use the quadratic formula to solve 11x² - 4x = 1.

We first need to rewrite the equation in the form ax² + bx + c = 0.

So,

11x² - 4x - 1 = 0

Now,

We can use the quadratic formula, which states that the solutions for the equation ax² + bx + c = 0.

x = (-b ± √(b² - 4ac)) / 2a

Now,

In our case,

a = 11, b = -4, and c = -1.

Substituting these values into the formula, we get:

x = (-(-4) ± √((-4)² - 4(11)(-1))) / 2(11)

x = (4 ± √(196)) / 22

x = (4 ± 14) / 22

So,

The solutions for the equation 11x² - 4x = 1

x = (4 + 14) / 22 = 9/11

x = (4 - 14) / 22 = -5/11

Therefore,

The values of x are 9/11 and -5/11.

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Answer:

  875 cm³

Step-by-step explanation:

You want the volume of the 15 cm high frustum of a 30 cm high pyramid with a 10 cm square base.

The volume of a pyramid is given by the formula ...

  V = 1/3Bh

Where B is the area of the base:

  B = s²

For the given pyramid, the volume is ...

  V = 1/3(10 cm)²(30 cm) = 1000 cm³

The volume of the frustum is the volume of the whole pyramid, less the volume of the part that is cut off. The part that is cut off has dimensions that are 1/2 of those of the whole pyramid, so its volume is ...

  V = (1/2)³ × (1000 cm³) = 125 cm³

Then the volume of the remaining frustum is ...

  1000 cm³ -125 cm³ = 875 cm³

The volume of the frustum is 875 cm³.

__

Additional comment

The volume can also be calculated from the areas of the two bases of the frustum and its height.

  V = (1/3)(B₁ +B₂ +√(B₁B₂))h

The top base is 5 cm square, so this evaluates to ...

  V = (1/3)(100 cm² +25 cm² +√(100·25) cm²)(15 cm) = 1/3(175 cm²)(15 cm)

  V = 875 cm³

Answer:

Step-by-step explanation: watch the video

6 school-supply kits can be put together in 30 minutes.

What do you mean by the Unitary method?

By using the unitary technique, we may determine the value of a single unit and, using that value, get the value of the necessary number of units.

According to the questions,

By applying the unitary method,

40 school supply kits can be put together in 8 minutes.

∴1 school supply kit can be prepared in (8/40) minutes

∴30 school supply kits can be prepared in (30/5) minutes

Hence,

6 school-supply kits can be put together in 30 minutes.

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The number of people the elevator would carry more if all passengers were children would be = 148 extra people.

An elevator is defined as the machine that is being installed in tall buildings which helps to transport individuals either to slower level or a higher level of the building.

The number of adults the elevator can carry at a time = 28 adults.

The number of children the elevator can carry at a time = 30 children.

During the course of the day the total capacity of the elevator= 28 × 74 = 2,072.

The number of people the elevator would carry more if all the passengers where children would be;

30 × 74 = $2,220

2,220 - 2,072 = 148 extra people.

Therefore, the number of people the elevator would carry more if all passengers were children would be = 148 extra people.

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The no. of ways could those question be ordered is  1307674368000 ways A combination is what?

When selecting components from a collection using the combination method, the sequence of selection is unimportant, in contrast to permutations. In simpler scenarios, the number of combinations can be counted.

The act of combining n objects into k groups, one at a time, without repetition Repetition-allowed combinations are usually referred to as k-selection or k-combinations with repetition.

Given

that, Total no of question in quiz is 15 The no. of ways could those question be ordered is 15! ways =  1307674368000 ways The number of possible ways for those questions is 1307674368000.

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now, the assumption in this implicit differentiation is that "y" is really a function in x-terms, whilst "x" is just a simple variable

[tex]x^2y-3x=y^3-3\implies \stackrel{product~rule}{\left( 2xy + x^2\cdot \cfrac{dy}{dx} \right)}-3=\stackrel{chain~rule}{3y^2\cdot \cfrac{dy}{dx}} \\\\\\ 2xy-3=3y^2\cdot \cfrac{dy}{dx}-x^2\cdot \cfrac{dy}{dx}\implies 2xy-3=\cfrac{dy}{dx}(3y^2-x^2) \\\\\\ \left. \cfrac{2xy-3}{3y^2-x^2}=\cfrac{dy}{dx} \right|_{(-1,2)}\implies \cfrac{2(-1)(2)-3}{3(2)^2-(-1)^2}\implies -\cfrac{7}{11}[/tex]

The angle ∠C is 130° by the alternative angles.

Given that,

In the figure we have a diagram.

We have to find the angle c.

The angles created on the opposing side of the transversal with regard to both straight lines when two straight lines are cut by it are referred to as alternative angles. Therefore, the angles that are on the opposing sides of the transversal and have distinct vertices are those.

We know that,

By alternative angles

∠M=∠C

So,

130°=∠C

Therefore, The angle ∠C is 130° by the alternative angles.

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The graph of line 3x-y= -1 will be as follows.

What is a line?

A line is an endlessly long, straight object that, despite being drawn with a minimum width, is considered to have no particular width in mathematics.

Main Body:

slope = m = 3     point = (0,1)

The formula for one point form for a line is -

y-y₁ = m(x-x₁)

y- 1 = 3(x-0)

3x-y =-1

Now the graph for the line will be plotted by using the point given and the slope--

on Graph mark the point (0,1)

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50 would be the reliability of that measure  by standard error.

What is the standard deviation?

A measure that has no random error and no true score (i.e., is only random error) has zero reliability. A measure that has random error.

50 would be the reliability of that measure .

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The number of the given statement will be inequality -2 < x <  4.

We have been given the statement "the sum of five times a number and three is between -7 and 23".

Let the number would be x

As per the given statement, we can represent this algebraic form with inequality as:

⇒ -7 < 5x + 3 < 23

Subtract 3 on both sides of the above inequality

⇒ -7 - 3 < 5x  < 23 - 3

⇒ -10 < 5x <  20

Divided by 5 into both sides of the above inequality

⇒ -2 < x <  4

Thus, the number of the given statement will be inequality -2 < x <  4.

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The question seems to be incomplete the correct question would be

Find the number if the sum of five times a number and three is between -7 and 23.

The greater factor of 432, if 12 is the greatest common factor between the two factors is 36

The Greatest Common Factor is defined as the largest number that is a factor of two or more numbers. For example, the GCF of 24 and 36 is 12, because the largest factor that is shared by 24 and 36 is 12. 24 and 36 have other factors in common, but 12 is the largest.

The factors of 432 are 36,12, 24 ,18,4,108

But the two factors of 432 that has a multiple of 12 is 12 and 36

12× 36 = 432

The factors of 12 = 1,2,3,4,6,12

The factors of 36 = 1,2,3,4,6,9,12,18,36

the common factors are ; 1,2,3,4,6 and 12

therefore the greatest common factor = 12

since the GCF between 12 and 36 is 12, the second number will be 36

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Based on the information illustrated, the analysis implies the following:

a. nonstatistical.

b. statistical.

c. nonstatistical

d. statistical

A statistical question is one that can be answered by collecting varying amounts of data. A statistical question is one that does not have a single answer. Instead, you should expect a range of responses.

Identifying a statistical question necessitates knowledge of statistics. Statistics is a mathematical study that involves the collection, analysis, and interpretation of changing data. A statistical question will ask a question with a variable answer; data must be collected and analyzed, and the answer will provide an explanation of the information.

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statistical or nonstatistical  What's the difference? is that statistical is of or pertaining to statistics while nonstatistical is not statistical.

Statistical sampling is more objective and uses probability to determine the appropriate sample size. While it is does not eliminate sampling risk, statistical sampling allows the auditor to measure sampling risk and take steps to control it. Nonstatistical sampling relies more on the auditor's judgment.

Thus, the correct answer is nonstatistical statistical nonstatistical statistical

Answer:

she has 2 half dollors and 1 dimes

Step-by-step explanation:

2 half dollors means 2x20=40 coins

1 dimes means 1x50=50 coins

when you total it you get 50+40=90

so it is 3 rolls and it totally has 90

Answer:

x=17

It just is. I don't know how to explain it.

He may keep 82 movies on each shelf, using up to 492 movies and leaving 3 movies to retain.

Arithmetic operations is a field of mathematics that studies numbers and the operations on numbers that are helpful in all other disciplines of mathematics. It consists mostly of operations like addition, subtraction, multiplication, and division. Arithmetic Operator is used to conduct mathematical operations on the supplied operands such as addition, subtraction, multiplication, division, modulus, and so on. Arithmetic operators carry out operations on numbers. Variables are assigned values using assignment operators. Logical operators compare two values and return either "true" or "false" depending on whether the comparison is true (or false).

Here,

Movies that movie store has=495 movies

Number of shelves=6

If the owner wanted to make sure each shelf had the same number of movies,

=495/6

=82.5

He can keep 82 movies in each shelf that will use up to 492 movies and 3 movies will be left to keep.

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The greatest number of bags Caesar can make is 16 bags. Each of these bags will have 5 boxes of pasta and 8 jars of sauce.

Find the greatest common factor of 32 and 48

The greatest common factor of 32 and 48 is 16

So, the greatest number of bags Caesar can make is 16 bags

Number of pasta in each bag = 32/16

= 5 boxes of pasta per bag

Number of sauce in each bag = 48/16

= 8 jars of sauce per bag

If Caesar made fewer bags, he would have boxes of pasta and jars of sauce remaining.

He could use 8 bags but this is not the greatest number he could use.

Therefore, Caesar can use the greatest common factor to determine the highest number of bags he could use.

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⇒ Is 4x + 7y divisible by 2?⇔ This question simply is asking you if there is a possibility that you can take out the highest common factor of 2 in the expression 4x+7y.

⇒ We cannot take out the highest common factor of 2 in this expression since there is the term 7y that has the coefficient 7 which is NOT divisible by 2. the expression 4x+7y

cannot be written in the form a(b+c)

⇒∴ 4x + 7y is not divisible by 2

If you want me to clarify more in this question please say so as soon possible so that I can make time for you.

The ratio of 15 and square of m is 15/m².

A ratio simply refers to a mathematical expression that is typically used for denoting the proportion of two (2) or more quantities with respect to one another and the total quantities. This ultimately implies that, a ratio can be expressed as a quotient.

In Mathematics, quotient can be defined as a mathematical expression that is simply used to represent the division of a numerical value by another numerical value or variable.

In this scenario, the numerical value 15 would be the numerator while the variable m would be the denominator, and it should be expressed as follows:

Ratio = 15/m²

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Answer:

The point does not lie in the solution sets of the given system of inequalities

Step-by-step explanation:

We need to check whether the point (1,-5) is a solution to the system of inequality

We substitute x=1 and y=-5 into the top inequality:

. This is true

We substitute x=1 and y=-5 into the bottom inequality:

. This is false.

Since the point does not satisfy both inequalities, it is not a solution to the system of inequalities.

your profile pic is pretty btw: and hope my answer helped

Answer: 70%

Step-by-step explanation:

Percentage is always out of 100. And 10x10 =100 so you do the same to 7 multiply it by ten then your answer is 70 which is 70%.

Answer: 695.52

Step-by-step explanation:

The area of each triangle is [tex]\frac{1}{2}(12)(14.49)[/tex].

There are 8 triangles in the figure, so the area is [tex]8(1/2)(12)(14.49)=695.52[/tex].

On solving the system of equations by substitution method , the solution is x = 0 , y = 1 and x = 4 , y = 9    .

In the question ,

it is given that

the system of equation is

y = x² - 2x + 1

y = 2x + 1

by using substitution method ,

Substituting y = 2x + 1 in y = x² - 2x + 1

we get

2x [tex]+[/tex] 1 [tex]=[/tex] x² - 2x [tex]+[/tex] 1

x² - 2x [tex]+[/tex] 1 - 2x - 1 [tex]=[/tex] 0

x² - 4x = 0

x(x-4) = 0

So , x=0      or    x = 4

for x=0 , y = 2x+1 = 1

for x = 4, y = 2(4) + 1 = 9

Therefore, the solution for the system of equations is x=0 , y=1 and x=4 , y=9    .

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Eight decimeters are the most logical measurement after eight weeks, according to the statistics.

A line is described as a collection of points that stretches in both directions indefinitely. It has a single-length dimension. Collinear points are points that are located on the same line. Two points form a line, which is shown below an arrowhead.

If a line intersects two spots [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the line's equation,

y - [tex]y_1[/tex] = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex](x - [tex]x_1[/tex])

It is evident from the above graph that the line goes through points (0,0) & (1,1). Consequently, the trend line's equation is

y - 0 = [tex]\frac{1 - 0}{1 - 0}[/tex](x - 0)

y = x

To determine the most acceptable measurement after 8 weeks, change x = 8 in the equation above.

y = 8

After eight weeks, 8 decimeters are the most realistic measurement.

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The question is -

Alexander was studying the effect of playing rock music on plant growth. One of the plants was exposed to rock music 24 hours a day for 6 weeks. Data on the growth of the plant was collected at the end of each week and plotted in a graph, with time in weeks on the X-axis and height in decimeters on the Y-axis. Based on the data, which would be the MOST reasonable measurement at the end of 8 weeks?

A) 2 decimeters

B) 6 decimeters

C) 8 decimeters

D) 16 decimeters

Answer:

Step-by-step explanation:

they will sprint 75 yard in total

Answer:

1870

Step-by-step explanation:

10 x 2 = 20

25 x 2 = 50

50 x 2 = 100

20 + 50 + 100 = 170

170 x 11 = 1870

I cried over this problem so you dont have to :)

The two trains will pass each other after 7 hours.

Both trains need to cover a distance of 525 miles before they cross each other.

We know, d = s × t

where d ⇒ total distance travelled

s ⇒ speed of the train

t ⇒ time taken for both trains to meet

For train A,

s = 30 miles per hour

Distance covered by train A in t hours = 30 × t

For train B,

s = 45 miles per hour

Distance covered by train B in t hours = 45 × t

As the total distance is 525 miles,

30t + 45t = 525

75t = 525

t = 7 hours

Hence, the trains will pass each other after 7 hours.

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24 different seatings are possible when five people are to be seated around a circular table such that two seatings are considered the same if one is a rotation of the other.

A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle. It asserts that if there are n ways to do something and then m ways to do something else, then there are nm methods to do both of these acts. The Fundamental Principle of Counting assists in determining how selection is made based on available options. The Fundamental Principle of Counting streamlines the method to choosing by taking into account all of the available options and their combinations in order to calculate the Probability.

Here,

Since there are 5 peoples,

let us fix the first person and remaining will be set according to that.

this can be arranged in,

(5-1)!=4!

=24 ways

When five persons are sitting around a circular table, 24 distinct seatings are available, with two seatings regarded the same if one is a rotation of the other.

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Two similar triangles have,

The ratio of two sides of one triangle  = Ratio of two sides of the other triangle

The distance between Alanton and Bishop is 14 miles.

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

Alanton:

16 miles from Oakley.

8 miles from Crawford.

28 miles from Fayeville

We can have two similar triangles as shown below.

Two similar triangles have,

The ratio of two sides of one triangle  = Ratio of two sides of the other triangle

AB / AC = DE/ DF

8 / 16 = x / 28

1/2 = x/28

x = 28/2

x = 14

Thus,

The distance between Alanton and Bishop is 14 miles.

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The values of a and b are 8 and - 9.

Given that:

f(x) = x + a/x + b ........ (1)

f(1) = 0, f(2) = - 3

Putting the value of x = 1 in equation (1). We get,

f(1) = 1 + a/1 + b

f(1) = 1 + a + b ....... (2)

Putting the value of x = 2 in equation (1). We get,

f(2) = 2 + a/2 + b

f(2) = (4 + a + 2b)/2 ........ (3)

Putting the value of f(1) = 0 in equation (2). We get,

a + b = - 1 ......... (4)

Putting the value of f(2) = -3 in equation (3). We get,

=> -3 = (4 + a + 2b)/2

=> -6 = (4 + a + 2b)

=> a + 2b = - 10 ......... (5)

To find the value of a and b we have to solve equations (4) and (5) by elimination method.

So, for that subtract equation (4) from (5).

We got the value of b = - 9.

Then put the value of b in equation (4).

We got the value of a = 8.

Checking the value of a and b satisfies the value of the function's output and input.  

Hence,  the values of a and b are 8 and - 9 respectively.

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