Consider the calculation x - y + (- z) where x and z are positive real numbers and y is a negative real number. i) What are the directions of motion for this calculation ? ii) Is the final answer positive , negative , or undetermined ? i) Right, left , left ii) Undetermined i) Right , right , left ii) Undetermined i) Right , left , left ii) Negative i) Right right , left ii) Positive

The factors of the quadratic equation are found as the 7 and -3/2

For the given question, the quadratic equation is give as;

2x² - 11x - 21 = 0

Find the factors of -21×2 = 42 such that on subtraction it gives -11.

2x² - 14x + 3x - 21 = 0

Take 2x common from the first two terms and 3 from the last two terms.

2x(x - 7) + 3(x - 7) = 0

Take (x - 7) common from the terms.

(x - 7)(2x + 3) = 0

Then,

x - 7 = 0

x = 7

and, 2x + 3 = 0

x = -3/2

Thus, the factors of the quadratic equation are found as the 7 and -3/2.

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We are asked to determine the arc length of HJ. To do that we will use the following formula:

Given two secant lines that intercept outside a circle as follows:

We have the following relationship:

Substituting the values we get:

Now, we multiply both sides by 2:

Now, we subtract 96 from both sides:

Solving the operations:

Now, we multiply both sides by -1:

Therefore, the measure of the arc length of HJ is 38.

Answer:

-3

Step-by-step explanation:

We know that,

( + ) × ( + ) = ( + )

( - ) × ( - ) = ( + )

( + ) × ( - ) = ( - )

Accordingly, let us solve the given fraction.

-7 - ( - 4 )

-7 + 4

-3

Answer: [tex]x=15[/tex]

Step-by-step explanation:

By the consecutive interior angles theorem,

[tex]150+3x-15=180\\\\3x-15=30\\\\3x=45\\\\x=15[/tex]

The way in which the graph of 2y − x = 1 compare with the graph of 3y − x = 1 is that: A. the graph of 2y − x = 1 has a steeper slope than the graph of 3y − x = 1.

In Mathematics, a steeper slope simply means that the slope of a line is bigger than the slope of another line. This ultimately implies that, a graph with a steeper slope has a greater (faster) rate of change in comparison with another graph.

Mathematically, the standard form of the equation of a straight line is given by;

y = mx + c

Where:

For the graph of 2y − x = 1, the slope is given by:

2y − x = 1

2y = x + 1

y = x/2 + 1/2  

Slope, m₁ = 1/2 or 0.5.

For the graph of 3y − x = 1, the slope is given by:

3y − x = 1

3y = x + 1

y = x/3 + 1/3

Slope, m₂ = 1/3 or 0.3.

Therefore, m₁ > m₂ (steeper slope).

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Since we are measuring bank preference, we want to see the data in order of importance, then, the pareto chart is the most useful graph in this situation

Answer:

0

Step-by-step explanation:

Whole numbers are 0.1.2.3...  Follows that pattern forever.

Answer:

using the quadratic formula

Step-by-step explanation:

x= 3/2

The measure of angle UVX is 30°

What is an angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles. The angle formed by the rays lying perpendicular to the two crossing curves at the point of junction is another property of intersecting curves. Angle can also refer to the length of a rotation or an angle. The arc is centered at the vertex and defined by the sides in the case of a geometric angle.

Given, measure of angle UVW = 72°

measure of angle XVW = 42°

So, the measure of angle UVX = 72° - 42° = 30°

Hence, the measure of angle UVX is 30°

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The profuct of the given expression (x-2)³ is (x³ - 6x² + 12x - 8).

So, (x-2)³:

Do, the product as follows:

Perfect cube root formula: (a - b)³ = a³ - 3a²b + 3ab² -b³

Simplify:

Therefore, the profuct of the given expression (x-2)³ is (x³ - 6x² + 12x - 8).

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The area of a circle can be calculated as follows:

Using the area given in the problem and solving for the radius r:

Finally, the diameter is twice the radius:

Then the answer is the first option 3.27 in

From the given table that represents the population in a small coastal communityfor the period 1997 to 2006, let's answer the following questions.

(a) Average rate of change of the population between 1999 and 2002.

To find the average rate of change, apply the formula below:

Where:

x1 = 1999

x2 = 2002

y1 = the population in 1999 = 1,336

y2 = the population in 2002 = 1,483

Thus, we have:

Therefore, the average rate of change of the population between 1999 and 2002 is

49

(b) What was the average rate of change of the population between 2001 and 2005.

To find the average rate of change, apply the formula:

Where:

x1 = 2001

x2 = 2005

y1 = population in 2001 = 1591

y2 = population in 2005 = 801

Thus, we have:

Therefore, the average rate of change in the population between 2001 and 2005 was -197.5

(c) For what period of time was the population increasing.

From the given table, we can see the table was increasing from 1997 to 2001

The population was increasing from 1997 to 2001

(d) For what period was the population decreasing.

From the table, the population was decreasing from 2002 to 2006

The population was decreasing from 2001 to 2006

ANSWER:

• (a) 49

• (b) -197.5

• (c) 1997 to 2001

• (d) 2001 to 2006

Answer:

A. y - 2 = 2/3 (x - 0)

Step-by-step explanation:

I will ask my question here

is p(x)

bye :)

Considering the Graph and reading the distance blocks from the store to the bank we see a progression of 3blocks

This is further explained below.

Generally, There is a concept referred to as distance that may be used to quantify, either quantitatively or qualitatively, the distance that separates two items or sites.

When speaking about physics or using the phrase in everyday language, "distance" may either refer to a literal measurement or an estimate based on a number of other parameters.

Both meanings are appropriate when discussing or using the term.

The progression of existence and events that occur in what seems to be an unstoppable order beginning in the past, continuing through the present, and moving into the future is what we refer to as time.

Time may be broken down into three distinct parts: the past, the present, and the future.

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The graph that is hardest to write the transformation using algebraic notation is the second top graph counting from left to right

A graph is a pictorial representation of data

A transformation is a movement that can be represented in a cartesian plane.

There several types of movement involved in transformation, some of them are:

The first top graph counting from the left is a translation to the left.

The first graph at the bottom counting from the left is a translation downwards

The next bottom graph is reflection along x axis and translation downwards

The most difficult which is the second at the top counting from left involves dilation.

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The most appropriate choice for exponent will be given by-

Fourth option is correct

What are exponent?

Exponent tells us how many times a number is multiplied by itself.

For example : In [tex]2^4 = 2\times 2\times 2 \times 2[/tex], here, 2 is multiplied by itself 4 times.

If  [tex]a^m = a\times a\times a \times.....\times a[/tex] (m times), a is the base and m is the index.

The laws of index are

[tex]a^m \times a^n = a^{m + n}\\\\\frac{a^m}{a^n} = a^{m-n}\\\\a^0 = 1\\\\(a^m)^n = a^{mn}\\\\(\frac{a}{b})^m = \frac{a^m}{b^m}\\\\a^mb^m = (ab)^m[/tex]

Here,

For first option

[tex]\frac{4^{11}}{4^{14}}\\\frac{1}{4^{14 - 11}}\\\frac{1}{4^3}\\\frac{1}{64} < 1[/tex]

For second option

[tex](5^4)^2 \times 5^{-11}\\5^8 \times 5^{-11}\\5^{8-11}\\5^{-3}\\(\frac{1}{5})^3\\\frac{1}{125} < 1[/tex]

For the third option,

[tex](2^3)^{-2}\\2^{-6}\\(\frac{1}{2})^6\\\frac{1}{64} < 1[/tex]

For the fourth option
[tex]\frac{(3^5)^2}{3^4}[/tex]

[tex]\frac{3^{10}}{3^4}\\3^{10 - 4}\\3^6\\ 729 > 1[/tex]

Fourth option does not have an expression greater than 1

Fourth option is correct.

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Step-by-step explanation:

I assume, based on what I see, that the solid line is just cos(x), right ?

and we need to find the equation that draws the dotted line, correct ?

the notation is strange, as it seems we need to find a multiplication factor for x in the cos function.

but there is no multiplication factor that moves the cosine wave by pi to the left or to the right (so that the max. happens, where originally the minimum happens, and vice versa).

so, we need to add (or subtract) pi in the cosine function.

the rest is clear :

the normal distance between min. and max. of the cosine function is 2 (between +1 and -1). the target is 4. so we need to multiply by 2.

and since the values of that function have to be between -4 and 0 (instead of -2 and +2), we have to subtract overall 2.

giving us the function :

y = 2×cos(pi + x) + -2

The outer perimeter of the no-slip surface is equal to 78 feet.

Perimeter is a term used to describe the sum of the outside edge lengths or it can also be described as the whole of the outer edge or boundary.

The outer perimeter of this swimming pool can be determined by adding 3 feet twice to all the sides of the rectangular swimming pool and then adding these sides together.

Since it is a 12-ft-by-15-ft rectangular swimming pool, this means that two sides of this swimming pool are 12 feet and two sides of this pool are 15 feet, therefore;

12 + 6 = 18

15 + 6 = 21

Now the perimeter can be determined by adding all the sides as follows;

18 + 21 + 18 + 21 = 78 feet

Hence, the outer perimeter of the no-slip surface is calculated to be 78 feet.

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According to the combination method, there are 6 ways for the selection to be made if one worker is to be a receptionist, one a secretary, and one a technical typist.

Combinations:

A combination is all about grouping. The number of different groups which can be formed from the available things can be calculated using combinations.

The standard form for calculating the combinations is,

[tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex]

where,

0 ≤ r ≤ n.

This formula is sometimes also called as ncr formula.

Given,

An executive hires 3 office workers from 8 applicants.

Here we need to find how many ways can the selection be made if one worker is to be a receptionist, one a secretary, and one a technical typist.

Here we have to split the problem like the following,

We know that the total number of office workers is 3.

Like, if one worker is to be a receptionist, the the combination is like,

So, the value of n = 3 and r = 1.

Then, according to the ncr formula,

=> ³C₁ = [tex]\frac{3!}{1!(3-1)!}[/tex]

=> 3!/1!2!

=> (3 x 2 x 1) / 1 x 2 x 1

=> 3

Similarly,  if one worker is to be a secretary,

Here the value of n = 2 (Because we have already select one person as receptionist) and r = 1

So,

=> ²C₁ = (2!)/1!(2-1)!

=> (2x1)/ 1 x 1

=> 2

Similarly,  if one worker is to be a technical typist,

Here the value of n = 1 (Because we have already select one person as receptionist) and r = 1

So,

=> ¹C₁ = 1

Therefore, the total number of possible ways are,

=> 3 x 2 x 1

=> 6

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We were told that Ben earned 625.5 points out of 700 on an essay. Expressing his score in the essay in terms of percentage, it becomes

625.5/700 x 100 = 89.29%

Also, he scored 65 out of 70 on an assignment. Expressing his score in the assignment in terms of percentage, it becomes

65/70 x 100 = 92.86%

We would find the average between the two percentages

Average = sum of percentages/number of percentages

Average = (89.29 + 92.86)/2

Average = 91.075

Average is approximately 91%

Since in order to earn an A in the class, he needed to average a 91 on these two

assignments and he got an average of 91%, then we can conclude that he got an A

Answer:

The equation is an example of the associative property of addition.

Step-by-step explanation:

Associative property of addition: changing the grouping of addends does not change the sum.

For example: A+(B+C) = (A+B)+C.

Answer:

a.) Let x be Kim's sister's age.  Kim's age would therefore be 2x.

b.) 2x + x = 36

c.) 2x + x = 36  

          3x = 36

             x = 12

d.) So Kim's sister (x) is 12.

e.) Since Kim's age is 2x, Kim is 24.

Step-by-step explanation:

See above.

The expression to find the population of fruit flies on 6th day in Lavania's laboratory can be (9+5x) where x is the number of fruit flies on the first day. After evaluating the expression, the number of fruit flies on 6th day will be 109.

According to the question,

We have the following information:

Lavania observes 20 fruit flies on the first day of her study.

On 6th day, the number of fruit flies would be nine more than 5 times as many fruit flies as when she begun her study.

Now, let's take the number of fruit flies on first day to be x.

So, we have:

x = 20

Now, the expression to find the number of fruit flies on 6th day would be:

9+5x

Now, putting the value of x:

9+5*20

9+100

109

Hence, the required expression is (9+5x) and the number of fruit flies on 6th day are 109.

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Answer:

32.5

Step-by-step explanation:

What is 25% of 130?

0.25 * 130 = 32.5

The correct statement about the function is the y-intercept is (0.71), and 71 represents the starting temperature.

A graph can be described as a pictorial representation of data. A graph has a y-axis and a x-axis. The x-axis in this question represents time and the y-axis is the temperature.

The function shown in the graph is a linear function. This is because the curve is a straight line.  The y-intercept is the point where the line crosses the y-axis. The y-intercept is the value of the data set when x is zero. The y-intercept represents the initial temperature or the starting temperature.

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The simplified form of the given expression is option c 1 1/2x - 1 3/4

Given,

The expression; 1/4 (3x - 7) + 3/4x

We have to simplify this expression;

Simplification of expressions;

To simplify a phrase, create an equivalent expression without any terms that are identical. The expression will then be rewritten using the fewest terms feasible.

Then,

1/4 (3x - 7) + 3/4x

= 1/4 × 3x - 1/4 × 7 + 3/4x

= 3/4x - 7/4x + 3/4x

= 6x/4 - 7/4

= 3x/2 - 7/4

= 1 1/2x - 1 3/4

Therefore,

The simplified form of the given expression is option c 1 1/2x - 1 3/4

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Answer:

3.456e+12
or

3,456,000,000,000

Step-by-step explanation:

400 x 600 = 240,000

240,000 x 800 = 192,000,000

192,000,000 x 150 = 28,800,000,000

28,800,000,000 x 120 = 3,456,000,000,000

hope this helps you :D

Given data:

The given figure of the trapezium.

The expression for the area of the trapezium is,

Thus, the area of the given trapezium is 360 sq-m.

I'm pretty sure it's 6>p-3