Writing and solving radical equations: Mastery Test
PLEASE HELP

Writing And Solving Radical Equations: Mastery TestPLEASE HELP

Answers

Answer 1

The equation has 2 valid solutions; no extraneous solutions.

What are functions?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

What is factorization  and radicals?

Factorisation : The process of breaking or decomposing an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorisation or factoring.

Radicals :In the same way that addition is the opposite of subtraction in mathematics, a radical, also known as a root, is the opposite of an exponent. The square root, denoted by the symbol  is the smallest radical.

The given equation is:

First, we determine the solutions

Add 5 to both sides

Square both sides

Expand

Collect like terms

Expand again

Factorize

Factor out x - 2

Split

The above values are valid values of x.

Hence, the equation has 2 valid solutions; no extraneous solutions

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Related Questions

describe your sketch. the solid has no negative x-values. the solid has both positive and negative y-values. the solid has no negative z-values. the solid has a straight side and a curved side in the x y-plane. the solid has ---select--- in the x z-plane. the solid has ---select--- in the y z-plane.

Answers

The solid has a straight side in the x y-plane and a curved side in the x y-plane. In the x z-plane, the solid has a curved side, and in the y z-plane, the solid has a straight side.

The solid has no negative x-values, meaning all x-values are positive. It has both positive and negative y-values, indicating that it is symmetrical around the x-axis. The solid has no negative z-values, meaning all z-values are positive. In the x y-plane, the solid has a straight side and a curved side. In the x z-plane, the solid has a curved side and in the y z-plane, the solid has a straight side.

The solid has a straight side in the x y-plane and a curved side in the x y-plane. In the x z-plane, the solid has a curved side, and in the y z-plane, the solid has a straight side.

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1) Differentiate following equations with respect to x.

a) x² + xy + y² = 0

b) 1/x + 1/y =e^y


Answers

The differential equations are dy/dx = -x/y and dy/dx = e^y * (-1/x² + 1/y²).

What is the differential equation?

A solution of a differential equation is an expression for the dependent variable in terms of the independent one(s) which satisfies the relation. The general solution includes all possible solutions and typically includes arbitrary constants (in the case of an ODE) or arbitrary functions (in the case of a PDE.)

a) To differentiate x² + xy + y² = 0 with respect to x, we can use the power rule and the chain rule.

The power rule states that the derivative of x^n is nx^(n-1)

The chain rule states that if y = f(u) and x = g(u) then dy/dx = dy/du * du/dx

x² + xy + y² = 0

dx/dx (x² + xy + y²) = dx/dx (0)

2x + y = 0

dy/dx = -x/y

b) To differentiate 1/x + 1/y = e^y with respect to x, we can use the chain rule and the reciprocal rule.

The chain rule states that if y = f(u) and x = g(u) then dy/dx = dy/du * du/dx

The reciprocal rule states that the derivative of 1/x is -1/x²

1/x + 1/y = e^y

dy/dx = dy/dx (e^y)

dx/dx (1/x + 1/y) = dx/dx (e^y)

-1/x² - 1/y² = e^y

dy/dx = e^y * (-1/x² + 1/y²)

Hence, the differential equations are dy/dx = -x/y and dy/dx = e^y * (-1/x² + 1/y²).

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Dr. Chandler wants to print copies of
his thesis in hardcover book format. He
could use Washington Printing, paying a
setup fee of $41 and $6 for every book
printed. Or, he could go through Fairfax
University, paying an up-front fee of
$32 and $9 per book. For how many
books will the costs be the same? How
much is that?

Answers

Answer:

For 3 books, costs are the same

$59

Step-by-step explanation:

x = number of books

$41 + ($6/book)(x) = $32 + ($9/book)(x)

41 - 32 = 9x - 6x

9 = 3x

x = 9/3 = 3

41 + 6(3) = 32 + 9(3) = $59

what is the slope through the line of (9, 10) and (7, 2)

Answers

Answer:4

Step-by-step explanation:

Distributive property c3/c when c=3

Answers

Answer: The answer is 9

Step-by-step explanation: 3^3/3=9

a child's toy harp is in the shape of a trapezoid as shown. in square inches, what is the area of the harp?

Answers

The area of a trapezoid is given by the formula A = 1/2(b1 + b2)h. In this case, b1 = 4, b2 = 3, and h = 8.

The area of a trapezoid can be determined using the formula A = 1/2h(b1 + b2), where A is the area, h is the height, and b1 and b2 are the lengths of the top and bottom bases of the trapezoid, respectively. To determine the area of a child's toy harp in square inches, we need to know the length of the top and bottom bases and the height of the trapezoid.

Therefore, the area of the harp is 1/2(4 + 3)8 = 20 square inches. To find the area of the harp, we first need to know the measurements of the base lengths, b1 and b2, as well as the height, h. Once we have these measurements, we can plug them into the formula for the area of a trapezoid and solve for A. In this case, the area of the harp is 20 square inches.

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Answer:

20 square inches

Correct Answer 100%. Pls, give me brainliest. Thank You.

The graph shows the number of gallons of water in a large tank as it is being filled. Based on the trend​ line, predict how long it will take to fill the tank with gallons of water.

Answers

The required time it will take to fill the tank with gallons of water is 18 minutes.

What is a line?

A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.

Here,
From the figure, the equation of the trend line is given as,
y = 20.83x

Where y =  gallons of water and x is time in minutes

Now, put y = 375
375 = 20.83x
x = 18 min

Thus, the required time it will take to fill the tank with gallons of water is 18 minutes.

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Complete question,

Make Sense and Persevere The graph shows the number of gallons of water in a large tank as it is being filled. Based on the trend line, predict how long it will take to fill the tank with 375 gallons of water.

15. For the graph below, which of the following is a possible function for g?

Answers

The graph demonstrates that the function g's line goes through the locations (0,2) and (2,8). The slope of the line is 3, implying that its equation is g(x) = 3x + 2.

What is a slope?

The steepness or inclination of a line, route, or surface is measured by slope. It is the vertical distance divided by the horizontal distance between two locations on a line, route, or surface.

According to the graph, the function g is a line with a slope of 3 and a y-intercept of 2. This suggests that the line's equation is g(x) = 3x + 2. According to this equation, increasing the y-coordinate by one increases the x-coordinate by three. The line connects the points (0, 2) and (2, 8), which means that when x = 0, y = 2 and when x = 2, y = 8. This may be demonstrated by plugging the x-values into the equation, which will produce the matching y-values.

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my grade depends on this, help!!

Answers

Answer:

x ≥ - 3

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

We observe on the graph:

The relation is not a function because it fails the vertical line test. You can see the graph intersects with the y-axis twice.

The domain is restricted at x = -3 and unrestricted on the positive side.

The domain is:

x ≥ - 3

Please Hurry!
A box of apples sells for $17. At this rate, which expression represents the cost, in dollars, of 100 apples?

A) 5/17•20
B) 5/20•17
C) 100/17•20
D) 100/20•17
E) 17•5•20

Answers

Answer: D

Step-by-step explanation:

20 apples cost $17

100 apples = 100/20 * 17 = D

Which is the common difference for this arithmetic series? 8, 30, 52, 74, 96, 118 a. d = 8 b. d = 22 c. d = 32 d. d = 38

Answers

Answer:

d = 22

Step-by-step explanation:

you add 22 to a number in the sequence to get the next number

8 + 22 = 30

30 + 22 = 52 and so on...

what is the slope of the line through the points (-2,9) and (-4,6) ?

Answers

Answer:

The slope is [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

The slope formula would be: [tex]\frac{y2-y1}{x2-x1}[/tex]

So for (-2,9) and (-4,6), we can plug in the variables: (x1, y1) and (x2, y2)

Let's use the numbers in the equation provided above:

[tex]\frac{6-9}{-4-(-2)}[/tex]

= [tex]\frac{-3}{-2}[/tex]

= [tex]\frac{3}{2}[/tex]

Answer:

3/2

Step-by-step explanation:

[tex]\frac{y2-y1}{x2-x1} = \frac{6-9}{-4-(-2)} = \frac{-3}{-2} =\frac{3}{2}[/tex]

please help solve it

Answers

Note that if the family is to spend less than $60 dollars without further expenses, then they will have to spend nothing more than 6 hours. The inequality expression is given as: 36+4h < 60

What is the justification for the above result?

First, the inequality expression is given as:

36+4h < 60

Where h is the number of hours they could spend.

We arrive at the above because we were given the following:

Cost of Movie = $36

Cost of parking Per Hour= $4

The maximum amount to be spent = $60

Thus, to find the number of hours the can spend without overshooting $60, we must find h. To do this, we must make h the subject of the formula by first removing 36 from both sides:

36+4h-36 < 60-36

4h < 24

h < 24/4

h < 6

What the above result show is that the number of hours that must be spent must be less than 6.

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Why is f not a function from R to R if
a) f (x) = 1/x?

Answers

The domain of the function is not the set of all real numbers, that is why it is not from R to R

Why is f not a function from R to R?

Here we want to see why the function f is not a function from R to R, where R is the set of the real numbers.

The function here is:

f(x) = 1/x

Notice that x is on the denominator, so we can't evaluate that function on x = 0.

So there is a real number that we can't use on that function, then the domain is not R, is R minus the element {0}

That is why f(x) is not a function from R to R, because the domain is not the set of the real numbers.

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URGENT PLEASE HELP!!!!!!

Answers

Answer:

یه گل یک گل بام میی مه فیلم بام حس بام حس فمس یکم باشگاه هی یک گل یه حس سیم هی فکریه خشک پیل هر یک حس صب زی صب هم گچ نی بلن هر بر قل هم بی دو حس قیین

Step-by-step explanation:

سبک حس بام نی شیک حس

یا کمی سیم حس او

نی یک حس بکشم یک حس بام نی که خیلی تنیام که اما الا دیه انجام نمییم ای موضوع که دعوا خیلی تخفیف خیلی خوعه ای موضوع که اما الا دیمش خوش

۳ خشک هی یک هی بام نی با که اما ۷غ هه بام نی بلن کف بام نی بکر

به نمییم هی بام میی لاک حس بام

بلن هی یک

حالم ای زبونه فراموش که

فخ بیم فک

Nancy and Martin are making kites. The kites are similar figures. The side lengths of Nancy's kite are 16 inches, 16 inches, 24 inches, and 24 inches. The side lengths of Martin's kite are (5x + 5) inches, (5x + 5) inches, 10x inches, and 10x inches. Assume that 10x > 5x + 5. Find the perimeter of Martin's kite.​

Answers

Answer: 100 inches

Step-by-step explanation:

Corresponding sides of similar figures have proportional side lengths, so:

[tex]\frac{10x}{24}=\frac{5x+5}{16} \\\\\frac{2x}{24}=\frac{x+1}{16}\\\\\frac{x}{12}=\frac{x+1}{16}\\\\16x=12x+12\\\\4x=12\\\\x=3\\\\[/tex]

So, the perimeter is [tex]5x+5+5x+5+10x+10x=100[/tex].

three friends went to an icecream store and tried a new flavor the store was testing. After
trying the flavor, they were asked to rate the icecream on 9-point rating scale ranging from
1-Hate it to 9-Love it. The friends ratings were: Destiny 9, Taylor 6, Jeremiah 5. What is the
mean of their ratings?

Answers

The mean of their ratings is 7.

How to calculate the mean of their ratings?

Mean (also called the average) is used to describe the central tendency of a set of numerical data. It is calculated by summing up all the values in the data set and dividing by the number of values.

Since We have the ratings:

Destiny 9, Taylor 6, Jeremiah 5

Mean = (9 + 6 + 5)/3 = 20/3 = 7

Note: we divide by 3 because there are 3 people

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The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.25, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.

A. Equally likely and unlikely
B. Likely
C. Unlikely
D. This value is not possible to represent probability of a chance event.

Answers

The baker made a batch of chocolate chips, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.25, the likelihood of randomly selecting a chocolate chip is B. Likely.

What is probability?

Generally,  Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.

A probability of 0.5, for example, would indicate that an event has a 50% chance of occurring. Probability can be used to make predictions and inform decision-making in a wide range of fields, including statistics, finance, and engineering.

A probability of 0.25 represents a 25% chance of a randomly selected cookie from the batch being a chocolate chip cookie, which is considered "likely" to occur.

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. The following list of monthly expenses for a first-year student at a post-secondary
institution are presented. The student has a monthly income of $1,450. Is the student
following the recommended rule of allocating 50% of monthly income to needs, 30% to
wants and 20% to savings or debt?
Income: $1,450

Answers

Based on the information provided, it can be concluded the student is not following the rule of allocating 50% to needs, 30% to wants, and 20% to savings.

What percentage is the student allocating for each category?

Needs: 300 +10 + 50 +150 + 100 + 100=  $710

Now, let's calculate the percentage this represents:

710 x 100 / 1450 = 48%

Wants: 9.99 + 9.95 +9.99 + 19.99 + 25 + 500 + 65= $639.92

Now, let's calculate the percentage this represents:

639 x 100/ 1450 = 44%

Savings: 48 + 44 = 92 which means he can save 8%

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toss a coin three times, and let x be the number of heads. find the probability mass function of x.

Answers

The probability mass function of x  is P(0)= 1/8, P(1)= 3/8, P(2)= 3/8, P(3)= 1/8.

Here number of trials = 3

In tossing a coin for once, the outcomes of the trial are either head or tail.

The trials are independent.

probability of getting head(success)=p=1/2

probability of getting tail(failure)=1-p=1-(1/2)=1/2

Number of success=X

Since there are two mutually exclusive outcomes of independent trials, the probability mass function of Binomial = (nx)px(1−p)n−x(nx)px(1 − p)n−x {in this case n=3}

The probability distribution of X is -

= X=0, P(X=0)=1/8

= X=1, P(X=1)=3/8

= X=2, P(X=2)=3/8

= X=3, P(X=3)=1/8

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Which equation can be used to find the area in square feet of the piece of glass?

Answers

Answer:

Area = length x width (in feet)

Step-by-step explanation:

The area of a 2-dimensional shape can be found by multiplying its length by its width. The equation to find the area of a rectangle is:

Area = length x width

So if you know the length and width of a piece of glass in feet, you can use the above equation to find its area in square feet. For example, if the length of the glass is 10 feet and the width is 5 feet, the area would be:

Area = 10 feet x 5 feet = 50 square feet

So the equation to find the area of a piece of glass in square feet is:

Area = length x width (in feet)

It's worth noting that this equation applies to any 2-dimensional shape that has a length and a width, not just a rectangle.

(07.01 mc) select the general solution to x squared dy over dx equals 3 plus 2y period one half ln absolute value of quantity 3 plus 2y close absolute value equals ln absolute value of x squared close absolute value plus c one half ln absolute value of quantity 3 plus 2y close absolute value equals negative 1 over x plus c

Answers

The general solution to x squared dy over dx equals 3 plus 2y is given by 1/2 ln|3 + 2y| = -1/x + c, where c is an arbitrary constant.

To calculate this, we begin by taking the derivative of both sides of the equation with respect to x. We then rearrange the equation to yield 2y + x^2 dy/dx = 3. We divide both sides by x^2 so that dy/dx is isolated on one side of the equation, yielding dy/dx = (3 - 2y) / x^2. We can then integrate both sides of the equation, with respect to x, to yield 1/2 ln|3 + 2y| = -1/x + c, where c is an arbitrary constant. This equation is the general solution to x squared dy over dx equals 3 plus 2y.

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A person borrowed $2100 from his home equity line of credit to pay off his car loan. He then borrowed another $1200 to have his kitchen repainted. Represent how much
he owed on his home equity line of credit as a real number.
What is the real number that represents the amount he owed on his home equity line of credit?

Answers

The real number that represents the amount he owed on his home equity line of credit would be = $3,300

What is a real number?

A real number is defined as the type of number that can be used to represent a one directional measurement which can be rational or irrational.

The first amount of money borrowed by a person from his home equity line of credit = $2100

The second amount of money borrowed by a person from his home equity line of credit = $1200

Therefore, the total amount that was borrowed= 2100+1200 = $3,300.

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The graph below represents the distance of a dog from a trainer after a command is given.

A graph titled Dog Obedience School. The horizontal axis shows Time (seconds), numbered 1 to 10, and the vertical axis shows Distance (yards) numbered 4 to 40. The line shows an increase, then decrease, then constant distance.

Which statement could describe the dog’s movement at 5 seconds once the command was given?

The dog stopped to lie down and obey the trainer’s command.
The dog was running towards the trainer.
The dog was running away from the trainer.
The dog was stopped but began running towards the trainer.

Answers

The correct statement regarding the dog’s movement at 5 seconds once the command was given is given as follows:

The dog was running towards the trainer.

How to obtain the correct statement regarding the graph?

The input and output variables for the function graphed are given as follows:

Input: time.Output: distance.

At a time of 5 seconds, the distance between the dog and the trainer is decreasing, meaning that the dog was moving towards the trainer, and thus the second option is the correct option.

Missing Information

The graph is given by the image presented at the end of the answer.

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Answer:

The dog was running towards the trainer.

k2 is 11,194.21 feet higher than mt. kenya. enter and solve an equation to find the elevation of mt. kenya. use x to represent the elevation of mt. kenya.

Answers

The elevation of mountain mt.kenya is, x = 17,057.1 feet by substitution method from the elevation of mountain K2 given.

Given that,

K2 is 11,194.21 feet higher than mt.Kenya, write and solve an equation to find the elevation of mt.Kenya.

x = mt. Kenya ( since given that x represents the elevation of mt.kenya)

Let us consider/assume ,

y = K2 (say)

Therefore, the relation between x and y:

                   x = y - 11,194.21    ( or )

                   y = x + 11,194.21  

( since given that K2 is 11,194.21 more than mt.Kenya )

The elevation of K2 Mountain = 28251.31 feet

                                                  = y

substitute the value of y in x = y - 11,194.21

                                            x = 28251.31 - 11,194.21

                                       ∴ x = 17,057.1 feet.

Therefore the elevation of mt.kenya found to be, x = 17,057.1 feet by substitution method.

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The complete question is :

K2(Which is 28251.31) is 11,194.21 feet higher than Mt.Kenya Write and solve an equation to find the elevation of Mt.Kenya. use x to represent the elevation of mt. kenya.

5 divided by 4/5???????????????????????????????????????????????????????

Answers

Answer:

6.94??????‽??????????????

Step-by-step explanation:

5÷4/5?????????

5×5?????????‽?/4

2.777777778/4

=69.4????????????????????

find each measure m < 5

Answers

The measure of all the angles are estimated.

∠1 = 104 ;  ∠4 = 45 ; ∠3 = 65 ; ∠2 = 79.Explain the term linear pair?When two lines cross at one point, a linear pair with angles is created. If the angles follow the intersection of both the two lines in a straight line, they are classified as linear. A linear pair's total angles are indeed equal to 180°.

For the stated question:

For ∠1

∠1 = 68 + 36 (sum of opposite interior angle equals exterior angle).

∠1 = 104

For ∠4.

∠4 = 180 - 70 - 65 (linear pair)

∠4 = 45

For ∠3.

∠3 = 65 (vertically opposite angle)

For ∠2.

∠2 = 180 - 65 - 36  (sum of angles of triangle are 180)

∠2 = 79

Thus, the measure of all the angles are estimated.

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What inverse operation is used to solve the equation?

x + 2 = 5
Responses
A multiply by 2 on both sidesmultiply by 2 on both sides
B divide by 2 on both sidesdivide by 2 on both sides
C add 2 to both sidesadd 2 to both sides
D subtract 2 from both sides

Answers

Answer:

D subtract 2 from both sides

Step-by-step explanation:

x + 2 - 2 = 5- 2

==>    x = 3

The solution of the equation is x = 3.

What is an equation?

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

An equation,

x + 2 = 5.

To solve the equation:

Subtract 2 from both sides,

x +2 -2 = 5 -2

x = 3

Therefore, the solution is x = 3.

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Given f(x) = 3x^3+kx-13, and x-1 is a factor of f(x), then what is the value of k?

Answers

Answer: k=10

Step-by-step explanation:

pls help me

Josh is the owner of CranBog, a Cranberry Bog in Massachusetts. Cranberry production at CranBod can be represented by the inequality y ≤ 150x - 3100
under normal climate conditions, where y
is the annual production of cranberries at CranBog, in thousands of pounds, and x
is the number of acres of land that produce cranberries.

Answers

The TRUE statements about the inequality y ≤ 150x - 3100 are:

A) For a solution to be viable, both x and y must be integers.E) The ordered pair (40, 2900) is a solution to the inequality and means that with 40 acres of land, CranBog can produce 2,900 (in thousands of) pounds of cranberries.

What is inequality?

Inequality is a mathematical statement showing that two or more mathematical expressions are unequal or not equivalent.

Inequalities are represented by the following types and inequality symbols:

Less than (<)Greater than (>)Not equal to (≠)Less than or equal to (≤)Greater than or equal to (≥).

Check:

Ordered pairs (40, 2900)

y ≤ 150x - 3100

y ≤ 150(40) - 3100

y ≤ 6,000 - 3100

y ≤ 2900

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Which of the following represents all solutions (x,y) to the system of equations created by the linear equation and the quadratic equation y=x^2+9 a financial statement showing the revenue and expenses for a fiscal period. 1/3x + 2y + 5/3x - 4y pls I have a 0 in math I need help with this "Design for production" takes into account the capabilities of the organization to produce or deliver a given product or service. True or False when you save a document for the first time, which tab displays in backstage? how each of the following would pass through the plasma membrane: gases, large polar molecules, charged molecules (like ions), hydrophobic molecules, and small polar molecules. Pls help is more than 30 point you work for a large company that has over 1,000 computers. each of these computes uses a wireless mouse and keyboard. therefore, your company goes through a lot of alkaline batteries. when these batteries can no longer power the intended device, you need to decide what to do with them. unless otherwise dictated by your local authorities, which of the following would be the easiest way to deal with these batteries? why is hemoptysis a clinical manifestation of pulmonary embolus? How doe power play out in a relationhip,pleae write 4-5 entence explaining and ill give brainliet measurements of a stream taken over 5 years indicate that its velocity decreased. the stream's decreased velocity was most likely caused by? 1) a decrease in gradient2) a decrease in transpiration3) an increase in atmospheric transparency4) an increase in atmospheric surface winds which of the following traits is associated with creative people today? stubbornness questioning talent intuition students are listed by the neighborhood they live in. the psychologist assigns numbers to each neighborhood and randomly selects one neighborhood and then surveys every student living in that neighborhood Match a system of equations to each description.System with one solution: (-1, 3)System with no solutionsSystem with infinite number of solutions2x + 2y = -8 and 3x + 3y = - 12- 3x + 3y = 12 and 5x + 5y = 10y +4 =-x and y = -x + 2 how are solar eruptions influenced by the sunspot cycle which of the following would be true if the actual rate of inflation were less than the expected rate of inflation? A child's realization that others may have beliefs that the children knows to be false best illustrates that the child is not completelyA. EgocentricB. ImprintedC. HabituatedD. AccommodatedE. Postconcentional the data set shows the number of passengers on the flights leaving the columbus airport in the next hour. what is the median number of passengers on the flights? round answer to tenths place. if answer is a whole number then put a zero in your answer for the tenths place for it to be counted correct 39, 48. 25, 25, 53, 22, 70, 36 Did Jas graph and find the solution correctly? If not, what was her mistake? Nomadic pastoralism is an extensive agricultural system practiceda) In the dry regions of Africa and Asiab) In the tropical region of Africa and Asiac) In the hinterland of Australiad) By Native American Buffalo hunterse) By people shift location in pursuit of rain clouds