Determine if the given point is a solution of the system of inequalities.
Help please.

4 m/s is the final speed of the 3.0 kg cart.

When two bodies of different masses move together each other and have a head-on collision, they travel in the same or different directions after a collision. This phenomenon is called the conservation of momentum.

The external force is not working here, so the initial momentum is equal to the final momentum. For elastic collision, the final velocities are different for both bodies.

m₁u₁ +m₂u₂ = m₁v₁ +m₂v₂

A 2.0  kg cart moving right at 5.0  m/s on a frictionless track collides with a 3.0 kg cart initially at rest. The 2.0 kg cart has the final speed of 1.0 m/s  to the left.

Substitute the values, m₁ = 2kg, m₂ =3kg, u₁ =5 m/s and u₂ =0 m/s, then the final velocity will be

3x0 +2x5 = -2x1 + 3v₂

v₂ = 4 m/s

Thus, the final velocity 3.0  kg cart is  4 m/s.

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d=2 and (a-1/2)2=2 hence 2a-1=2 hence a=3/2=first term and the common difference=d=2

S1, S2,... Sn can be written as:

A (first term) (first term)

A+r (r is a common difference) (r is a common difference),

A+2r

A+3r

A +(n-1)r

It is possible to calculate the sum as A +A +... +A (n times) + r +2r +3r.... +(n-1)r.

Giving n*A +r*(1+2+3....+n-1)

1+2+3….+n-1= n*(n-1)/2 =n^2 - n/2

The first N terms are added together as follows: n*A + r/2 *n2 - r*n/2

= r/2 *n^2 + (A - r/2)*n

This equals n2 - 2n for any n given the questions, so

A-r/2 = 2 AND r/2 = 1

=> r = 2 and A = 3 with r = 2

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Full question

The sum of the first n terms of an arithmetic sequence is given by Sn= n^2-2n. What are the first term and the common difference?

The coordinates of the vertices of quadrilateral A’B’C’D’ after a translation along vector <2, -3> is: A. A' (-2, 5), B' (1, 7), C' (2, 5), D' (1, 3).

In Mathematics, the translation of a geometric figure to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image or function.

Note: We would move in the opposite direction of the given vector <2, -3>.

By applying a translation to the pre-image of quadrilateral ABCD vertically up by 3 units and horizontally left by 2 unit, the coordinates of the image of triangle A'B'C' include the following:

(x, y)                               →                  (x - 2, y + 3)

Coordinate A = (0, 2)   →    Coordinate A' (0 - 2, 2 + 3) = (-2, 5)

Coordinate B = (3, 4)   →    Coordinate B' = (3 - 2, 4 + 3) = (1, 7)

Coordinate C = (4, 2)   →   Coordinate C' = (4 - 2, 2 + 3) = (2, 5)

Coordinate D = (3, 0)   →    Coordinate D' = (3 - 2, 0 + 3) = (1, 3)

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An artist draws a stained glass window to scale. The actual window will have a length of 5ft and a width of 2ft. The scale from the drawing to the window is 2in to 1 ft. The width of the drawing is 4 inches.

To find the width of the drawing, we need to determine how much the width of the window has been scaled down on the drawing.

We know that the scale of the drawing is 2 inches to 1 foot, so for every 1 foot in the window, there are 2 inches in the drawing.

Since the width of the window is 2 feet, and the scale is 2 inches to 1 foot, the width of the drawing is (2 inches/foot) * (2 feet) = 4 inches.

Therefore, the correct answer is as given above 4 inches.

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Answer: B) 2x²-3y=9

Step-by-step explanation:

This is not a linear function because the equation for a linear function is mx+b=y this means that x cannot have an exponent which in B it does.

This type of data is cross-sectional data.

In statistics and econometrics, cross-sectional data, or a cross-section of a study population, is a type of data gathered by monitoring numerous subjects (such as individuals, firms, countries, or regions) at one point or throughout the course of time. It's also possible that the analysis disregards variations in time. Cross-sectional data analysis often entails contrasting the variations among pre-selected respondents.

Time series data, in which the same small-scale or aggregate entity is seen multiple times in time, differs from cross-sectional data. A different kind of data called panel data (also known as longitudinal data) combines the concepts of cross-sectional and time series data and examines how the topics (firms, people, etc.) develop throughout a time series. Panel data differs from cross-sectional data that has been pooled over time.

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Answer:

3,271,000

Step-by-step explanation:

There is no explanation for this problem.

Answer: is 3,271,000

A line passing between the points (1, 6) and (1, 31) has an undefined slope.

What is the slope?

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

The slope of a line can be found using the formula:

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

where m is the slope of the line, (x1, y1) and (x2, y2) are two points on the line.

In this case, we have (x1, y1) = (1, 6) and (x2, y2) = (1, 31). Plugging these values into the formula:

m = (31 - 6) / (1 - 1)

Hence, the denominator is zero, the slope is undefined. This means that the line is a vertical line and has no slope.

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The number of clients that Belvedere train using Plan I if the total training time was 310 minutes will be 2 clients

From the information, Belvedere is a personal trainer and uses two different workout plans with his clients. Plan I takes 50 minutes to complete and Plan Il takes 35 minutes. Belvedere trained 6 clients using Plan Il last weekend.

The number of clients can be given as x.

The number of clients that Belvedere train using Plan I if the total training time was 310 minutes will be:

50x + 35(6) = 310

50x + 210 = 310

Collect the like terms

50x = 310 - 210

50x = 100

Divide

x = 100 / 50

x = 2

The clients are 2.

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Answer:

Step-by-step explanation: make a table of values, followed be a column for the 1st and another for the 2nd difference

0 0

1 1 -- 1

2 4-- 3 -- 2

3 9 --5 -- 2

4 16 --7 -- 2

5 25 --9 --2

6 36 ------- etc

looks like the 2nd difference is 2

Answer: You have a 1/6 chance to roll a 2 when you role a dice since there is 6 sides

Step-by-step explanation:

The graph of equations y - 1 = - 3(x - 2) and y = - 3x + 7 is illustrated below with the attached image.

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, An equation of a line y - 1 = - 3(x - 2) in point-slope form.

y - 1 = - 3x + 6.

y = - 3x + 7.

The next equation is 3y = x - 9.

y = (1/3)x - 3.

Now, The graph of these two equations can be sketched by assuming two or more arbitrary values of 'x' that correspond to different values of 'y'.

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Answer: 12

Step-by-step explanation:

x + 9 + 9 = 7x

9 + 9 = 6x

18 = 6x

x = 3

DE = x + 9 = 3 + 9 = 12 :>

Answer:

DE = 12

Step-by-step explanation:

DF = DE + EF

7x = x+9 + 9

7x = x + 18

6x = 18

x = 3

DE = 3 + 9

DE = 12

The analysis of the figure, comprising of concentric circles, in the shape of a hollow cylinder cross-section is as follows;

12) Part A; The area of the deck is about 691.15 square feet

Part B; The minimum number of treatment gallons needed is four gallons

Part C; The total cost to cover the patio with weather treatment is $143.8

The cross-sectional area of a hollow cylinder is; A = π·(R² - r²)

Where;

R = The radius of the outer circle of the cylinder

r = The radius of the smaller (open) circle at the center of the cylinder.

Part A

The outside diameter of the deck, D = 32 feet

The radius of the swimming pool = 6 feet

The area of the deck, A = The area of the circle with diameter 32 feet less the area of the swimming pool

A = π·D²/4 - π·r²

A = π × 32²/4 - π × 6² = 220·π ≈ 691.15

Part B

The area covered per gallon of weather treatment = 204.5 square feet per gallon

The minimum number of gallons of weather treatment, n, that will need to be purchased to cover the deck with weather treatment is therefore;

n ≈ 691.15/204.5 ≈ 3.38

Therefore, the minimum number of gallons that needs to be purchased, since 3 gallons is not enough, is four gallons of weather treatment

Part C; The cost per gallon of weather treatment excluding tax = $35.95

The total cost in dollars excluding tax to cover the patio with weather treatment, C, is presented as follows;

C = Number of gallons needed × Cost per gallon

Number of gallons needed to cover the deck = 4 gallons

Cost per gallon = $35.95/gallon

Therefore;

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Answer: Gabriella's distance from the stadium is modeled by the function G(t) = 550 - 25t.

Ian's distance from the stadium is modeled by the function I(t) = 950 - 50t.

To find the number of hours after noon when Gabriella and Ian are the same distance from the stadium, we need to set the two equations equal to each other and solve for t:

G(t) = 550 - 25t = I(t) = 950 - 50t

Combining like terms we get:

25t = 400

t = 16

So, 16 hours after noon, Gabriella and Ian will be the same distance away from the stadium.

To graph the functions, we can substitute different values of t into the equations to find the corresponding values of G(t) and I(t). Then we can plot the points on a coordinate plane and connect them to form the graph of the two functions.

It is important to note that we are assuming that both Gabriella and Ian don't make any stops, so the speed is constant through the whole trip and no time is wasted.

Step-by-step explanation:

The equation 12x + 1 = 3(4x + 1) – 2 have infinite solutions

An equation is a mathematical statement that shows that two mathematical expressions are equal. In other terms we say that an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

To solve this problem, we can proceed to solve this equation by collecting like terms and then dividing through to know the coefficient of x.

⇒ 12x + 1 = 3(4x + 1) – 2

⇒ 12x + 1 = 12x + 3 – 2

⇒ 12x + 1 = 12x + 1

So that, The equation have infinite solutions.

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This problem have two question:

1) How many solutions exist for the given equation? 12x + 1 = 3(4x + 1) – 2

2) Which of the following shows the graph of y = –(2)x – 1?

we are giving the answer of question no.1

The numbers that Austin could choose from are: 80, 100 which have 4, 5, and 10 as their multiples

The numbers between 61 and 107 are:

62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106

we will observe that only 70, 80, 90 and 100 have 10 and 5 as their multiple, amongst which, only 80 and 100 have 4 as their multiple.

Therefore, Austin must choose only the two numbers 80 and 100 which have 4, 5, and 10 as their multiples.

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a) Angular acceleration is 0.53 rad/s^2

b) Tangential acceleration is 2.56 m/s^2

c) Centripetal acceleration is 2.56  rad/s^2

We know that the angular acceleration can be obtained from the equations of circular motion. We know that we have the equation for the circular motion as;

α = ω2 -  ω1/t

α =  angular acceleration

ω2 = final angular velocity

ω1 = initial angular velocity

α = 0.8 - 0/1.5

= 0.53 rad/s^2

b) The tangential acceleration = v^2/r

But V = ωr

V = 0.8 * 4

V = 3.2 m/s

Then;

(3.2)^2/4

= 2.56 m/s^2

c) Centripetal acceleration = ω^2 r

= (0.8)^2 * 4

= 2.56 rad/s^2

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a) (i) Working out the value of x2 gives -6

(ii) Working out the value of x3 gives -11

b) Working out the solution to 6 decimal places is undefined.

a) (i) To find the value of x2, we substitute x1 = -1 into the iterative equation:

x2 = ((-1)^(2/3)) - 5 = (-1)^(2/3) - 5 = -1 - 5 = -6

(ii) To find the value of x3, we substitute x2 into the iterative equation:

x3 = ((-6)^(2/3)) - 5 = (-6)^(2/3) - 5 = -6 - 5 = -11

b) To find the solution to 6 decimal places, we would need to continue iterating the process until the desired level of accuracy is reached. But in this case, the equation does not have solution as the equation is not defined for negative values of x. The cube root of a negative number is complex numbers and not real numbers.

Therefore, the values are -6, -11, and undefined respectively.

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The two processes that caused the puddle to form and then disappear were evaporation and infiltration.

Evaporation is the process in which liquid water turns into vapor and rises into the atmosphere. It occurs when the air around the puddle is warmer than the liquid, causing the water molecules to move faster and spread out. This allows the water to evaporate into a gas. The rate of evaporation is proportional to the water surface area and the difference in temperature between the air and the water.

Infiltration is the process in which water is absorbed into the ground. It occurs when the water in the puddle is drawn into the soil due to gravity and capillary action. This process is influenced by the soil type, the amount of water, and the soil's porosity. The rate of infiltration is proportional to the soil's permeability, which is a measure of how quickly water can move through the soil.

The combination of evaporation and infiltration caused the puddle to form and then disappear. As the water evaporated, the puddle shrank until it was gone. Simultaneously, the water that remained was absorbed into the ground until all of the puddle was gone.

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Answer: 50 cattle for 24500 is cheaper than 18870 for 37 cattle

Step-by-step explanation: divide 24500/50= $490 per cattle

vs

18870/37= $510 per cattle

proving that 24500 for 50 is overall a better deal

The total number of 18,181 bottles should be sold to break the business even based on the investment.

Firstly calculating the profit earned on each soft drink. Based on this, the formula for profit to be used is -

Profit = Selling price - cost price

Keep the values in formula

Profit = 1.20 - 0.65

Performing subtraction on Right Hand Side of the equation

Profit = $0.55

For the business to break even, the total profit earned by company must be equal to the investment. So, let the number of bottles required to break even the business be x.

0.55 × x = 10,000

Performing multiplication on Left Hand Side of the equation

0.55x = 10000

x = 10,000/0.55

Performing division on Right Hand Side of the equation

x = 18181.8

Rounding off = 18181.

Thus, 18,181 bottles need to be sold.

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At store B, they charge $0.09 more for pineapple juice than store A.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

Given that, Brody was comparing the price of pineapple juice at two stores.

Equation to represent the cost of pineapple juice at store A is

y=0.7x

Equation to represent the cost of pineapple juice at store B is

From the table, we have (9, 7.11) and (13, 10.27)

Now, slope m= (10.27-7.11)/(13-9)

= 3.16/4

= 0.79

Substitute m=0.79 and (x, y)=(9, 7.11) in y=mx+c, we get

7.11=0.79(9)+c

7.11=7.11+c

c=0

So, the equation is y=0.79x

Cost of 1 bottle juice at store A is $0.7 and Cost of 1 bottle juice at store B is $0.79

Difference in cost =0.79-0.7=$0.09

Therefore, at store B, they charge $0.09 more for pineapple juice than store A.

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The fraction of fence that George can build at a constant rate of 1/3 in 1 hour is 2/3.

Divide implies to distribute anything evenly. After learning about whole number division, let's move on to fraction division. The numerator and the denominator are the two components of a fraction. Fractional division is roughly the same as fractional multiplication. When dividing fractions, we multiply the smaller of the two fractions by their reciprocals.

Given that George builds the fence at a rate of 1/3 section per 1/2 hour.

The fraction of fence that George build per hour can be obtained as:

1/3 = 1/2 hour

x = 1 hour

Using the butterfly method for multiplication we have:

x = (1/3) ÷ (1/2)

x = (1/3) × (2)

x = 2/3

Hence, the fraction of fence that George can build at a constant rate of 1/3 in 1 hour is 2/3.

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The required function that represent the given situation is y = 10x + 350.

In order to write the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The slope is the ratio of the y-to-x change. Find two locations on the line and create a sloping triangle connecting the two places.

Rental fee is $350 for the first week and $10 for each additional day or any portion of a day.

So, The equation that represent this problem is;

Let cost y (in dollars) to rent the dumpster for x days.

y = 350 + 10x (y in dollar)

y = 10x + 350

Here, slope of function is 10 and y- intersect is 350.

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Where there is a jump at x = 7 from y = 350 to y = 350 + 10 * (x - 7). Before x = 7, the cost would remain constant at $350. After x = 7, the cost would increase by $10 for each additional day.

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[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to 1.75\%\to \frac{1.75}{100}\dotfill &0.0175\\ t=years\dotfill &6 \end{cases} \\\\\\ I = (5000)(0.0175)(6) \implies I = 525[/tex]