Write an expression that represents the height of a tree that begins at 9 feet and increases by 3 feet per year. Let y represent the number of years.

A system of linear equations: y + 2x = -5 and 8x + 4y = -20  has infinitely many solutions.

The 3 possible solutions of a linear system are:

- Unique or one solution

- Infinite solutions

- No solution

If the linear equations are exactly (or can be transformed to exactly) the same equations, the solution is infinite.

The given linear system is:

y + 2x = -5           ....... (equation 1)

8x + 4y = -20     ..........(equation 2)

Rearrange equation 1 to:

2x + y = -5

Multiply both sides by 4:

8x + y4 = -20

Hence, equation 1 is equivalent to equation 2. Hence, the given linear system has infinitely many solutions.

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The term "total moles of a solute contained in a kilogram of a solvent" exists utilized to define molality. The amount of water required exists 252ml.

Given: Mass of urea = 25 g

Required Molality = 1.65m

Density of water = 1000 kg/m³

Formula for urea = CH₄N₂O

Mass of Carbon atom = 12 u

Mass of Oxygen atom = 16 u

Mass of Nitrogen atom = 14 u

Mass of Hydrogen atom = 1 u

Molecular Mass of Urea

= (1)12 + (4)1 + (2)14 + 16

= 12 + 4 + 28 + 16

= 60 u

Molar mass = 60 g

No of moles = Given mass/Molar mass

No of moles = 25/60 = 5/12

Molality = Mass of solute / Mass of solvent(g)

Let the weight of water be x kg

1.65 = (5/12)/x

simplifying the above equation, we get

1.65 x = (5/12)

x = (5/12) / 1.65

x = 5 / 1.98

x = 0.2525

Mass of water = 0.252 kg.

Volume of water = 0.252 ÷ 1000 kg/m³

= 0.000252 m³

= 0.252 liters

= 252 ml

Therefore, the require amount of water is 252 ml.

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Answer:

10x=1/2(x+3)

Step-by-step explanation:

option b is the answer

Answer: it is D

Step-by-step explanation:

The surface area of the larger prism is 3 times larger than the surface area of the smaller prism.

A prism is a three-dimensional geometric shape that has two identical polygonal bases connected by rectangular faces. The surface area of a prism refers to the total area of all its faces.

The surface area of a prism is usually expressed in square units, such as square centimeters (cm²) or square meters (m²).

It represents the total amount of space that would need to be covered if all the faces of the prism were completely filled in.

Calculating the surface area of a prism is important in various real-world applications, such as architecture, engineering, and manufacturing, where understanding the amount of material needed or the amount of surface that will be exposed is necessary.

To determine how many times larger the surface area of the larger prism is compared to the smaller prism, we need to divide the surface area of the larger prism by the surface area of the smaller prism.

Let's denote the surface area of the larger prism as \(A_{large\) and the surface area of the smaller prism as \(A_{small\).

If we divide \(A_{large}\) by \(A_{smal\), we get:

\(A_{large} / A_{small} = 6 / 2\)

= 3.

Therefore, the surface area of the larger prism is 3 times larger than the surface area of the smaller prism.

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The equation to calculate the distance will be 12 × 2.

From the information given, she travels at 12 miles per hour and the total travel time is 2 hours.

It should be noted that:

Distance = Speed × Time

Therefore,

Distance = 12 × 2

The distance is 24 miles.

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Answer:

f(4) = - 1

Step-by-step explanation:

To evaluate f(4) substitute x = 4 into f(x) , that is

f(4) = 5(4 - 7) + 14 = 5(- 3) + 14 = - 15 + 14 = - 1

Answer:

x = 2

Explanation:

The given expression is

7x - 4 - 3x = -3x + 10

First, we need to add the like terms on the left side

(7x - 3x) - 4 = -3x + 10

4x - 4 = -3x + 10

Add 4 to both sides

4x - 4 + 4 = -3x + 10 + 4

4x = -3x + 14

Add 3x to both sides

4x + 3x = -3x + 14 + 3x

7x = 14

Finally, divide by 7

7x/7 = 14/7

x = 2

Therefore, the answer is x = 2

Given the topological spaces X = {D, O, R, K} with the topology Tx and Y = {M, A, T, H} with the topology Jy, we are asked to determine whether the set E = {0, K} is open in X and open in Y.

To determine whether the set E = {0, K} is open in the topological spaces X and Y, we need to check if E belongs to the respective topologies, Tx and Ty.

In X, the topology Tx is given by: Tx = {Ø, {0}, {D, O}, {O, R}, {D, O, R}, X}. We can see that E = {0, K} is not explicitly listed in Tx. Therefore, E is not open in X since it does not belong to the topology.

In Y, the topology Ty is given by: Jy = {0, {M}, {M, A}, {M, A, T}, Y}. Again, E = {0, K} is not explicitly listed in Ty. Hence, E is not open in Y as it does not belong to the topology.

In both cases, the set E = {0, K} is not open in the respective topological spaces X and Y because it is not a member of the defined topologies.

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Answer:

what can i help u with

Step-by-step explanation:

The graph of x = |y| is as shown in the figure.

When we draw a vertical line, it intersects the graph at two points.

This means for the same value of x , we have two values of y.

Or in other words, for the same pre image, we have two images.

Hence it is not a function.

But for every value of x, we do have a value of y, hence it is a relation.

x = |y| is a relation but it is not a function

Answer:

:B

Step-by-step explanation:

hope that can help

The derivative of g(x) is (-4x²-3x+1)cos(1+2x) - (2x³ - 2x^2 + x)tcos(1+2x) + t(1+2x)sin(1+2x) + C, where C is a constant of integration.

The derivative is a mathematical concept that represents the rate at which a function changes. It is essentially the slope of the tangent line to the curve of the function at a given point.

Integration is the process of finding the integral of a function, which involves calculating the area under its curve. It is the reverse of differentiation and is used in calculus and mathematical analysis.

According to the given information:

To find the derivative of g(x), we first need to evaluate the integral:

g(x) = ∫[1, 2x+1] (1-2t)sin(t) dt

Using the product rule of differentiation, we have:

g'(x) = (d/dx) [∫[1, 2x+1] (1-2t)sin(t) dt]

= (2-2x)sin(2x+1) - ∫[1, 2x+1] 2sin(t) dt

Simplifying the second term, we get:

g'(x) = (2-2x)sin(2x+1) - 2[cos(2x+1) - cos(1)]

Therefore, the derivative of g(x) is g'(x) = (2-2x)sin(2x+1) - 2[cos(2x+1) - cos(1)].

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Answer:

Variance ≈ 63.1

Standard Deviation ≈ 7.9

Therefore, the variance is approximately 63.1 and the standard deviation is approximately 7.9.

Step-by-step explanation:

To calculate the variance and standard deviation for the given random sample data, we'll follow these steps:

Calculate the mean of the data.

Calculate the squared difference between each data point and the mean.

Calculate the variance by taking the average of the squared differences.

Calculate the standard deviation by taking the square root of the variance.

Let's perform the calculations:

Calculate the mean:

Mean = (18.4 + 19.4 + 16.7 + 28.2 + 3.5) / 5

Mean = 17.24

Calculate the squared difference between each data point and the mean:

(18.4 - 17.24)² = 1.34² = 1.7956

(19.4 - 17.24)² = 2.16² = 4.6656

(16.7 - 17.24)² = (-0.54)² = 0.2916

(28.2 - 17.24)² = 10.96² = 120.2416

(3.5 - 17.24)² = (-13.74)² = 188.5476

Calculate the variance:

Variance = (1.7956 + 4.6656 + 0.2916 + 120.2416 + 188.5476) / 5

Variance ≈ 63.10

Calculate the standard deviation:

Standard Deviation ≈ √63.10

Standard Deviation ≈ 7.95

Rounding to one decimal place:

Variance ≈ 63.1

Standard Deviation ≈ 7.9

Therefore, the variance is approximately 63.1 and the standard deviation is approximately 7.9.

Answer:

Negative infinity, positive infinity

Step-by-step explanation:

The x values go forever in both ways

Answer:

Negative infinity, positive infinity

Step-by-step explanation:

Considering the volume of a rectangular prism, the limitations are given as follows:

Upper: 500, Lower: 0.

The volume of a rectangular prism of length l, width w and height h is given by:

V = lwh.

For the toy, the dimensions are of 1 inch, hence:

V = 1 x 1 x 1 = 1 inch³.

For the box, the dimensions are of 10 x 10 x 5 inches, hence:

V = 10 x 10 x 5 = 500 inches³.

500/1 = 500, hence the upper limit is of 500, while the lower limit is of 0.

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The position value, r(t) is equals to the (t³/6)k + 2j and velocity value, v(t) is equals to ( t²/2 )k + 4i , for a(t) = tk, v(0) = 4i, r(0) = 2j.

Acceleration is defined as the rate of change of the velocity of an object with respect to time. Accelerations are vector quanty.

a = dv/dt

We have the following informations are available,

Initial velocity, v(0) = 4i

Initial position, r(0) = 2j

Acceleration at any time "t",

a(t) = tk

we have to determine the value of v(t) and r(t).

As we know, a(t) = dv(t)/dt = tk

integrating the above equation ,

v(t) = ∫tk dt = ( t²/2 )k + c

at t = 0 , v(0) = 0 + c = 4i ( since, v(0) = 4i

=> c = 4i

So, v(t) = ( t²/2 )k + 4i

Also, velocity is calculated by derivative of postion (r) with respect to time.

=> v(t) = dr(t) /dt

=> r(t) = ∫ v(t) dt

=> r(t) = ∫ ( t²/2 )k dt

integrating value of the right hand side,

r(t) = ( t³/2×3 )k +d

= (t³/6)k + d

At t = 0, r(0) = (0/6)k + d

=> r(0) = d = 2j

so, r(t) = (t³/6)k + 2j

Hence, the required position and velocity are

(t³/6)k + 2j and ( t²/2 )k + 4i.

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To solve for angle A and angle B in the given triangle, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle.

In this case, we have side a with length 2 and side c with length 9. Let's denote angle A as angle opposite side a and angle B as angle opposite side b (which is unknown).

Using the Law of Sines, we have:

sin(A) / a = sin(B) / b

Plugging in the known values, we get:

sin(A) / 2 = sin(B) / 9

To find angle A, we can use the arcsine function:

A = arcsin((sin(B) / 9) * 2)

To find angle B, we can rearrange the equation:

sin(B) = (sin(A) / 2) * 9

B = arcsin((sin(A) / 2) * 9)

Now we can calculate the angles using a calculator:

A ≈ 19.5 degrees (rounded to one decimal place)

B ≈ 84.1 degrees (rounded to one decimal place)

Therefore, angle A is approximately 19.5 degrees and angle B is approximately 84.1 degrees.

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The probability of getting at least one head is 15/16.

What is probability?

The ratio of positive outcomes to all possible outcomes of an event is known as the probability.

Formula for probability = favourable outcomes/ total outcomes

Main body:

if 4 coins are tossed , total no. of outcomes = 2⁴ = 16

In a toss there are 2 outcomes T or H

so, Probability of getting Head = 1/2

The probability of getting at least 1 head = 1- probability of getting no heads

⇒1 - Probability of getting tail in 4 tosses

⇒ 1 - (1/2)⁴

⇒ 1 - 1/16

⇒ 15/16

So the probability of getting at least one head is 15/16.

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Answer:

They are exactly the same size and shape

Step-by-step explanation:

The congruence postulates covered in this lesson are

- Side-Side-Side (SSS)

- Side-Angle-Side (SAS)

- Angle-Side-Angle (ASA)

- Angle-Angle-Side (AAS)

Answer:

KE=112 \(\frac{kg * m^{2} }{s^{2} }\)

Step-by-step explanation:

Kinetic Energy (KE) = (1/2)*mass*v^2

KE=(1/2)*.14*40^2

KE=112 \(\frac{kg * m^{2} }{s^{2} }\)

Answer:

Graph 1

Step-by-step explanation:

Given that the equation of the line in the diagram is `y = 5 - x`. The line cuts the y-axis at P. So, the coordinates of point P are (0,5) and the gradient of the line is `-1`.

The equation of the line can be written as `y = -1x + 5`.Therefore, the y-intercept of the line is 5. Therefore, the coordinates of point P are (0,5).

To find the gradient of the line, we have to write the equation of the line in the form of `y = mx + c`.

We can rewrite `y = -1x + 5` as `y = (-1)x + 5`.From the above form of the equation, we can see that the gradient `m` is `-1`.Therefore, the gradient of line 1 is `-1`.Hence, the required answer is: Coordinates of point P is `(0,5)`.The gradient of the line is `-1`.

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Answer:

333.33 miles

Step-by-step explanation:

Let x be the number of miles Mike and Juan drive.

They only have $300, however, so let's set an equation that will tell us how many miles, x, does it take to result in a total bill of $300.  The mileage fee will be ($0.75/mile)*(x miles driven).   Start with the $300 and subtract both the fixed fee of $50 and the mileage fee of 0.75x and set the result to zero, the point at which they spend $300.

$300 - $50 - ($0.75)x = 0

$250 - ($0.75)x = 0

- ($0.75)x = -$250

x = -($250)/(-$0.75)

x = 333.33 miles

CHECK:

Would Mike and Juan spend $300 on the rental car if they drove 333.33 miles?

                                            Rental Fee:     $50

Mileage:  ($0.75/mile)*(333.333 miles) = $250

                                             Total Cost:   $300  YES

Nothing left for burgers,

Graphs that represent direct variation are proportional functions

The graph represents a direct variation

From the graph, we have the following ordered pairs

(x,y) = (0,0), (2,4) and (3,9)

Rewrite as:

(x,x^2) = (0,0^2), (2,2^2) and (3,3^2)

The above means that, the equation of the graph is:

\(y = x^2\\\)

i.e. y varies directly to the square of x

Where the proportionality constant is 1

Hence, the graph represents a direct variation

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The correct answer is a) the probability of precipitation is 72%. and b)  the probability of precipitation is 2%.

The given formula to determine the probability of precipitation (PoP) is PoP = (C * A) * 100 percent where C represents the confidence that precipitation will occur somewhere in the forecasted area and A represents the percentage of the area that will receive measured precipitation if it occurs.

(a) If a forecaster expresses confidence that there is an 80% chance of precipitation in the forecasted area, and it is expected to produce measurable precipitation over 90% of the area, then the probability of precipitation is given as follows: PoP = (C * A) * 100 per cent C = 80%A = 90%PoP = (80% * 90%) * 100%

PoP = 72%.

Therefore, the probability of precipitation is 72%.

(b) If a forecaster expresses confidence that there is a 20% chance of precipitation in the forecasted area, and it is expected to produce measurable precipitation over 10% of the area, then the probability of precipitation is given as follows: PoP = (C * A) * 100 per cent C = 20%A = 10%PoP = (20% * 10%) * 100%PoP = 2%

Therefore, the probability of precipitation is 2%.

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Answer:

The answer to this equation is 9+4n

Answer: See picture

Step-by-step explanation:

For this problem, we need to know how to graph the inequality. First, let's establish that we will have a solid line because the inequality is greater than or equal to. If the inequality was only greater than, then it would be a dotted line. For -4/3x-7, you would start at (0,-7) as the y-intercept. Then you would go down by 4 and go to the right by 3 units. Now, we have to do shading. Since we know that y is greater than or equal to, the shading will be on top of the line, where y is greater.

The two distances are equal, which means the points (2, -8) and (0, -8) are symmetric about the axis of symmetry x = 1, or the vertex (1, -9).

What is the quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The vertex of a parabola in standard form, f(x) = a(x - h)² + k, is at the point (h, k).

We can rewrite the given equation, f(x) = x² - 2x - 8, in standard form by completing the square:

f(x) = x² - 2x - 8

= (x² - 2x + 1) - 1 - 8

= (x - 1)² - 9

So the vertex of the parabola is at the point (1, -9), where h = 1 is the x-coordinate of the vertex, and k = -9 is the y-coordinate of the vertex.

To verify that points (2, -8) and (0, -8) are symmetric about the vertex, we can calculate the axis of symmetry, which is x = h, or x = 1 in this case.

The distance between the vertex (1, -9) and the point (2, -8) is the same as the distance between the vertex and the point (0, -8), since these points have the same y-coordinate:

d((1, -9), (2, -8)) = d((1, -9), (0, -8))

Using the distance formula, we can calculate the left-hand side:

d((1, -9), (2, -8)) = √((2 - 1)² + (-8 - (-9))²)

= √(1 + 1)

= √(2)

Using the distance formula again, we can calculate the right-hand side:

d((1, -9), (0, -8)) = √((0 - 1)² + (-8 - (-9))²)

= √(1 + 1)

= √(2)

Hence, the two distances are equal, which means the points (2, -8) and (0, -8) are symmetric about the axis of symmetry x = 1, or the vertex (1, -9).

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An effective sampling method is not cast doubt on the usefulness of the sample

The effective sample is a calculation of the approximate sample size needed to obtain the same degree of accuracy as a simple random sample. It is denoted mathematically by the formula n/D, where n represents the sample size and D denotes the design effect. It is employed as a means of condensing the volume of data.

Effective sample size calculations are mostly used for qualitative analyses of the sample size. The sample size calculates the total number of measurements or observations made during an experiment or survey. The effective sample size—rather than the actual sample size—is utilized in this assessment since it is thought that a sample size of 30 is necessary for an analysis to be valid.

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