Kate has a serving account that contains $230. She decides to deposit $5 each month from her monthly earnings for baby-sitting after school. Write an expression to find how much money Mata will have in her savings account after x months. Let x represent the number of months. Then find out how much she will have in her account after 1 year

2.25

Consider the square ...

... (x+a)² = x² +2ax +a²

The constant term (a²) is the square of half the x-coefficient: a² = (2a/2)².

The x-coefficient in your expression is 3. The square of half that is ...

... (3/2)² = 9/4 = 2.25

Adding 2.25 to both sides gives ...

... x² +3x + 2.25 = 6 + 2.25

... (x +1.5)² = 8.25 . . . . completed square

(3/2)^2

I believe it is (3/2)^2 because I tried working it out and got something like it. I did get an answer of x = ±[tex]\sqrt{33}[/tex] over 2.

Most sources appear to give 2.25, which is equal to 3/2 squared.

Attached some work.

Answer:

Step-by-step explanation:

Josie's balance would be -8 dollars.

47-55=-8

the second number to the right of the decimal point is 5 so you need to round the 2 up to 3

 so the number becomes 49.3

Out of given expressions, only expression A results in a positive value. Expression B, C, and D all result in a negative value.

To determine which expression results in a positive value, evaluate each:

So, "only expression A results in a positive value".

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The equation representing the set of points that are 2 units from the point (-2,-6) is a circle with equation (x + 2)^2 + (y + 6)^2 = 4

The question asks for an equation that represents the set of points that are exactly 2 units from the point (-2,-6) in a coordinate system. This set of points forms a circle with a radius of 2 units centered at (-2,-6). The equation for a circle with radius r and center (h, k) is (x - h)² + (y - k)² = r². Thus, the equation of the circle is (x + 2)² + (y + 6)² = 2² or (x + 2)² + (y + 6)² = 4

Using incentive spirometry is an effective intervention to prevent atelectasis in a postsurgical client.

To prevent atelectasis in a postsurgical client, the nurse can implement the following intervention:

Using the incentive spirometer, the client is instructed to exhale normally, place their lips around the mouthpiece, and take a slow, deep breath. They should hold the breath for a few seconds before exhaling and repeating the process multiple times throughout the day.

This intervention is effective because it encourages deep breathing and lung expansion, preventing the collapse of alveoli in the lungs and promoting better gas exchange.

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To prevent atelectasis in a postsurgical client, the nurse can implement interventions such as deep breathing exercises, mobilization and ambulation, and pain medication.

To prevent atelectasis in a postsurgical client, the nurse can implement several interventions:

These interventions help prevent the collapse of alveoli and promote proper lung function after surgery.

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The work done by force field on a particle moving from one point to another in space is calculated using the concept of dot-product. The force field is represented as a function and the movement of the particle is treated as a path. By integrating the dot product of the force field and the derivative of path over the interval, we get the work done.

To calculate the work done by force field on a particle, you need to apply the concept of dot product in vector calculus. The force field is defined as f(x, y, z) = x − y², y - z², z - x² and the movement of the particle is from (0, 0, 1) to (3, 1, 0). We treat this movement as a line segment in the 3-dimensional space.

The work done by the force field on the particle is calculated as W = F . dr = ∫ F(r(t)) . r'(t) dt from t1 to t2. In this case, the force field F is f(x, y, z) and the line segment can be treated as a path r(t) = t * (3, 1, 0) + (1 - t) * (0, 0, 1) and t varies from 0 to 1. Hence, r'(t) = (3, 1, 0) - (0, 0, 1).

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Answer:

Step-by-step explanation:

Integer factors of 117 include ...

... 117 = 1×117 = 3×39 ≈ 9×13

The last factor pair is two factors that differ by 4. We can take these to be the dimensions of the rectangle.

_____

If you want to write an equation for width (w), it might be ...

... w(w+4) = 117

... w² +4w -117 = 0

The factorization problem for this quadratic is the problem of finding two factors of 117 that differ by 4. That is what we have done, above.

If you want to solve this by completing the square, you can to this:

... w² +4w = 117

... w² +4w +4 = 121 . . . . . add 4 = (4/2)² to complete the square

... (w+2)² = 121

... w + 2 = ±√121 = ±11 . . . . take the square root

... w = -2 ± 11 . . . . . we're only interested in the positive solution

... w = 9, then w+4 = 13 and the dimensions are 9 cm by 13 cm.

Answer:

the answer is 3cm

HOPE THIS WORKED

Step-by-step explanation:

I JUST ANSWERED THIS ON EDG

The volume of a cube is given as 512 cubic cm then the side length of the cube is 8 mm.

The volume of a cube can be calculated as the cube of the sides of a given figure.

The volume of a cube = [tex]sides^3[/tex]

We have been given that the volume of a cube is 512 cubic cm. We need to find the side length of the cube.

The volume of a cube = [tex]sides^3[/tex]

                                64  =  [tex]sides^3[/tex]

Now we will take cube-root on both sides of the equation;

∛ 512 = ∛ s^3

∛ 8^3 = ∛ s^3

8 = s

Therefore, the side length of the cube is 8 cm.

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Final answer:

The velocity of the top of the ladder at time t = 1 sec is -4 ft/sec.

Explanation:

To find the velocity of the top of the ladder at time t = 1 sec, we can use the concept of similar triangles. Let x be the distance between the bottom of the ladder and the wall at time t = 1 sec. Since the bottom of the ladder slides away from the wall at a rate of 4 ft/sec, we have x = 5 + 4t.

The height of the ladder remains constant at 15 ft, so if we consider the triangle formed by the ladder, the wall, and the ground, we have the ratio of the height to the base is always 15 / x. Therefore, the velocity of the top of the ladder can be found by taking the derivative of the height with respect to time.

Let h be the height of the ladder at time t. Since h = 15, we have 15 / x = 15 / (5 + 4t). Taking the derivative of both sides, we get d/dt (15 / x) = d/dt (15 / (5 + 4t)). Using the quotient rule, we have d/dt (15 / x) = (0 - 15)(0 - (5 + 4t)-2)(4) = -60 / (5 + 4t)². This gives us the velocity of the top of the ladder at time t = 1 sec: v = -60 / (5 + 4(1))² = -4 ft/sec.

The present Age of Chloe is 2x - 4 years old.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Bertie is x years old now.

Four years Ago,

Chloe was twice as old as Bertie.

Bertie Age four years ago = x - 4

So, Chloe  Age four years ago = 2(x- 4) = 2x- 8

Now, Chloe is 4 years older than she was 4 years ago,

Then, Chloe present age is  (2x - 8) + 4 = 2x - 4 years old.

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The clown bought a total of 70 heart-shaped balloons. This is found by multiplying the number of bags (5) by the number of balloons in each bag (14).

The question involves a basic multiplication operation in mathematics. The clown bought 5 bags of heart-shaped balloons and each bag contains 14 balloons. To find the total number of balloons, you multiply the number of bags (5) by the number of balloons in each bag (14). This is done as follows:

So, the clown bought a total of 70 heart-shaped balloons.

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