Which products result in a difference of squares? Check all that apply.

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To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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Step-by-step explanation:

Slope 1/2    point    5,1  

  in point slope form would be

    (y-1) = 1/2 (x-5)

Answer: 80.04 squared

Step-by-step explanation:

The numbers are 1 and 8.

We have,

Let's assume the lesser number as "x" and the greater number as "8x".

According to the given information, when the lesser number is subtracted from the greater, the result is 2 more than 5 times the lesser number:

8x - x = 5x + 2

Simplifying the expression:

7x = 5x + 2

Subtracting 5x from both sides:

2x = 2

Dividing both sides by 2:

x = 1

So, the lesser number is 1 and the greater number is 8 times that, which is 8.

Therefore,

The numbers are 1 and 8.

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11

In slope formula: \(m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

Substitute and calculate: \(m=\frac{2}{5}\)

Substitute and calculate: \(b=\frac{17}{5}\)

Substitute: \(y=\frac{2}{5} x+\frac{17}5}\)

Answer= \(y=\frac{2}{5} x+\frac{17}5}\)

(Let me know if you want to know how I got my answer)

Answer:

Using distributive property to solve \((x+12)8\) we get \(\mathbf{8x+96}\)

Step-by-step explanation:

We need to used distributive property to solve (x+12)8

The distributive property of multiplication or addition states that: \(a(b+c)=ab+ac\)

Using the property:

\((x+12)8\\=8x+8*12\\=8x+96\)

So, using distributive property to solve \((x+12)8\) we get \(\mathbf{8x+96}\)

Answer:

-0.12

Step-by-step explanation:

0.0844/(-0.72)=-0.11722222222

-0.11722222222 rounded to the nearest hundredths in -0.12

Answer:

- 0.11722222222

Step-by-step explanation:

- 0.0844 ÷ - 0.72 = - 0.11722222222

There will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

To calculate the amount in Nathan's daughter's RESP after 25 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount (amount in the account after 25 years)

P = Principal amount (amount deposited every 2 months)

r = Annual interest rate (in decimal form)

n = Number of times the interest is compounded per year

t = Number of years

In this case, Nathan deposits $940 every 2 months, so the principal amount (P) is $940. The annual interest rate (r) is 3.99% or 0.0399 in decimal form. Since the interest is compounded quarterly, the compounding frequency (n) is 4. The number of years (t) is 25.

Since Nathan deposits every 2 months, we need to calculate the total number of deposits made over 25 years. There are 12 months in a year, so in 25 years, there will be 25 * 12 = 300 months. However, since Nathan deposits every 2 months, the number of deposits (m) is 300 / 2 = 150.

Now, we can substitute these values into the formula:

A = 940(1 + 0.0399/4)^(4*25)

Calculating the exponent first:

(1 + 0.0399/4)^(4*25) ≈ 2.703236

Now, substituting the calculated exponent and the number of deposits into the formula:

A = 940 * 2.703236 * 150 ≈ $594,311.34

Therefore, there will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

It's important to note that this calculation assumes Nathan makes the same $940 deposit every 2 months consistently over the 25-year period and does not make any withdrawals from the account during that time. Additionally, the actual amount may vary slightly due to rounding and any potential changes in interest rates over the years.

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The quotient of the expressions −48.132 and −0.84 will be 57.30. Then the correct option is C.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

Given −48.132 ÷ −0.84.

Then the value of the expression will be

⇒ −48.132 / −0.84

If in the numerator and the denomination, the negative sign is present, then both will cancel out each other.

⇒ 48.132 / 0.84

⇒ 57.30

The quotient of the expressions −48.132 and −0.84 will be 57.30.

Then the correct option is C.

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Answer: (6,11π/6).

Step-by-step explanation:We need to find the radius r and the angle θ. Remember that r2=x2+y2, so

because of the signs of x and y, our angle is in quadrant IV. Therefore, we find that θ=11π/6.

So the final answer is (6,11π6).

The critical points for the equation \(f(x)=(x^{2} +64)^{\frac{1}{11} }\) is

\((x,f(x))\) = \((0,2^{\frac{6}{11} })\) = \((0,1.46)\). at x=0

The absolute maximum is at \((x,f(x))\\\) = \((9,\sqrt[11]{145} )\) =  \((9,1.6)\), at x=9.

What is the absolute maximum of an equation?

The highest conceivable values for f are represented by the absolute maximum (sometimes called the global maximum) of a function f(x) (x). Let's imagine the function's critical value, x=c, is present within its domain. If the inequality f(c) \(\geq\) f(x), x is a domain, then the function f(x) is said to satisfy an absolute maximum when x=c.

To find the critical points, we find the value of f'(x) and equate to 0.

\(\frac{d}{dx} (\sqrt[11]{x^{2}+64} )=0\)

we get x=0.

We see that f'(x) exists for all x between [-8,9].

We also find the endpoints, that is -8 and 9.

Then we calculate f(x) at critical points and endpoints.

We calculate f(x) at 0, -8, and 9.

We get,

for x=0, f(x)= \(2^{\frac{6}{11} }\)

for x=-8, f(x)= \(2^{\frac{7}{11} }\)

for x=9, f(x)= \(\sqrt[11]{145}\)

We see that the value is maximum at x=9, and f(x) becomes \(\sqrt[11]{145}\).

Hence we get the absolute maximum is \((x,f(x))\\\) = \((9,\sqrt[11]{145} )\) = \((9,1.6)\)

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The sum of the geometric sequence in this problem is given as follows:

5.77.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number, which is called the common ratio q.

The first term, the common ratio and the number of terms for this problem are given as follows:

\(a_1 = 10, q = -\frac{2}{3}, k = 8\)

The formula for the sum of the first n terms is given as follows:

\(S_n = a_1\frac{1 - r^n}{1 - r}\)

Hence the sum for this problem is given as follows:

\(S_8 = 10 \times \frac{1 - \left(-\frac{2}{3}\right)^8}{1 + \frac{2}{3}}\)

\(S_8 = 5.77\)

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Answer: 519 120

Step-by-step explanation:

84*84=7056

7056/7=1008

1008*515=519 120

Plotting the lines y = 1 and x = 1, we get the following graph:

From the graph, we see that:

• the line y = 1 intersects the curve 3 times,

• the line x = 1 intersects the curve 1 time.

• The line ,y = 1, intersects the curve ,3 times

• The line ,x = 1, intersects the curve ,1 time

Answer:

a) It is a one-tailed test

Step-by-step explanation:

The number of plants he sets up in the room, n = 20

The number of plants that grew more with Miracle Grow = 14

The alpha level α = 0.01

A one-tailed test is used when the critical-area of interest in the distribution is either to the left or right of a value on the number line. That is the test is concerned if the test result is either less than or more than a value

In the test the farmer subjects all 20 plants to the same test treatment without any control experiment, therefore, the farmer evaluates the plants based on how much they grow compared to each other, that is if they grow more or less than their pairs

Therefore a one-tailed test should be used.

Answer:

Explanation:

Here, we want to get the functions which are fourth degree polynomials

A fourth degree polynomial will have the highest power as 4 in its expression

Let us take a look at the values one after the other:

a) This is not a fourth degree polynomial. It is a third degree polynomial. This is because the highest power we can see is 3

b) This is a fourth degree polynomial. This can be see with the power x^4

c) This is not a fourth degree polynomial. It is not because it has been divided. If it stood alone and not being a dividend to 1, then it would have being a fourth degree polynomial

d) This is a fourth degree polynomial since the highest power is 4

Conclusively, we can see that the second and last options are the fourth degree polynomials here

Answer:

Below.

Step-by-step explanation:

x^2 - 6x = -5

x^2 - 6x + 9 = -5 + 9            c = 9

(x - 3)^2 = 4

x - 3 = +/- sqrt4

x - 3 = +/- 4

x - 3 = 2 gives x = 5  and

x - 3 = -4 gives x = -1.

The matrix multiplication is possible for option (b) 1 × 3 by 3 × 3, and option (c) 2 × 1 by 1 × 2.

What is a matrix?

A matrix is a rectangular array or table with numbers or other objects arranged in rows and columns. Matrices is the plural version of matrix. The number of columns and rows is unlimited. Matrix operations include addition, scalar multiplication, multiplication, transposition, and many others.

It is known that if the number of columns of a matrix A be equal to the number of rows of another matrix B then the product of matrix A and matrix B i.e. AB is defined.

a)  In this option no of columns in first matrix is 1 and the no of rows in second matrix is 2.

That means no of columns in first matrix is not equal to no of rows in second matrix.

Hence, in this case matrix multiplication is not possible.

Therefore, option (a) is incorrect.

b)  In this option no of columns in first matrix is 3 and the no of rows in second matrix is also 3.

That means no of columns in first matrix is equal to no of rows in second matrix.

Hence, in this case matrix multiplication is possible.

Therefore, option (b) is correct.

c)  In this option no of columns in first matrix is 1 and the no of rows in second matrix is 1.

That means no of columns in first matrix is equal to no of rows in second matrix.

Hence, in this case matrix multiplication is possible.

Therefore, option (c) is correct.

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Answer:

b

Step-by-step explanation:

edge

Answer:

B

Step-by-step explanation:

Given the figure of the circle P

RT is a diameter

The measure of the angle R = 38

The measure of the arc RU = 90

The measure of the arc is twice the inscribed angle opposite to it

So,

The measure of the arc WT = 2 * 38 = 76

The measure of the arc WR = 180 - 76 = 104

The measure of the arc TU = 180 - 90 = 90

And the measure of the angle T = 90/2 = 45

Answer:

50

Step-by-step explanation:

i got it correct on the iready quiz

The graph of the line does not change except only in the y - intercept. The slope of the line remains same.

        y = mx + c

        [m] : slope of line.

        [c] : y - intercept

Given is a graph that shows the relationship between time and the distance a train travels.

From the graph, we can write the coordinates as -

(1, 60) and (2, 120)

So, we can write the slope of the line as -

m = (120 - 60)/(2 - 1)

m = 60/1

m = 60

Therefore, the slope of the line given in the graph will be 60 miles/hr.

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In order to find the height of 2 different 3-D shapes, we must identify which dimension represents the height for each individual shape and then add them together.

The first thing is that we must identify which dimension represents the height for each individual shape, for instance, if one shape is a rectangular prism, its height would be the length of one of its sides.

After we identified the height for each shape, you can add them together to get the total height of the composite figure, but, we must understand that this method assumes that the two shapes are stacked vertically on top of each other with their bases aligned.

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Answer:

x = 6

Step-by-step explanation:

This is a bit of a tricky equation, and it's what we call an exponential equation since it involves some exponents. The way we begin to solve these kinds of problems is make the base on each side of the equals sign the same. On one side, we have 9 as our base, and on the other side, we have 3 as our base. 9 = 3², so we can rewrite our equation as shown below:

(3²)⁴ˣ⁻¹⁰ = 3⁵ˣ⁻²

From there, we can use the exponent rule (xᵃ)ᵇ = xᵃᵇ to simplify the left side of the equation.

3²⁽⁴ˣ⁻¹⁰⁾ = 3⁵ˣ⁻²

3⁸ˣ⁻²⁰ = 3⁵ˣ⁻²

Since our bases are now the same, we can take just the exponents and turn it into a new equation as shown below:

8x - 20 = 5x - 2

Hopefully at this point, this problem becomes easy for you, but I'll show how I solved this new equation below in case it doesn't make sense.

8x - 20 = 5x - 2

8x - 20 - 5x = 5x - 2 - 5x

3x - 20 = -2

3x - 20 + 20 = -2 + 20

3x = 18

3x/3 = 18/3

x = 6

Hopefully that's helpful! Let me know if you need more help. :)

The price of a ticket to the homecoming dance to maximize the council's profit is 4830.

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Answer:

$2 each ticket

Step-by-step explanation:

I don't really know how it's 2, but it's in the vertex of the graph. I just got my test back which the answer was 2. I'm sorry if you expected reasoning but I only got an answer. You can make a table for the equation and then see that 2 results in the highest profit though. 2 being substituted for t equates to the greatest profit.