Evaluate (18)^2-(15)^2
Please show working.

It would take approximately 11.7 years to pay off the credit card balance of $3052.41 with a monthly payment of $55 and an annual interest rate of 18%.

To calculate the time it will take to pay off a credit card balance, we need to consider the interest rate, the balance, and the monthly payment. In your question, you mentioned an annual interest rate of 18% and a monthly payment of $55.

First, let's convert the annual interest rate to a monthly interest rate. We divide the annual interest rate by 12 (the number of months in a year) and convert it to a decimal:

Monthly interest rate = (18% / 12) / 100 = 0.015

Next, we can calculate the number of months it will take to pay off the balance. Let's assume there are no additional charges or fees added to the balance:

Balance = $3052.41

Monthly payment = $55

To determine the time in months, we'll use the formula:

Number of months = log((Monthly payment / Monthly interest rate) / (Monthly payment / Monthly interest rate - Balance))

Using this formula, the calculation would be:

Number of months = log((55 / 0.015) / (55 / 0.015 - 3052.41))

Calculating this equation gives us approximately 140.3 months.

Since we want to find the number of years, we divide the number of months by 12:

Number of years = 140.3 months / 12 months/year ≈ 11.7 years

Therefore, it would take approximately 11.7 years to pay off the credit card balance of $3052.41 with a monthly payment of $55 and an annual interest rate of 18%.

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Answer:

75

Step-by-step explanation:

Scores for his first tests were 65, 67, 69.

Rate of change: +2

y=2x+63; 63 is the 0th test he took, his first test was 65, so 65-2=63. 2x is the rate of change, his tests scores increase by 2 each time.

x=6, 6th test score

y=2(6)+63

y=12+63

y=75

So, on his 6th test he will get a score of 75

Any non-empty subset of Rⁿ, where any linear combination of vectors in S is again a vector in S, is a subspace of Rⁿ.

Given that S is a non-empty subset of Rⁿ such that any linear combination of vectors in S is again a vector in S. Therefore, to prove that S is a subspace of Rⁿ, we have to show that S satisfies three conditions. These conditions are as follows;

The condition for being a subspace of Rⁿ

Firstly, a subspace must be closed under addition. In other words, if x and y are any two vectors in S, then their sum x + y must be in S.

Secondly, a subspace must be closed under scalar multiplication. In other words, if x is any vector in S and c is any scalar, then cx must be in S.

Finally, a subspace must contain the zero vector, denoted by 0.S is a subspace of Rⁿ

From the conditions mentioned above, we can show that S is indeed a subspace of Rⁿ, since S satisfies all the required conditions.

Therefore, we can say that any non-empty subset of Rⁿ, where any linear combination of vectors in S is again a vector in S, is a subspace of Rⁿ.

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IT IS REQUIRED OF YOU TO SOLVE FOR X

\(x - 3x = 17 + 3 \\ - 2x = 20 \\ \frac{ - 2x}{ - 2} = \frac{20}{ - 2} \\ x = - 10\)

Answer:

x = -10

Step-by-step explanation:

x-3 = 3x + 17

-2x -3 = 17

-2x = 20

x = -10

Check:

Does x-3 = 3x + 17 when x = -10?

x-3 = -13

3x+17 = -30+17 = -13  YES

The inequality that models the situation is x + y <= 10 and two possible sizes for the sandbox are (5, 4) and (5, 5)

The given parameter is:

The use of no more than 20 linear feet of lumber to make the sides of the sandbox.

This means that the perimeter of the sandbox is not more than 20 linear feet

Represent the dimensions of the sandbox with x and y

The perimeter is calculated as:

P = 2 * (x + y)

The perimeter of the sandbox is not more than 20 linear feet

So, we have:

2 * (x + y) <= 20

Divide both sides by 2

x + y <= 10

Hence, the inequality that models the situation is x + y <= 10.

See attachment for the graph of the inequality that models the situation

Make y the subject in x + y <= 10

This gives

y <= 10 - x

Let x = 5

So, we have:

y <= 10 - 5

y <= 5

A possible solution here is (5, 4) and (5, 5)

Hence, two possible sizes for the sandbox are (5, 4) and (5, 5)

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The error term is a random variable with an expected value of zero.2. The error term is normally distributed

The assumptions underlying the simple linear regression model `y = Bo + B1x + e` are: 1.

The variance of the error term e is constant across all values of x.Thus, the assumptions that are underlying the simple linear regression model `y = Bo + B1x + e` are the second and the third options, which are "The error term is normally distributed." and "The variance of the error term e is constant across all values of x." respectively.

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Answer:

43.5 cm

Step-by-step explanation:

The original photocopy's length is 15 cm. If Mona enlarges the photo's length to be 45 cm, we would need to find how much 15 is multiplied by to get 45, so that we can multiply 14.5, the width, by the same amount.

45/15 = 3

14.5 * 3 = 43.5 cm

Answer:

43.5

Step-by-step explanation:

The correct simplification of (4x - 3)(3x^2 - 4x - 3) is 12x^3 - 25x^2 + 9.To simplify the expression (4x - 3)(3x^2 - 4x - 3), we need to multiply the two binomials together using the distributive property.

To simplify the expression, we will multiply each term in the first binomial (4x - 3) by each term in the second binomial (3x^2 - 4x - 3) and combine like terms.

Multiply the first term of the first binomial (4x) by each term in the second binomial:

4x * 3x^2 = 12x^3

4x * (-4x) = -16x^2

4x * (-3) = -12x

Multiply the second term of the first binomial (-3) by each term in the second binomial:

-3 * 3x^2 = -9x^2

-3 * (-4x) = 12x

-3 * (-3) = 9

Combine the like terms obtained from the multiplications:

12x^3 - 16x^2 - 12x - 9x^2 + 12x + 9

Simplify further by combining like terms:

12x^3 - 25x^2 + 9

Therefore, the correct simplification of (4x - 3)(3x^2 - 4x - 3) is 12x^3 - 25x^2 + 9.

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Answer:

None

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

2x < -10

Step 2: Solve for x

Here we see that any value x smaller than -5 would work as a solution.

Step 3: Identify

Answer choices.

I. -2

II. 2

III. 10

We see that none of these numbers are less than -5. Therefore, non of the answer choices are correct.

A. To show "half" of the graph, we can restrict the domain to only include values of x that result in non-negative values of y. This can be done by setting the expression inside the square brackets to be greater than or equal to zero and solving for x:

3 * (x + 2) ^ 2 - 7 ≥ 0

(x + 2) ^ 2 ≥ 7/3

|x + 2| ≥ sqrt(7/3)

x + 2 ≤ -sqrt(7/3) or x + 2 ≥ sqrt(7/3)

x ≤ -2 - sqrt(7/3) or x ≥ -2 + sqrt(7/3)

So the restricted domain would be [-2 - sqrt(7/3), -2 + sqrt(7/3)].

B. To find the equation for the inverse function, we start by swapping the x and y variables and solving for y:

x = 3 * (y + 2) ^ 2 - 7

x + 7 = 3 * (y + 2) ^ 2

(y + 2) ^ 2 = (x + 7) / 3

y + 2 = ±sqrt((x + 7) / 3)

y = -2 ± sqrt((x + 7) / 3)

To show "half" of the graph, we need to choose one of the two possible values for y. Since we want the inverse function to pass the vertical line test, we choose the positive square root. So the equation for the "half" graph of the inverse function is:

y = -2 + sqrt((x + 7) / 3)

C. The domain of the inverse function is the range of the original function, which is [0, ∞). The range of the inverse function is the domain of the original function, which is (-∞, ∞).

The expanded form of 500,000 is (5*100,000) + (0*10,000) + (0*1,000) + (0*100) + (0*10) + (0*1), which on simplifying can be written as (5*100,000).

In math, the expanded form enables us to comprehend a number more clearly. Take the number 875294831 as an example. This amount is impossible to comprehend. Here, an expanded form enables us to comprehend each numeral according to its place value. Let's try to determine the extended form of the straightforward number 423. The expanded form of 423 is (4*100) + (2*10) + (3*1). It denotes that there are 4 hundred, 2 tens, and 3 ones in this number. Through its expanded form, a number's meaning for each digit is clearly understood.

In the question, we are asked to write the expanded form of 500,000.

Similar to our example, we can write the expanded form of 500,000 as

(5*100,000) + (0*10,000) + (0*1,000) + (0*100) + (0*10) + (0*1),

which when simplified can be shown as (5*100,000).

Thus, the expanded form of 500,000 is (5*100,000) + (0*10,000) + (0*1,000) + (0*100) + (0*10) + (0*1), which on simplifying can be written as (5*100,000).

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Answer:

I think it's 120??

Step-by-step explanation:

10 x 10 = 100

12 x 10 = 100

Answer:

if 10%=12

then

1%=12/10

or,1%=1.2

then, for 100%

100%=1.2*100

hence, 100%=120...

4 more students have 2 or 3 siblings than 4 or 5 siblings in Austin's swim class.

To determine how many more students have 2 or 3 siblings than 4 or 5 siblings in Austin's swim class, we'll count the number of responses for each category.

Step 1: Count the number of students with 2 or 3 siblings.

Responses: 2 students, 2 students, 8 students, 8 students, 9 students, 9 students

There are 6 students with 2 or 3 siblings.

Step 2: Count the number of students with 4 or 5 siblings.

Responses: 11 students, 11 students

There are 2 students with 4 or 5 siblings.

Step 3: Subtract the number of students with 4 or 5 siblings from the number of students with 2 or 3 siblings.

6 students (2 or 3 siblings) - 2 students (4 or 5 siblings) = 4 students

So, 4 more students have 2 or 3 siblings than 4 or 5 siblings in Austin's swim class.

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Answer:

21

Step-by-step explanation:

21

1. 2x + 3y = 1470

   3y = -2x + 1470

   y = -2/3x + 490 <== slope intercept form

==================

2. y = -2/3x + 490....slope = -2/3.....y int = (0,490)

   to graph, start at (0,490)....since the slope is -2/3, we will go down 2       spaces, then to the right 3 spaces, then down 2 spaces, and to the right 3 spaces. It helps to find the x int which can be found by subbing in 0 for y into the equation and finding x. So ur x int is (735,0)...this is where ur line should cross the x axis.

===================

3. function notation : f(x) = -2/3x + 490...not sure how to explain the meaning...sorry

===================

4. graph the function....it will be the same line as the graph I explained before...y = -2/3x + 490

y int = (0,490)

x int = (735,0)

===================

5. original :                            new :

   2x + 3y = 1470                 2x + 3y = 1593

   3y = -2x + 1470                3y = -2x + 1593

    y = -2/3x + 490                y = -2/3x + 531

similarities : Both of these equations will have the same slope, which is -2/3. Both lines are descending. Both lines are parallel to each other.

differences : These lines will have different x and y intercepts

y = -2/3x + 490 : y int = (0,490), x int = (735,0)

y = -2/3x + 531 : y int = (0,531), x int = (796.5,0)

======================

6. pick 2 points on the line.....(0,300) and (450,0)

find the slope using the slope formula : slope = (y2 - y1) / (x2 - x1)

(0,300)....x1 = 0 and y1 = 300

(450,0)...x2 = 450 and y2 = 0

now we sub and find the slope

slope = (0 - 300) / (450 - 0) = -300/450 reduces to -2/3

now we use y = mx + b

slope(m) = -2/3

use either of ur points...(450,0)...x = 450 and y = 0

now sub and find b, the y int

0 = -2/3(450) + b

0 = - 300 + b

300 = b

so ur equation is : y = -2/3x + 300....or  2x + 3y = 900

Answer: 2, 3, 5, 6, 9, 10,

Step-by-step explanation:

The equations are written as;

Slope - intercept form : y = mx + c

Point- slope form; y − y₁= m(x − x₁).

Standard form; y - mx + c = 0

First, we need to know that the general formula representing the equation of a line of graph is expressed as;

y = mx + c

Such that the parameters of the formula are;

From the information given, we have that the graph is a straight line.

Then, we have;

y = mx + c

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Answer:

0.85(x - 350)

Step-by-step explanation:

x - This is the employees salary before tax exempts

$350 - This is the amount of tax exempted from the employers salary

Income left after tax exempt expenses have been deducted = (x - 350)

If 15% of taxed income is collected, the remaining income would be - 100% - 15% = 85%

85% / 100 = 0.85

Therefore, the remaining salary that the employees take home is 0.85(x - 350)

To find the two real solutions of the equation x^4 - 3x^3 - 3x^2 - 3x + 3 = 0 using Newton's method, we start by selecting initial guesses for the solutions.

Since we have no prior knowledge about the solutions, we can make reasonable initial guesses based on the given equation.

Let's choose x1 = 0 as the first initial guess and x2 = 1 as the second initial guess. We will use these values to iterate through Newton's method until we converge to the desired solutions.

Using Newton's method, the iterative formula to find the next approximation is given by:

xn+1 = xn - f(xn) / f'(xn)

We repeat this process until we reach a desired level of accuracy. Let's perform the iterations to find the solutions:

For the first initial guess, x1 = 0:

x2 = x1 - f(x1) / f'(x1) = 0 - (0^4 - 3(0)^3 - 3(0)^2 - 3(0) + 3) / (4(0)^3 - 9(0)^2 - 6(0) - 3) = 1.00000

For the second initial guess, x2 = 1:

x3 = x2 - f(x2) / f'(x2) = 1 - (1^4 - 3(1)^3 - 3(1)^2 - 3(1) + 3) / (4(1)^3 - 9(1)^2 - 6(1) - 3) = 1.30612

We continue this iteration process until we reach the desired level of accuracy. After further iterations, we find the two real solutions of the equation:

x1 ≈ 0.82913

x2 ≈ 1.68232

These values represent the two real solutions of the equation x^4 - 3x^3 - 3x^2 - 3x + 3 = 0, obtained using Newton's method with the initial guesses x1 = 0 and x2 = 1.

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Using implicit differentiation, we found that dy/dx = \((18x) / (5y^4)\). When solving the equation explicitly for y, we obtained y =\((9x^2)^(1/5) - 2^(1/5)\), and differentiating this expression gave dy/dx = \((18/5) * x^(-2/5) * (9x^2)^(1/5)\).

A) To find y' by implicit differentiation, we differentiate both sides of the equation with respect to x using the chain rule and product rule:

d/dx (9x^2) - d/dx (y^5) = d/dx (2)

Simplifying, we get:

18x - 5y^4 * (dy/dx) = 0

Rearranging the equation and solving for dy/dx, we have:

dy/dx = (18x) / (5y^4)

B) To solve the equation explicitly for y, we isolate y:

9x^2 - y^5 = 2

9x^2 = y^5 + 2

Taking the fifth root of both sides, we get:

\((9x^2)^(^1^/^5^) = (y^5 + 2)^(1^/^5^)y = (9x^2)^(^1^/^5^) - 2^(^1^/^5^)\)

Now, we differentiate y with respect to x using the power rule:

dy/dx = \((1/5) * (9x^2)^(-4/5) * (18x)\)

Simplifying further:

dy/dx =\((18/5) * x^(-2/5) * (9x^2)^(1/5)\)

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By differentiating the given equation implicitly and then solving for y', we get y' = (18x) / (5y^4). Alternatively, if we first solve for y and then differentiate, we get the same expression for y'.

The given equation is \(9x^2 - y^5 = 2\). We will differentiate it implicitly and solve for y' for part A, and solve for y first and then differentiate to find y' for part B.

Differentiating with respect to x gives 18x - 5y'^4y = 0. Solving this equation for y', we get, \(y' = (18x) / (5y^4).\)

First, solve the equation for y to give y = [(9x^2 −2 )]^(1/5). Differentiating this with respect to x, we find \(y' = 2/5*9x * [(9x^2 -2 )]^(-4/5)\) which simplifies to \(y' = (18x) / (5y^4).\)

Therefore, whether we use implicit differentiation (Part A) or solve for y and differentiate (Part B), we get the same expression for y' in terms of x.

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\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)

Let's solve ~

\(\qquad \sf  \dashrightarrow \: y = 2x - 3\)

plug the value of x = -5 :

\(\qquad \sf  \dashrightarrow \: y = 2( - 5) - 3 \)

\(\qquad \sf  \dashrightarrow \: y = - 10 - 3\)

\(\qquad \sf  \dashrightarrow \: y = - 13\)

The probability of picking a blue marble at random out of the bag is 2/13.

The probability of an incident occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an occurrence may be known to us or unknown to us. When this happens, we state that there is a chance that the event will happen or not. In general, probability has many great uses in games, in business to make predictions based on probability, and in this new branch of artificial intelligence.

The probability of picking a blue marble at random out of the bag can be calculated by dividing the number of blue marbles by the total number of marbles in the bag:

P(picking a blue marble) = number of blue marbles / total number of marbles

P(picking a blue marble) = 4 / (4 + 12 + 8 + 2)

P(picking a blue marble) = 4 / 26

P(picking a blue marble) = 2 / 13

Therefore, the probability of picking a blue marble at random out of the bag is 2/13.

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Answer:

A

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

A is the variable.

Answer:

Step-by-step explanation:

You want the area of a 16-unit circle using different values for pi.

The formula for the area of a circle is ...

  A = πr² . . . . . . where r is half the diameter

For the different values of pi, this will be (in square units) ...

  π(8²) = 64π . . . . exact

  3.14(8²) = 200.96 . . . . using 3.14 for π, slightly low

  22/7(8²) = 201 1/7 . . . . using 22/7 for π, slightly high

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Answer:

-3/2

Step-by-step explanation:

Count the rise = -3

Count the run= 2

Rise/run= -3/2

Answer:

-7/-4 or 1.75

Step-by-step explanation:

Another formula for the slope of a line is (y2-y1)÷(x2-x1)

So all we need is to find the points (x1, y1) and (x2, y2)

Point 1: (1, -3)

Point 2: (-3, 4)

Sub this into the equation:

(-3-4) ÷ (-3-1) = -7 ÷ -4 = 1.75

Answer:

c; y = 2x

Step-by-step explanation:

if it was without the coupon the fee would be the $2 per mile (2x) with the $35 which would be

y = 2x + 35

but with the coupon the $35 reservation is removed so only 2x is left

y = 2x

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

Answer:  \(\textsf{Option C, 3}\sqrt{2}\)

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

Given:  \(\sqrt{18}\)

Find: \(\textsf{Simplify the expression}\)

Solution: In order to get a number outside of the square root there must be two of them inside of the square root.  The first step that we need to take is to break down the number 18 into it's lowest factors and then take out the numbers can be taken out.

Break down the number 18

Take 3 outside of the square root

Therefore, the option that would best match the results that were solved for is option C, \(\textsf{3}\sqrt{\textsf{2}\)

It will take approximately 23.1 weeks for the ant population to double.

To find out how long it will take for the ant population to double, we need to use the formula for exponential growth, which is:

N = N0(1+r)^t

Where N is the final population, N0 is the initial population, r is the growth rate, and t is the time it takes for the population to reach N.

In this case, we know that N0 is 4,000, r is  3 percentage per week (or 0.03), and we want to find out t when N is double the initial population, or 8,000.

So, we can plug in these values into the formula:

8,000 = 4,000(1+0.03)^t

Dividing both sides by 4,000, we get:

2 = (1+0.03)^t

Taking the natural logarithm of both sides, we get:

ln(2) = t ln(1.03)

Dividing both sides by ln(1.03), we get:

t = ln(2) / ln(1.03)

Using a calculator, we find that t is approximately 23.1 weeks.

Therefore, it will take approximately 23.1 weeks for the ant population to double.

In summary, the ant colony has a population size of 4,000 ants and is increasing at a rate of 3% per week. To find out how long it will take for the ant population to double, we used the formula for exponential growth and found that it will take approximately 23.1 weeks.
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Answer:

$5.78

Step-by-step explanation:

brainliest?

The parameters for computing the area of triangle is first listed out and the expression for the area of triangle was used to find the algebraic method

Parameters for find the area of triangle are

Let the base be x, and let the height be y

We know that the expression for the area of triangle is given as

Area = 1/2 (Bass* Height)

Substituting our parameters we have

Area = 1/2*x*y

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