Which graph represents a linear function?

The equation 2 = -x√(x + 2) - x has two potential solutions: x = -1 and x = -8. However, x = -8 does not satisfy the equation, so the set of all solutions is {x = -1}.

To find the set of solutions to the equation 2 = -x√(x + 2) - x, we can solve it algebraically.

Starting with the given equation, we can simplify it step by step:

2 = -x√(x + 2) - x

Adding x to both sides:

2 + x = -x√(x + 2)

Squaring both sides to eliminate the square root:

(2 + x)^2 = (-x√(x + 2))^2

Expanding and simplifying:

4 + 4x + x^2 = x^2(x + 2)

Simplifying further:

4 + 4x = x^3 + 2x^2

Rearranging terms:

x^3 + 2x^2 - 4x - 4 = 0

Factoring the equation:

(x + 1)(x^2 + x - 4) = 0

Setting each factor to zero:

x + 1 = 0 or x^2 + x - 4 = 0

Solving the first equation, we find x = -1.

For the second equation, we can use the quadratic formula:

x = (-1 ± √(1^2 - 4(1)(-4))) / (2(1))

x = (-1 ± √(1 + 16)) / 2

x = (-1 ± √17) / 2

However, when we substitute x = (-1 + √17) / 2 into the original equation, it does not satisfy the equation. Therefore, x = -8 is not a solution.

Hence, the set of all solutions to the equation is {x = -1}.

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The size of the quarterly deposits in Shelby's RRSP account was approximately $147.40.

Let's denote the size of the quarterly deposits as \(D\). The total number of deposits made over 9 years is \(9 \times 4 = 36\) since there are 4 quarters in a year. The interest rate per period is \(r = \frac{3.50}{100 \times 12} = 0.0029167\) (3.50% annual rate compounded monthly).

Using the formula for the future value of an ordinary annuity, we can calculate the accumulated value of the RRSP fund:

\[55,000 = D \times \left(\frac{{(1 + r)^{36} - 1}}{r}\right)\]

Simplifying the equation and solving for \(D\), we find:

\[D = \frac{55,000 \times r}{(1 + r)^{36} - 1}\]

Substituting the values into the formula, we get:

\[D = \frac{55,000 \times 0.0029167}{(1 + 0.0029167)^{36} - 1} \approx 147.40\]

Therefore, the size of the quarterly deposits, rounded to the nearest cent, is approximately $147.40.

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Answer: A

Step-by-step explanation:

Okay so f-g = (2x+3)-(3x+2) = 2x+3-3x-2 = -x+1

A

Answer:

6c-8-2c+(-16)=0

6c-2c-8-16=0

6c-2c=16+8

4c=24

c=24/4

c=6

Answer:

4c - 24

Step-by-step explanation:

6c−8−2c−16

(6c−2c)+(−8−16)

4c - 24

The running time is O(n log(n)) since we sort two vector.

We solve the problem with the following algorithms:  

1. Order A is in the increasing order.

2. Order B is in the decreasing order.

3. Return (A,B).

We must demonstrate that this is the best answer. without sacrificing generality, we can assume that a₁ ≤ a₂ ......≤ aₙ in the optimal solution.

Since the payoff is \(\prod_{i}^{n}=1^{a_{i}^{bi}}\), the payoff will always increase if we make a change so that \(b_{i+1} > b_{i}\).

Therefore the optimal solution will be found if B is sorted.

Thus, the running time is O(n log(n)) since we sort two vector.

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Answer:

The equation in the standard form is

\(y+2x=5\)

Step-by-step explanation:

Given the points

Finding the slope between (6, -7) and (4, -3)

\(\left(x_1,\:y_1\right)=\left(6,\:-7\right),\:\left(x_2,\:y_2\right)=\left(4,\:-3\right)\)

\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)

\(m=\frac{-3-\left(-7\right)}{4-6}\)

\(m=-2\)

As the point-slope form is defined as

\(y-y_1=m\left(x-x_1\right)\)

substituting the values m = -2 and the point (6, -7)

\(y-y_1=m\left(x-x_1\right)\)

\(y-\left(-7\right)=-2\left(x-6\right)\)

Writing the equation in the standard form form

As we know that the equation in the standard form is

\(Ax+By=C\)

where x and y are variables and A, B and C are constants

converting the equation in standard form

\(y-\left(-7\right)=-2\left(x-6\right)\)

\(y+7=-2\left(x-6\right)\)

subtract 7 from both sides

\(y+7-7=-2\left(x-6\right)-7\)

\(y=-2x+5\)

\(y+2x=5\)

Therefore, the equation in the standard form is

\(y+2x=5\)

The driver's percent value-added time is approximately 18.57%.

The percent value-added time, we need to consider the total time spent in non-value-added activities (waiting in line, eyes tested, and photograph taken) compared to the total time spent, including value-added activities.

Total time spent = Time in line + Time for eyes test + Time for photograph = 57 minutes + 9 minutes + 4 minutes = 70 minutes

Value-added time = Time for eyes test + Time for photograph = 9 minutes + 4 minutes = 13 minutes

Percent value-added time = (Value-added time / Total time spent) * 100

= (13 minutes / 70 minutes) * 100

≈ 18.57%

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Answer: x²

Step-by-step explanation: If your number is doubled, it is squared. Hence, ².

3435 were children visited the India gate.

What is a linear equation in math?

Given,

             men = 1265

            women = 1150

Total women and men -

        men + women = 2415

         = 5450-2415  ⇒ 3435

Therefore,  3435 were children visited the India gate.

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Answer:

a) x =  7.5

b) x = 1

Step-by-step explanation:

a)

b)

Answer:

Step-by-step explanation:

Answer:

Please refer to the attachment

Hope it helps

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Answer:

the missing blank for forks is 0 and the missing blank for spoons is 20

Step-by-step explanation:

Rotating a triangle 270 degrees counterclockwise is the same as rotating a figure 90 degrees clockwise. The solution has been obtained using the concept of rotation.

What is rotation?

A rotation in mathematics is a transformation that revolves a shape around a fixed point.

We have a specific rule that we can use to do this that is based on the fact that a 270° anticlockwise rotation is the same as a 90° clockwise rotation. One such rotation is to rotate a triangle 270° anticlockwise.

On a graph, we can rotate a triangle 270° anticlockwise by passing each of its vertices through the transformation shown below:

Change the x and y coordinates after multiplying the x coordinate by a negative number.

Consequently, (x,y) becomes (y,-x).

Hence, this way we can rotate a triangle 270 degrees counterclockwise.

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The toy cars Anna must sell for her revenue to equal her expense is 4 toy cars. The result is obtained by using the concept of calculating algebra.

To calculate the algebra with one variable, sum up all the same variable and count the value.

Anna want to sell toy car at a craft fair. Each car is sold at a price of $ 12. The material for each car cost $ 3.50 and the table rental at the fair is 34 dollar for the day.

Find the toy cars must Anna sell for her revenue to equal her expense!

We have

Let's say

Revenue = Expense

a × $12 = (a × $3.5) + $34

12a = 3.5a + 34

12a - 3.5a = 34

8.5a = 34

a = 4 toy cars

Hence, Anna must sell 4 toy cars so that her revenue is equal to expense.

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The statement that knowing the value of x tells you nothing about the value of y can be explained by several scenarios. One possible scenario is when the values of x and y are not related in any way. In other words, there is no mathematical or logical connection between them.

Another scenario where knowing the value of x tells you nothing about the value of y is when there are multiple possible values of y for a given value of x. This occurs when the relationship between x and y is not one-to-one. For instance, if x represents a person's age and y represents their height, knowing someone's age does not determine their height since there are different heights for different ages.

Furthermore, it is possible that there is a relationship between x and y, but the value of y is affected by other factors besides x. For example, if x represents the amount of time a student spends studying and y represents their grade on a test, knowing the value of x does not completely predict the value of y because other factors like natural ability and test-taking skills may also play a role in determining the grade.

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Answer:

-6/-2<-2x/-2

divide both sides by-2 to remain with the x variable on one side

I hope this helps

The type of function that fits the given description is D. Exponential decay.

In an arithmetic sequence, the difference between consecutive terms remains constant. If the y-values of a function form an arithmetic sequence that decreases in value, it means that the difference between consecutive terms is negative.
Exponential decay functions exhibit a constant ratio between consecutive terms, resulting in a decreasing sequence. As the x-values increase, the y-values decrease at a consistent rate. This is represented by the formula y = ab^x, where b is a constant between 0 and 1.
In contrast, linear functions have a constant difference between consecutive terms, resulting in an arithmetic sequence. However, since the y-values are decreasing, the function cannot be linear.
Exponential growth functions, on the other hand, have a constant ratio between consecutive terms, but they result in an increasing sequence. The y-values of an exponential growth function increase as the x-values increase.

Therefore, based on the given information, the most appropriate type of function is D. Exponential decay.

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The proportion null hypothesis is a specific type of hypothesis that tests for significant differences in proportions between two groups.

In statistics, a hypothesis is a statement that is being tested through data analysis. The null hypothesis is a specific type of hypothesis that assumes there is no significant difference or relationship between two variables being studied. The proportion null hypothesis specifically applies to situations where the variable being studied is a proportion or percentage.

The proportion null hypothesis states that there is no significant difference in the proportions of two groups being compared. This can be represented mathematically as

H0 => p1 = p2, where H0 represents the null hypothesis, p1 represents the proportion in the first group, and p2 represents the proportion in the second group.

To test this hypothesis, researchers will collect data from both groups and calculate the proportion for each group. They will then use statistical tests to determine whether the difference in proportions is significant or could have occurred by chance. If the difference is not significant, then the null hypothesis is accepted, and it can be concluded that there is no real difference in the proportions of the two groups.

It is important to note that the proportion null hypothesis is just one type of hypothesis that can be tested in statistics.

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Answer:

A

Step-by-step explanation:

it is A for for two outgoing (y)there is one in going(x)

Answer:

The answer is (A)

Step-by-step explanation:

Answer:

r= -6

Step-by-step explanation:

Answer:

2.25 should be the right answer

Answer:

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

Each coordinate of the midpoint is the average of endpoints:

Therefore M is (13, 14).

Answer:

Y= 2x - 2

Step by step explanation

Answer: 1.8125 gallons = 29 cups

Step-by-step explanation:

There are 16 cups in a gallon. Therefore, to convert gallons to cups we multiply the number of gallons by 16.

The number of gallons, in this case, is: 1.8125

So, we need to multiply 1.8125 by 16

1.8125 ⋅ 16 = 29

In the final analysis, 1.8125 gallons is equal to 29 cups.

,  Hope this helps :)

Have a great day!!

Answer: \( 8 \sqrt{147} \)

Step-by-step explanation:

It goes like this \( 2 \times 4 \sqrt{147} = (2 \times 4) \sqrt{147} = (8)\sqrt{147} = 8\sqrt{147}. \)

Hence, the simplest radical form is \(8\sqrt{147}\).

What is the simplest radical form?

Simplifying a radical so that there are no more square roots, cube roots, 4th roots, etc left to find. It also means removing any radicals in the denominator of a fraction.

Here given that,

To find out the product of \(2\) and \(4\sqrt{147}\) in simplest radical form

So,

\((2\) ×\(4)\sqrt{147}\) \(=8\sqrt{147}\).

Hence, the simplest radical form is \(8\sqrt{147}\).

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The formula for the nth term of the given sequence is an = 0.4 * (5^n-1), where n is the position of the term in the sequence starting from n = 1.

To determine the formula for the nth term of the sequence, we can observe that each term is obtained by multiplying the previous term by 5. We start with the first term, 0.4. To obtain the second term, we multiply 0.4 by 5, resulting in 2. To get the third term, we multiply 2 by 5, giving us 10. Similarly, to obtain the fourth term, we multiply 10 by 5, resulting in 50.
In general, to find the nth term, we multiply the previous term by 5. Mathematically, this can be expressed as: an = 5 *a^(n-1  )  .   However, in this case, the first term is not multiplied by 5 to obtain itself. Instead, it is multipliemultipliedd by 5 raised to the power of (n-1). Therefore, the formula for the nth term of the sequence can be written as: an = 0.4 * (5^n-1), where n represents the position of the term in the sequence starting from n = 1.

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The power series expansion of f(x) = ln(1 + x²) about a=0 can be found using geometric series, differentiation, and integration of power series. The expansion is given by:

ln(1 + x²) = x² - (1/2)x⁴ + (1/3)x⁶ - (1/4)x⁸ + ...

To find the power series expansion, we start by considering the geometric series expansion of ln(1 + x). Using the formula for the sum of an infinite geometric series, we have:

ln(1 + x) = x - (1/2)x² + (1/3)x³ - (1/4)x⁴ + ...

Now, we substitute x² for x in the above series to get the power series expansion for ln(1 + x²):

ln(1 + x²) = x² - (1/2)(x²)² + (1/3)(x²)³ - (1/4)(x²)⁴ + ...

Simplifying the terms, we have:

ln(1 + x²) = x² - (1/2)x² + (1/3)x⁶  - (1/4)x⁸ + ...

The interval of convergence for this power series expansion is -1 < x < 1, which means the expansion is valid for values of x within this interval. The radius of convergence is 1, which indicates that the series converges absolutely for values of x within the interval -1 < x < 1.

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The number of nickel coins and dime coins are 11 and 20 respectively.

Ceci has $2.55 in nickels and dimes

Nickel coin is worth 5 cents and the dime coin is worth 10 cents

1$ = 100 cents

Total money Ceci has is 2.55 x 100 cents = 255 cents

Let the number of nickel coin be x

then the number of dime = x + 9

5x + 10(x + 9) = 255

5x + 10x + 90 = 255

15x = 255 - 90

15x = 165

x = 11

The number of nickel coin = 11

dime coin = x + 9

= 11 + 9 = 20

Therefore. the number of nickel coins and dime coins are 11 and 20 respectively.

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Answer:

\(\huge\boxed{y-27=8(x-3)}\)

Step-by-step explanation:

The point-slope form of an equation of a line:

\(y-y_1=m(x-x_1)\)

where

\(m=\dfrac{y_2-y_1}{x_2-x_1}\)

We have the points (3, 27) and (-8, -61).

Calculate the slope m:

\(m=\dfrac{-61-27}{-8-3}=\dfrac{-88}{-11}=8\)

Susbtitute to the equation of a line:

\(y-27=8(x-3)\)