The following information supposedly collected on a particular country by the CIA. Consumption Expenditures$3,600 million Imports$1,200 million Depreciation$300 million Government Expenditures$1,000 million Gross Private Domestic Investment$1,000 million Tax Revenues$700 million Exports$800 million Implicit GDP Deflator 2.00 (1996 = 1.00) Nominal GDP is equal to: $4,900 million $5,200 million $5,600 million $6,000 million

The domain of the function is a semicircle with a radius of 5 and centered at the origin, where y is non-negative.

The domain of a function is the set of all possible input values for which the function is defined. In this case, the function is defined as:

\(f(x,y) = \sqrt{y} + \sqrt{[25 - x^2 - y^2} ]\)

To find the domain of this function, we need to determine the values of x and y that would result in the function producing a real-valued output.

For the square root of y to be real, y must be non-negative. That is, y ≥ 0.

For the square root of [\(25 - x^2 - y^2\)] to be real, we must have:

\(25 - x^2 - y^2 \geq 0\\x^2 + y^2 \leq 25\)

This is the equation of a circle with radius 5 centered at the origin. Therefore, the domain of the function is the set of all points (x, y) that lie inside or on this circle and have y ≥ 0.

In interval notation, we can write:

Domain: {(x, y) |\(x^2 + y^2 \leq 25, y \geq 0\)}

To sketch the domain, we can plot the circle with radius 5 centered at the origin and shade the region above the x-axis. This represents all the valid input values for the function. The boundary of the domain is the circle, and the domain includes all points inside the circle and on the circle itself, but not outside the circle.

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Answer:

-10

Step-by-step explanation:

2x+6 = x-4

2x = x - 4 - 6

2x = x -10

2x -x = x-x - 10

x = -10

Please mark my answer as brainest

This is due tο the fact that as x grοws, the quadratic cοmpοnent in g(x) and f(x), respectively, predοminates οver the cοnstant term and the linear term.

A functiοn is a mathematical fοrmula that relates every element in οne set, knοwn as the dοmain, tο a single element in anοther set, knοwn as the range. The relatiοnship between input and οutput, the relatiοnship between a variable and its rate οf change, and many οther real-wοrld phenοmena are all examples οf this basic mathematical idea. Algebraic expressiοns, graphs, tables, and even wοrds can be used tο describe functiοns. They are a crucial instrument in many disciplines, including cοmputer science, statistics, and calculus.

given:

Fοr rising values οf x, the fοllοwing functiοn exhibits the fastest grοwth:

h(x) = 6x² + 1.

This is due tο the fact that as x grοws, the quadratic cοmpοnent in g(x) and f(x), respectively, predοminates οver the cοnstant term and the linear term. As a result, οf the functiοns listed, h(x) grοws at the fastest pace.

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Answer:

49+0.89c

Step-by-step explanation:

From the given function  f(x) = x² - 4,  f inverse (5) equals 3

An inverse function in mathematics is a function that undoes another function.

In other words, if f(x) yields y, then y entered into the inverse of f yields the output x. x .

An invertible function is one that has an inverse, and the inverse is represented by the symbol f - 1.

Hence inverse functions like in the problem. the output of f(x) when substituted into the input of g(x) gives same out put

f(x) = y = x² - 4 solving for the inverse

y + 4 = x²

x = √(y + 4)

interchanging the variables

y = √(x + 4)

f inverse (5) = √(5 + 4)

= √(9)

= 3

f inverse (5) equals 3

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The activation energy of the reaction is approximately 126.8 kJ/mol. The calculation was done using the Arrhenius equation and the natural logarithm of the rate constants at the two temperatures.

To calculate the activation energy of a reaction, we can use the Arrhenius equation:

k = A * e⁽⁻ᴱᵃ/ᴿᵀ⁾

where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.

We have two rate constants at different temperatures, so we can set up two equations:

k₁ = A * e⁽⁻ᴱᵃ/ᴿᵀ₁⁾

k₂ = A * e⁽⁻ᴱᵃ/ᴿᵀ₂⁾

We want to solve for Ea, so we can take the natural logarithm of both sides of each equation:

ln(k₁) = ln(A) - Ea/RT₁

ln(k₂) = ln(A) - Ea/RT₂

We can subtract the second equation from the first to eliminate ln(A):

ln(k₁) - ln(k₂) = Ea/R * (1/T₂ - 1/T₁)

Now we can solve for Ea:

Ea = -R * (ln(k₁) - ln(k₂)) / (1/T₂ - 1/T₁)

Plugging in the given values, we get:

Ea = -8.314 J/mol/K * (ln(6.20 x 10⁻⁴) - ln(2.39 x 10⁻²)) / (1/760 K - 1/700 K)

Ea ≈ 126.8 kJ/mol

Therefore, the activation energy of the reaction is approximately 126.8 kJ/mol.

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Answer:

Step-by-step explanation:

Answer: C

Step-by-step explanation:

i did the quiz

Answer:

rise over run is 1/4

Step-by-step explanation:

Here, we want to calculate the ratio of the rise to the run

Mathematically, this is simply referring to the slope

To get the slope, we need to select any two points and then apply the slope formula

The two points selected are;

(8,-6) and (-4,-9)

The slope formula is;

m = (y2-y1)/(x2-x1) = (-9 -(-6))/(-4-8) = -3/-12 = 1/4

The length and the width of the rectangle are 10 inches and 6 inches respectively.

In the question, we are given that the length of a rectangle exceeds its width by 4 inches, and the area is 60 square inches.

We are asked for the length and the width of the rectangle.

We assume the width (w) of the rectangle to be x inches.

Its length (l), exceeds its width (w) by 4 inches.

Thus, its length (l) = x + 4 inches.

Now, the area can be calculated using the formula, A = l*w, where A is its area, l is its length, and w is its width.

Thus, the area = (x + 4)x = x² + 4x.

But, we are given that the area is 60 square inches.

Putting the value, we get a quadratic equation:

x² + 4x = 60.

or, x² + 4x - 60 = 0,

or, x² + 10x - 6x - 60 = 0,

or, x(x + 10) - 6(x + 10) = 0,

or, (x - 6)(x + 10) = 0.

By the zero-product rule, we get:

Either, x - 6 = 0, or, x = 6,

or, x + 10 = 0, or, x = -10, but this is not possible as the width of a rectangle cannot be negative.

Thus, the width = x = 6 inches.

The length = x + 4 = 10 inches.

Thus, the length and the width of the rectangle are 10 inches and 6 inches respectively.

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Answer:

$15.25

Step-by-step explanation:

Answer:

- 7

Step-by-step explanation:

d = a₂ - a₁ = a₃ - a₂ = - 2 - 5 = - 9 - (- 2) = - 7

The given statement is True because If the sample mean is close to the population parameter, it suggests representative sampling regarding the variable of interest, although other factors should be considered too.

When the sample mean closely approximates the population parameter, it indicates that the sample is capturing the central tendency of the population. The mean is a measure of central tendency that reflects the average value of the variable of interest in the population.

If the sample mean is similar to the population mean, it suggests that the sample is a good representation of the population in terms of that particular variable.

However, it is important to note that representativeness is a relative concept. A sample may be considered representative in one sense but not necessarily in all aspects. Other factors, such as the sampling method, sample size, and sampling bias, also influence the representativeness of a sample.

In summary, when the obtained mean of the observations in a research study is close to the population parameter, it provides evidence that the sample is representative of the target population to some degree, indicating that the sample captures the central tendency of the population for the variable under investigation.

However, representativeness should be assessed in consideration of other factors as well.

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Answer:

x = 1.4

Step-by-step explanation:

12x - 15 = 6 - 3x

12x + 3x = 6 + 15

15x = 21

x = 1.4

Check:

12(1.4) - 15 = 1.8

6 - 3 (1.4) = 1.8

The value of x which makes the equation 12x minus 15 = 6 minus 3x true is 1.4

Given:

12x minus 15 = 6 minus 3x

12x - 15 = 6 - 3x

collect like terms

12x + 3x = 6 + 15

15x = 21

x = 21 / 15

x = 1.4

Therefore, the value of x which makes the equation 12x minus 15 = 6 minus 3x true is 1.4

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Answer:

1/3 X 2 = 2/6, 2/6 + 1/6 = 1/2

1- 1/2 = 1/2 THE ANSWER IS ONE HALF

Step-by-step explanation:

Answer:

1/2 :)

Step-by-step explanation:

(a) 95% confidence interval for the difference between female and male times is (11.954, 255.591).

(b) The assumptions and conditions for the two-sample t-test are met, so we can use the results of the test and confidence interval.

a) To construct a 95% confidence interval for the difference between female and male times, we can use a two-sample t-test. Let's denote the mean time for female swimmers as μf and the mean time for male swimmers as μm. We want to test the null hypothesis that there is no difference between the two means (i.e., μf - μm = 0) against the alternative hypothesis that there is a difference (i.e., μf - μm ≠ 0).

The formula for the two-sample t-test is:

t = (Xf - Xm - 0) / [sqrt((s^2f / nf) + (s^2m / nm))]

where Xf and Xm are the sample means for female and male swimmers, sf and sm are the sample standard deviations for female and male swimmers, and nf and nm are the sample sizes for female and male swimmers, respectively.

Using the data from the plots, we get:

Xf = 917.5, sf = 348.0137, nf = 15

Xm = 783.7273, sm = 276.0625, nm = 28

Plugging in these values, we get:

t = (917.5 - 783.7273 - 0) / [sqrt((348.0137^2 / 15) + (276.0625^2 / 28))] = 2.4895

Using a t-distribution with (15+28-2) = 41 degrees of freedom and a 95% confidence level, we can look up the critical t-value from a t-table or use a calculator. The critical t-value is approximately 2.021.

The confidence interval for the difference between female and male times is:

(917.5 - 783.7273) ± (2.021)(sqrt((348.0137^2 / 15) + (276.0625^2 / 28)))

= 133.7727 ± 121.8187

= (11.954, 255.591)

Therefore, we can be 95% confident that the true difference between female and male times is between 11.954 and 255.591 minutes.

b) Assumptions and conditions for the two-sample t-test:

Independence, We assume that the observations for each group are independent of each other.

Normality, We assume that the populations from which the samples were drawn are approximately normally distributed. Since the sample sizes are relatively large (15 and 28), we can rely on the central limit theorem to assume normality.

Equal variances, We assume that the population variances for the female and male swimmers are equal. We can test this assumption using the F-test for equality of variances. The test statistic is,

F = s^2f / s^2m

where s^2f and s^2m are the sample variances for female and male swimmers, respectively. If the p-value for the F-test is less than 0.05, we reject the null hypothesis of equal variances. If not, we can assume equal variances. In this case, the F-test yields a p-value of 0.402, so we can assume equal variances.

Sample size, The sample sizes are both greater than 30, so we can assume that the t-distribution is approximately normal.

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The margin of error is (31.15, 32.85).

The margin of Error is a statistical expression that is used to determine the percentage point by which the result arrived will differ from the value of the entire population, and it is calculated by dividing the standard deviation of the population by the sample size and lastly multiplying the resultant with the critical factor. A higher error indicates a high chance that the result of the sample reported may not be the true reflection of the whole population. The formula for the margin of error is calculated by multiplying a critical factor (for a certain confidence level) with the population standard deviation. Then the result is divided by the square root of the number of observations in the sample.

Mathematically, it is represented as,

Margin of Error = Z * ơ / √n

Given:

Number of people = n = 16

Mean = μ = $32

Standard deviation = σ = $7

Confidence level = 95%

Thus, the z value would be 1.96.

The confidence interval can be calculated as follows:

Confidence interval = μ ± z(σ/√n)

= 32 ± 1.96 × (7/16)

= 32 ± 0.85

= (31.15, 32.85)

Thus, the margin of error is (31.15, 32.85).

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Answer:

Option A

Step-by-step explanation:

Let us take this number as x, translating this description of the equation into mathematical language;

\(x^2 = 3x - 2\)

Now let us solve for x;

\(x^2 = 3x - 2,\\x^2+2=3x-2+2,\\x^2+2=3x,\\x^2+2-3x=3x-3x,\\x^2-3x+2=0,\\\\Factored = \left(x-1\right)\left(x-2\right)=0,\\Zero Factor Principle, \\x = 1, x = 2\\\\Solution - Option A\)

* Note that for the the previous problem I solved, I set up a similar equation that had two values for the width, one negative and the other positive. Now the width could only be a positive number, so there was only one solution out of the two.

Answer:

Answer:

C

Step-by-step explanation:

Answer:

x=-6

Step-by-step explanation:

i got a hundred on the test

The probability that the sample mean would differ from the true mean by less than 0.5 dollars is approximately 0.0000.By calculating the z-score for a difference of 0.5 dollars, we can then determine the probability using the standard normal distribution.

To calculate the probability that the sample mean would differ from the true mean by less than 0.5 dollars, we can use the Central Limit Theorem. Given that the mean cost of a five pound bag of shrimp is $46 with a standard deviation of $7, and a sample size of 49 bags, we can consider the distribution of sample means. Since the sample size is large (n ≥ 30), we can assume that the distribution of sample means will be approximately normal.

According to the Central Limit Theorem, for a sample size of 49 or larger, the distribution of sample means will be approximately normal, regardless of the shape of the original population. In this case, the mean cost of a five pound bag of shrimp is $46 with a standard deviation of $7. Since we are interested in the probability that the sample mean differs from the true mean by less than 0.5 dollars, we need to calculate the z-score for a difference of 0.5 dollars.

The z-score can be calculated using the formula: z = (x - μ) / (σ / sqrt(n)), where x is the desired difference (0.5 dollars), μ is the true mean ($46), σ is the standard deviation ($7), and n is the sample size (49). Substituting the values into the formula, we get: z = (0.5 - 46) / (7 / sqrt(49)) = -45.5 / (7 / 7) = -45.5 / 1 = -45.5.

Now, we can use the standard normal distribution table or a calculator to find the probability corresponding to the z-score of -45.5. However, since the z-score is extremely large, the probability will be extremely close to 0. Therefore, we can round the answer to four decimal places and conclude that the probability that the sample mean would differ from the true mean by less than 0.5 dollars is approximately 0.0000.

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The probability that exactly 4 out of the 5 randomly selected employees are cashiers is approximately 0.00549 or 0.549%

To calculate the probability that exactly 4 out of the 5 employees selected to work on Labor Day are cashiers, we need to use the concept of combinations and probabilities.

First, let's determine the total number of ways to select 5 employees out of the 22. This can be calculated using the combination formula:

C(n, k) = n! / (k!(n-k)!)

where n is the total number of employees (22) and k is the number of employees selected (5).

C(22, 5) = 22! / (5!(22-5)!)

= 22! / (5! * 17!)

= (22 * 21 * 20 * 19 * 18) / (5 * 4 * 3 * 2 * 1)

= 22,957

So, there are a total of 22,957 ways to select 5 employees out of the 22.

Next, let's determine the number of ways to select exactly 4 cashiers out of the 9 cashiers. This can also be calculated using combinations:

C(9, 4) = 9! / (4!(9-4)!)

= 9! / (4! * 5!)

= (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1)

= 126

Now, let's calculate the probability of selecting exactly 4 cashiers out of the 5 employees randomly selected for overtime pay:

P(4 cashiers) = Number of ways to select 4 cashiers out of 9 / Total number of ways to select 5 employees from 22

= C(9, 4) / C(22, 5)

= 126 / 22,957

≈ 0.00549

Therefore, the probability that exactly 4 out of the 5 randomly selected employees are cashiers is approximately 0.00549 or 0.549%

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The value of x that maximizes the expression is x = 4/7.

(a) Find the derivative of the given expression with respect to x

To find the derivative of the expression dx/dx (x^2 - 18x + 21) + 12, we can use the power law and the constant differentiation rule.

The power law states that the derivative of \(x^n\) with respect to x is n*x^(n-1), and the constant law states that the derivative of a constant with respect to x is zero.

These apply the rule to the given expression:

\(dx/dx (x^2 - 18x + 21) + 12\)

= \(2x^1 - 1*18x^(1-1) + 0 + 0\)

= 2x - 18

Therefore the derivative of the expression is 2x - 18.

(b) To find the derivative of the expression dx/dx (1/4) ln(2x - 4) we can use the chain rule of differentiation.

According to the chaining rule, given a compound function f(g(x)), the derivative of f(g(x)) with respect to x is f`(g(x)) * g'(x). increase. .

Applies the chain rule to the given expression:

dx/dx (1/4) ln(2x - 4)

= (1/4) * (1/(2x - 4)) * 2

= 1/ ( 2x - 4)

So the derivative of the expression is 1/(2x - 4).

(c) To find the derivative of the expression dx/dx (2x^3 - 4x)^2 we can use the chain rule and the power law.

Apply chain rule:

dx/dx \((2x^3 - 4x)^2\)

= 2 * \((2x^3 - 4x)^(2-1) * (6x^2 - 4)\)

Simplification :

= 2 *\((2x^3 - 4x) * (6x^2 - 4)\)

= 4x\((6x^2 - 4)(2x^3 - 4x)\)

So the expression \(4x(6x ^2)\) The derivative is - 4) \((2x^3 - 4).\)

Bonus: To solve the optimization problem that maximizes the expression 1/4 ln(3(1-x)) + 4/3 ln(x), take the derivative of the expression with respect to x and use it as Set equal to: Set it to zero and solve for x.

d/dx (1/4 ln(3(1-x)) + 4/3 ln(x)) = 0

To solve this problem, use the chain rule and the power law to find each term can be distinguished individually. .

d/dx (1/4 ln(3(1-x))) + d/dx (4/3 ln(x)) = 0

(1/4) * (1/(3(1- x)) x))) * (-3) + (4/3) * (1/x) = 0

Simplification:

-3/(12(1-x)) + 4/(3x) = 0

12x(1-x) Multiply and remove fractions:

-3x + 4(1-x) = 0

Simplify:

-3x + 4 - 4x = 0

- 7x + 4 = 0

-7x = -4

x = 4/7

So the value of x that maximizes the expression is x = 4/7.

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It should be noted that since the calculated value of F (4.289) is greater than the critical value (3.15), we reject the null hypothesis

The decision rule is: Reject H0 if F > critical value

Now, let's calculate the critical value of F:

df1 = n1 - 1 = 21 - 1 = 20

df2 = n2 - 1 = 18 - 1 = 17

Using an F-table or calculator, we find the critical value of F for α = 0.01 and (df1, df2) = (20, 17) to be approximately 3.15

Therefore, the decision rule is:

Reject H0 if F > 3.15

Now, let's calculate the value of F:

F = (s1²) / (s2²)

F = (45,600²) / (21,3302)

F ≈ 4.289

The value of F is approximately 4.289

Since the calculated value of F (4.289) is greater than the critical value (3.15), we reject the null hypothesis. We can conclude, at the 0.01 significance level, that there is more variation in the selling prices of oceanfront homes compared to homes one to three blocks from the ocean.

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The vertices of image L′M′N′ are L′(−5, −1), M′(0, −1), and N′(−5, −2).  

Rotating a figure 90° clockwise about the origin means that each point of the figure will be moved to a new position that is located 90° clockwise from its original position, with respect to the origin of the coordinate plane.

To rotate a figure 90° clockwise about the origin follow the steps:

1. Swap the x- and y-coordinates of each point.

2. Negate the new x-coordinates.

3. Leave the new y-coordinates as they are.  

Here we have

Triangle LMN has vertices at L(−1, 5), M(−1, 0), N(−2, 5)

Triangle LMN is rotated 90° clockwise about the origin.  

Using the above condition

L(−1, 5) => (−(5), −1) => (−5, −1)

M(−1, 0) => (−0, −1) => (0, −1)  

N(−2, 5) => (−(5), −2) => (−5, −2)    

Therefore,

The vertices of image L′M′N′ are L′(−5, −1), M′(0, −1), and N′(−5, −2).  

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Answer:

Numerical.

Step-by-step explanation:

A number sentence is a statement of equality between two numerical expressions!

Hope this helps!

To find an ε > 0 satisfying the given conditions, we need to examine the graph of the function f(x) = 4 - (-3x + 2). By analyzing the graph, we can identify a suitable ε value that ensures |f(x) - L| < ε for all x within the given range.

The function f(x) is given by f(x) = 4 - (-3x + 2), which simplifies to f(x) = 3x + 2. We are given that x = -2 and L = 4.7. To find ε, we need to determine the maximum distance between f(x) and L within the range 0 < |x - xo| < 6.

First, let's evaluate f(x) at the given x-value:

f(-2) = 3(-2) + 2 = -6 + 2 = -4.

Next, we calculate the absolute difference between f(-2) and L:

|f(-2) - L| = |-4 - 4.7| = |-8.7| = 8.7.

Since we want |f(x) - L| to be less than ε, we set ε = 0.2, which is a smaller value. As 8.7 > 0.2, ε = 0.2 does not satisfy the condition.

To find a suitable ε value, we examine the graph of f(x) = 3x + 2. By observing the graph, we can see that the maximum difference between f(x) and L occurs near x = -2.5. Let's evaluate f(-2.5):

f(-2.5) = 3(-2.5) + 2 = -7.5 + 2 = -5.5.

The absolute difference between f(-2.5) and L is:

|f(-2.5) - L| = |-5.5 - 4.7| = |-10.2| = 10.2.

As 10.2 > 0.2, ε = 0.2 is not suitable. We need a smaller ε value to satisfy the condition.

Continuing to analyze the graph, we can observe that the maximum difference between f(x) and L decreases as x moves away from -2.5. Thus, if we choose a smaller value for x, the difference between f(x) and L will be smaller as well. By selecting x = -3, we can evaluate f(-3) = 3(-3) + 2 = -7, and the absolute difference becomes:

|f(-3) - L| = |-7 - 4.7| = |-11.7| = 11.7.

As 11.7 > 0.2, ε = 0.2 does not satisfy the condition. Therefore, we need to select an even smaller ε value.

By analyzing the graph, we can determine that for x = -3.5, f(-3.5) = 3(-3.5) + 2 = -8.5, and the absolute difference is:

|f(-3.5) - L| = |-8.5 - 4.7| = |-13.2| = 13.2.

Since 13.2 > 0.2, ε = 0.2 is still not suitable. We continue this process until we find an x-value that satisfies the condition. By repeating the analysis, we eventually find that for x = -3.8, the absolute difference becomes:

|f(-3.8) - L| = |-9.4 -

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Answer:

56 ft

Step-by-step explanation:

Perimeter is the distance around the shape

18 x 2 + 10 x 2 =

36 + 20 =

56 ft

Answer:

56 feet

Step-by-step explanation:

First, we have to understand that since this is rectangle opposite sides are equal, and that perimeter is equal to the sum of all sides. From this, we know that in this question perimeter equals...

perimeter = 18 + 10 + 18 + 10 = 56 feet

Answer:

482.84

Step-by-step explanation:

\(A = 2 ( 1 +\sqrt{2} ) a^{2} = 2 multiply ( 1 +\sqrt{2} ) multiply 10^{2} = 482.84271\)

The image of the transformation is (-5, 11) (-4, 8) (-2, 14)

From the question, we have the following parameters that can be used in our computation:

Pre-image: (5, 15) (4, 12) (2, 18)

Transformation: Translate 4 units down, and then reflect over the y-axis.

Mathematically, this can be expressed as

(x, y) = (-x, y - 4)

Substitute the known values in the above equation, so, we have the following representation

(5, 15) (4, 12) (2, 18) = (-5, 11) (-4, 8) (-2, 14)

Hence, the image is (-5, 11) (-4, 8) (-2, 14)

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Answer:  solving for x would be x ≤ 3

Step-by-step explanation:

Hope this helps! have a good day!

Answer:

Inequality form:

x≤3

Interval Notation:

(-∞,3]

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

x=13

Step-by-step explanation:

Switch sides:

2x−9=17

Add 9 to both sides:

2x−9+9=17+9

Simplify

2x=26

Divide both sides by 2:

2x/2 =26/2

Simplify to get the result.

x=13

Answer:

x=13

Step-by-step explanation:

\(\sf 2x-9=17\)

\(\sf 2x-9+9=17+9\)

\(\sf 2x=26\)

\(\sf \cfrac{2x}{2}=\cfrac{26}{2}\)

\(\sf x=13\)