Find all real x in each of the following


X=(-27)^-2/3

The correct statement regarding the inverse function is given as follows:

[tex]f^{-1}(x) = 3 - \sqrt{\frac{x - 4}{2}}[/tex], with a domain of x ≤ 3.

The function for this problem is defined as follows:

f(x) = 2(x - 3)² + 4.

The axis of symmetry of the function is of x = 3, hence the domain of the inverse function is given as follows:

x ≤ 3.

The inverse function is obtained exchanging x and y and then isolating y, hence:

x = 2(y - 3)² + 4

2(y - 3)² = x - 4.

[tex](y - 3)^2 = \frac{x - 4}{2}[/tex]

[tex]y - 3 = \sqrt{\frac{x - 4}{2}}[/tex]

[tex]f^{-1}(x) = 3 - \sqrt{\frac{x - 4}{2}}[/tex]

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The solution to the given equation √(2x + 9) = 7 is x = 20.

Any equation that contains a radical symbol is considered a radical equation. To find the square roots, cubic roots, and higher, radical symbols are used.

The equation is given as follows:

√(2x + 9) = 7

Square both sides of the above equation,

2x + 9 = 7²

2x + 9 = 49

Subtract 9 from both sides of the above equation,

2x = 49 - 9

2x = 40

Divide by 2 into both sides of the equation,

x = 40/2

x = 20

Thus, the solution to the given equation is x = 20.

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The amount of depreciation to be recorded for year 2 using the straight-line method of calculating depreciation is $6,750.

Straight-line depreciation is calculated by dividing a fixed asset's depreciable base by its useful life. The depreciable base is the difference between an asset's all-in costs and the estimated salvage value at the end of its useful life.

By using the straight-line method of calculating depreciation, the annual depreciation expense would be calculated as follows:

= (Purchase Price - Salvage Value) / Useful Life

= ($60,000 - $6,000) / 8 years

= $54,000 / 8 years

= $6,750.

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Answer:

Valid

Step-by-step explanation:

This argument is Valid because there could be many other reasons she needs dress altercations, however the most likely one is that she did not have her baby before next week.

Answer:

Step-by-step explanation:

The argument is valid.

We can analyze it using the following symbols:

Let A be the event that Bryony has her baby before next week.

Let B be the event that Bryony needs dress alterations before her sister's wedding next month.

Then the argument can be represented as follows:

If A, then not B.

B.

Therefore, not A.

This is a valid deductive argument form called modus tollens. The conclusion follows logically from the premises. Therefore, the argument is valid.

Answer:

the original price of each costume was $25, and the sale price was $(25-3.50) = $21.50.

Step-by-step explanation:

Let the original price of each costume be $x. The sale price of each costume will be $(x-3.50). Ms. Monroe ordered 24 costumes, so the cost of 24 costumes at the sale price will be:

24 × (x-3.50) = $24x - $84

Ms. Monroe paid $516 in all, so we can write:

24x - 84 = 516

Adding 84 to both sides, we get:

24x = 600

Dividing both sides by 24, we get:

x = 25

Therefore, the original price of each costume was $25, and the sale price was $(25-3.50) = $21.50.

Answer: so Ms.Monroe got $84 off her entire purchase

Step-by-step explanation: I hope it helps

The order of these numbers from least to greatest is 2.7 x 10³, 2.3 x 10¹¹, 6.5 x 10^12, 4.8 x 10^21

Index forms are simple described as the mathematical expressions or models used to represent numbers that are large or small in more appropriate ways.

They are also termed as scientific notations or standard forms.

Examples of index forms are;

2³ = 8

2 ² = 4

3 ³ = 27

From the information given, we have that;

2.7 x 10³

This is represented as; 2.7 × 10 × 10 × 10

Multiply the values

2700

2.3 x 10¹¹

This is represented as 2. 3 multiply by 10 in 11 times

6. 5× 10^12

This is represented by 6.5 multiplied by 10 in 12 places

4.8 × 10^21

This is represented by 4.8 multiplied by 10 in 21 places.

Hence, the exponent shows the greatest number

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The two points with an x-coordinate of 2 and a distance of 5 from (-2, -4) are: (2, -4 + 2√13) and (2, -4 - 2√13)

What is distance formula?

Distance is a measurement of how far away two things or locations are, either numerically or occasionally qualitatively.

Distance formula: [tex]distance = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)}[/tex]

We can solve this problem using the distance formula, which gives us the distance between two points in a plane:

[tex]distance = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)}[/tex]

Let (x, y) be a point with an x-coordinate of 2. Then we can write the distance from (-2, -4) to (x, y) as:

[tex]distance = \sqrt{((x - (-2))^2 + (y - (-4))^2)}[/tex]

Simplifying this expression, we get:

[tex]distance = \sqrt{((x + 2)^2 + (y + 4)^2)}[/tex]

We know that the distance between (-2, -4) and (x, y) is 5. Therefore, we can write:

[tex]\sqrt{((x + 2)^2 + (y + 4)^2)} = 5[/tex]

Squaring both sides, we get:

[tex](x + 2)^2 + (y + 4)^2 = 25[/tex]

Expanding the left side, we get:

[tex]x^2 + 4x + 4 + y^2 + 8y + 16 = 25[/tex]

Simplifying this expression, we get:

[tex]x^2 + 4x + y^2 + 8y - 5 = 0[/tex]

To find all points with an x-coordinate of 2 that satisfy this equation, we can substitute x = 2 and simplify the resulting equation:

[tex]2^2 + 4(2) + y^2 + 8y - 5 = 0[/tex]

Simplifying this equation, we get:

[tex]y^2 + 8y + 3 = 0[/tex]

We can solve this quadratic equation using the quadratic formula:

y = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 8, and c = 3.

Plugging in these values, we get:

y = (-8 ± sqrt(8^2 - 4(1)(3))) / 2(1)

Simplifying this expression, we get:

y = (-8 ± √52) / 2

y = (-8 ± 2√13) / 2

y = -4 ± √13

Therefore, the two points with an x-coordinate of 2 and a distance of 5 from (-2, -4) are: (2, -4 + 2√13) and (2, -4 - 2√13)

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The number of hours till Ed and Julie were 875 miles apart was 7 hours.

Since Ed and Julie are traveling in opposite directions, we can think of their distances from Good Life City as two separate distances that are adding up to their total distance apart.

For Ed, his distance from Good Life City is:

= 60 t

For Julie :

=  65t

We want to know how many hours it took for their total distance to be 875 miles. So we can set up the equation:

875 = 60t + 65t

Simplifying, we get:

875 = 125t

t = 875 /  125

t = 7 hours

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Answer:

4/3, -3

Step-by-step explanation:

slope is the number in front of the variable x, and y intercept is when x=0

Answer:

Step-by-step explanation:

The equation written in slope-intercept form is: y=3x-2.

It is estimated that producing an additional 500 lb of paper once 10 tons have been produced would cost approximately $95,000.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To estimate the cost of producing an additional 500 lb of paper, we need to first convert 500 lb to tons.

1 lb = 0.0005 tons

So, 500 lb = 0.25 tons

Now, we can use the marginal cost formula:

MC = C'(t)

where MC is the marginal cost and C'(t) is the derivative of the cost function with respect to t.

We are given that C'(10) = 380, which means that the marginal cost of producing the 10th ton of paper is $380,000.

To estimate the cost of producing an additional 500 lb of paper once 10 tons have been produced, we need to find the marginal cost at t = 10.

Therefore, the estimated cost of producing an additional 500 lb of paper is:

MC(10) ≈ C'(10) ≈ $380,000 per ton

0.25 tons x $380,000 per ton = $95,000

Hence, it is estimated that producing an additional 500 lb of paper once 10 tons have been produced would cost approximately $95,000.

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The optimal strategy would be to fit several models to the data using equation mathematical software or tools, and then assess the goodness of fit using statistical metrics like R-squared or Mean Squared Error.

In a mathematical equation, the equals sign (=), which connects two claims and denotes equality, is utilized. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a space. Mathematical expressions can be used to describe the relationship between the two sentences on either side of a letter. The logo and the particular piece of software frequently correspond. like, for instance, 2x - 4 = 2.

The following exponential model could be a good fit for the data in the image:

[tex]f(x) = 7.5 * e^(0.1x) (0.1x)[/tex]

The data is assumed to develop exponentially with a base of e in this model, with a growth rate of 10% for each unit increase in x.

It is crucial to remember that this is only one potential model and that other exponential models with other parameters could also be able to satisfactorily match the data. The optimal strategy would be to fit several models to the data using mathematical software or tools, and then assess the goodness of fit using statistical metrics like R-squared or Mean Squared Error.

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Using arithmetic operations, The total cost of six sheets will be:

$27.00 + ($9.00 x 4) = $63.00

If each sheet costs $18.00, then the cost of the first sheet will be $18.00, and the cost of the second sheet will be 50% of $18.00, or $9.00.

So, two sheets will cost the cost of the first sheet plus the cost of the second sheet, which is:

Using addition,

$18.00 + $9.00 = $27.00

For six sheets, we can use the same logic: the first two sheets will cost $27.00, and the next four sheets will be half off. So, the cost of the next four sheets will be 50% of $18.00, or $9.00 each.

Hence, the total cost of six sheets will be:

$27.00 + ($9.00 x 4) = $63.00

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Answer:

10^9 = 1,000,000,000

2^6 = 64

7^1 = 7

10^3 = 1,000

10^8 = 100,000,000

0^4 = 0

7^6 = 117,649

Step-by-step explanation:

The exponent multiplies a number by itself by whatever value it is.

Answer:

↓ ↓ ↓

Step-by-step explanation:

1)

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3)

4)

5)

6)

7)

8)

9)

10)

________________________

Hope this helps! :)

Answer: the image didnt send with this try reposting

Step-by-step explanation:

this is a little funny out of context tho, best of luck be upon you

The similar triangles are Δ SRQ ~ Δ RPQ  ~ Δ SRP

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Given is right triangle PRQ, a perpendicular line is drawn to the side PQ from angle R

we need to tell the similar triangles,

From the figure we have,

Δ SRQ ~ Δ RPQ  ~ Δ SRP

And, according to the definition of similar triangle,

SP / RP = PR / RQ

PQ / RQ = RQ / SQ

Hence, the similar triangles are Δ SRQ ~ Δ RPQ  ~ Δ SRP

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The equation for calculating the area of a triangle is:

A = 1/2 * base * height

where A represents the area of the triangle, base represents the length of the base of the triangle, and height represents the height of the triangle measured perpendicularly to the base.

Answer:

25.12cm

Step-by-step explanation:

The area of a circle is (π) x (radius)^2.

Here, you are given the diameter.

To find the radius, divide the diameter by 2, which results in 4.

(π) x (4)^2

Now square the 4, which results in 16

3.14 x 16 = 50.24

50.24 would be the area of the circle not cut in half, so divide 50.54 by 2 to get half.

50.24/2 = 25.12

Answer:

Step-by-step explanation:

The area of Circle is [tex]\pi r^{2}[/tex]

So, the area of half circle is [tex]\frac{\pi r^{2} }{2}[/tex]

Diameter is given = 8cm

so radius will be 4 cm

[tex]A = \frac{\pi 4^{2} }{2} \\A = \frac{\pi 16}{2} \\A = 8\pi[/tex]

A = 8 × 3.14

A = 25.12cm Square

The interval where both functions are decreasing is {-1, 2} and it is shown on the number line below.

For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value (domain or x-value) is increased, then, the function is generally referred to as a decreasing function.

By critically observing the graph of g(x), we can logically deduce that the function g(x) decreases over the interval {-2, 2}. On the other hand (conversely), the function f(x) = -5|x + 1| + 10 decreases over the interval {-1, ∞}.

Therefore, the interval over which both functions decrease is denoted by the intersection of both functions;

Interval = {-1, 2}

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Answer:

the answer is px and at ako

The p-value for this sample is approximately 0.004655 which is smaller than the significance level of 0.005. This means that we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the population proportions are not equal.

To test the hypothesis Hₐ : p₁ ≠ p₂ at a significance level of α = 0.005, we can use the two-sample z-test for proportions, where the test statistic is given by:

z = (p₁ - p₂) / sqrt{p(1-p)(1/n₁ + 1/n₂)}

where p = (x₁ + x₂) / (n₁ + n₂) is the pooled sample proportion, x₁ and x₂ are the number of successes in the two samples, n₁ and n₂ are the sample sizes for the two samples, and p₁ and p₂ are the sample proportions for the two samples.

Plugging in the given values, we have:

p₁ = 119/687 ≈ 0.1732

p₂ = 137/577 ≈ 0.2374

n₁ = 687

n₂ = 577

p = (119 + 137) / (687 + 577) ≈ 0.202

z = (0.1735 - 0.2376) / √{0.202 * (1 - 0.202) * (1/687 + 1/577)} ≈ -2.83

The test statistic for this sample is approximately -2.83

To find the p-value for this sample, we need to find the probability of observing a test statistic as extreme as -2.83, assuming that the null hypothesis is true. Since this is a two-tailed test, we need to find the area in the tails of the standard normal distribution that corresponds to a significance level of 0.005:

α/2 = 0.005/2 = 0.0025

Using a standard normal table or a calculator, we can find that the z-score corresponding to an area of 0.0025 in the left tail of the standard normal distribution is approximately -2.81. The z-score corresponding to an area of 0.0025 in the right tail is approximately 2.81.

The p-value for this sample is the sum of the areas in the tails beyond the test statistic:

p-value = P(Z ≤ -2.83) + P(Z ≥ 2.83)

P = 0.004655

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Answer:

The answer should be D.)

The rhyme scheme of the poem is abab cdcd efef gg. The rhyme scheme creates a sense of symmetry and balance in the poem.

A poem's rhyme system is its regular pattern of final rhymes. It is written using alphabetical letters, each of which stands for a particular rhyme sound. A poem with the rhyme scheme ABAB, for instance, follows a pattern where the first and third lines rhyme, and the second and fourth lines rhyme.

The poem's rhyme scheme can be mathematically described by utilising letters to denote the various rhyming sounds. "Abab cdcd efef gg" is the rhyme pattern used in this poem. This can be written as follows using letters to represent the various sounds:

This pattern is repeated throughout the entire poem, creating a consistent and structured rhyme scheme.

Therefore the rhyme scheme is abab cdcd efef gg.

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The measures of the angles are JKN = 27 degrees and JNK = 126

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

The rectangle

On the rectangle, we have

JKN = NJK

Using the above as a guide, we have the following:

JKN = 27 degrees

The sum of angles in a triangle is 180

So, we have

JNK = 180 - 27 * 2

Evaluate

JNK = 126

Hence, teh angle is 126 degrees

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Answer:

try 1/2

Step-by-step explanation:

Answer:

Let's start by finding out how many muffins were there in total before the ogre stole 20 of them. Let's call that number "x".

If 5/8 of them were left after the ogre stole 20, then 3/8 of them were taken.

So we can set up an equation:

x - 20 = 3/8x

To solve for x, we can start by multiplying both sides by 8 to get rid of the fraction:

8(x - 20) = 3x

8x - 160 = 3x

Now we can solve for x by subtracting 3x from both sides:

5x - 160 = 0

5x = 160

x = 32

So there were originally 32 muffins.

Now we can find out how many are left:

5/8 of 32 = 20

So there are 20 muffins left.

Step-by-step explanation:

The percent discount being offered is 20%.

What is percentage ?

Percentage is a way of expressing a number as a fraction of 100. It is often denoted by the symbol %, which means "per cent" or "out of 100". Percentages are used to compare two quantities and express the relationship between them in terms of the fraction of one quantity that the other quantity represents.

To find the percent discount, we need to first calculate the amount of discount that is being offered. We can do this by subtracting the sale price from the original price:

Discount = Original Price - Sale Price

Discount = $79.95 - $63.96

Discount = $15.99

Next, we can calculate the percentage discount by dividing the discount by the original price and then multiplying by 100:

Percent Discount = (Discount / Original Price) x 100

Percent Discount = ($15.99 / $79.95) x 100

Percent Discount = 20%

Therefore, the percent discount being offered is 20%.

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Answer:

When the ball hits the ground, its height will be 0 meters. Therefore, we need to solve the equation:

h(t) = 0

8t - 5t^2 + 4 = 0

We can solve this quadratic equation by factoring or by using the quadratic formula, but in this case, it's easier to use factoring:

(5t - 4)(t - 1) = 0

From this equation, we can see that either 5t - 4 = 0 or t - 1 = 0. Solving for t in each case, we get:

5t - 4 = 0 ==> t = 0.8 seconds

t - 1 = 0 ==> t = 1 second

Therefore, the ball will reach the ground after either 0.8 seconds or 1 second, depending on the initial height of the ball.