can you simplify (1/4a^8b^5)^2 make sure you simplify it by hand-drawing it :)

Can You Simplify (1/4a^8b^5)^2 Make Sure You Simplify It By Hand-drawing It :)

Answers

Answer 1

Answer:

\(\frac{1}{16} a^{16} b^{10}\)

Step-by-step explanation:

\((\frac{1}{4} a^8b^5)^{2}\) =\((\frac{1}{4}) ^{2} a^{8*2} b^{5*2}\) =\(\frac{1}{16} a^{16} b^{10}\)

Answer 2
(ab)^n=a^n×b^n

So

\(\\ \rm\Rrightarrow (\dfrac{1}{4}a^4b^5)^2\)

\(\\ \rm\Rrightarrow 1/16a^{4×2}b^{5×2}\)

\(\\ \rm\Rrightarrow 1/16a^8b^{10}\)


Related Questions

What is mean reversion? How is mean reverting level x1 is calculated for time series? How is it interpreted?

Answers

Mean reversion is the tendency of prices or variables to return to their average level. The mean-reverting level, x1, is calculated using statistical methods and indicates potential future decreases or increases.

Mean reversion refers to the tendency of asset prices or economic variables to move back to their average or mean level over time. The mean-reverting level, x1, for a time series can be calculated using statistical methods like moving averages or exponential smoothing. These techniques estimate the average value or trend of the data.



The interpretation of x1 depends on the context. If the current value is above x1, it suggests a potential future decrease, reverting back to x1. Conversely, if the current value is below x1, it indicates a potential future increase, also reverting back to x1. The deviation from x1 provides insights into the strength or speed of the mean reversion process.



Therefore, Mean reversion is the tendency of prices or variables to return to their average level. The mean-reverting level, x1, is calculated using statistical methods and indicates potential future decreases or increases.

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Describe how to compare the two ratios 5:8 to 7:9. Tell each step to set up the ratios, then explain what to do to be able to compare the ratios. Finally make sure to answer how the ratios compare. ~ 100 POINTS AND ILL GIVE YOU BRAINLIEST IF YOU ANSWER CORRECTLY AND 5 SENTENCES NEEDED

Answers

Answer:

5/8 is smaller.

Step-by-step explanation:

A ratio is just a different type of fraction, a 5:8 ratio means 5/8 which is 0.625. A 7:9 ratio equals 7/9 which is 0.777777

Then to compare them you see which is smaller or bigger.

0.77777  is bigger than 0.625 so we know that 0.77777777 which was the 7:9 ratio is the bigger one.

Steps:-

First rewriteThen convert to fractionsThen divide both

\(\\ \rm\rightarrowtail 5:8::7;9\)

\(\\ \rm\rightarrowtail 5/8:7/9\)

\(\\ \rm\rightarrowtail \dfrac{5(9)}{8(9)}:\dfrac{7(8)}{9(8)}\)

\(\\ \rm\rightarrowtail \dfrac{45}{72}:\dfrac{56}{72}\)

\(\\ \rm\rightarrowtail \dfrac{45}{56}\)

Second one is bigger

find the absolute maxima and minima for f(x) on the interval [a, b]. f(x) = x3 x2 − x 8, [−2, 0]

Answers

To find the absolute maxima and minima of the function \(f(x) = x^3 - x^2 - x + 8\) on the interval [-2, 0], we need to evaluate the function at its critical points and endpoints within the interval.

Critical Points:

To find the critical points, we take the derivative of f(x) and set it equal to zero:

\(f'(x) = 3x^2 - 2x - 1\)

Setting f'(x) = 0 and solving for x, we find:

\(3x^2 - 2x - 1 = 0\)

This quadratic equation can be factored as:

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

So the critical points are x = -1/3 and x = 1.

Endpoints:

We need to evaluate the function at the endpoints of the interval, which are x = -2 and x = 0.

Evaluating the function:

Now we evaluate f(x) at the critical points and endpoints:

\(f(-2) = (-2)^3 - (-2)^2 - (-2) + 8 = -2 - 4 + 2 + 8 = 4\\\\f\left(-\frac{1}{3}\right) = \left(-\frac{1}{3}\right)^3 - \left(-\frac{1}{3}\right)^2 - \left(-\frac{1}{3}\right) + 8 = -\frac{1}{27} - \frac{1}{9} + \frac{1}{3} + 8 \approx 7.407\\\\f(0) = 0^3 - 0^2 - 0 + 8 = 8\\\\f(1) = 1^3 - 1^2 - 1 + 8 = 7\)

Finding the absolute maxima and minima:

Comparing the values of f(x) at the critical points and endpoints, we find:

Absolute maximum: \(f\left(-\frac{1}{3}\right) \approx 7.407\)

Absolute minimum: f(-2) = 4

Therefore, the absolute maximum value of f(x) on the interval [-2, 0] is approximately 7.407, and the absolute minimum value is 4.

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Please answer correctly !!!! Will mark brainliest !!!!!!!!!!

Please answer correctly !!!! Will mark brainliest !!!!!!!!!!

Answers

Answer:

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

Step-by-step explanation:

So just divide the areas by the length:

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

And that is your width.

Answer:

iddk

Step-by-step explanation:

in the garden, the ratio of roses to daises is 1:3. there are 8 roses. How many daises are there

Answers

There would be 24 roses.

8x3=24

I need help on this pls​

I need help on this pls

Answers

Answer:

Elephants are worth 4 the other one is worth 1.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

we have 2 elephants, and 4 horses are equal to 12 horses

First, lets form an equation. Let the elephants be e and the horses be h

2e + 4h = 12h

The horses are a variable that's equal on both sides, so we can remove them. Do this by subtracting 4h from both sides of the equals sign.

2e = 8h

Hence, 2 elephants are as strong as 8 horses. But, this equation is not simplified, the question asks for 1 elephant, so we divide by 2 on both sides of the equals sign.

hence, e = 4h

One elephant is as strong as 4 horses.

solve for x and show your work
-1/2 x<-12

Answers

Answer:

Your input: find x in the equation −x2−12=0

x=−24

Step-by-step explanation:

x>24
You can multiply both sides by -2 and then flip the inequality sign -2(-1/2)x>-2(-12)
2•1/2x>-2(-12) which one be x>-2(-12) then x>2•12 and in the end you’ll end up with x>24

I need help with step 3

I need help with step 3

Answers

\(f(x) = ( \frac{1}{4} ) {}^{x} \)

\(f(0) = ( \frac{1}{4} ) {}^{0} \)

\(f(0) = 1\)

\(f(1) = ( \frac{1}{4} ) {}^{1} \)

\(f(1) = \frac{1}{4} \)

\(f(2) = ( \frac{1}{4} ) {}^{2} \)

\(f(2) = \frac{1}{16} \)

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List the key features of the quadratic function y = -x^(2) + 4x - 3

A) x-intercepts: (1,0) and (3,0), y-intercept: (0,3), vertex: (2,–1)

B) x-intercepts: (–1,0) and (–3,0), y-intercept: (0,–3), vertex: (2,–1)

C) x-intercepts: (1,0) and (3,0), y-intercept: (0,–3), vertex: (–1,2)

D) x-intercepts: (1,0) and (3,0), y-intercept: (0,–3), vertex: (2,1)

Answers

The key features of the quadratic function y = -x² + 4x - 3 include the following: D) x-intercepts: (1, 0) and (3, 0), y-intercept: (0, –3), vertex: (2, 1).

What is y-intercept?

In Mathematics, the y-intercept of any graph such as a quadratic function, generally occur at the point where the value of "x" is equal to zero (x = 0).

When x = 0, the y-intercept is given by;

y = -x² + 4x - 3

y = -0² + 4(0) - 3

y = -3

Therefore, the y-intercept of this quadratic function y = -x² + 4x - 3 is given by the ordered pair (0, -3).

What is the x-intercept?

In Mathematics, the x-intercept can be defined as the point at which the graph of a quadratic function crosses the x-coordinate and the value of "y" is equal to zero (0).

By critically observing the graph of this quadratic function y = -x² + 4x - 3, the x-intercept include the following:

Ordered pair = (1, 0).Ordered pair = (3, 0).

In conclusion, the vertex of this quadratic function y = -x² + 4x - 3 is (2, 1).

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List the key features of the quadratic function y = -x^(2) + 4x - 3A) x-intercepts: (1,0) and (3,0),

HELP! I'LL GIVE BRAINLIEST ! ! ! ! ! ! ! !

Select all of the quadrants that the parabola whose equation is y = √x - 4 (principal square root) occupies.
a. IV b. III c. II d. I

Answers

Quadrants I and IV

When we graph y^2 = x - 4, we see that it is on the x axis, and goes up into Quadrant I, and down into Quadrant IV

Help pls I need the answer fast and today

Help pls I need the answer fast and today

Answers

Answer:

B.

Step-by-step explanation:

0.264172 is how many gallons are in one liter soooo yeah, the estimation of that is 0.26/1 which is B

Use context to determine the meaning of the word unabated as it is used in Narrative of the Life of Frederick Douglass, An American Slave. Write your definition of unabated here and tell how you found it.

Answers

The wοrd "unabated" is used in Narrative οf the Life οf Frederick Dοuglass, An American Slave.

The wοrd "unabated" in this cοntext can be interpreted tο mean "cοntinuing withοut any reductiοn in intensity οr strength." "That cheerful eye, under the influence οf slavery, swοre red with rage; that vice, made all οf sweet accοutrement, changed tο a οne οf harsh and hοrrid discοrd; and that angelic face gave way tο that οf a demοn."

The authοr is describing hοw the slavehοlder's pοwer οver the slaves cοrrupts the wοman's character, turning her previοusly kind demeanοur intο οne οf rage and discοntent. The wοrd "unabated" emphasises hοw persistent and unyielding this transfοrmatiοn is and hοw unlikely it is that it will diminish.

By examining the surrοunding text and cοmmοn usage, I was able tο determine the definitiοn οf the wοrd "unabated." In this sentence, the authοr's descriptiοn οf the slavehοlder's transfοrmatiοn is well-suited tο the wοrd "unabated," which is generally used tο describe sοmething that cοntinues withοut any lοss οf intensity οr strength.

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A floor which measures 15m x 8m is to be laid with tiles measuring 50cm by 25cm. Find the number of tiles required.

Answers

Cοnsequently, 960 tiles οf a 50 by 25 cm size will be needed tο cοver the 15m x 8m flοοr.

What is an example οf a measure ?

Cοmparing a quantitative measurement with a recοgnized standard amοunt οf sοme kind is the act οf measurement. Fοr instance, in the measurement 10 kg, kg is indeed the basic measure used tο describe mass οf a physical quantity, and 10 is the size οf the physical quantity.

Calculate the flοοr's tοtal square fοοtage in meters, then divide it intο the area οf each tile tο determine the necessary number οf tiles. The measurements must first be changed tο a cοmparable unit. By dividing by 100, we may cοnvert centimeters tο meters:

15m = 1500cm

8m = 800cm

In square meters, the flοοr space is as fοllοws:

1500cm x 800cm = 1200000cm² = 120m²

The area οf the each tiles in square meters must nοw be determined. The size οf each tile, which is 50 by 25 centimetres, is as fοllοws:

50cm x 25cm = 1250cm² = 0.125m²

Lastly, by dividing the entire flοοr area even by area οf each tile, we can determine the necessary number οf tiles:

120m² / 0.125m² = 960 tiles

The flοοr will therefοre need 960 tiles that are 50 cm by 25 cm in size tο cοver its 15 m × 8 m surface.

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If you were constructing a 99% confidence interval of the population mean based on a sample of n=30 where the standard deviation of the sample S=0.05, the critical value of t will be 2.7564 2.4922 2.7969

Answers

The critical value of t for constructing a 99% confidence interval with a sample size of 30 and a sample standard deviation of 0.05 is 2.7564.

A confidence interval is a range of values within which the population parameter is estimated to lie with a certain level of confidence. In this case, we are constructing a 99% confidence interval for the population mean. The critical value of t is used to determine the width of the confidence interval.

The formula for calculating the confidence interval for the population mean is:

Confidence interval = sample mean ± (critical value) * (standard deviation of the sample / square root of the sample size)

Given that the sample size is 30 (n = 30) and the standard deviation of the sample is 0.05 (S = 0.05), we need to find the critical value of t for a 99% confidence level. The critical value of t depends on the desired confidence level and the degrees of freedom, which is equal to n - 1 in this case (30 - 1 = 29). Looking up the critical value in a t-table or using statistical software, we find that the critical value of t for a 99% confidence level with 29 degrees of freedom is approximately 2.7564.

Therefore, the 99% confidence interval for the population mean would be calculated as follows: sample mean ± (2.7564) * (0.05 / √30). The final result would be a range of values within which we can be 99% confident that the true population mean lies.

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an employee makes $18.00 per hour. given that there are 52 weeks in a year and assuming a 40-hour work week, calculate the employee's yearly salary.

Answers

The employee's yearly salary is calculated as $37,440 using the arithmetic operations.  

The employee earns $18 per hour and works 40 hours per week. To calculate the weekly salary, we multiply the hourly wage by the number of hours worked:

Weekly salary = Hourly wage × Hours worked per week

Weekly salary = $18/hour × 40 hours/week = $720

Next, to calculate the yearly salary, we use the multiplication operation the weekly salary by the number of weeks in a year:

Yearly salary = Weekly salary × Weeks in a year

Yearly salary = $720/week × 52 weeks/year = $37,440

Therefore, the employee's yearly salary is $37,440. This calculation assumes a 40-hour work week and 52 weeks in a year. It's important to note that this calculation does not account for overtime pay or any other additional benefits or deductions that may affect the employee's total annual income.

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What is the complete factorization of the polynomial below?
x^3- 2x²+x-2
A. (x-2)(x + 1)(x - 1)
B. (x + 2)(x + 1)(x - 1)
C. (x + 2)(x - 1)(x - 1)
D. (x-2)(x - 1)(x - 1)

Answers

Answer:

Let's start by rearranging this polynomial.

x^3 - 2x^2 + x - 2

x^3 + x - 2x^2 - 2

Now, factor out the common terms in the first two terms, and the second t wo terms. So we have: x(x^2 + 1) - 2(x^2 +1)

Apply the distributive property, and you have: (x-2)(x^2+1), which can't be factored further.

There's definitely something wrong with the answer choices here, or the problem itself.

Hopefully this helps!

The complete factorization of the polynomial is,

⇒ (x + i) (x - i) (x - 2)

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The polynomial is,

⇒ x³ - 2x² + x - 2

Now, We can factor the polynomials as;

The polynomial is,

⇒ x³ - 2x² + x - 2

⇒ x² (x - 2) + 1 (x - 2)

⇒ (x² + 1) (x - 2)

⇒ (x + i) (x - i) (x - 2)

Therefore, The complete factorization of the polynomial is,

⇒ (x + i) (x - i) (x - 2)

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WILL MARK BRAINLIEST IF EXPLAINED! G with FA and FE tangent at A and E.

Find mADB Find mABD Find mAFE Find mACE

PLEASE EXPLAIN HOW YOU GOT YOUR ANSWER! :)

WILL MARK BRAINLIEST IF EXPLAINED! G with FA and FE tangent at A and E.Find mADB Find mABD Find mAFE

Answers

The first one is 44 and the second one is 49

Answer:

angle ADB = 41 degrees

angle ABD = 90 degrees

angle AFE = 70 degrees

angle ACE = 31 degrees

Step-by-step explanation:

angle ADB = 41 degrees because minor arc AB = 82 degrees and it's inscribed angle is 1/2 of it's arc.

angle ABD = 90 degrees because arc AED = 180 degrees and inscribed angles are equal to 1/2 of the arc.

arc ABD = 180

arc ABE = arc ABD + 70 degrees = 250 degrees

minor arc AE = 360 degrees-250 degrees = 110 degrees

angle AFE = 1/2 (250-110) = 70 degrees

angle ACE = 1/2(110-48) = 31 degrees

Please help me ASAP!!

Please help me ASAP!!

Answers

Answer:

x=30

Step-by-step explanation:

So we know that a shape with 4 angles equal 360 degrees and this has 4 angles. Since we know that 4x is one and 2x is one We cna use the vertical angles to find the other two. Since 4x is opposite of an unknown side it is also 4x becuase vertical angles are equal becuase they are opposite sides of each other. Same thing with 2x

Now add them all up

4x+4x+2x+2x which will equal 12x

now 12x=360

x=30

Jessie walked 4 miles. How many feet did she walk?

Answers

Answer:

?

Step-by-step explanation:

Answer: 21120

Step-by-step explanation: look up 4 miles to feet

If each exterior angle of a regular polygon is 30°, find how many sides the polygon has & the measure of an
interior angle of that polygon.

Answers

Answer:

12 sides and measure of each interior angle is 150...

Answer:

Step-by-step explanation:

Number of sides = 360°/30° = 12

Interior angle is the supplement of exterior angle = 180°-30° = 150°

Felipe makes a bracelet with 10 beads, 3 blue, 2 green, and 5 red. Which statement about Felipe's bracelet is true? * 1 point The ratio of green beads to red beads is 5 to 2. The ratio of green beads to total beads is 2 to 10. For every 3 blue beads, there are 2 red beads. For every 5 red beads, there are 5 total beads on the bracelet.

Answers

Answer:green to total 2/10

Step-by-step explanation:

The minute hand on a clock tower is 6 feet long. At 10 minutes after the hour, the tip
of the minute hand is 55 feet above the ground. How high above the ground is the
center of the clock face? Explain how you know.

Answers

Answer: 12:55 is the answer

Step-by-step explanation:

dont delete this brainly

The height of the center of the clock above the ground is 52 feet such that the length of the minute hand of the clock is 6 feet and at 10 minutes after the hour, the tip of the minute hand is 55 feet above the ground.

Sine trigonometric function

The trigonometric function, \(sin\theta=\dfrac{perpendicular}{hypotenuse}\) .

How to determine the length of the side using trigonometric function?

From the given information, the following pictorial representation can be made.

The distance between the centre of the clock and the the point of the minute hand 10 minutes after the hour is-

\(x=6sin30\\x=3\text{ft}\)

Now, from the figure,

The height of the center of the clock above the ground is-

d=6+(55-3-6)

=52 ft

Thus, the height of the center of the clock above the ground is \(52\text{ft}\)

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The minute hand on a clock tower is 6 feet long. At 10 minutes after the hour, the tipof the minute hand

2) find the equations of the straight lines given the slope m and one point. be prepared to show your work on paper to your teacher. m= -2 point (-1,-2) x1= _______ y1=_____ equation: _________________

Answers

The equation of the straight line is y = -2x - 4, the value of x₁ is -1 and the value of y₁ is -2.

To find the equation of a straight line given its slope and one point, we use the point-slope form of the equation:

−y − y₁​ = m(x−x₁ )

where m is the slope of the line, and (x₁, y₁) is the given point.

In this case, m = -2 and the point is (-1, -2). So we have:

x₁ = -1

y₁ = -2

m = -2

Substituting these values into the point-slope form, we get:

y−(−2)=−2(x−(−1))

Simplifying and rearranging terms, we get the equation of the line:

y + 2 = -2x - 2

y = -2x - 4

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can you apply the properties of rational exponents to an example?

Answers

We can simplify \((16x^4)^(-1/2) to 1/(4x^2)\) using the properties of rational exponents.

Certainly! Here's an example:

Simplify the expression: \((16x^4)^(-1/2)\)

We can apply the property of rational exponents which states that \((a^m)^n = a^(m*n)\). Using this property, we get:

\((16x^4)^(-1/2) = 16^(-1/2) * (x^4)^(-1/2)\)

Next, we can simplify \(16^(-1/2)\) using the rule that \(a^(-n) = 1/a^n\):

\(16^(-1/2) = 1/16^(1/2) = 1/4\)

Similarly, we can simplify \((x^4)^(-1/2)\) using the rule that \((a^m)^n = a^(m*n)\):

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

Substituting these simplifications back into the original expression, we get:

\((16x^4)^(-1/2) = 1/4 * x^(-2) = 1/(4x^2)\)

Therefore, the simplified expression is \(1/(4x^2).\)

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7.
Which of the following is a prime number between 80 and 90?
OA. 85
B.
86
O C. 81
OD
83
HELP!!

Answers

Answer:

D) 83 is the answer. this is because it doest divide more then 2wice like the rule

Answer:

D TRUST ME

Step-by-step explanation:

How do you find the center of enlargement of a triangle?

Answers

To find the center of enlargement, draw line segments between corresponding vertices of pre-image and image triangles, the point where they intersect is the center of enlargement, check that all the line segments intersect at the same point, or use the coordinates of the triangle and the scale factor.

You can follow these steps:

Identify the pre-image triangle. This is the original triangle that will be enlarged.Identify the image triangle. This is the enlarged version of the pre-image triangle.Draw a line segment between the corresponding vertices of the pre-image and image triangles.The point where these line segments intersect is the center of enlargement.To check that you have the correct center of enlargement, you can draw a line segment between any other corresponding vertices of the pre-image and image triangles and check that they intersect at the same point.

Another way to find the center of enlargement is to use the coordinates of the triangle and the scale factor. The center of enlargement is the point that remains the same distance from all points on the image and the pre-image. The center of enlargement is the point that the coordinates of the image triangle obtained from the coordinates of the pre-image triangle by multiplying each coordinate by the same scale factor greater than 1.

It's important to note that, the center of enlargement is the same as the center of dilation.

In both ways, it's important to have the pre-image triangle and the image triangle to find the center of enlargement.

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Christian had brochures printed for a new business venture. Christian

originally ordered 4 boxes of black-and-white brochures and 3 boxes of

color brochures, which cost a total of $134. After those ran out, Christian

spent $120 on 3 boxes of black-and-white brochures and 3 boxes of color

brochures. Which system represents this situation?

Answers

The following set of equations can be used to represent this situation:

4b + 3c = 134

3b + 3c = 120

In this approach, b stands for the price per box of monochrome brochures, whereas c stands for the price per box of color  brochures.

Christian ordered two batches of brochures; the first equation shows the cost of the first batch, and the second equation shows the cost of the second batch.

The replacement approach can be used to solve this system. By focusing on just one side of the first equation, we may find the value of b:

4b = 134 - 3c

The second equation can therefore be changed to use this expression for b in place of b :

3(134 - 3c) + 3c = 120

This equation can be written as:

402 - 9c + 3c = 120

Combining related concepts gives us:

-6c = -282

When we multiply both sides by -6, we get:

c = 47

The value of b can then be determined by reintroducing this value into the first equation as follows:

4b = 134 - 3(47) (47)

If we simplify, we get:

4b = 134 - 141

This equation can be written as:

4b = -7

When we multiply both sides by 4, we get:

b = -1.75

As a result, the price each box of monochrome brochures is $-1.75, whereas the price per box of color brochures is $47.

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Work with a partner. Supercooling is the process of lowering the temperature
of a liquid or a gas below its freezing point without it becoming a solid. Water
can be supercooled to 86°F below its normal freezing point (32°F) and still
not freeze.

a. Let x represent the temperature of water. Which inequality represents the
temperature at which water can be a liquid or a gas? Explain your reasoning.

Answers

Even when water is supercooled to 86 degrees Fahrenheit below its normal freezing point (32 degrees Fahrenheit), it will not freeze. Therefore, x-32≥-86

Define supercooling.

The process of lowering a liquid or gas's temperature below its melting point without causing it to solidify is known as supercooling, sometimes known as undercooling. It accomplishes this in the absence of a seed crystal or nucleus around which a crystal structure can form.

Let temperature be x

The temperature at which water turns into a liquid or a gas is represented by inequality is x-32≥-86

The reason is that as water will not freeze even when supercooled to 86°F below its typical freezing point (32°F).

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What is the solution to the equation? ​

What is the solution to the equation?

Answers

X=63


Hope this helps you ☺️

Answer:

C. x = 63

Step-by-step explanation:

X ÷ 3 = 21 is the same as 3 × 21 which is 63.

(EASY POINTS)The accompanying table shows the value of a car over time that was purchased for 18400 dollars, where x is years and y is the value of the car in dollars. Write an exponential regression equation for this set of data, rounding all coefficients to the nearest hundredth. Using this equation, determine the value of the car, to the nearest cent, after 9 years.

(EASY POINTS)The accompanying table shows the value of a car over time that was purchased for 18400 dollars,

Answers

i. The exponential regression equation for this data is

y ≈ 35125.61(0.8276)^x

ii. The value of the car after 9 years is approximately $3,444.20.

The exponential regression

To find an exponential regression equation for this data, we can use the form of the equation y = ab^x, where y is the value of the car in dollars, x is the number of years since it was purchased, and a and b are coefficients to be determined.

Using the given data points, we can set up a system of equations:

a b^0 = 18400 (the initial value of the car)

a b^1 = 14593

a b^2 = 12503

a b^3 = 9934

a b^4 = 8490

a b^5 = 7613

a b^6 = 6348

Dividing the second equation by the first, the third by the second, and so on, we get:

b = 14593/18400 = 0.7938 (rounded to four decimal places)

b = 12503/14593 = 0.8554

b = 9934/12503 = 0.7943

b = 8490/9934 = 0.8545

b = 7613/8490 = 0.8967

b = 6348/7613 = 0.8346

Taking the average of these values for b, we get b ≈ 0.8276.

Substituting this value of b into any of the equations above, we can solve for a:

a ≈ 18400/b^0 ≈ 18400

a ≈ 14593/b^1 ≈ 25395.22

a ≈ 12503/b^2 ≈ 31298.57

a ≈ 9934/b^3 ≈ 36475.19

a ≈ 8490/b^4 ≈ 42344.76

a ≈ 7613/b^5 ≈ 48022.39

a ≈ 6348/b^6 ≈ 58468.11

Taking the average of these values for a, we get a ≈ 35125.61.

Therefore, the exponential regression equation for this data is:

y ≈ 35125.61(0.8276)^x

To determine the value of the car after 9 years, we can simply plug in x = 9 into this equation:

y ≈ 35125.61(0.8276)^9 ≈ 3444.20

Therefore, the value of the car after 9 years is approximately $3,444.20.

Learn more on exponential regression here https://brainly.com/question/9302810

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