solving by elimination
2x+8y=6
5x+20y=15
​

A rational equation is defined as the quotient of two polynomials, with the denominator not being zero. It is a type of algebraic expression that involves variables and rational functions with rational exponents.

The error in the given rational equation is that it's not allowed to cancel out the x-2 and X+2 terms, as they are in the denominators. It is because of the fact that it may make the denominator zero, which would result in undefined expressions. Therefore, we need to find the least common multiple (LCM) of the denominators and then convert the equation into equivalent forms with the same denominator.B):

Correction of the error1-2/x-2 = x+1/X+2Given rational equation can be re-written as:((1 - 2)/(x - 2)) = ((x + 1)/(X + 2))The LCM of x - 2 and X + 2 is (x - 2) (X + 2).Multiplying the numerator and denominator of the left side by (X + 2) and the numerator and denominator of the right side by (x - 2) we get,(1 - 2)(X + 2) = (x + 1) (x - 2)Now simplify the equation:2X - 3x = -3The given rational equation becomes 2X - 3x = -3 after correction.Note: You should always double-check if the obtained solution satisfies the initial equation.

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The possible lengths( in whole elevation) for the third side is

9 elevation< x< 45 elevation, i.e in between 9 and 45 elevation.

 For the below question, we've a rule from the properties of triangle, the sum of the length of any two  sides of the triangle must be lesser than the length of the third side.

Hence

She has two sides of length 18 elevation and 27 elevation

Let the third side = x

Hence

a) 18 27> x

45> x

b) 18 x> 27

x> 27- 18

x> 9

thus, the possible lengths( in whole elevation) for the third side is

elevation< x< 45 elevation

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If there is no difference between the distributions of scores in two groups, the effect size will be equal to zero.Effect size is a measure used to quantify magnitude of a difference or relationship between variables.

It provides information about the practical significance or importance of an observed effect. In the context of comparing distributions of scores between two groups, a non-zero effect size indicates that there is a difference between the groups.

However, when there is no difference between the distributions of scores in the two groups, it implies that the effect size is zero. This means that the observed effect or relationship is negligible, indicating that the groups are essentially similar and there is no meaningful distinction between them.

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Answer:  the value of f′′′(4) is 3/256.

Step-by-step explanation:

Given the third-degree Taylor polynomial:

f(x) = (x−4)³/512 − (x−4)²/64 + (x−4)⁴/2

To find the value of f′′′(4), we need to differentiate the polynomial three times and evaluate it at x = 4.

First derivative:

f'(x) = 3(x−4)²/512 − 2(x−4)/64 + 4(x−4)³/2

Second derivative:

f''(x) = 6(x−4)/512 − 2/64 + 12(x−4)²/2

Third derivative:

f'''(x) = 6/512 + 24(x−4)/2

Now, substitute x = 4 into f'''(x):

f'''(4) = 6/512 + 24(4−4)/2

= 6/512 + 0

= 6/512

= 3/256

Therefore, the value of f′′′(4) is 3/256.

The circle intersects the x-axis at x = -17 and x = 17 and y-axis at y = -17 and y = 17.

To determine where the circle intersects the x-axis and y-axis when the point (8,15) lies on a circle centered at (0,0), we can use the equation of a circle.

The equation of a circle with center (h, k) and radius r is given by:

\((x-h)^{2}\) + \((y-k)^{2}\) = \(r^{2}\)

In this case, the center of the circle is (0,0), so the equation becomes:

\(x^{2}\) + \(y^{2}\) = \(r^{2}\)

Substituting the point (8,15) into the equation, we have:

\(8^{2}\) + \(15^{2}\) =  \(r^{2}\)

64 + 225 =  \(r^{2}\)

289 =  \(r^{2}\)

Taking the square root of both sides, we find:

r = 17

Therefore, the equation of the circle is:

\(x^{2}\)  +  \(y^{2}\)  = \(17^{2}\)

Now, to determine where the circle intersects the x-axis, we set y = 0 in the equation:

\(x^{2}\)  + \(0^{2}\) = \(17^{2}\)

\(x^{2}\)  = 289

Taking the square root, we find:

x = ±17

So, the circle intersects the x-axis at x = -17 and x = 17.

To determine where the circle intersects the y-axis, we set x = 0 in the equation:

\(0^{2}\) +  \(y^{2}\)  = \(17^{2}\)

\(y^{2}\)  = 289

Taking the square root, we find:

y = ±17

Thus, the circle intersects the y-axis at y = -17 and y = 17.

By substituting the point (8,15) into the equation of the circle, we were able to determine its radius. Then, by setting y = 0 and x = 0 in the equation, we found the points where the circle intersects the x-axis and y-axis.

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The area of the rectangle is 200 square centimeters

The area of a rectangle can be found by multiplying its length and width. In this case, the width is given as w and the length is given as 2w.

Therefore, the area of the rectangle can be found using the expression 2w^2.

If the width of the rectangle is 10 centimeters, we can substitute this value into the expression for the area to find the area in square centimeters.

Area = 2w^2

= 2(10)^2

= 2(100)

= 200 square centimeters

Therefore, the area of the rectangle is 200 square centimeters

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Using the concept of percentages the total earning of Cara can be found to be $4200.

Percentage is a number expressed as a fraction of 100. The % sign means to divide the number by 100.

Cara's earning = commission + basic salary

basic salary = $1800 (this is constant)

commission = 6% of $40000

= (6/100)*40000

= $2400

Cara's earning = 1800 + 2400

Hence, her earning is $4200

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We can  rewrite (z ≤ −1.75) in order to  4%.

We have given that  (z ≤ −1.75).

We have to use the Normal Distribution is symmetrical

The normal distribution is symmetric and has a skewness of zero.

\(P(z \leq -1.75)\)

\(P(z > > 1.75)\)

\(1 - P(z \leq 1.75)\)

\(1 - 0.9599\)

\(0.04001 \times 100=4.001 \%\)

That is nothing but the 4%

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Answer:

Step-by-step explanation:

Answer:

n^2 + 3.

Step-by-step explanation:

4 7 12 19

Differences are 3 5 7   so this a quadratic sequence.

2nd difference = 2 2

So the first part of the expression is n^2

Terms:  4  7  12  19

n^2       1    4   9  16

Difference = 3 3 3 3 3

So the answer is n^2 + 3.

Answer:

11 shelves

Step-by-step explanation:

96/9= 10.6666

since you have more books you cannot round down you have to round up. so you need 11 shelves

Answer:

11

Step-by-step explanation:

96/9=10.6666

than round up

hope this helps

Answer: 1,2,3,4

Step-by-step explanation:

The domain consists of every x value

Answer:

there are 575 seats left empty

Step-by-step explanation:

First you must subtract 25 from 600 because the teachers are using only 25 seats leaving 575 seats left to sit on for students

Using the factor theorem, it is found that the polynomial is:

\(f(x) = x^3 - 2x^2 - 3x + 6\)

Given by the first option

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

Given a polynomial f(x), this polynomial has roots \(x_{1}, x_{2}, x_{n}\) using the factor theorem it can be written as: \(a(x - x_{1})*(x - x_{2})*...*(x-x_n)\), in which a is the leading coefficient.

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

In this question:

Thus:

\(f(x) = (x - 2)(x - \sqrt{3})(x + \sqrt{3})\)

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

\(f(x) = x^3 -2x^2 - 3x + 6\)

Which is the polynomial.

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Answer: inscribed angle

Answer:

the above answer is correct

Step-by-step explanation:

I got it right on the test

Answer:

A = (1/4)πr^2

where r is the radius of the circle.

If the side and base mentioned in the question refer to the radius of the circle, then the area of the quadrant can be calculated as follows:

Given, radius (r) = 8 cm

The area of the quadrant = (1/4)πr^2

= (1/4)π(8)^2

= 16π square cm

= 50.27 square cm

The particular solution to the given differential equation dy/dx = sin(x^2) with the initial condition y(√π) = 4 is (B) y = -cos(x^2)/(2x) + 4 - 1/(2√π).

To find the particular solution, we integrate the given function sin(x^2) with respect to x. However, since there is no direct antiderivative for sin(x^2), we cannot find a simple closed form expression for the integral. Hence, we need to use numerical or approximative methods to evaluate the integral.

None of the given options (A), (C), or (D) provide a correct representation of the particular solution. Option (B) includes the term -cos(x^2)/(2x), which is a common approximation method for the integral of sin(x^2). The other terms in (B) account for the initial condition y(√π) = 4. Therefore, (B) y = -cos(x^2)/(2x) + 4 - 1/(2√π) is the correct particular solution to the differential equation with the given initial condition.

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Answer:

11

Step-by-step explanation:

Let the number be x,

2x+4 = 3x-7

Collect like terms

2x-3x= -4-7

-x =. -11

Multiply both sides by -1

x. =. 11

Oh and I think you made a typo and missed the 2, " if you multiply the number by 2 to end at 4..........."

Hope This Helps :)

Named constants are used rather than numbers for token codes because they make the code more readable and easier to understand.

Constants are also used to avoid any errors that may occur if a number is mistyped. By using named constants, it is easier to update the value of the constant if it needs to be changed in the future. Additionally, using named constants can help prevent mistakes, such as accidentally using the wrong number in a calculation. Overall, named constants provide a more organized and efficient way of coding.

For example, consider the following code:

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\(x^{\frac{8}{15} }\) is the value of yz when x=y⁵=z³  and x is positive.

Two or more expressions with an Equal sign is called as Equation.

Since x=y⁵=z³

Solve for yz as follows:

we can take the fifth root of x to get y, and the cube root of x to get z:

We can solve for yz as follows:

\(y=x^{\frac{1}{5} }\)

\(z=x^{\frac{1}{3} }\)

Now yz=\(x^{\frac{1}{5} }.x^{\frac{1}{3} }\)

=\(x^{\frac{8}{15} }\)

Hence, option A is correct, if  x=y⁵=z³  then yz is \(x^{\frac{8}{15} }\)

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Ratio analysis can be made more meaningful in all the following ways except by focusing more on long-term solvency than on short-term solvency.

Ratio analysis is a mathematical technique for analyzing a company's financial documents, such as the balance sheet and income statement, to gather knowledge about its liquidity, operational effectiveness, and profitability. Fundamental equity research is built on ratio analysis.

In order to get insights into profitability, liquidity, operational effectiveness, and solvency, ratio analysis examines line-item data from a company's financial statements.

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The full question:

ratio analysis can be made more meaningful in all the following ways except by?

Answer: A) 1/2

Step-by-step explanation:

Answer:

If you flip a coin three times in the air, what is the probability that tails lands up all three times?

Step-by-step explanation:

1/2

The formula for the surface area of the box, in terms of the length of one side of the square base (s), is A = s^2 + 4s^2 = 5s^2.

The derivative of the surface area function with respect to s, denoted as dA/ds, gives us the rate of change of the surface area with respect to the length of one side of the base.

1. The surface area of the box consists of the area of the square base and the four equal sides. The area of the square base is s^2, and each side has a length of s. Therefore, the total surface area is given by A = s^2 + 4s^2 = 5s^2.

2. To find the derivative of the surface area function, we differentiate 5s^2 with respect to s using the power rule of differentiation. The power rule states that if we have a function f(x) = cx^n, then the derivative is f'(x) = cnx^(n-1).

  Applying the power rule, we have dA/ds = d(5s^2)/ds = 10s.

3. The derivative, dA/ds = 10s, represents the rate of change of the surface area with respect to the length of one side of the square base. This means that for every unit increase in s, the surface area increases by 10s units.

  The derivative does not provide information about minimizing the amount of material used. To find the dimensions of the box that minimize the amount of material used, we need to set up an optimization problem and solve for the critical points. This involves setting the derivative equal to zero and finding the values of s that satisfy this equation. However, since the problem statement does not provide a specific volume constraint or objective function, we cannot proceed with the optimization process.

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The overall DPMO for the boards would be 4750.

Boardwalk Electronics manufactures 200,000 circuit boards per month. A random sample of 4,000 boards is inspected every week for seven characteristics. During a recent week, seven defects were found for one characteristic, and two defects each were found for the other six characteristics. If these inspections produced defect counts that were representative of the population, the dpmo's for the individual characteristics and what is the overall dpmo for the boards would be as follows:To calculate the DPMO, the formula used is:DPMO = (Number of defects / Number of Opportunities) × 1,000,000For Characteristic

1:Number of defects = 7Number of opportunities = 4000DPMO = (7/4000) × 1,000,000= 1750For Characteristic 2:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500For Characteristic 3:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500For Characteristic 4:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500For Characteristic 5:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500For Characteristic 6:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500For Characteristic 7:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500The overall DPMO for the boards would be the sum of the DPMO of all characteristics which would be 1750 + 500 + 500 + 500 + 500 + 500 + 500 = 4750.

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Answer: 3

Step-by-step explanation:

Divide the x numbers by 3 to then get the y numbers

Example: 3 divided by 1 is 3, 6 divided by 2 is 3, and it goes on!

once again the final answer is 3

hope this helps!

The answer is 6 divided by f

sannie =w=

If the beginning inventory is worth $838 and 40 units are purchased for $14.05 each, the new total cost of goods available for sale is $1,400.

The cost of goods available for sale is the sum of the beginning inventory and the current period's purchases.

When the ending inventory is subtracted from the cost of goods available for sale, the result is the cost of goods sold.

The beginning inventory of 60 units at $13.96 ≈ $838

Purchases of 40 units at $14.05 each = $562

Cost of goods available for sale = $1,400 ($838 + $562)

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Two other examples of linear relationships are changes of units and finding the total cost for buying a given item x times.

Two examples of linear relationships that are useful are:

Changes of units:

These ones are used to change between units that measure the same thing. For example, between kilometers and meters.

We know that:

1km = 1000m

So if we have a distance in kilometers x, the distance in meters y is given by:

y = 1000*x

This is a linear relationship.

Another example can be for costs, if we know that a single item costs a given quantity, let's say "a", then if we buy x of these items the total cost will be:

y = a*x

This is a linear relationship.

So linear relationships appear a lot in our life, and is really important to learn how to work with them.

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Answer:

Slope is 20 (rise/run)

y = 20x

(no y-intercept)

Step-by-step explanation:

Hope this helps. Pls give brainliest.

Answer:

Slope is 20

Step-by-step explanation:

The formula for slope is Y2-Y1 divided by X2-X1

Hope this helped :)

Answer:

18 degrees Fahrenheit

Step-by-step explanation:

Given

\(F = 32 + 1.8C\)

Required

Determine change in F if change in C is 10

A 10 degrees change in C is represented as: C + 10

The equivalent change in F is F + x, where x represents the change in F

So: If \(F = 32 + 1.8C\)

Then

\(F + x = 32 + 1.8(C + 10)\)

Open brackets

\(F + x = 32 + 1.8C + 18\)

Collect Like Terms

\(F + x = 32 + 18+ 1.8C\)

\(F + x = 50+ 1.8C\)

Make x the subject

\(x = 50+ 1.8C - F\)

Recall that: \(F = 32 + 1.8C\)

So:

\(x = 50+ 1.8C - F\) becomes

\(x = 50 + 1.8C - (32 + 1.8C)\)

Open Bracket

\(x = 50 + 1.8C - 32 - 1.8C\)

\(x = 50 - 32+ 1.8C - 1.8C\)

\(x = 50 - 32\)

\(x = 18\)

Hence:

A change of 10 degrees Celsius will bring a change of 18 degrees Fahrenheit

Answer:

18 degrees Fahrenheit

Step-by-step explanation:

I got it right on Khan Academy