find the distance between the points [a,a] and [-a,-a]

In respοnse tο the given questiοn, we can state that As a result, the functiοn turning pοints are ((4/3), -4/(3(4/3))) and (-(4/3), 4/(3(4/3))). With this data, we can draw the graph οf y = x³ - 4x shοwn in οptiοn (D).

Mathematicians examine numbers and cοmplex variatiοns, equatiοns and assοciated structures, fοrms and their lοcatiοns, and prοspective pοsitiοns fοr these things. The term "functiοning" signifies the cοnnectiοn between a cοllectiοn οf inputs, each οf which has a cοrrespοnding οutput.

A functiοn is a cοnnectiοn οf inputs and results in which each input leads tο a single, identifiable οutcοme. Each functiοn is assigned a dοmain, a cοdοmain, οr a scοpe. The letter f is widely used this tο denοte functiοns (x). The symbοl fοr admissiοn is an x. The fοur primary types οf usable functiοns are οn οperatiοns, οne-tο-οne capabilities, sο multiple functiοnality, in capabilities, and then οn functiοns.

Optiοn (D) is a design that might depict the graph οf y = x³ - 4x since it cοntains a single hump with a rοοt at x = 0 and intersects the y-axis at y = 0.

We may use the fοllοwing prοcedures tο sοlve the functiοn y = x³ - 4x:

The value οf the y-intercept is (0, 0).

We set y = 0 and sοlve fοr x tο determine the x-intercepts:

\(x^3 - 4x = 0\)

\(x( x^2 -4) = 0\)

\(x = 0 , x = -2 , x = 2\)

As a result, the x-intercepts are (-2, 0), (0, 0), and (2, 0).

\(3x^2 - 4 = 0\)

x = ±√(4/3)

As a result, the turning pοints are ((4/3), -4/(3(4/3))) and (-(4/3), 4/(3(4/3))).

With this data, we can draw the graph οf y = x³ - 4x shοwn in οptiοn (D).

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The distance between the skew lines given by the equations \(X = y + 73, z = 0 and 2x - 1 = X = z + 3\) is equal to \(\sqrt{(d^2 - p^2)}\), where d is the distance between the parallel planes that contain the lines, and p is the perpendicular distance between the lines and one of the planes.

To find d, we need to determine the normal vectors of the planes that contain the lines. For the first line, the direction vector is (1, 1, 0), and for the second line, it is (2, -1, 1). Taking the cross product of these two vectors, we obtain the normal vector of the plane containing the first line as (1, -1, -3).

Next, we find the perpendicular distance p between the lines and one of the planes. Substituting the coordinates of any point on the first line into the equation of the second line, we get \(2(y + 73) - 1 = y + 3\), which gives y = -35. Therefore, the perpendicular distance between the lines and the plane is \(|-35 - 0| = 35.\)

Finally, we can calculate the distance between the skew lines:

\(\sqrt{((-35)^2 - 35^2)}\)

\(=\sqrt{(-35^2)}\)

= 35.

Hence, the distance between the skew lines X = y + 73, z = 0 and 2x - 1 = X = z + 3 is 35 units.

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Answer:

13

Step-by-step explanation:

-5+5=0

0+8=8

5+8=13

Answer: 13

Step-by-step explanation:

Inverse distance weighting is a useful tool for estimating values at unsampled locations in geostatistics. Another advantage of inverse distance weighting is that it allows for the incorporation of multiple variables into the estimation process.

Inverse distance weighting is a method used in geostatistics to estimate values at unsampled locations based on values at surrounding sample locations. It works by assigning weights to the sample points based on their proximity to the unsampled point. The closer a sample point is to the unsampled point, the higher its weight. The weights are then used to calculate a weighted average of the sample values, which is used as the estimate for the unsampled location.
The benefit of inverse distance weighting over a simple average is that it takes into account the spatial variability of the data. A simple average treats all sample points equally, regardless of their distance from the unsampled point. This can lead to inaccurate estimates if there is a high degree of spatial variability in the data. In contrast, inverse distance weighting gives more weight to sample points that are closer to the unsampled point, which is likely to provide a more accurate estimate.
Another advantage of inverse distance weighting is that it allows for the incorporation of multiple variables into the estimation process. For example, if there are two variables of interest (e.g., temperature and precipitation), inverse distance weighting can be used to estimate values for both variables simultaneously. This is not possible with a simple average.
Overall, inverse distance weighting is a useful tool for estimating values at unsampled locations in geostatistics. Its ability to account for spatial variability and incorporate multiple variables makes it a powerful technique for analyzing spatial data.

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The formula for the general term of the sequence is:

an = (-1)^(n+1) * (2n-1) / 2^n

Looking at the first few terms, we can observe the following pattern:

a1 = -9/2

a2 = 11/4

a3 = -13/8

a4 = 15/16

a5 = -17/32

Notice that the numerator alternates between odd and even values, while the denominator doubles with each term. Based on this pattern, we can write the general term as:

an = (-1)^(n+1) * (2n-1) / 2^n

Therefore, the formula for the general term of the sequence is:

an = (-1)^(n+1) * (2n-1) / 2^n

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Answer:

Step-by-step explanation:

Dont do it. Just take the detention

Work Shown:

|x-12.2| = 0.3

x-12.2 = -0.3 or x-12.2 = 0.3

x = -0.3+12.2 or x = 0.3+12.2

x = 11.9 or x = 12.5

The min length is 11.9 cm and the max length is 12.5 cm

Subtracting 12.2 from either x value leads to a positive difference of 0.3 which is the margin of error.

Answer:

obtuse

Step-by-step explanation:

hope this helps

and can you tell me if I was right or wrong?

Nastya's annual payments on the loan will be approximately $7,350.68 (rounded to the nearest cent).

To find Jean's equity as a percent of the house value, we need to calculate the equity and divide it by the house value, then multiply by 100 to get the percentage.

Jean's equity is the difference between the house value and the mortgage amount. So, the equity is $792078.31 - $600,000 = $192,078.31.

To calculate the percentage, we divide the equity by the house value and multiply by 100: ($192,078.31 / $792078.31) * 100 = 24.26%.

Therefore, Jean's equity as a percent of the house value is 24.26%.

Now, let's move on to Nastya's question.

To calculate Nastya's annual payments on a fully amortizing loan, we need to use the formula for calculating the monthly payment:

P = r * PV / (1 - (1 + r)^(-n))

Where:
P = Monthly payment
r = Monthly interest rate (annual interest rate / 12)
PV = Present value of the loan
n = Total number of payments

Given:
PV = $622,422
Annual interest rate = 5.2%
n = 10 years

First, we need to convert the annual interest rate to a monthly interest rate: 5.2% / 12 = 0.43333%.

Next, we substitute the values into the formula and solve for P:

P = (0.0043333 * 622422) / (1 - (1 + 0.0043333)^(-10))

Using a calculator, we get P ≈ $7,350.68.

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Using the concepts of probability, we got 0.5 is the probability of drawing the sum $20 or more when  two bills are drawn randomly without replacement.

We have an envelope contains 8 bills;

Two of $1 bills, Two of $5 bills, Two of $10 bills, Two of $20 bills.

When two bills are drawn randomly without replacement, we have to find the probability that their sum is $20 or more.

Total  outcomes = 2 x 2 x 2 x 2 = 16

Total possible outcomes, more than 20;

(1, 20), (20, 1), (5, 20), (20, 5), (10, 10), (20, 10), (10, 20), (20, 20) = 8 cases

That is,

The total possible outcomes is 8.

Now,

The probability of bill to be $20 or more = Possible outcome / Total outcome

Probability = 8/16 = 1/2=0.5

Hence, When two bills are drawn randomly without replacement,  the probability that their sum is $20 or more is 0.5.

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(Complete question)

an envelope contains eight bills: 2 ones, 2 fives, 2 tens, and 2 twenties. two bills are drawn at random without replacement. what is  the probability that their sum is $20 or more?

A system having ΔG equal to zero means that the system is at equilibrium at standard conditions. This is option c. In a chemical reaction, ΔG represents the change in Gibbs free energy, which is a measure of the energy available to do work.

When ΔG is equal to zero, it indicates that the system is balanced, with the forward and reverse reactions occurring at the same rate. At equilibrium, the concentrations of reactants and products remain constant over time. For example, consider the reaction A ⇌ B. Initially, if we have more A than B, the forward reaction will be favored until equilibrium is reached. At equilibrium, the rate of the forward reaction equals the rate of the reverse reaction, and the concentrations of A and B remain constant. In this case, ΔG is zero.

It is important to note that while a ΔG of zero indicates equilibrium, it does not provide information about whether the reaction is spontaneous or nonspontaneous. The spontaneity of a reaction is determined by the sign of ΔG. If ΔG is negative, the reaction is spontaneous, while a positive ΔG indicates a nonspontaneous reaction.

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The first digit must be 1. The remaining seven ones must be either 0 or 1.

Therefore, there can be formed \(2^7=128\) different numbers.

The economist would need a total sample size of 3,792 individuals for a 95% confidence interval with an interval width of no more than $100.

To calculate the required sample size, we can use the formula:

n = [(Z * σ) / E]^2

Where:

n is the required sample size

Z is the Z-score corresponding to the desired confidence level (for a 95% confidence level, Z ≈ 1.96)

σ is the population standard deviation ($1,000 in this case)

E is the desired margin of error ($100 in this case)

Plugging in the values, we have:

n = [(1.96 * 1000) / 100]^2 = 3841.44

Since we can't have a fraction of a sample, we round up to the nearest whole number, resulting in a required sample size of 3,842.

However, since the economist already has a sample of 50 individuals, they would need an additional sample size of 3,842 - 50 = 3,792 to meet the desired criteria.

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The total amount to be repaid on a simple interest loan of $4,000 for 3 years at an interest rate of 11% p.a. is $5,320.

In order to calculate the total amount to be repaid on a simple interest loan of $4,000 for 3 years at an interest rate of 11% p.a., we need to use the formula for simple interest:

Total amount = Principal + Interest

The principal is $4,000 and the interest rate is 11% per year. Let's convert the rate to a decimal:11% = 0.11We also need to know the time period in years. In this case, it's 3 years.

Now, we can use the formula:

Interest = Principal x Rate x Time

I = 4000 x 0.11 x 3 = 1320

The interest on the loan is $1,320. Therefore, the total amount to be repaid is:

Total amount = Principal + Interest = $4,000 + $1,320 = $5,320

Therefore, the total amount to be repaid on a simple interest loan of $4,000 for 3 years at an interest rate of 11% p.a. is $5,320.

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Answer:

The answer is h(x)=(1/4)x

Step-by-step explanation:

The derivative of g(z) is g'(z) = cos(-√(1 - x² - y²)). The given triple integral simplifies to the surface integral of g(z) over the region B+.



To find g'(z), we differentiate g(z) = z * cos(-√(1 - x² - y²)) with respect to z, treating x and y as constants. Applying the chain rule, g'(z) = cos(-√(1 - x² - y²)).

Next, we consider the region B+ defined by x² + y² + z² ≤ 1 and z ≥ 0. We want to evaluate the triple integral of 2π√(₁₂) + cos(√((1 - x² - y²) - ₁²)) - ₂√(1 - x² - y²) * √(1 - x² - y²) * ln(√(1 - x² - y²)) over B+.

By applying Gauss's theorem, we relate the triple integral to the flux of a vector field F = (0, 0, g(z)) across the surface ∂B. The divergence of F is g'(z), so we substitute it into the triple integral. This allows us to convert the volume integral into a surface integral, resulting in the expression ∯_∂B g(z) dS. Since we are integrating over B+, the unit outward normal vector points in the positive z-direction, simplifying the expression to ∯_∂B g(z) dS = ∭_B g(z) dV. Therefore, the original triple integral is equivalent to the surface integral of g(z) over B+.

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Answer:

Yes, because x is rasied to the power of 3

Step-by-step explanation:

Linear algebra is the branch of mathematics concerning linear equations such as:

{\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b,}{\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b,}

linear maps such as:

{\displaystyle (x_{1},\ldots ,x_{n})\mapsto a_{1}x_{1}+\cdots +a_{n}x_{n},}{\displaystyle (x_{1},\ldots ,x_{n})\mapsto a_{1}x_{1}+\cdots +a_{n}x_{n},}

and their representations in vector spaces and through matrices.[1][2][3]

Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to spaces of functions.

Linear algebra is also used in most sciences and fields of engineering, because it allows modeling many natural phenomena, and computing efficiently with such models. For nonlinear systems, which cannot be modeled with linear algebra, it is often used for dealing with first-order approximations, using the fact that the differential of a multivariate function at a point is the linear map that best approximates the function near that point.

13.50<= 1.20c + 3 is the inequality

We can see that it costs her $3 in addition to the $1.20 she receives for each task she completes, which is "C," for a total of $13.50.

Start by deducting her initial investment ($3) from the total ($13.50) to find the solution. By doing this, you'll discover that Janie needs to earn $10.50 in order to meet her goal, and since she receives $1.20 for EVERY chore, you'll also want to determine how many chores it will take her to reach that amount. You can calculate this by simply dividing $10.50 by $1.20, which gives you the total number of tasks she must complete, which is 8 and third tasks.

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Answer:

\(slope=\frac{4}{5}\)

Step-by-step explanation:

\(y=\frac{4}{5} x-3\)

This is written in slope-intercept form:

\(y=mx+b\)

m is the slope and b is the y-intercept. x and y are the corresponding points (x,y).

Therefore, the slope is \(\frac{4}{5}\).

:Done

Answer:

greater

Step-by-step explanation:

this is true because it is like going from feet to inches 1ft=12in the number gets larger

Answer:

242pi or about 760.266cm

Step-by-step explanation:

V=pi5.5^2 times 8

V=30.25pi times 8

V=242pi

V is about 760.266cm

Answer:

242pi or  760.266cm

Step-by-step explanation:

Answer:

multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.

Have a great day luv!

-Ary

Answer:

To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.

The formula for the area of a triangle is A = 1/2 * b * h, where b is the length of the base and h is the height of the triangle. To solve for h, rearrange the formula to 2*A/bh = 2*28/10h = 5.6 yards.

Height is a measure of vertical distance, often measured from the ground up. Its most typical application is to express the size of a person, object, or other item. Height is often measured in inches, feet, and millimetres. It is also used to determine the elevation of a piece of land or a building.

To calculate the height of a triangle, use the area of a triangle formula, A = 1/2 * b * h, where b is the length of the base and h is the height of the triangle. Because we know the triangle's area is 28 square yards and its base length is 10 yards, we can rearrange the formula to find h:

h = 2*A/b

h = 2*28/10

h = 5.6 yards

As a result, the triangle's height is 5.6 yards.

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Step-by-step explanation:

The program I used tells me the lengths, though I could use the law of cosines or Pythagoras's Therom for this.

AB: 2

BC: 3

AC: About 3.61

Also, point A is (-2, 4), point B is (-2, 2), and point C is (1, 2)

Hope this helps!

The equation of the line in slope-intercept form is y = 6x + 55.

Equations can involve variables, which are placeholders for unknown values that we wish to find. For example, the equation x + 3 = 7 asserts that the value of x plus 3 is equal to 7. We can solve for x by subtracting 3 from both sides of the equation, obtaining x = 4.

Equations can be linear or nonlinear, and they can involve one or more variables. They can be represented in various forms, such as standard form, slope-intercept form, or quadratic form.

To find the equation of the line in point-slope form, we need to first find the slope of the line. We can use any two points from the table to find the slope using the formula:

slope = (change in y)/(change in x)

Let's use the first and last points in the table:

slope = (295 - 175)/(40 - 20) = 120/20 = 6

Now we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is any point on the line. Let's use the first point (20, 175):

y - 175 = 6(x - 20)

To write this equation in slope-intercept form, we need to isolate y:

y - 175 = 6x - 120

y = 6x + 55

So the equation of the line in slope-intercept form is y = 6x + 55.

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Answer:

\(f(x)=x^3-7x^2-6x+72\)

Step-by-step explanation:

\(f(x)=a(x-p)(x-q)(x-r)\\\\f(x)=1(x-6)(x+3)(x-4)\\\\f(x)=(x^2-3x-18)(x-4)\\\\f(x)=x^3-4x^2-3x^2+12x-18x+72\\\\f(x)=x^3-7x^2-6x+72\)

This is because \(x=6\) is the solution to \(x-6=0\), \(x=-3\) is the solution to \(x+3=0\), and \(x=4\) is the solution to \(x-4=0\).

Answer:

8: 12 ,5

9 : 18, 7

10 : 17,5

But Not Sure

Answer:

No

Step-by-step explanation:

Does anyone have to do DELTA-MATH

Answer: Can you send the question that you have.

Step-by-step explanation:

Answer:

10/49

Step-by-step explanation:

make it (5)(4)/(14)(7)

20/98

divide it by the greatest common factor, 2

10/49