given two points on a line and a third point not on the line, is it possible to draw a plane that includes the line and the third point?

\(2x\pm3=45\\2x=42 \vee 2x=48\\x=21 \vee x=24\)

Answer:

x = 21 or 24

Step-by-step explanation:

That ± tells you we are setting up two different equations to solve for x, as both answers can satisfy the equation.

We do 2x + 3 = 45 and 2x -  3 = 45.

Let's solve them each separately.

2x + 3 = 45
subtract 3 from both sides to get 2x on its own:
2x + 3 - 3 = 45 - 3
simplify:
2x + 0 = 42 or 2x = 42
divide both sides by 2 to isolate variable x
(2x / 2) = (42 / 2)
x = 21

2x - 3 = 45
add 3 to both sides to get 2x on its own:
2x - 3 + 3 = 45 + 3
simplify:
2x + 0 = 48 or 2x = 48
divide both sides by 2 to isolate variable x
(2x / 2) = (48 / 2)
x = 24

x = 21, 24 is your answer

Answer:

f(6) = 27

Step-by-step explanation:

f(6) means what is the value of f(x) when x = 6

substitute x = 6 into f(x)

f(6) = 2(6) + 15 = 12 + 15 = 27

Answer: about 0.79

Step-by-step explanation:

First divide 8 by 9 --> (8/9) = about 0.8889

then square that value --> (0.8889)^2 = about 0.79.

PEMDAS is your friend!

Answer:

second dot choice thing

Answer:

The second dot that is the answer.

Step-by-step explanation:

hope this helps.

Answer:

im not sure if my answer is correct

Answer:

So a = -2, b = 3 or 2, and c = 5.

Step-by-step explanation:

An equation like this is usually setup as: ax + by + c = 0

So assuming that with 3 x 2 one of the is y you can rearrange:

-2x + 3 x 2 + 5 = 0

So a = -2, b = 3 ( or 2 depending on which one is y), and c = 5.

To eliminate the roots in 1.1 and 1.2, we can use trigonometric substitution. In 1.1, we can substitute x = 4 sin(theta) to eliminate the root of 4. In 1.2, we can substitute z = 7 sin(theta) to eliminate the root of 7.

1.1. V64+2 + 1 We can substitute x = 4 sin(theta) to eliminate the root of 4. This gives us:

V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3 1.2. V4z2 – 49

We can substitute z = 7 sin(theta) to eliminate the root of 7. This gives us:

V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta) (2 – 1) = 7 sin(theta)

Here is a more detailed explanation of the substitution:

In 1.1, we know that the root of 4 is 2. We can substitute x = 4 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 2.

When we substitute x = 4 sin(theta), the expression becomes V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3

In 1.2, we know that the root of 7 is 7/4. We can substitute z = 7 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 7/4.

When we substitute z = 7 sin(theta), the expression becomes: V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta)

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Answer:

I have no idea!!!!!!!!!!!!!

Answer: y = -3/5x - 6

Step-by-step explanation:

There are a few equations that can be used for this, but the simplest one would be y = mx + b

We are given:

y = -3

m = -3/5 (slope)

x = -5

b = ?

Our equation is this, we are solving for b

==> -3 = -3/5 ( -5) + b

==> -3 = -3/5 ( -5) + b ( multiply the brackets)

==> -3 = 3 + b ( subtract 3 to both sides)

==> -6 = b

Now we can make the desired equation in slope intercept form;

y = -3/5x - 6

Hope this helped! Have a great day :D

The orthogonal trajectories of a family of curves are a new set of curves that intersect the original curves at right angles. To find the orthogonal trajectories of the family of ellipses given by the equation 2x^2 y^2, follow these steps:

Differentiate the equation of the family of ellipses with respect to x or y (whichever is more convenient). In this case, let's differentiate with respect to y: d/dy (2x^2 y^2) = 4x^2y Find the slope of the tangent line to the family of ellipses at any given point by setting the derivative equal to -1 divided by the slope of the tangent line: 4x^2y = -1/m where m represents the slope of the tangent line.

Solve the resulting equation for y in terms of x to obtain the equation of the orthogonal trajectories: y = -1/(4x^2m) By following these steps, you can find the equation of the orthogonal trajectories of the family of ellipses. Differentiate the equation of the family of ellipses with respect to x or y (whichever is more convenient).

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The value of the given expression is 35 when M = 3 and N = 2.

The given expression is M³ + N³ for M = 3, N = 2.

Thus,

M³ + N³ = 3³ + 2³= 27 + 8= 35.

Therefore, the value of the given expression is 35 when M = 3 and N = 2.

The given expression is M³ + N³ for M = 3, N = 2.

Thus, M³ + N³ = 3³ + 2³ = 27 + 8 = 35.

Therefore, the value of the given expression is 35 when M = 3 and N = 2.

The sum of cubes formula for two numbers is a³ + b³ = (a + b)(a² – ab + b²).

The formula to calculate the sum of the cubes of two numbers is a³ + b³ = (a + b) (a² – ab + b²).

Thus, putting a = m and b = n, we can rewrite the given expression as: M³ + N³ = (M + N)(M² – MN + N²).

Substituting the values of M and N in the formula, we get:

M³ + N³ = (3 + 2) (3² – 3 × 2 + 2²)

= 5 × (9 – 6 + 4)

= 5 × 7

= 35.

Therefore, the value of the given expression is 35 when M = 3 and N = 2.

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The Reimann sum with n rectangle will be given as \(\sum^{n-1}_{i = 0} f{(x_i)} \Delta x\)

Let us suppose that f is a non-negative function, defined over a closed interval represented by [a, b].

The integral of f with respect to x signifies the area between the graph of f and X-axis. This area would be called definite integral of a function f from a to b. Then Riemannian method of determining this area is:

“if the area is divided into n rectangles of very small breadth, then it would be simpler to calculate the area of such rectangles and then we can add them up

(i ) The width of each rectangle will be denoted as Δx

Δx = b-a/n,

where , a is lower bound

b is upper bound of the integral

(ii) The right-hand endpoints of each rectangle are refer as \(x_i\) and we can find the right endpoints by \(x_i\) = a + Δx.i

(iii) The height of each rectangle is the value of the function at the upper point of the interval.

a + (b-a)/n for the first rectangle , a + 2(b-a)/n for the second rectangle and so on

(iv) The area of the each rectangle will be

Area = Width × height

=> A = (b-a)/2 × a + i(b-a)/2

(v) The Riemann sum with n rectangles is

Area of rectangle = \(\sum^{n-1}_{i = 0} f{(x_i)} \Delta x\)

Which is also known as Reimann sum

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Answer:

slope=9

Step-by-step explanation:

whole equation=y = 9x – 31

hope that helps

please mark as brainliest if correct

thank you

have a great day/night

Answer:

length =105 width =10

Step-by-step explanation:

L=10*W+5

P=230

P=2(L+W)

230=2(10W+5+W)

SOLVE FOR W

W=10

L=10*W+5

=10*10+5

L=105

Yes, this community of 36 homes was unusual during the economic crisis because it lost more value than the average home in the region. The difference between the average value of homes in the community and the region is $5232 ($9232 - $8700), which is greater than one standard deviation ($1500) from the average.

To determine if the community of 36 homes was unusual during the economic crisis, we can use a z-score to compare the average home value loss in the community to the average home value loss in the region.

Step 1: Calculate the z-score.
z = (X - μ) / (σ / √n)

Where:
X = average home value loss in the community ($9232)
μ = average home value loss in the region ($8700)
σ = standard deviation of home value loss in the community ($1500)
n = number of homes in the community (36)

Step 2: Plug in the values and solve for z.
z = ($9232 - $8700) / ($1500 / √36)
z = ($532) / ($1500 / 6)
z = $532 / $250
z = 2.128

Step 3: Interpret the z-score.
A z-score of 2.128 indicates that the average home value loss in the community was 2.128 standard deviations above the regional average. Generally, a z-score greater than 1.96 or less than -1.96 is considered unusual, as it falls in the top or bottom 2.5% of the distribution.

Since the z-score for this community is 2.128, it is considered unusual due to the higher average home value loss compared to the regional average during the economic crisis.

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The smallest possible inside length of the cubical steel tank that can hold 275 liters of water is approximately 0.640 meters.

The side length of the cube is found by converting the volume of water from liters to cubic meters, as the unit of measurement for the side length is meters.

Given that the volume of water is 275 liters, we convert it to cubic meters by dividing it by 1000 (1 cubic meter = 1000 liters):

275 liters / 1000 = 0.275 cubic meters

Since a cube has equal side lengths, we find the side length by taking the cube root of the volume. In this case, we find the cube root of 0.275 cubic meters:

∛(0.275) ≈ 0.640

Rounded to the nearest 0.001 meters, the smallest possible inside length of the tank is approximately 0.640 meters.

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The work done by the force F on a particle that is moving counterclockwise around the closed path C is 3276/7 for given a particle that is moving counterclockwise around the closed path C. F(x, y) = (9x² + y)i + 3xy²j C: boundary of the region lying between the graphs of y = √x, y = 0 and x = 9 & using Green's-Theorem

Green's Theorem states that the line integral around a simple closed curve C of the vector field F is equal to the double integral over the plane area D bounded by C of the curl of F.

It is given by:

∮C F ⋅ dr = ∬D curl F ⋅ dA

Using Green's Theorem, we can calculate the work done by the force F on a particle that is moving counterclockwise around the closed path C.

Given,F(x, y) = (9x² + y)i + 3xy²j

C: boundary of the region lying between the graphs of y = √x, y = 0 and x = 9

Here, D is the region enclosed by the curve C.

Boundaries of D: y = 0 to y = √x; x = 0 to x = 9

We know that ∮C F ⋅ dr = ∬D curl F ⋅ dA

We need to calculate curl F for the given function F(x, y).

So, curl F is given by:curl F = (∂Q/∂x - ∂P/∂y)

Here,P = 9x² + y and

Q = 3xy²

So,∂P/∂y = 1∂Q/∂x

               = 6xy

Using above formula,curl F = (∂Q/∂x - ∂P/∂y)

                                             = 6xy - 1

Now, applying Green's Theorem,∮C F ⋅ dr = ∬D curl F ⋅ dA

                                                                      = ∬D (6xy - 1) dA

Here, D is the region enclosed by the curve C. Boundaries of D: y = 0 to y = √x; x = 0 to x = 9

Now, calculating the integral of the above expression, we get:

∬D (6xy - 1) dA= [3x²y - x]dydx where, y varies from 0 to √x and x varies from 0 to 9.

[3x²y - x]dydx= ∫[0, 9]dx ∫[0, √x] [3x²y - x]dy

                      = ∫[0, 9]dx [(x³y - x²/2)]|√x0

                      = ∫[0, 9]dx [(x^5/2 - x²/2)]

So, ∮C F ⋅ dr = ∬D curl F ⋅ dA

                   = ∬D (6xy - 1) dA

                    = ∫[0, 9]dx [(x^5/2 - x²/2)]0

                    = 3276/7

Thus, the work done by the force F on a particle that is moving counterclockwise around the closed path C is 3276/7.

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A standard piece of paper typically has dimensions of 8.5 inches by 11 inches (21.59 cm by 27.94 cm).

These dimensions refer to the North American standard paper size known as "Letter" or "US Letter." It is commonly used for various purposes such as printing documents, letters, and reports. The dimensions are based on the traditional imperial measurement system, specifically the United States customary units. The longer side of the paper is known as the "letter" or "long" side, while the shorter side is called the "legal" or "short" side.

The 8.5 by 11 inch size provides a versatile and widely accepted format for printing and documentation needs.

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Answer:

60%

Step-by-step explanation:

24/40 = .6 x 100 = 60

Answer:

See below

Step-by-step explanation:

To find the mean, you take each data point, add them together, and divide it by the number of data points.

Problem 1

Mean of High Temperatures = (65+67+54+52+63+69+75)/7 = 445/7 = between 63 and 64

Problem 2

Mean of Low Temperatures = (61+55+37+29+34+42+54)/7 = 312/7 = between 44 and 45

Answer:

y=4x-7   3(4x-7)-21x=-21     12x-21-12x=-21 -21=-21

Step-by-step explanation:

Answer:

Step-by-step explanation:

C

Answer:

\(-1.4\)

Step-by-step explanation:

The slope of a line is the change in the line. It can be found using the formula;

\(\frac{rise}{run}\) or \(\frac{y_2-y_1}{x_2-x_1}\).

Substitute in the given points, and solve for the slope;

\(\frac{y_2-y_1}{x_2-x_1}\\\\= \frac{2-9}{11-6}\\\\= \frac{-7}{5}\\\\= -1.4\)

Answer:

-7/5

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(2-9)/(11-6)

m=-7/5

The maximum distance that trigonometric parallax will work and allow for a reliable distance determination is approximately 1,000 parsecs or 3,260 light-years.

Trigonometric parallax is a method used to measure the distances to nearby stars by observing their apparent movement in the sky as Earth orbits the Sun.
This method involves observing a star from two different positions in Earth's orbit, typically six months apart, and measuring the angular shift in the star's position against more distant background stars. The angular shift, or parallax angle, is then used to calculate the distance to the star using basic trigonometry. However, this method becomes less accurate as the distance to the star increases because the parallax angle becomes too small to measure precisely.
One factor limiting the accuracy of trigonometric parallax is the resolving power of telescopes, which restricts the ability to detect very small angles. Improvements in telescope technology and the use of space-based observatories, such as the Gaia satellite, have increased the accuracy and range of trigonometric parallax measurements. However, even with these advancements, the maximum reliable distance for trigonometric parallax remains at around 1,000 parsecs or 3,260 light-years.
In summary, trigonometric parallax is a reliable method for determining the distance to stars within 1,000 parsecs or 3,260 light-years. Beyond this range, other methods such as spectroscopic parallax and standard candles are used to estimate distances in astronomy.

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The appropriate p-value for the given test statistic and hypotheses is approximately 0.0253.

Tο determine the apprοpriate p-value fοr the given hypοthesis test, we need tο use the t-distributiοn and the t-statistic value οbtained.

Given:

Null hypοthesis (H0): μ = 130 (pοpulatiοn mean)

Alternative hypοthesis (HA): μ > 130 (pοpulatiοn mean)

T-statistic: t = 2.73

Degrees οf freedοm: df = 5

Tο calculate the p-value, we cοmpare the t-statistic tο the t-distributiοn.

Since the alternative hypοthesis is μ > 130, it is a οne-tailed test, and we are interested in the right tail οf the t-distributiοn.

Using a t-table οr a statistical sοftware, we can determine the p-value assοciated with the t-statistic and the degrees οf freedοm.

Fοr a t-statistic οf 2.73 with 5 degrees οf freedοm, the p-value is apprοximately 0.0257 (assuming a twο-tailed test).

Since we have a οne-tailed test, the apprοpriate p-value is half οf the twο-tailed p-value:

p-value = 0.0257 / 2 = 0.01285

Therefοre, the apprοpriate p-value fοr the given hypοthesis test is apprοximately 0.01285.

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To compute the value of the correlation coefficient, we can use the given values of ∑x, ∑x^2, ∑y, ∑y^2, and ∑xy. The correlation coefficient, denoted as r, is calculated as:

r = (n∑xy - ∑x∑y) / √((n∑x² - (∑x)²)(n∑y² - (∑y)²))

Using the given values, we can substitute them into the formula to find the value of r.

Once we have the value of r, we can determine whether y should tend to increase or decrease as x increases from 3 to 25 months based on the sign of the correlation coefficient.

The computation table allows us to calculate the necessary summations for each column, including x², y², and xy.

By summing each column, we obtain ∑x² = 1070, ∑y² = 90,230, and

∑xy = 9,528.

These values can then be used to calculate the correlation coefficient, r, using the formula mentioned earlier.

After obtaining the value of r, we can determine the direction of the relationship between x and y.

If r is positive, it implies a positive correlation, indicating that as x increases, y tends to increase as well.

Conversely, if r is negative, it implies a negative correlation, meaning that as x increases, y tends to decrease.

The value of r will help us understand the relationship between the variables x and y in terms of their tendency to increase or decrease together.

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Answer:

D

Step-by-step explanation:

The graph clearly shows that x=>3

The average tangential acceleration of a point on the wheel's edge is 0.45 m/s².

The radius of the grinding wheel r = 0.15 m Angular speed,ω = 12.0 rad/s Time taken, t = 4.0 s Formula used, Tangential acceleration = rα where r is the radius of the wheel α is the angular acceleration of the wheel. Multiplying both sides by r, we get, α = a/r Where a is the tangential acceleration. Using the formula Angular acceleration,α = ω/t= 12.0 rad/s4.0 s = 3.0 rad/s²Putting values in α = a/r, we get, a = α × r = 3.0 rad/s² × 0.15 m= 0.45 m/s². Therefore, the average tangential acceleration of a point on the wheel's edge is 0.45 m/s².

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Answer:

x=9

Step-by-step explanation:

13x-32 and 7x+22 are equal to each other (angles) so

13x-32=7x+22

13x-7x=22+32

6x=54

x=54/6

x=9