The coordinates of a triangle PQR are P(2,-3) Q(-3,5) and R(-1,-2). If the points of the triangle are reflected across the x -axis, what are the coordinates of the reflected points​

Answer:

6.83and 7.03 this is the answer

Answer:

6.83, 6.93, 7.03, 7.13, 7.23, 7.33 always add .10 each time.

Step-by-step explanation:

Answer:

.

Step-by-step explanation:

(x+2)(x+4)

=x(x+4)+2(x+4)

=x²+4x+2x+8

=x²+6x+8

Answer:

Hi, there for the graph it will be not a function

For the equation it is also not a function

Step-by-step explanation:

For the graph use   vertical line test to see if the x value are the same if they are that's means it is not a function.

The X value can't be the same and can't be used twice.

The reason why because given an equation, there should be only one corresponding y value for any x value.

The probability that at least 96 of the 244 students admitted to binge drinking in the last week is approximately equal to 0.999996 or 0.9999 (rounded to four decimal places).

We can calculate it using the binomial probability distribution as follows:

follows:

P(X ≥ 96) = P(X = 96) + P(X = 97) + ... + P(X = 244 - n)

P(X ≥ 96) = 1 - P(X < 96)

P(X < 96) = P(X ≤ 95)

P(X < 96) = Σ_(k=0)⁹⁵ (244 C k) (0.44)^k (0.56)⁽²⁴⁴⁻k⁾

P(X ≥ 96) = 1 - P(X < 96)P(X ≥ 96) = 1 - P(X ≤ 95)

Now we can use any statistical calculator or standard normal distribution table to find the cumulative probability corresponding to the probability value of P(X < 96).

Using an online calculator, we get:

P(X ≥ 96) ≈ 1 - 3.124 x 10⁻⁶

P(X ≥ 96) ≈ 0.999996

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Answer:

g(g(-2))

g(-8)

-32

This is the correct solution

Tthe population of the colony after 2 hours is 64a

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

Rate = doubles every 20 minutes

Represent the initial population with a

So, we have the following representation

f(t) = a(2)^t

Where t is the number of 20 minutes in the time

The time is given as 2 hours

So, we have

t = 2 hours/20 minutes

Evaluate

t = 6

The function becomes

f(t) = a(2)^6

Evaluate

f(t) = 64a

hence, the population is 64a

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The volume of a cone is given by the formula:

volume = (1/3) * pi * r^2 * h

where r is the radius of the base of the cone (half of the diameter), and h is the height of the cone.

We can rearrange this formula to solve for the height:

h = (3 * volume) / (pi * r^2)

Substituting the given values and solving for h gives:

h = (3 * 226 m^3) / (3.14159 * (12 m / 2)^2)

h = (3 * 226 m^3) / (3.14159 * 6^2 m^2)

h = (3 * 226 m^3) / (3.14159 * 36 m^2)

h = (3 * 226 m^3) / 113.097 m^2

h = 6.49 m

So the height of the cone is approximately 6.49 m.

A 3D object's volume is the amount of actual space it occupies. It is a 2D shape's 3D equivalent of area. It is quantified in cubic units like cm3. By multiplying its length, height, and width, you may determine this.

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Answer:

22( w + 2 ) =77 and the amount of the water bottle would be 1.50

Step-by-step explanation:

As per the curve the derivative of the curve and integrating it over the interval 1 <= t <= 4.

A curve is a geometric shape defined by a set of points. It can be represented mathematically by a function that maps points in space to a real number.

In this case, the curve is defined by the function r(t) = (7t², 8t², 2√2t²),for 1 <= t <= 4.

The parameter t is not an arc length parameter, as it does not represent the distance along the curve. Instead, it represents the position along the curve at a particular time.

To determine whether a curve uses arc length as a parameter, we need to calculate the arc length of the curve and compare it to the value of the parameter.

If the parameter is equal to the arc length, then the curve uses arc length as a parameter. In this case, the parameter t is not equal to the arc length of the curve, so the curve does not use arc length as a parameter.

Complete Question:

Determine whether the following curve uses arc length as a parameter. If not, find a description that uses arc length as a parameter r(t) = (7t², 8t², 2√2t²), for 1 less than or equal to t less than or equal to 4.

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Answer:

A. \(x^{3} + 3x^{2} +5x+3\)

B. \(2x^{3} -3x^{2} -5x+6\)

C. \(3y^{3} - 4y^{2} -11y+4\)

D. \(x^{2} - 2xy+y^2+x - y\)

E.  \(3m^2-2mn-n^2+6m+2n\)

F.  \(4x^4+4x^3+5x^2+2x+1\)

Answer:

9/4 or 2 1/4

Step-by-step explanation:

2 7 /8 -5/8 which gives you 9/4

(x+3) x (x+2)

Step-by-step explanation:

it should be *(x+3) x (x+2)* because area of rectangle = length x breadth

Answer:

So first we need to determine what the exponential growth function would look like.  Exponential growth functions look like \(P(t) = P_0*e^{r*t}\) and in our case \(P_0\) would be the initial population which is 6.63 million.  R is the next variable that we need to fill out which is the rate of change which in our case is 3.01% or 0.0301.

This is how our function should look now \(P(t)=6.63*e^{0.0301*t}\)

Moving onto part b, we need to estimate the population of the city in 2018 which 6 years from 2012 and we plug that into t and solve.

\(P(t) = 6.63 * e^{0.0301*6}\)

\(P(t) = 6.63*e^{0.1806}\)

\(P(t) = 6.63 *1.1979\)

\(P(t) = 7.9423\ million\)

Moving onto part c, we need to find when the population of the city will be 11 million which will be done by setting P(t) to 11 million and solving for t.

\(11 = 6.63*e^{0.0301*t}\)

\(\frac{11}{6.63} = \frac{6.63*e^{0.0301*t}}{6.63}\)

\(1.659=e^{0.0301*t}\)

\(ln(1.659)=ln(e^{0.0301*t})\)

\(\frac{0.506}{0.0301}=\frac{0.0301*t}{0.0301}\)

\(16.818\ years = t\)

Moving onto part d, we need to find the doubling time.  This will be similar to the previous part but we will be finding the time it takes to double our population.  So instead of putting 11 million for P(t) we put 6.63 * 2 in there which is 13.26.

\(13.26 = 6.63*e^{0.0301*t}\)

\(\frac{13.26}{6.63} = \frac{6.63*e^{0.0301*t}}{6.63}\)

\(2=e^{0.0301*t}\)

\(ln(2)=ln(e^{0.0301*t})\)

\(\frac{0.693}{0.0301}=\frac{0.0301*t}{0.0301}\)

\(23.028\ years = t\)

Hope this helps!  Let me know if you have any questions

Answer:

1/3 plus 5\6 si equal to 7\6

Step-by-step explanation:

1\3 X 2 is equal to 2\6 add it to 5\6 it will equal 7\6

Answer:

the correct answer is 2/6+5/6=7/6.

Step-by-step explanation:

hope this helps!

Answer:

A.

Step-by-step explanation:

6, 11,14,14,19,20

Adding these 6 numbers we get  84.

84 / 6 = 14 = mean.

Median =  middle number(s) = 14

Mode = number occurring most = 14.

S is transitive. Since S is reflexive, symmetric, and transitive, it is an equivalence relation.

To prove that S is an equivalence relation, we need to show that it satisfies three conditions: reflexivity, symmetry, and transitivity.

Reflexivity: For any ordered pair (a, b), we have a + b = b + a. So, (a, b) S (a, b), and S is reflexive.

Symmetry: If (a, b) S (c, d), then a + d = b + c. Rearranging this equation gives us d + a = c + b, which implies that (c, d) S (a, b). Therefore, S is symmetric.

Transitivity: If (a, b) S (c, d) and (c, d) S (e, f), then we have a + d = b + c and c + f = d + e. Adding these two equations gives us a + 2d + f = b + 2c + e. Rearranging this equation, we get (a, b) S (e, f). Hence, S is transitive.

Since S is reflexive, symmetric, and transitive, it is an equivalence relation.

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Answer:

d(-6,-9),e(3,-9),f(3,-3),g(-6,-3

Step-by-step explanation:

first you look at the location of the point and follow in the direction of which number it is on the X line, then in the direction of which number it is on the Y line and in the parentheses of the coordinates, first write the number from the X line, then from the Y line

ps: I hope I helped you a bit :)

To find the mass and center of mass of the solid bounded by the paraboloid z = 8x^2 + 8y^2 and the plane z = a, we can use cylindrical coordinates.

In cylindrical coordinates, the paraboloid can be expressed as z = 8r^2, where r is the radial distance and z is the height.

To find the mass of the solid, we need to integrate the density function over the volume of the solid. Since the solid has constant density k, the mass can be expressed as:

M = ∭ k dv

Using cylindrical coordinates, the volume element (dv) is given by dv = r dz dr dθ.

The bounds for the integral are as follows:

r: from 0 to √(a/8) (due to the paraboloid equation z = 8r^2)

θ: from 0 to 2π (to cover the entire azimuthal angle)

z: from 0 to a (due to the plane z = a)

Now, let's evaluate the integral for the mass:

M = ∭ k dv = ∫[z=0 to a] ∫[θ=0 to 2π] ∫[r=0 to √(a/8)] k r dz dr dθ

The integration process will yield the mass M of the solid.

To find the center of mass, we need to evaluate the triple integral:

(x_cm, y_cm, z_cm) = (1/M) ∭ (x, y, z) k dv

Where (x_cm, y_cm, z_cm) represent the coordinates of the center of mass.

The integrals for each coordinate can be set up similarly to the mass integral, using the appropriate expressions for x, y, and z in terms of cylindrical coordinates. Then, divide each integral by the mass M to obtain the coordinates of the center of mass.

Note that the calculations can be quite involved, so it's recommended to use software or a computer algebra system to perform the integrations and simplify the expressions.

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Answer:

To find ? we use sine

sin ∅ = opposite / hypotenuse

From the question

The hypotenuse is 50

The opposite is 25

So we have

sin ? = 25 / 50

sin ? = 1/2

? = sin-¹ 1/2

To find ? we use tan

tan ∅ = opposite / adjacent

From the question

the opposite is 8

the adjacent is 33

So we have

tan ? = 8/33

? = tan-¹ 8/33

? = 13.62

Hope this helps you

The required equation is 135 + 9x > 250.

The number of lawns Ed must mow is assumed to be x.

The amount Ed charges for each lawn he mows is $9.

Thus, the total amount Ed earns by mowing x lawns = $9x.

The savings which Ed has is $135.

Thus, the total amount Ed will have to spend can be written as the expression, $(135 + 9x).

The cost of the video game is given to be $250.

We are asked to write an equation, that can be used to find the number of lawns Ed mow, that is x so that the amount Ed has will be more than the amount he needs to buy the video game.

This can be shown as the equation:

Total amount Ed has > Cost of the video game,

or, 135 + 9x > 250.

Thus, the required equation is 135 + 9x > 250.

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Answer:

\(let \: the \: angle \: be \: \alpha \\ \tan( \alpha ) = \frac{p}{b} \\ \tan(16.8) = \frac{2.7}{x} \\ x = \frac{2.7}{0.30 } \\ x = 9 \\ now \: by \: using \: pythagoras \: theorem \: \\ h = \sqrt{p {}^{2} } + b {}^{2} \\ h = \sqrt{ {2.7}^{2} } + {9 }^{2} \\ h = 9.396\)

Sketching a graph of the function f(x) = e-x+ 2 and state its domain and range in interval notation:Let's first discuss the domain of the given function which is all real numbers, as there are no restrictions for the input value (x) of the function. Therefore, the domain of f(x) = e-x+ 2 is:Domain: (-∞,∞)

Next, we will discuss the range of the given function, which is all real numbers greater than or equal to 2. We can see that the function e-x is always greater than zero because e is a constant whose value is approximately 2.718 and x is always negative. When we add 2 to e-x, we get values of f(x) greater than or equal to 2.

the range of f(x) = e-x+ 2 is:Range: [2,∞)Let's now sketch the graph of the given function:Image attached shows the graph of the given function, f(x) = e-x+ 2.

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The characteristic polynomial of A is \(λ^3 - 5λ^2 + 8λ - 4.\) The eigenvalues of A are λ = 1, 2, and 2. The eigenspaces corresponding to the different eigenvalues are spanned by the vectors\([1 0 -1]^T\) and \([0 1 -1]^T\). A is diagonalizable with the matrix P = [1 0 -1; 0 1 -1; -1 -1 0] and the diagonal matrix D = diag(1, 2, 2) such that \(A = PDP^{(-1)}\).

(a) To find the characteristic polynomial of A and the eigenvalues of A, we need to find the values of λ that satisfy the equation det(A - λI) = 0, where I is the identity matrix.

Using the given matrix A:

A = [3 2 2; 1 2 0; 2 1 0]

We subtract λI from A:

A - λI = [3-λ 2 2; 1 2-λ 0; 2 1 0-λ]

Taking the determinant of A - λI:

det(A - λI) = (3-λ) [(2-λ)(0-λ) - (1)(1)] - (2)[(1)(0-λ) - (2)(1)] + (2)[(1)(1) - (2)(2)]

Simplifying the determinant:

det(A - λI) = (3-λ) [(2-λ)(-λ) - 1] - 2 [-λ - 2] + 2 [1 - 4]

det(A - λI) = (3-λ) [-2λ + λ^2 - 1] + 2λ + 4 + 2

det(A - λI) \(= λ^3 - 5λ^2 + 8λ - 4\)

Therefore, the characteristic polynomial of A is \(p(λ) = λ^3 - 5λ^2 + 8λ - 4\).

To find the eigenvalues, we set p(λ) = 0 and solve for λ:

\(λ^3 - 5λ^2 + 8λ - 4 = 0\)

By factoring or using numerical methods, we find that the eigenvalues are λ = 1, 2, and 2.

(b) To find the eigenspaces corresponding to the different eigenvalues of A, we need to solve the equations (A - λI)v = 0, where v is a non-zero vector.

For λ = 1:

(A - I)v = 0

[2 2 2; 1 1 0; 2 1 -1]v = 0

By row reducing, we find that the general solution is \(v = [t 0 -t]^T\), where t is a non-zero scalar.

For λ = 2:

(A - 2I)v = 0

[1 2 2; 1 0 0; 2 1 -2]v = 0

By row reducing, we find that the general solution is \(v = [0 t -t]^T\), where t is a non-zero scalar.

(c) To prove that A is diagonalizable and find the invertible matrix P and diagonal matrix D, we need to find a basis of eigenvectors for A.

For λ = 1, we have the eigenvector \(v1 = [1 0 -1]^T.\)

For λ = 2, we have the eigenvector \(v2 = [0 1 -1]^T.\)

Since we have found two linearly independent eigenvectors, A is diagonalizable.

The matrix P is formed by taking the eigenvectors as its columns:

P = [v1 v2] = [1 0; 0 1; -1 -1]

The diagonal matrix D is formed by placing the eigenvalues on its diagonal:

D = diag(1, 2, 2)

PDP^(-1) = [1 0; 0 1; -1 -1] diag(1, 2, 2) [1 0 -1; 0 1 -1]

After performing the matrix multiplication, we find that PDP^(-1) = A.

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To ensure the preservation of the clinical specimen for viral isolation, it should be stored at a specific temperature. The recommended temperature for storing the specimen is generally between 2 to 8 degrees Celsius (36 to 46 degrees Fahrenheit).

Storing the clinical specimen in viral transport medium at a temperature range of 2 to 8 degrees Celsius (36 to 46 degrees Fahrenheit) is commonly advised for preserving the viability of the virus. This temperature range helps to slow down the viral activity and prevents the specimen from deteriorating while awaiting processing. It provides an environment that can maintain the integrity of the viral particles until laboratory procedures can be carried out the following week. It's important to follow the recommended storage temperature to ensure accurate results and successful viral isolation from the specimen.

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Answer: I believe the answer is -8.32

Answer:

Step-by-step explanation:−8.32

Answer:

It would be C

Step-by-step explanation:

So, shows in the graph, you can see that the change in rise is 100, because to get to 150 from 50, you add 100

And the run is 1, because to go from 0 to 1, you add 1

Meaning the slope is 100/1

Hope this helped!

Generally, using a protractor we see x to be an angle 32 degrees

Hence, we solve

since the angle in point is given by 360 and x=35

Therefore

y=360-x

y=360-32

y=328 degrees

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The measure of angle x would be 35° and the measure of angle y would be 325°

From the question, we are to determine the measures of angle x and angle y.

The measure of angle x can be determined with the aid of a protractor.

From the given diagram, we can observe that angle x is an acute angle. That is, the measure of angle x is less than 90°.

After determining the measure of angle x by using a protractor, for example, let us say the measure of angle x is 35°.

We can determine the measure of angle y by using the sum of angles at a point theorem.

Sum of angles at a point is 360°.

Thus, we can write that

x + y = 360°

Then,

35° + y = 360°

y = 360° - 35°

y = 325°

Hence, the measure of x = 35° and the y = 325°

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The first step is converting both the velocity and the wind in vector form, as follows:

Then the true speed of the plane is given by the addition of these two vectors, as follows:

\(\vec{v_1} + \vec{v_2} = \sqrt{|v_1|^2 + |v_2|^2 + 2 \cdot |v_1| \cdot |v_2| \cdot \cos(\theta)}\)

The magnitudes of each vector are given as follows:

The angle between these two vectors is given as follows:

\(\theta = 100^\circ - 42^\circ = 58^\circ\)

Thus the resulting speed is obtained as follows:

\(\vec{v_1} + \vec{v_2} = \sqrt{180^2 + 30^2 + 2 \cdot 180 \cdot 30 \cdot \cos(58^\circ)} = 197.54\)

The resulting angle of the plane is then obtained as follows:

\(\angle = \arctan\left(\frac{|v_1| \cdot \sin(\theta) + |v_2| \cdot \sin(\theta_2)}{|v_1| \cdot \cos(\theta) + |v_2| \cdot \cos(\theta_2)}\right)\)

Hence:

\(\angle = \arctan\left(\frac{180 \cdot \sin(58^\circ) + 30 \cdot \sin(42^\circ)}{180 \cdot \cos(58^\circ) + 30 \cdot \cos(42^\circ)}\right)\)

\(\angle = 59.87^\circ\)

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Answer:

  197.5 km/h

Step-by-step explanation:

You want the resultant speed with an airplane at a speed of 180 km/h at 100° is acted upon by a wind at a speed of 30 km/h at 42°. Angles are bearings CW from north.

A vector calculator makes short work of this. The resultant speed is ...

  197.5 km/h at 92.6°

The law of cosines can be used to find the side opposite the known angle in the triangle with sides 30 km/h and 180 km/h. The known angle is ...

  180° -(100° -42°) = 122°

So, the resultant speed is ...

  c = √(a²+b²-2ab·cos(C))

  = √(30² +180² -2(30)(180)·cos(122°)) ≈ √39023.13

  c ≈ 197.543

The true speed of the plane is about 197.5 km/h.

__

Additional comment

You will notice that we used bearing angles directly in the calculator computation. As long as angles are consistently measured, it doesn't matter how they're measured.

When plotting the vectors on the Cartesian plane, we need to subtract the bearing angles from 90° to make them correspond to the vectors plotted on a map with north at the top.

Answer:

Distance = ✓2

Midpoint = (-4, 10)

Step-by-step explanation:

a.) (-3,8) and (-5,12)

These coordinates are (x,y)

Let's subtract the X's

-5-(-3) = -2

And for the Y's

12-8 = 4

Next, you would add these together

-2+4 = 2

Last step is squaring rooting this number

✓2, you can either find the actual square root by calculator or leave it as ✓2. This would be your distance.

Finding the midpoint is like the average. Right in the middle. So you would do the same with these.

To find X you'll add them then divide by 2 since there are 2 x coordinates

-3+-5 = -8

Divided by 2 = -4

Same with Y

8+12 = 20

Divided by 2 = 10

Now we can say the midpoint is (-4, 10)