The coordinates of a triangle are (2, 3), (3, 1), and (4, 5). Find the coordinates of thetranslated triangle if it is enlarged by a scale factor of 3.

Answer:

X > 2

Step-by-step explanation:

2x + 14 < 3x + 12

-x < -2

x > 2

Answer:

x >2

Step-by-step explanation:

steps:

1: write the question nicely.

2: the number outside multiply with what is in the bracket.(EXPAND).

3: collect the like terms.

4: 2x-3x=-1x

:12-14=-2

5: divide by negative 1 on both side.

6:remember when u solve something including the inequalities sign....if u divide it by a negative number u should change the sign .

the ans will be x>2

Answer:

If the radius is 10mi, height is 22mi, the answer is V≈6911.5

If the radius is 22mi, height is 10mi,  the answer is V≈15205.31

The correct option is B.

The symbolic statement (p ∨ q) ∧ ~r represents "The chair is broken or it is time to sleep, and I do not study".

The statement (p ∨ q) ∧ ~r can be broken down as follows:

p ∨ q represents "The chair is broken or it is time to sleep".~r represents "I do not study".

The ∧ symbol represents "and".Therefore, the entire statement can be written as "The chair is broken or it is time to sleep, and I do not study"."It is time to sleep or the chair is broken and I do not study".

Hence the correct option is B.

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Answer:

B. 336. 38

Step-by-step explanation:

So, what you want to do is multiply the original price ($299) by the first markup percentage (150%)

299*1.50= $448.50

that is your markup price!

then you have to do the sale % (25%)

so you'll multiply your (25%) by your new price ($448.50)

448.50*.25= $112. 125

THIS IS NOT YOUR ANSWER!

don't forget that!

you will then subtract the sale price ($112.125) by the upcharged price ($448.50)

448.50-112.125= 336. 375

Round up then there is your answer!

= $336. 38

hope this helps!!

We are given the following equation

We are asked to solve the equation for y.

Solving for y means that we have to separate the variable y.

Step 1:

Subtract 3x from both sides of the equation

The Boolean expression that is not equivalent to the given expression "num * -1 ≥ 10" is option D: "NOT num * -1 < 10."

What is Boolean expression?

A Boolean expression is an expression or equation that evaluates to true or false. It includes the use of logical operators such as AND, OR, and NOT, as well as comparison operators such as equal to (=), greater than (>), less than (<), and more.

The Boolean expression that is not equivalent to the expression "num * -1 ≥ 10" is option D: "NOT num * -1 < 10."

Let's break down each option and evaluate its equivalence to the given expression:

A. (num < 0) AND (num * -1 = 10)

This expression checks if "num" is negative and if the absolute value of "num" is equal to 10. It does not directly represent the condition "num * -1 ≥ 10," so it is not equivalent.

B. (num < -10) OR (num = -10)

This expression checks if "num" is less than -10 or if "num" is exactly equal to -10. It also does not directly represent the condition "num * -1 ≥ 10," so it is not equivalent.

C. (num * -1 > 10) OR (num = -10)

This expression checks if the negative value of "num" is greater than 10 or if "num" is exactly equal to -10. Although it involves the negative value of "num," it represents the condition "num * -1 > 10" when "num" is positive. Therefore, it is equivalent to the given expression.

D. NOT num * -1 < 10

This expression checks if the negative value of "num" is not less than 10. While it involves the negative value of "num," it does not directly represent the condition "num * -1 ≥ 10." Additionally, the use of "NOT" operator flips the condition, which makes it different from the original expression. Hence, it is not equivalent.

Therefore, the Boolean expression that is not equivalent to the given expression "num * -1 ≥ 10" is option D: "NOT num * -1 < 10."

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The map x → Ax is neither onto nor one-to-one for the given matrix A.

(a) Example of a matrix A such that the map x → Ax is one-to-one but not onto:

Consider the matrix A = [[1, 0], [0, 0]]. This is a 2x2 matrix with the first column being [1, 0] and the second column being [0, 0].

To show that the map x → Ax is one-to-one, we need to demonstrate that for any two distinct vectors x₁ and x₂, the corresponding products Ax₁ and Ax₂ are also distinct.

Let's assume x₁ = [x₁₁, x₁₂] and x₂ = [x₂₁, x₂₂] are two distinct vectors. Then:

Ax₁ = [[1, 0], [0, 0]] * [x₁₁, x₁₂] = [x₁₁, 0]

Ax₂ = [[1, 0], [0, 0]] * [x₂₁, x₂₂] = [x₂₁, 0]

Since x₁₁ ≠ x₂₁ (because x₁ and x₂ are distinct), Ax₁ and Ax₂ are also distinct.

However, the map is not onto because there is no vector x such that Ax = [0, 1]. The second element of the product Ax will always be zero.

(b) Example of a matrix A such that the map x → Ax is onto but not one-to-one:

Consider the matrix A = [[1, 0], [0, 0]]. This is the same matrix as in part (a).

To show that the map x → Ax is onto, we need to demonstrate that for any vector y, there exists a vector x such that Ax = y.

Let's assume y = [y₁, y₂] is an arbitrary vector. We can choose x = [y₁, 0]:

Ax = [[1, 0], [0, 0]] * [y₁, 0] = [y₁, 0] = y

Therefore, for any vector y, there exists a vector x such that Ax = y, making the map onto.

However, the map is not one-to-one because different vectors x can result in the same product Ax. For example, if x₁ = [1, 0] and x₂ = [2, 0], both will result in Ax = [1, 0]. Hence, multiple inputs can produce the same output.

(c) Example of a matrix A such that the map x → Ax is onto and one-to-one:

Consider the identity matrix I. This is a square matrix with ones on the diagonal and zeros elsewhere.

To show that the map x → Ax is onto, we need to demonstrate that for any vector y, there exists a vector x such that Ax = y.

For any given vector y, we can choose x = y. Then Ax = Iy = y. Thus, for any vector y, there exists a vector x such that Ax = y, making the map onto.

The identity matrix is also one-to-one. This is because different vectors x will always produce different products Ax. If Ax₁ = Ax₂, then Ix₁ = Ix₂, which implies x₁ = x₂. Therefore, the map is one-to-one.

(d) Example of a matrix A such that the map x → Ax is neither onto nor one-to-one:

Consider the matrix A = [[0, 1], [0, 0]]. This is a 2x2 matrix with the first column being [0, 0] and the second column being [1, 0].

The map is not onto because there is no vector x such that Ax = [1, 0]. The first column of the product Ax will always be zero.

The map is not one-to-one because different vectors x can produce the same product Ax. For example, if x₁ = [0, 1] and x₂ = [1, 1], both will result in Ax = [1, 0]. Hence, multiple inputs can produce the same output.

Therefore, the map x → Ax is neither onto nor one-to-one for the given matrix A.

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Answer:

Area = 6. 76 square cm

Explanation

Each side of the square = 2.6 cm

Area of a square = s^2

Where s = 2.6cm

Area = 2.6^2

Area = 6.76 square cm

Therefore, the area of the square is 6. 76 square cm

Answer:

Your slope would be -1/10

Step-by-step explanation:

To find the slope from two points, you would use the formula y2-y1/x2-x1

In this case, the equation would look like -4-(-3)/5-(-5)

-4 - (-3) = -1

5 - (-5) = 10

-1/10 = -1/10

Answer:

2x-1

Step-by-step explanation:

Answer:

= 2x + (-1)

Step-by-step explanation:

Let's simplify step-by-step.

2x+4−5

=2x+4+−5

Combine Like Terms:

=2x+4+−5

=(2x)+(4+−5)

=2x+−1

Answer:

5

Step-by-step explanation:

To find the largest nth root of 3 that is less than 1.001 using Maple, you can use an "until" loop in combination with the "root" function. The loop will continue until the nth root of 3 is greater than or equal to 1.001, and it will keep decrementing the value of n until the condition is met.

In Maple, you can use the "root" function to calculate the nth root of a number. To find the largest nth root of 3 that is less than 1.001, you can implement an "until" loop that decrements the value of n until the condition is satisfied.

Here's an example of the code:

Maple

Copy code

n := 2;

until root(3, n) < 1.001 do

 n := n - 1;

end do;

n;

In this code, we initialize the value of n as 2, and then the loop continues until the nth root of 3 is less than 1.001. Inside the loop, we decrement the value of n by 1. Once the condition is met, the loop terminates, and the value of n is the largest integer for which the nth root of 3 is less than 1.001.

Running this code in Maple will give you the desired result.

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The partial derivative diffusivity equation for spherical flow is ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t, and for hemispherical flow, it is the same equation.

1. The partial derivative diffusivity equation for spherical flow is derived from the spherical coordinate system and applies to radial flow in a spherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

2. The partial derivative diffusivity equation for hemispherical flow is derived from the hemispherical coordinate system and applies to radial flow in a hemispherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

1. For the derivation of the partial derivative diffusivity equation for spherical flow, we consider a spherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the polar angle (φ). By assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in spherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

2. Similarly, for the derivation of the partial derivative diffusivity equation for hemispherical flow, we consider a hemispherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the elevation angle (ε). Again, assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in hemispherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

In both cases, the term ϕμC/k ∂p/∂t represents the source or sink term, where ϕ is the porosity, μ is the fluid viscosity, C is the compressibility, k is the permeability, and ∂p/∂t is the change in pressure over time.

These equations are commonly used in fluid mechanics and petroleum engineering to describe radial flow behavior in spherical and hemispherical geometries, respectively.

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To find the point Q such that R is the midpoint of PQ, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint M between two points A(x₁, y₁, z₁) and B(x₂, y₂, z₂) can be calculated as follows:

M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2, (z₁ + z₂) / 2).

In this case, we have the point P(9, 7, 10) and the midpoint R(10, 2, 1). We want to find the coordinates of point Q, where R is the midpoint of PQ. Let's denote the coordinates of point Q as (x, y, z).

Using the midpoint formula, we can set up the following equations:

(x + 9) / 2 = 10,  

(y + 7) / 2 = 2,  

(z + 10) / 2 = 1.

Simplifying these equations, we get:

x + 9 = 20,  

y + 7 = 4,  

z + 10 = 2.

Solving for x, y, and z, we find:

x = 20 - 9 = 11,  

y = 4 - 7 = -3,  

z = 2 - 10 = -8.

Therefore, the point Q is Q(11, -3, -8).

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Step-by-step explanation:

there u have it, since y is 0, we make a straight line that passes through 2 and shade the numbers that are <2

Answer:

180 meters

Step-by-step explanation:

Distance from the balloon to the boat = 108 meters

Distance from the boat to the shore = 144 meters

Since the boat is directly below the balloon, the problem forms a right triangle in which the distance from the balloon to shore is the hypotenuse.

Let the length of the hypotenuse = l

Using Pythagoras Theorem

\(l^2=108^2+144^2\\l^2=11664+20736\\l^2=32400\\l=\sqrt{32400} \\l=180$ meters\)

The distance from Fossett's balloon to the shore is 180 meters.

Fossett's balloon is 180m from the shore

data;

To solve this problem we can assume this is situation forms a right angle triangle and we can solve this using pythagoras theorem.

\(x^2 = y^2 + z^2\\\)

Let's substitute the values and solve

\(x^2 = y^2 + z^2\\x^2 = 108^2 + 144^2\\x^2 = 32400\\x = \sqrt{32400} \\x = 180m\)

Fossett's balloon is 180m from the shore

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\(3 \sqrt{3} \)

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The probability that Marshall wins a prize on his second spin =  0.1875

Consider an event X = the number of spins until Marshall wins a prize.

Given that a prize wheel with 4 segments of equal size, one of which is labeled winner.

So, the sample space n = 4

For given event x, the possible outcomes = 1

Using the formula of probability,

p = x/n

p = 1/4

p = 0.25

So, the probability of success p = 0.25

q = 1 - p

q = 1 - 0.25

q = 0.75

To find the probability that Marshall wins a prize on his 2nd spin.

Using formula, \(P(X = k) = (1 - p)^{k-1}p\)

For  k = 2,

\(P(X = 2) = (1 - 0.25)^{2-1}\times 0.25\)

P(X = 2) = 0.75 × 0.25

P(X = 2) = 0.1875

Thus, the required probability is  0.1875

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The exact value of the integral ∭E (xy + z²) dV, where E = {(x, y, z) | 0 ≤ x ≤ 3, 0 ≤ y ≤ 4, 0 ≤ z ≤ 7}, is 3045.

To find the exact value of the integral ∭E (xy + z²) dV, where E = {(x, y, z) | 0 ≤ x ≤ 3, 0 ≤ y ≤ 4, 0 ≤ z ≤ 7}, we can evaluate it using any of the three orders of integration. Let's use the order of integration: x, y, z.

∭E (xy + z²) dV = ∫₀³ ∫₀⁴ ∫₀⁷ (xy + z²) dz dy dx

Integrating with respect to z:

∫₀³ (xyz + (1/3)z³) [z]₀⁷ dy dx

= ∫₀³ (7xy + (1/3)7^3) dy dx

= ∫₀³ (7xy + 343/3) dy dx

Integrating with respect to y:

∫₀⁴ (7xy² + 343/3)y [y]₀³ dx

= ∫₀⁴ (7x(4³) + 343/3)(4) dx

= ∫₀³ (448x + 343) dx

Integrating with respect to x:

(448/2)x² + 343x [x]₀³

= (448/2)(3²) + 343(3) - (448/2)(0^2) - 343(0)

= (448/2)(9) + 343(3)

= 2016 + 1029

= 3045

Therefore, the exact value of the integral ∭E (xy + z²) dV is 3045.

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The point on the line y = (-6/7) x + 6 that is closest to the origin is (2.96, 8.54)

The equation of the line is,

y = (-6/7) x + 6

So each point on the given line can be expressed as (x, (-6/7) x + 6).

So the distance of the point on the line to the origin (0, 0) is given by,

d = √[x² + {(-6/7) x + 6}²]

d² = x² + {(-6/7) x + 6}²

d² = x² + {(-6/7) x}² + 6² + 2 (-6/7)x * 6

d² = x² + 36x²/49 + 36 - 72x/7

d² = 85x²/49 - 72x/7 + 36

Let, z = 85x²/49 - 72x/7 + 36

differentiating the above relation with respect to 'x' we get,

dz/dx = 170x/49 - 72/7

d²z/dx² = 170/49

Now, dz/dx = 0. So,

170x/49 - 72/7 = 0

170x/49 = 72/7

x = (72*49)/(7*170)

x = 252/85

At x = 252/85, d²z/dx² = 170/49 > 0

So, at x = 252/85, z is minimum.

So, at x = 252/85, d² is minimum thus d is minimum.

So, the point is = (252/85, [(-6/7)(252/85) + 6]) = (2.96, 8.54) [Rounding off to nearest hundredth].

Hence the required point is (2.96, 8.54).

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Answer:

63/210 or 3/10

B.

Step-by-step explanation:

14 · 15 = 210

9 · 7 = 63

Answer:

B- 3/10

Step-by-step explanation:

9/14 x 7/15

multiply across so you would now get 63/210 and we can divide the top and bottom by 21  so it will simplify to 3/10

Answer:

1 0 0 2

0 1 0 1

0 0 1 -1

Step-by-step explanation:

Answer:

picture below

Step-by-step explanation:

A scatter plot chart of stock returns versus past stock returns will typically appear as a random pattern mostly concentrated in the top-right and lower-left quadrants.

This pattern indicates that there is a positive correlation between past and current stock returns, but there are also instances where current returns are negative despite past positive returns.

The top-right quadrant represents instances where both past and current returns are positive, while the lower-left quadrant represents instances where both past and current returns are negative.

The random pattern indicates that stock returns cannot be predicted with certainty based on past returns alone.

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The required required angles are ∠1 = 111 degree and ∠2 = 26 degree.

In a triangle, there are three points. These angles are created by the triangle's two edges coming together at the triangle's vertex. Three interior angles added together make 180 degrees. The side length creates an exterior angle if we extend it outside.

We will use sum of angles on straight line is 180 degree

180 - 128 = 52 degree

Then

52 + 17 + ∠1 = 180

∠1 = 180 - 69 = 111 degree

Similarly

180 - 111 = 69 degree

Then,

69 + 85 + ∠2 = 180

∠2 = 180 + 154

∠2 = 26 degree.

Thus, required angles are ∠1 = 111 degree and ∠2 = 26 degree.

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Answer:

x=-7

Step-by-step explanation:

Move all terms that don't contain  x  to the right side and solve.

Answer:

-7

Step-by-step explanation:

16 - (-5) = 21

21 / -3 = -7

Answer:

x=8

Step-by-step explanation:

lol so easy

Answer and Step-by-step explanation:

First, let's solve for z.

3z - 1 ≥ -7

We add 1 to both sides.

3z ≥ -6

Now we divide both sides by 3.

z ≥ -2

Since we got this as our answer, that means  Answer choice D is the correct answer.

#teamtrees #WAP (Water And Plant)