4
Use a truth table to show the following equivalence: p^q=~(p+4)

Answer:

yes

Step-by-step explanation:

no

The equation of the conic with Points at (1,−1) directrix along x−y+1=0 and with eccentricity 2​ is 2xy - 4x -4y +1 = 0 .

Equation:

An equation is a formula that connects two expressions with the equal sign = to indicate that they are equal. Solving an equation involving variables involves determining which values ​​of the variables make the equation true. The variables for which the equation must be solved are also called unknowns, and the values ​​of the unknowns that satisfy the equation are called solutions of the equation. There are two types of comparisons: identity comparisons and conditional comparisons. The identity is true for all values ​​of the variable. Conditional comparisons are only true for certain values ​​of variables

According to the Question:

Let P(x, y) be any point on conic. Then,

    \(\sqrt{(x-1)^2+(y+1)^2}\)  = \(\sqrt{2} (\frac{x-y+1}{\sqrt{2} } )\)

⇒ (x-1)²+(y+1)² = (x- y+ 1)²

⇒ 2xy - 4x -4y +1 = 0

The above equation is the required equation of conic.

Complete Question:

The equation of the conic with focus at (1,−1) directrix along x−y+1=0 and with eccentricity 2​ is.

1) x²− y²=1O

2) xy =1O

3) 2xy−4x+4y+1 =0

4) 2xy+4x−4y−1 =0

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The time it would take Colleen alone to clear the yard of leaves is 40 minutes (option d). So the answer is d. 40 minutes

Let's set up the equation based on the given information:

1/24 is the rate at which Sean and Colleen work together (clearing the yard in 24 minutes).

Let's denote the time it takes Colleen to clear the yard alone as c minutes. According to the given information, it would take Sean 20 minutes longer than Colleen to clear the yard alone, so Sean's time is (c + 20) minutes.

To set up the equation, we can combine their individual rates of work:

1/c is Colleen's rate of work (clearing the yard in c minutes).

1/(c + 20) is Sean's rate of work (clearing the yard in c + 20 minutes).

Given that their combined rate is 1/24, we can set up the equation:

1/c + 1/(c + 20) = 1/24

To solve this equation and find the value of c, we can multiply both sides by the common denominator of 24c(c + 20):

24(c + 20) + 24c = c(c + 20)

Simplifying and rearranging the equation:

24c + 480 + 24c = c^2 + 20c

48c + 480 = c^2 + 20c

Rearranging the terms and setting the equation equal to zero:

c^2 - 28c - 480 = 0

Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. By factoring, we find:

(c - 40)(c + 12) = 0

This gives two possible values for c: c = 40 or c = -12.

Since time cannot be negative, we discard the solution c = -12.

Therefore, the time it would take Colleen alone to clear the yard of leaves is 40 minutes (option d).So the answer is d. 40 minutes.

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Answer:

Your answer would be X ≥ -3

Step-by-step explanation:

Answer:

explain yourself

Step-by-step explanation:

explain yourself, rather than writing the answer as x=88 explain why it is, for example we can say that

"since a four sided shapes total interior angles are 360⁰ we can add up the angles that we know, here 156, 69 and 47, giving us 272, subtracting that from 360 gives us 88 which is the answer for x"

Answer:

answer below

Step-by-step explanation:

angles in quadrilateral add up to 360°

Answer:

A

Step-by-step explanation:

Measurement is the numerical quantification of the attributes of an object or event, which can be used to compare with other objects or events.

Measurement is used to compare or determine the relation of a quantity, physical or not, with a certain  numerical value.

We have to determine, which is used to compare or determine the relation of a quantity, physical or not, with a certain  numerical value

According to the question,

The process of measurement is required to measure or compare physical quantities in day-to-day life.

Thus, to measure each of the standard quantities, we choose certain units for them that are accepted worldwide.

Other similar quantities can also be expressed in terms of these units and can be measured accordingly.

The physical quantities are measured in terms of the unit and are known as a standard of that physical quantity.

The length of the foot, the width of a finger, and the distance between two different places were commonly measured by different units of measurements.

For unique measurement properties, scientists accepted standard units of measurement all over the world.

Hence, Measurement is used to compare or determine the relation of a quantity, physical or not, with a certain numerical value.

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Answer:

SA = 94 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 4

w = 5

h = 3

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 5(4) + 3(4) + 3(5) )

SA = 2 ( 20 + 12 + 15 )

SA = 2 ( 47 )

SA = 94 ft²

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Answer:

32 units.

Step-by-step explanation:

look up a picture of a 306090 triangle, it will make sense :)

Answer:

32

Step-by-step explanation:

cos 30 = \(\frac{\sqrt{3} }{2}\)

\(\frac{\sqrt{3} }{2}\) = 16\(\sqrt{3}\) / n

n = 16\(\sqrt{3}\) * \(\frac{2}\sqrt{3} }\)

n = 32 units

The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.

To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:

We have:

Point: (0, 1)

Slope: 5xy

We can start by integrating the slope function to find the equation of the curve:

∫(dy/dx) dx = ∫(5xy) dx

Integrating both sides:

∫dy = ∫(5xy) dx

Integrating with respect to y on the left side gives us:

y = ∫(5xy) dx

To solve this integral, we treat y as a constant and integrate with respect to x:

y = 5∫(xy) dx

Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:

y = 5 * (1/2) * x^2y + C

Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:

1 = 5 * (1/2) * (0)^2 * 1 + C

1 = C

Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:

y = 5 * (1/2) * x^2y + 1

Simplifying further, we have:

y = (5/2) * x^2y + 1

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Given:

The interval notation is,

Required:

To fill the blanks.

Explanation:

The interval notation [1,3) represents the set of real numbers between 1 and 3, including 1 but not 3.

Final Answer:

The interval notation [1,3) represents the set of real numbers between 1 and 3, including 1 but not 3.

Answer:

\(\text{area of sector} = \frac{320\pi}{3} \text{ mi}^2\)

Step-by-step explanation:

Let's use the formula for the area of the sector:
\(\text{area of sector} = (\frac{\theta}{360^\circ}) \pi r^2\),
where r is radius and θ the angle in degrees.

Given information:

r = 16 mi

θ = 150°

Using the formula:

\(\text{area of sector} = (\frac{\theta}{360^\circ}) \pi r^2 =\\\\ = (\frac{150^\circ}{360^\circ}) \pi (16\text{ mi})^2 =\\\\ = (\frac{150 \cdot 16^2}{360}) \pi \text{ mi}^2 =\\\\ = (\frac{320}{3}) \pi \text{ mi}^2 =\\\\ = \frac{320\pi}{3} \text{ mi}^2\)

Answer:

B

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = 4 , then

y = 4x + c ← is the partial equation

to find c substitute (- 3, - 1 ) into the partial equation

- 1 = - 12 + c ⇒ c = - 1 + 12 = 11

y = 4x + 11 ← equation of line

Answer:

.

Step-by-step explanation:

Answer:

10.7a-8.1b

Step-by-step explanation:

Answer: 24.3a - 8.1 + 0.29

Step-by-step explanation:

YOUR WELCOME

The slope of a line is a measure of its steepness and can be calculated using the formula:

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

In this case, the points (0,3) and (36,0) represent the coordinates of two points on the ramp. To find the slope of the ramp, we can plug these values into the formula:

slope = (0 - 3) / (36 - 0) = -3 / 36 = -1/12

The slope of the ramp is -1/12. This indicates that the ramp is relatively flat, as a negative slope means that the line is sloping downward.

To find the slope of the second ramp, represented by the function g(x) = -1/4x + 2, we can take the derivative of the function. The derivative of a function represents the slope of the function at any given point, and it is calculated using the formula:

derivative = f(x) = -1/4

The derivative of the function g(x) is a constant value of -1/4, which means that the slope of the second ramp is also -1/4. This is a steeper slope than the first ramp, as the value of the derivative is larger in magnitude.

Without knowing the specific form of the velocity function v(t), it is not possible to determine the exact distance traveled.

The total distance traveled by a particle can be found by integrating its velocity over time. If the velocity of the particle at time t is given by the function v(t), then the total distance traveled between time t1 and t2 is given by:

distance = ∫v(t)dt from t1 to t2

In this case, we want to find the distance traveled between time 0 and time 16, so t1 = 0 and t2 = 16. Without knowing the specific form of the velocity function v(t), it is not possible to determine the exact distance traveled.

Velocity is a vector quantity that describes the rate at which an object changes its position in space. It is a combination of both speed and direction and is typically represented by the symbol v.

In physics, velocity is defined as the derivative of position with respect to time. If the position of an object at time t is given by the function x(t), then its velocity at time t is given by:

v(t) = dx(t)/dt

This means that velocity is the rate of change of position with respect to time. For example, if an object moves in a straight line from position x1 to x2 in time t, its average velocity during that time is given by:

v = (x2 - x1)/t

Velocity is an important concept in mechanics, as it is used to describe the motion of objects and to calculate various physical quantities, such as force and acceleration.

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Aryabhata, also called Aryabhata I or Aryabhata the Elder, (born 476, possibly Ashmaka or Kusumapura, India), astronomer and the earliest Indian mathematician whose work and history are available to modern scholars. He is also known as Aryabhata I or Aryabhata the Elder to distinguish him from a 10th-century Indian mathematician of the same name. He flourished in Kusumapura—near Patalipurta (Patna), then the capital of the Gupta dynasty—where he composed at least two works, Aryabhatiya (c. 499) and the now lost Aryabhatasiddhanta.

Aryabhatasiddhanta circulated mainly in the northwest of India and, through the Sāsānian dynasty (224–651) of Iran, had a profound influence on the development of Islamic astronomy. Its contents are preserved to some extent in the works of Varahamihira (flourished c. 550), Bhaskara I (flourished c. 629), Brahmagupta (598–c. 665), and others. It is one of the earliest astronomical works to assign the start of each day to midnight.

Aryabhatiya was particularly popular in South India, where numerous mathematicians over the ensuing millennium wrote commentaries. The work was written in verse couplets and deals with mathematics and astronomy. Following an introduction that contains astronomical tables and Aryabhata’s system of phonemic number notation in which numbers are represented by a consonant-vowel monosyllable, the work is divided into three sections: Ganita (“Mathematics”), Kala-kriya (“Time Calculations”), and Gola (“Sphere”).

Answer:

1 to 20 that have the same mean, median, and range. ... The set {3,3,5,6,8} contains 5 whole numbers whose mean, median, and range are 5

Answer:

hyperbola?

\(\frac{(y+4)^{2} }{36}\) - \(\frac{(x-6)^{2} }{49}\) =1

Enter your answer in point-slope form by filling in the boxes. Enter the slope as a simplified fraction.

Answer:

1096.6

Step-by-step explanation:

The answer would be 1096.63316, but since you are rounding to the nearest tenth, then your answer would be 1096.6.

Answer:

1096.6.

Step-by-step explanation:

e = about 2.7

2.7^7is about 1046

Answer:

4 ft shadow=3 ft tall

?(x)=6 ft

4×6=3x

24=3x

24/3=x

8=x

that's my answer I think

John's savings amount as a function of time is S(t) = $24,000 / 25. Initially, he needs to save $24,000 for a new car. After the first month, he has saved $1,000. The savings amount is directly proportional to the time elapsed. The constant of proportionality is 1/24. Thus, John's savings amount can be determined based on the remaining amount he needs to save.

John's savings amount can be represented as a function of time and is proportional to the amount he still needs to save. Let's denote the amount John needs to save as N(t) at time t, and his savings amount as S(t) at time t. Initially, John needs to save $24,000, so we have N(0) = $24,000.

We know that John has saved $1,000 after the first month, which means S(1) = $1,000. Since his savings amount is proportional to the amount he still needs to save, we can write the proportionality as:

S(t) = k * N(t)

where k is a constant of proportionality.

We need to find the value of k to determine John's savings amount at any given time.

Using the initial values, we can substitute t = 0 and t = 1 into the equation above:

S(0) = k * N(0)  =>  $1,000 = k * $24,000  =>  k = 1/24

Now we have the value of k, and we can write John's savings amount as a function of time:

S(t) = (1/24) * N(t)

Since John's savings amount is proportional to the amount he still needs to save, we can express the amount he still needs to save at time t as:

N(t) = $24,000 - S(t)

Substituting the expression for N(t) into the equation for S(t), we get:

S(t) = (1/24) * ($24,000 - S(t))

Simplifying the equation, we have:

24S(t) = $24,000 - S(t)

25S(t) = $24,000

S(t) = $24,000 / 25

Therefore, John's savings amount at any given time t is S(t) = $24,000 / 25.

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Answer: I'd say reflection

Answer:

It is a reflection

Step-by-step explanation:

In Geometry, a reflection is known as a flip. A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.

Answer:

The triangle is a right triangle.

Step-by-step explanation:

Since The Pythagorean Theorem only works on right triangles, we can use this knowledge to prove whether this triangle is right:

\(a^2 + b^2 = c^2\\10^2 + (2\sqrt{39})^2 = 16^2\\100 + (4 \times 39) = 256\\100 + 156 = 256\\256 = 256\)

Therefore, the triangle is right.

The average speed was 60\(\frac{k+300}{96+t}\)

We are given that a plane travelled k miles in 96 minutes. Since we need the average speed in miles per hour we can convert 96 minutes to hours.

96 minutes = 96/60 =8/5 hours

We are also given that the Plane completed the remaining 300 miles in t minutes. We must also convert t minutes to hours.

t minutes = t/60 hours

Now we can calculate the average speed for the entire trip, using the formula for average speed.

Average Speed = total distance/ total time

Average Speed = (k +300)/(8/5 + t/60)

Average speed = (k + 300) / ((96 + t)/60)

Hence, Average Speed = 60(k + 300)/ (96 + t)

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The values of the given expressions are respectively,  -5.33, 5.33, -6,  -6,  6

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Here are the calculations for each expression:

1. (-8) x 2/3

  = (-8) x 2/3

  = -16/3

  = -5.33

2. (-8) x (-2/3)

   = (-8) x (-2/3)

   = 16/3

   = 5.33

3. -18/3 = -6

4. 18/(-3) = -6

5. (-18)/(-3) = 18/3

                 = 6

So, the values of each expression are -5.33..., 5.33..., -6, -6, and 6, respectively.

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Yes, the equation C-1(A+X)B-1=In has a solution, X. To find the solution, first use C-1(A+X)B-1=In to simplify to C-1 AB-1=In+X. Next, use matrix multiplication to expand C-1AB-1 to In+X = AC-1B-1-B-1C-1. Subtract In from both sides of the equation to get X=AC-1B-1-B-1C-1-In. This is the solution for X, where A, B, and C are nan invertible matrices.

Given that A, B, and C are invertible nan matrices, we have to check if the equation C-1(A+X)B-1=In has a solution or not, and if there is a solution, we have to find X.

Let's solve it. Let's multiply both sides of the equation by B and C, respectively, we get C-1(A+X)B-1B = IB and C-1(A+X) = B. Now, we have to multiply both sides by C on the left, so we get C*C-1(A+X) = CB, which becomes A+X = CB.

Now we have to multiply both sides by B-1 on the right, so we get A + XBB-1 = CBB-1, which becomes A + XB-1 = CB-1.Now, we have to multiply both sides by C-1 on the left, so we get C-1A + C-1XB-1 = I.

Now, we have to multiply both sides by B and C, respectively, which results in C-1AC-1B + XC-1B = B. Finally, X = B(C-1AC-1B)B-1 - C-1B + I. We know that if A and B are matrices of the same order, then (AB)-1 = B-1A-1. By using this property, we can write the solution as X = B-1(A-1 + C-1)-1B-1 - C-1B + I. So, the solution exists for the given equation.

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Answer:

B

Step-by-step explanation:

On a coordinate plane, parallel lines have the same slope as geometric figures are true. Thus option B is correct.

Marks, splines, spheres, and curved are used to build enclosed geometric shapes. We can see these shapes all around us. Illustrations of geometric shapes include circles, rectangles, triangles, and others. Any configuration of points, columns, or angles is a geometry figure.

A point is the most fundamental algebraic concept because it has no boundaries. Simply put, a point upon that plane is a location. A dot is used to symbolize it. A plane can be identified by three non-straight-line points.

As two or much more vectors seldom cross each other and are located on the same dimension, these are said to be parallel. The slope of these lines is constant. Coplanar lines that seem to be parallel are the ones that don't cross. Therefore, option B is the correct option.

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