3. It took Juan 48 minutes to drive 12 miles. Calculate his speed in miles per hour.

Answer:

y - 3y^2 + 4y^2 - 12y

y^2 - 11y

Step-by-step explanation:

The equivalent equation for the expression y = 3x-6 is none.

Equivalent equation:

If the two equations are said to be equivalent when they have the same solution set. Then it is called as Equivalent equation.

Given,

Here we have the expression y = 3x-6

Now, we need to find the equivalent equation.

In order to find the equivalent equation, we have to take some sample values for x,

The sample value of x as 1, 2, 3

Now, we have to apply these values on the given expression first,

Then we get,

x = 1 => y = 3(1) - 6 = -3

x = 2 => y = 3(2) - 6 = 0

x = 3 => y = 3(3) -6 = 9

Now, we have to apply these to the given equation and which has the same value of the given expression,

x = 1 => 3(1) - 2y = 6 = -2y = 6 - 3 => y = -3/2

x = 2 => 3(2) - 2y = 6 = -2y = 6 - 6 => y = 0

x = 3 => 3(3) - 2y = 6 = -2y = 6 - 9 => y = 3/2

This is not equal one.

Move on to the second one,

x = 1 => 2(1) + 3y = -6 => 3y = -6 - 2 => y = -8/3

x = 2 =>  2(2) + 3y = -6 = 3y = -6 - 4 => y = -10/3

x = 3 =>  2(3) + 3y = -6 = 3y = -6 - 6 => y = -4

This is not a equivalent one.

Move on to the third expression,

x = 1 => 3(1) - 2y = 12 = -2y = 12 - 3 => y = -9/2

x = 2 => 3(2) - 2y = 12 = -2y = 12 - 6 => y = -3

x = 3 => 3(3) - 2y = 12 = -2y = 12 - 9 => y = -3/2

This is not a equivalent one.

Finally we have to use the last one, then  we get,

x = 1 => 2(1) - 3y = 18 => -3y = 18 - 2 => y = -16/3

x = 2 =>  2(2) - 3y = 18 => -3y = 18 - 4 => y = -14/3

x = 3 =>  2(3) - 3y = 18 => -3y = 18 - 6 => y = -4

Therefore, none of them are the equivalent one.

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The particular solution satisfying the initial conditions is y(t) = (1/2)*cos(2t) - (1/8)*sin(2t) + (1/4)t - 1/2 and the graph has been plotted.

The given differential equation is y′′ + 4y = (t − ) − (t − 2). To solve this equation, we will first find the general solution to the homogeneous part, y′′ + 4y = 0, and then find a particular solution to the non-homogeneous part, (t − ) − (t − 2).

The characteristic equation for the homogeneous part is obtained by assuming the solution is of the form. Substituting this into the equation, we get r² + 4 = 0. Solving this quadratic equation, we find two complex roots: r = ±2i. Therefore, the general solution to the homogeneous part is y_h(t) = c₁cos(2t) + c₂sin(2t), where c₁ and c₂ are arbitrary constants.

To find a particular solution to the non-homogeneous part, we will use the method of undetermined coefficients. Since the non-homogeneous part contains terms (t − ) and (t − 2), we assume a particular solution of the form y_p(t) = At + B, where A and B are constants to be determined.

Taking the derivatives, we have y′_p(t) = A and y′′_p(t) = 0. Substituting these into the differential equation, we get 0 + 4(At + B) = (t − ) − (t − 2). Equating the coefficients of the like terms on both sides, we get 4A = 1 and 4B = -2.

Solving these equations, we find A = 1/4 and B = -1/2. Thus, the particular solution is y_p(t) = (1/4)t - 1/2.

The general solution to the original differential equation is given by the sum of the homogeneous and particular solutions: y(t) = y_h(t) + y_p(t).

y(t) = c₁cos(2t) + c₂sin(2t) + (1/4)t - 1/2.

We are given the initial conditions y(0) = 0 and y′(0) = 0.

Substituting these values into the general solution, we get:

y(0) = c₁cos(0) + c₂sin(0) + (1/4)*0 - 1/2 = 0.

This equation simplifies to c₁ - 1/2 = 0, which gives c₁ = 1/2.

Differentiating the general solution with respect to t, we get:

y′(t) = -2c₁sin(2t) + 2c₂cos(2t) + 1/4.

Substituting t = 0 and y′(0) = 0 into the above equation, we have:

y′(0) = -2c₁sin(0) + 2c₂cos(0) + 1/4 = 0.

This equation simplifies to 2c₂ + 1/4 = 0, which gives c₂ = -1/8.

Therefore, the particular solution satisfying the initial conditions is:

y(t) = (1/2)*cos(2t) - (1/8)*sin(2t) + (1/4)t - 1/2.

The graph will show how the solution varies with the input value t. It will illustrate the oscillatory nature of the cosine and sine functions, along with the linear term (1/4)t, which represents a gradual increase. The initial condition y(0) = 0 ensures that the graph passes through the origin, and y′(0) = 0 implies the absence of an initial velocity.

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Answer:

The answer is D. x=-1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. Divide both sides by 10.

2. Add 4 to both sides.

3. Subtract 10x from both sides.

4. Divide both sides by -8.

The answer is D.

Answer:

a / 3(a + b).

Step-by-step explanation:

3a / (9(a + b))

The 3/9 cancels to 1/3 so the answer is

a / 3(a + b)

Answer:

a/3(a+b)

Step-by-step explanation:

We can divide both the top and bottom of the expression by 3 to reduce the fraction. This gives us a/3(a+b), which is fully reduced.

Therefore, the distance between points P and Q to the nearest tenth is about 10.6 units.

The Pythagorean Theorem is a mathematical formula that describes the relationship between the sides of a right triangle. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical notation, the theorem can be expressed as: c² = a² + b² where c is the length of the hypotenuse, and a and b are the lengths of the other two sides. The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery. The Pythagorean Theorem has many practical applications in fields such as architecture, engineering, physics, and trigonometry. It can be used to solve a wide range of problems involving right triangles, such as finding the distance between two points in a coordinate plane, calculating the height or length of an object, or determining the angle of elevation or depression.

Here,

To find the distance between points P(3, 2) and Q(10, 10), we can use the distance formula or the Pythagorean theorem. Since the prompt asks us to use the Pythagorean theorem, we can create a right triangle with points P and Q as two of its vertices and find the length of the hypotenuse using the theorem.

First, we need to find the lengths of the legs of the right triangle. The horizontal leg is the difference between the x-coordinates of the two points:

leg₁ = 10 - 3 = 7

The vertical leg is the difference between the y-coordinates of the two points:

leg₂ = 10 - 2 = 8

Now, we can use the Pythagorean theorem to find the length of the hypotenuse (c), which is the distance between points P and Q:

c² = leg₁² + leg₂²

c² = 7² + 8²

c² = 49 + 64

c² = 113

c ≈ √113 ≈ 10.6 (rounded to the nearest tenth)

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Answer:

d

Step-by-step explanation:

-3(4x+2)-2x

-12x+6-2x

-14x+6

Answer:

*error* error* This account is here to assist CodeName: ELA/ LANGUAGE ARTS/ ENGLISH. Please say RESET in order for me to go back to ELA/ LANGUAGE ARTS/ ENGLISH.

Step-by-step explanation:

Answer:

Hi there!

Your answer is:

B) 25/100 × 64

C) .25× 64

Step-by-step explanation:

25% of 64 is

100% is 64

/100

1% is .64

× 25

25% of 64 is 16!

A) 25× 64 = 1600 NO

B) 25/100 × 64 = 16 YES ✓

C) .25 × 64 = 16 YES✓

D) 64 ÷ 25/100= 256 NO

E) 25÷ 64/100= 39.0625 NO

Hope this helps!

In general, the exponential growth/decay formula is

If 1+r>1, the function is growing while 1+r<1 implies that it is decaying.

In our case,

Furthermore,

Finally, notice that t stands for the number of days; therefore, 24t implies that the function exponentially decays 60% a total of 24 times per day, and 24 times per day is equivalent to 1 time every hour.

Answer:

I think the answer is A

Sorry if i am wrong

Step-by-step explanation:

The condition for the first dark fringe through a single slit of width w is when the path difference between the light waves at the edges of the slit equals a half wavelength= (λ/2).

This can be expressed mathematically as:
w * sin(θ) = (m + 1/2) * λ, where m = 0 for the first dark fringe, w is the slit width, θ is the angle of the dark fringe from the central maximum, and λ is the wavelength of light.
When light passes through a single slit, it diffracts and creates an interference pattern with alternating bright and dark fringes on a screen. The dark fringes occur when light waves from the edges of the slit interfere destructively, which means their path difference must be an odd multiple of half a wavelength (λ/2).
For the first dark fringe, we set m = 0 in the equation:
w * sin(θ) = (0 + 1/2) * λ
So, the condition for the first dark fringe is:
w * sin(θ) = λ/2

Hence, The condition for the first dark fringe through a single slit of width w is when the path difference between the light waves at the edges of the slit equals a half wavelength (λ/2). This can be represented by the equation w * sin(θ) = λ/2.

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Refer to the image for the graph of the lines.

The common form of the equation of a line is y = mx + c, where m is the slope of the line and c is a constant.

We need to draw any line with a slope m = 2, and

another line with a slope m = -2.

Disclaimer: Let us assume that the constant c = 0.

Then the equation to the line with a slope of "positive" 2 is given by

y = 2x

Then the equation to the line with a slope of "negative" 2 is given by

y = -2x

Refer to the attached image for the graph of the lines with the slope of "positive" 2 and "negative" 2.

f: green line indicates a line with a slope of "positive" 2.

g: blue line indicates a line with a slope of "negative" 2.

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u⃗ and v⃗ are the desired pair of vectors.To find a pair of vectors u⃗ and v⃗ in ℝ⁴ that span the set of all vectors x⃗ ∈ ℝ⁴ ,

that are mapped into the zero vector by the transformation x⃗ ↦ ax⃗, we need to find the nullspace (or kernel) of the matrix A.

The nullspace of a matrix A consists of all vectors x⃗ such that Ax⃗ = 0.

Given the matrix A:

A = [[10, 3, -5, 1], [-3, -1, 1, -5], [11, 5, -11, 5], [0, 0, 0, 0]]

We can set up the following equation:

Ax⃗ = 0

Multiplying the matrix A by the vector x⃗ and setting it equal to the zero vector:

[[10, 3, -5, 1], [-3, -1, 1, -5], [11, 5, -11, 5], [0, 0, 0, 0]] * [x₁, x₂, x₃, x₄]ᵀ = [0, 0, 0, 0]

This gives us the following system of linear equations:

10x₁ + 3x₂ - 5x₃ + x₄ = 0

-3x₁ - x₂ + x₃ - 5x₄ = 0

11x₁ + 5x₂ - 11x₃ + 5x₄ = 0

0 = 0 (This equation represents the trivial condition)

To find the nullspace of A, we can solve this system of equations using row reduction or Gaussian elimination. The solutions to the system of equations will give us the values of x₁, x₂, x₃, and x₄ that make Ax⃗ = 0.

Solving the system of equations, we find that the nullspace of A is spanned by the vectors:

u⃗ = [1, -1, -2, 0]ᵀ

v⃗ = [3, -1, 0, 1]ᵀ

These two vectors, u⃗ and v⃗, form a pair that spans the set of all vectors x⃗ ∈ ℝ⁴ that are mapped into the zero vector by the transformation x⃗ ↦ Ax⃗.

Therefore, u⃗ and v⃗ are the desired pair of vectors.

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A. The fixed effects regression model: The slope coefficients are allowed to differ across entities, but the intercept is "fixed" (remains unchanged).

B. In a log-log model, may include logs of the binary variables, which control for the fixed effects. C. The fixed effects regression model does not specifically address heteroskedasticity, so it does not "fix" or address the effect of heteroskedasticity. D. The fixed effects regression model includes n different intercepts, one for each entity or observation in the dataset.

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Answer:

  75

Step-by-step explanation:

Let t and u represent the tens and units digits, respectively.

  t = u + 2 . . . . the tens digit exceeds the units digit by 2

  t + 2u = 17 . . . . the sum of the tens digit and twice the units digit is 17

Substituting for t in the second equation, we get ...

  (u +2) +2u = 17

  3u = 15 . . . . . . . . subtract 2

  u = 5 . . . . . . . . . . divide by 3

  t = u+2 = 7

The number is 75.

_____

Check

7 exceeds 5 by 2. 7 + twice 5 = 7 + 10 = 17.

There are 84 possible codes that can be formed using the given conditions.

The set X has 3 elements (A, E, C) and the set Y has 4 elements (3, 6, 5, 2). The code consists of 2 different symbols selected from X followed by 4 symbols (not necessarily different) from Y. To calculate the number of possible codes, we need to determine the number of ways to select 2 symbols from X and the number of ways to select 4 symbols from Y.

The number of ways to select 2 symbols from X can be calculated using combinations. Since order does not matter, we use the formula for combinations: C(n, r) = n! / (r!(n-r)!). In this case, n = 3 (number of elements in X) and r = 2 (number of symbols to be selected). So, C(3, 2) = 3! / (2!(3-2)!) = 3.

The number of ways to select 4 symbols from Y can be calculated using permutations since repetition is allowed. Using the formula for permutations with repetition, we have P(n+r-1, r) = (n+r-1)! / r!(n-1)!. In this case, n = 4 (number of elements in Y) and r = 4 (number of symbols to be selected). So, P(4+4-1, 4) = 11! / 4!(11-1)! = 11! / 4!7! = 330.

To calculate the total number of possible codes, we multiply the number of ways to select symbols from X and Y: 3 * 330 = 990.

Therefore, there are 990 possible codes that can be formed using the given conditions.

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To find the surface area of the solid obtained by rotating the curve y = 1/4\(x^2\) - 1/2ln(x) about the y-axis, we can use the formula for the surface area of revolution:

A = 2π ∫[a,b] y ds

Where a and b are the limits of integration, y is the function representing the curve, and ds is the differential arc length element.

First, let's find ds:

ds = √(1 + (dy/dx)^2) dx

Taking the derivative of y with respect to x:

dy/dx = 1/2x - 1/(2x)

Now, we can substitute this into the ds equation:

ds = √(1 + (1/2x - 1/(\(2x))^2\)) dx

  = √(1 + 1/4\(x^2\) - 1/x + 1/(4\(x^2\))) dx

  = √(5/4\(x^2\) - 1/x) dx

The limits of integration are 2 ≤ x ≤ 4.

Now, we can calculate the surface area using the formula:

A = 2π ∫[2,4] y ds

  = 2π ∫[2,4] (1/4\(x^2\) - 1/2ln(x)) √(5/4\(x^2\)- 1/x) dx

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As per the concept of Simple interest, the value of x that refers the time is 0.000057.

Simple interest:

Simple interest is obtained by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

Give,

Here we have the expression like the following:

p*r*t=I

4350 * 4 * x =1

Here we need to find the value of x.

While we looking into the expression, we have identified that the value of

Principal amount (p) = 4350

rate of interest (r) = 4

Time = x

Interest amount (I) = 1

So, while we execute this expression then we get the value of times as,

=> 4350 x 4 x x = 1

Here we need the value of x so, we have to move the other to the right hand side, then we get,

=> x = 1/(4350 x4)

=> x = 1/17400

=> x = 0.000057

Therefore, the value of x is 0.000057.

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Answer:

ABC Sports

Step-by-step explanation:  Because $50 off is $200, and the rest would be like $10 off. Please give Brainliest! :D

Answer:

The answer is ABC Mart D is the correct answer

Step-by-step explanation:

If the function approaches a specific value (y = c) as x approaches infinity or negative infinity, then it has a horizontal asymptote at y = c.

To determine if a function has a horizontal asymptote, consider the behavior of the function as x approaches positive or negative infinity. The main idea is to analyze the end behavior of the function.

Degree of Polynomials:

If the degree of the numerator is less than the degree of the denominator, the function has a horizontal asymptote at y = 0 (the x-axis). If the degree of the numerator is equal to the degree of the denominator, divide the coefficients of the highest degree terms. The resulting ratio determines the horizontal asymptote. If the degrees are unequal, there is no horizontal asymptote.

Limits:

Take the limit of the function as x approaches positive or negative infinity. If the limit evaluates to a finite value, that value represents the horizontal asymptote. If the limit is infinite (∞) or does not exist, there is no horizontal asymptote.

Infinity:

If the function involves terms like exponential functions or logarithmic functions, analyze their behavior as x approaches infinity. Exponential functions with positive exponents tend to infinity, while those with negative exponents approach zero. Logarithmic functions tend to negative infinity as x approaches zero.

By considering these methods, you can determine if a function has a horizontal asymptote and find its equation or behavior as x approaches infinity or negative infinity. Remember to apply these techniques with caution and consider the specific characteristics of the function being analyzed.

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Answer:

Vertical line (straight up and down)

Step-by-step explanation:

The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0).

Answer:

Step-by-step explanation:

the slope of any line is rise/run. What this means is that you have the change in y value divided by the change in x. If you have two points whos x value stays the same, or does not change, you have the change in y divided by 0. Dividing any number by 0 gives you the answer “undefined”.

Answer:

It's undefined since it's a vertical line.

Step-by-step explanation:

Answer:

He can invite 11 people and pay the rest for the party

Step-by-step explanation:

6 x 11 is

66 + 60 is 126

Answer:

The coordinate of the initial point is given below as

The coordinate of the terminal point is

Concept:

The formula below will be used to calculate a linear form of v

By substituting the values, we will have

Hence,

The final answer is

The FIRST OPTION is the right answer

The required number of children and adults for sitting in the theater are 300 and 50 respectively.

A equation is supposed to be linear equation in two factors in the event that it is written as hatchet + by + c=0, where a, b and c are genuine numbers and the coefficients of x and y, i.e an a and b separately, are not equivalent to nothing. For instance, 10x+4y = 3 and - x+5y = 2 are straight equation in two factors.

Let be consider number of children be x and that of adults is y.

We have,

x + y = 350-------(1)

y = 350 - x

And 5x + 10y = 2000------------------(2)

Put value of y in equation (2)

5x + 10( 350 - x) = 2000

5x + 3500 - 10x = 2000

-5x = -1500

x = 300

Then

y = 350 - x = 350 - 300 = 50

Thus, There will be 300 children and 50 adults in the  theater .

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Answer:

x = 11

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

7x = 4x + 33

3x = 33 Bring the x's to one side.

x = 11

The standard error of this measurement is 6.32

The standard error of measurement is simply the estimate of how repeated measures of an entity on the same instrument tend to be distributed around the entity' “true” score.

In this case, we have the following parameters

Standard deviation = 20

Reliability = 0.90

The standard error of measurement from the standard deviation and the reliability is calculated using the following formula

Standard error of measurement = Standard deviation * √1 - reliability

Substitute the known values in the above equation, so, we have the following representation

Standard error of measurement = 20 * √1 - 0.90

This gives

Standard error of measurement = 20 * √0.10

Evaluate

Standard error of measurement = 6.32

Hence, the standard error in this case is 6.32

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Answer:

Solution Given:

let ABC be an equilateral triangle with the vertex A(2,-1) and slope =-1.

and

∡ABC=∡BAC=∡ACB=60°

slope of BC\([ m_1]=-1\)

we have

\(\theta\)=60°

Slope of AB=\([ m_2]=a\)

now

we have

angle between two lines is

\(Tan\theta =±\frac{m_1-m_2}{1+m_1m_2}\)

now substituting value

tan 60°= ± \(\frac{-1-a}{1+-1*a}\)

\(\sqrt{3}=±\frac{-1-a}{1-a}\)

doing criss-cross multiplication;

\((1-a)\sqrt{3}=±-(1+a)\)

\(\sqrt{3}-a\sqrt{3}\)=±(1+a)

taking positive

\(-a-a\sqrt{3}=1-\sqrt{3}\)

\(-a(1+\sqrt{3})=1-\sqrt{3}\)

a=\(\frac{1-\sqrt{3}}{-(1+\sqrt{3})}=\frac{\sqrt{3}-1}{1+\sqrt{3}}\)

taking negative

\(a-a\sqrt{3}=-1-\sqrt{3}\)

\(a(1-\sqrt{3})=-1-\sqrt{3}\)

a=\(\frac{-(1+\sqrt{3})}{(1-\sqrt{3})}=\frac{\sqrt{3}+1}{-1+\sqrt{3}}\)

Equation of a line when a =\(\frac{\sqrt{3}-1}{1+\sqrt{3}}\)

and passing through (2,-1),we have

\( y-y_1=m(x-x_1)\)

y+1=\(\frac{\sqrt{3}-1}{1+\sqrt{3}}\)(x-2)

y=\(\frac{\sqrt{3}-1}{1+\sqrt{3}}x-2\frac{\sqrt{3}-1}{1+\sqrt{3}}\)-1

Equation of a line when a =\(\frac{\sqrt{3}+1}{-1+\sqrt{3}}\)

and passing through (2,-1),we have

\( y-y_1=m(x-x_1)\)

y+1=\(\frac{\sqrt{3}+1}{-1+\sqrt{3}}\)(x-2)

y+1=\(\frac{\sqrt{3}+1}{-1+\sqrt{3}}x -2\frac{\sqrt{3}+1}{-1+\sqrt{3}}\)

y=\(\frac{\sqrt{3}+1}{-1+\sqrt{3}}x -2\frac{\sqrt{3}+1}{-1+\sqrt{3}}-1\)