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James determined that these two expressions were equivalent expressions using the values of x = 4 and x = 6. Which statements are true? Check all that apply.

The slope of the line perpendicular to the given line is calculated by taking the negative reciprocal of the given slope.The slope of the given line is 4/3. The slope of the line perpendicular to the given line is -3/4.

To find the slope of a line perpendicular to the given line, we need to take the negative reciprocal of the slope of the given line. The equation of the given line is y = 4/3x - 5/3. To calculate the slope, we need to rearrange the equation to the form y = mx + b, where m is the slope and b is the y-intercept. Rearranging the equation to the form y = mx + b, we get y = 4/3x - 5/3 which can be written as 4/3x - y = 5/3. The slope of the given line is 4/3. To find the slope of the line perpendicular to the given line, we take the negative reciprocal of 4/3 which is -3/4. Therefore, the slope of the line perpendicular to the given line is -3/4.

y = 4/3x - 5/3

4/3x - y = 5/3.

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Answer:

the division of (x^4 − 5x^3 + 17x + 3) by (x − 3) is equal to x^3 - 3x^2 + 4x - 3, with a remainder of 0.

Step-by-step explanation:

To divide (x^4 − 5x^3 + 17x + 3) by (x − 3), we can use polynomial long division. This involves dividing the polynomial by the divisor (x - 3) and expressing the result as a quotient plus a remainder. The remainder will be a polynomial of degree less than the degree of the divisor.

Here is how the division would look:

x  -3      x^4   -5x^3   17x   3

--- -----   ----  -----   ---  ---

 x  -3      x^3   -5x^2   17    0

           x^3  -3x^2   -2x^2   3

            0    -2x^2  -2x^2   0

            0      0     -4x^2   3

            0      0       -4x^2 -9

            0      0         0   -9

            0      0         0    0

From this division, we can see that the quotient is x^3 - 3x^2 + 4x - 3, and the remainder is 0. Therefore, we can express the division as:

(x^4 − 5x^3 + 17x + 3) / (x − 3) = (x^3 - 3x^2 + 4x - 3) + 0

This means that the division of (x^4 − 5x^3 + 17x + 3) by (x − 3) is equal to x^3 - 3x^2 + 4x - 3, with a remainder of 0.

Given equation= (x^4 - 5 x^3 + 17 x + 3)/(x - 3)

alternate form-x^3 - 2 x^2 - 6 x - 1 (for x!=3)

expanded form-x ((x - 2) x - 6) - 1 (for x!=3)

x^4/(x - 3) - (5 x^3)/(x - 3) + (17 x)/(x - 3) + 3/(x - 3)

quotient form and reminder-x^4 - 5 x^3 + 17 x + 3 = (x^3 - 2 x^2 - 6 x - 1)(x - 3) + 0.

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Yes, it is hard but with a lot of practice and putting effort one can also find it easy.

Physics requires the ability to solve problems, which can only be acquired via practice. In addition to these difficult ideas, there are theoretical concepts, mathematical calculations, and laboratory experiments.

It is better to comprehend the derivations than to memorise the formulas. Making a mess of several formulas will just increase your anxiety over the topic. Instead, if you strive to comprehend where they originate, you will begin to appreciate physics and its applications.

Physics is a difficult topic since it combines science and arithmetic, which may be challenging for the best of us. Nevertheless, despite how difficult it is, you can achieve if you follow a few simple guidelines and put yourself through some practice.

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The previous population of the city was 32,000.

Percentage is a measurement to find value of given number out of hundred.

Given that,

The current population of the city = 20,800.

Let the previous population was 100%.

Since, The population of the city decreased by 35%,

So, the current population of the city = 100 - 35 = 65%

According to given condition,

65 % = 20800

1 % = 20800 / 65

1 % = 320

100% = 320 x 100

         = 32,000

Hence, the initial population was 32,000.

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The equation 3x² + 5x + 2 = 0 has two solutions, x = -2 and x = -1/3. This means that when the equation is set equal to zero and then solved, the two values of x that will make the equation true are -2 and -1/3.

To solve 3x² + 5x + 2 = 0, we must first find the roots of the equation. To do this, we can use the quadratic formula to solve for the two roots. The quadratic formula is x = [-b ± √(b² - 4ac)]/2a, where a, b, and c are the coefficients of the equation. To apply this to our equation, we have a = 3, b = 5, and c = 2, so the formula becomes x = [-5 ± √(5² - 4(3)(2))]/2(3). Simplifying this equation gives us x = [-5 ± √29]/6. The two solutions of this equation are x = -2 and x = -1/3. This means that when the equation is set equal to zero and then solved, the two values of x that will make the equation true are -2 and -1/3.

x = [-5 ± √29]/6

x = [-5 + √29]/6 = -2

x = [-5 - √29]/6 = -1/3

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The system of equations that can be used to find the roots of the equation 4x 5 12x is:x = -5/8

1. Set up the equation: 4x - 12x = 5

2. Simplify the equation on the left side: -8x = 5

3. Solve for x: x = -5/8

To find the roots of the equation 4x - 12x = 5, we must first set up the equation. On the left side of the equation, we can simplify it to -8x = 5. Then, we can solve for x by dividing both sides by -8, giving us x = -5/8. This is the solution to the system of equations, and the root of the original equation.

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Answer:

2. One inch on the photograph represents 1.6 yards of the real bridge.

Step-by-step explanation:

1 yd = 36 in.

8 yd = 36 in./yd × 8 yd = 288 in

1 ft = 12 in.

5/12 ft × 12 in./ft = 5 in.

5 in. in the picture equals 288 inches real.

1 in. in the picture equals 57.6 inches real.

57.6 in. × (1 yd)/(36 in.) = 1.6 yd

1 in. in the picture equals 1.6 yd real

Answer:

2. One inch on the photograph represents 1.6 yards of the real bridge.

Answer:jkd

Step-by-step explanation:

d

I think

h(t)=480t–16t^2

Max height is the vertex of the parabola at t = -b/2a

t = -480/-32 = 15 seconds

--> h(15)

Linear equations are one-degree equations. So, the two solutions of the equation is (0,-4)(6,0).

It is a straight-line equation. A linear equation with parameters a and b equal to zero has the conventional form ax + by + c = 0. A linear equation has the following standard form: ax + by + c = 0.

Here, variables are x and y and constants a, b, and c are used. Also, a ≠ 0, and b ≠ 0.

We can find the solution of the linear equation by putting x = 0 and y = 0 so that two points form which are the solution of the linear equation,

Put x = 0 in the linear equation 2x - 3y = 12,

2 × (0) - 3y = 12

or, - 3y = 12

or, y = -4

The points is (0,-4)

Put y = 0 in the linear equation 2x - 3y = 12,

2x - 3 × (0) = 12

or, 2x = 12

or, x = 6

The points is (6,0)

Therefore, the two solutions of the equation is (0,-4)(6,0)

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The complete question is as follows:

What is the answer for 2x - 3y = 12?

Answer:

Step-by-step explanation:

Answer:

I would say the length  is near 8

Answer:

In the given right angled triangle,

base(b)=2 mm and perpendicular(p)=7mm

hypotenuse (h)=?

By using Pythagoras theorem,

h²=p²+b²

or,h²=(7)²+(2)²

or,h²=49+4

or,h²=53

or,h=√53

or,h=7.28

The length of unknown side is 7.28 mm and it is not determined exactly.

The length 7.28 mm is between integers 7 and 8 and it is more closer to 7.

Your research question can also be answered by the alternative hypothesis (Ha). The populace, according to the assertion, is affected.

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On solving the provided question we can say that - The range of f(x) is a subset of this range, which is the range of -3x-2  (-14,∞)

The range of values that may be plugged into a function is known as its domain. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set. Let y = f(x) be a function where x and y are the independent and dependent variables. If a function f offers a means of successfully generating a single value y while employing a value for x to that end, then the selected x-value is said to belong to the domain of f.

f(x)=  -3x-2     x <4

       3/4x-1   x [tex]\geq[/tex] 4

Domain =

The range of f(x) is a subset of this range, which is the range of -3x-2  (-14,∞).

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Answer:

34.064516129

Step-by-step explanation:

[tex]32 \times \frac{33}{31} = \frac{1056}{31} [/tex]

[tex] = 34.064516129[/tex]

i hope this helps

The coeficient of y² in the expression is the number 3

An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

In the given expression we have the following:

3y² + 4x

 As we are asked for the coefficient of the variable "y" then we must take the number that is just before the letter which in this case is the number 3.

3 is the coefficient of y²

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The duplicate number on a given integer array in Python can be found  through two loops.

We need to print the duplicate elements present in the array. This can be done through two loops. The first loop will select an element and the second loop will iteration through the array by comparing the selected element with other elements. If a match is found, print the duplicate element.

ALGORITHM:

STEP 1: Declare and initialize an array.

STEP 2: Duplicate elements can be found using two loops. The outer       loop will iterate through the array from 0 to length of the array. The outer loop will select an element. The inner loop will be used to compare the selected element with the rest of the elements of the array.

STEP 3: If a match is found which means the duplicate element is found then, display the element.

PYTHON PROGRAM:

#Initialize array    

arr = [ ];    

print("Duplicate elements in given array: ");    

#Searches for duplicate element    

for i in range(0, len(arr)):    

   for j in range(i+1, len(arr)):    

       if(arr[i] == arr[j]):    

           print(arr[j]);  

The duplicate number on a given integer array in Python can be found  through two loops.

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The relationship between a scalene triangle and the location of its centroid is; A: The centroid will always be inside the scalene

triangle, since the centroid is always inside any type of triangle.

A scalene triangle is a triangle in which all three sides have different lengths. Also the angles of a scalene triangle have different measures.

Some right triangles can be a scalene triangle when the other two angles or the legs are not congruent.

Now, a centroid of a triangle is defined as the point formed by the intersection of the medians of the triangle. Now, the medians of a triangle always lie within a triangle. This means that their intersection point which is the centroid of a triangle always lies inside a triangle.

Thus, the centroid of the scalene triangle can be concluded to always lie inside the triangle.

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The frictional force between the box and the surface is 100 newtons .

Since the body being dragged across the surface is not accelerating, the acceleration of the body is 0m/s².

From Newtons second law of motion, F = ma where;

F is the sum of the forces acting on the body

m is the mass of the body

a is the acceleration

If the box is dragged along a straight line by a force of 100 N, its moving force (Fm) is 100 N and the frictional force (Ff) will act opposite to this force.

Resultant force acting on the box along the horizontal will be Fm+(-Ff)

Therefore;

Fm+(-Ff) = ma

Fm-Ff = ma

Since a = 0m/s²

Fm-Ff = m(0)

Fm-Ff = 0

Fm = Ff

This shows that for a static body, the moving force acting on the body will be the same as the frictional force. Since Fm = 100 N

Frictional force (Ff) = 100 N

Therefore, the frictional force between the box and the surface is 100 N

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Answer:

Look at the image I attached to my response.

Step-by-step explanation:

For proof #3, I did it according to the way I was taught how to do proofs in my state/school, so what you wrote could be correct.

To find the x-intercept of a rational function we put y=0 in the given and find the corresponding value of x.To find the y-intercept of a  rational function we put x=0 in the function and the value of y.

The x-intercept is the point where a line crosses the x-axis.At this point y=0 and the y-intercepts is the point where a line crosses the y-axis.At this point x=0

It is point where the graph of the rational function intersects the x-axis or y-axis.

For Horzontal asymptotes

The horizontal asmptotes of a rational function can be determined by looking at the degree of the numerator and denominator.if Nis the degree of numerator and Dis the degree of denominator.Then N<D

So horizontal asymtote is y=0

To finding horizontal asymptotes we can just focus on degree of numerator and denominator.

For vertical asymptotes

vertical asymptotes occur where the denominator of a rational function approaches zero.A rational function cannot cross a vertical asymptotes because it would be dividing by zero. we set denomintor to zero and solve value of x.The values of x are vertical asymptotes.

Hence we can find easily horizontal and vertical asymptotes of rational function.

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Step-by-step explanation:

the multiplication result is found by row×column multiplications.

1st row × 1st column = a

2×1 + 1×-1 + 0×0 = 2 - 1 = 1 = a

1st row × 2nd column = b

2×-1 + 1×-2 + 0×1 = -2 + -2 = -4 = b

1st row × 3rd column = c

2×2 + 1×1 + 0×1 = 4 + 1 = 5 = c

Lin's family make a trip of length 50 miles.

What is a trip?

People move between far-off geographic regions when they travel. Travel can be done with or without luggage, on foot, by bicycle, car, rail, boat, airline, ship, or by another mode of transportation. It can also be one way or round trip.

Given that Lin's family had completed 60% of a trip.

Thus they have to travel (100 - 60)% = 40% of the trip.

Also given that, they have traveled 30 miles..

Therefore,

60% of the trip is equal to 30 miles.

1% of  the trip is equal to 30/60% miles.

100%  the trip is equal to (30× 100%)/60% miles.

                                         = 50 miles.

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The value of x + y is 5.

What is linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Given linear equations are

2x + 3y = 12  ....(i)

2x - y = 4    ......(ii)

To solve the give linear equation, using elimination method.

Subtract equation (ii) from equation (i)

2x + 3y = 12

2x - y = 4

(-)  (+)   (-)

________

   4y = 8

Divide both sides by 4:

y = 2

Putting y = 2 in equation (ii)

2x - 2 = 4

Add 2 with both sides:

2x = 6

Divide both sides by 2

x = 3

Putting x = 3 and y =2 in x + y:

x + y = 3 + 2 =5

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Answer:

You can tell if a function is positive or negative by checking the Y values. If all the Y values are above the x-axis it should be positive, and if the all y values are below the x-axis the function should be negative.

Good luck!

The integration is as follow

Finding an antiderivative of a function is the process of integration. If a function can be integrated and its integral across the domain is finite with the given bounds, then the integration is definite.

Given:

first, [tex]\int\limits {e^{4x} / 19 - e^{8x}} \, dx[/tex]

= [tex]\int\limits {e^{4x} / 19 - e^{(4x)}^2} \, dx[/tex]

let [tex]e^{4x}[/tex] = z

4[tex]e^{4x}[/tex] dx = dz

= 1/4 [tex]\int\limits {dz / \sqrt{19} ^2 -z^2} \,[/tex]

= 1/4 x 1/2√19 log|(z+ √19)/(z-√19)| + C

= 1/8√19 log|([tex]e^{4x}[/tex] + √19)/ ([tex]e^{4x}[/tex] - √19)| + C

Second,

[tex]\int\limits {33 sec^5 (x)} \, dx[/tex]

= 33 [ 1/4 tan x sec³x + 3/4 ∫sec³x dx]

= 33/4  tan x sec³x + 99/4[ 1/2 tan x sec x +1/2 ∫sec x dx]

=  33/4  tan x sec³x + 99/8 tan x sec x +99/8 log (sec x+ tan x) + C

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The number of different outfits is 576

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

8 pairs of pants, 6 t-shirts, 6 sweaters or hoodies, and 2 pairs of shoes

The number of different outfits is the products of the count of each apparel

This is represented as

Different outfits = Pants * T-shirts * Sweaters or hoodies * Pairs of shoes

Substitute the known values in the above equation

Different outfits = 8 * 6 * 6 * 2

Evaluate

Different outfits = 576

Hence, there are 576 different outfits

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Answer:

True False True False

Step-by-step explanation:

Yes, √3x² - 2x is a polynomial.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

√3x² - 2x

This is in the form of ax² - bx

This is a polynomial with degree 2.

Thus,

√3x² - 2x is a polynomial.

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