Mrs. Crosland asked students to factor the expression 28x−8. The students offered the answers shown in the box.



Which student(s) offered answer(s) equivalent to the original expression?

Responses

only Danny
only Danny

only Irene
only Irene

both Carlos and Danny

both Carlos and Danny

both Carlos and Irene
both Carlos and Irene

The equation of the linear line that best fit the given points is y = (7/8)x + 7/8.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

The line passes through points (-1,0) and (7,7) will be the best fit as it is at the smallest distance between all points.

The linear function associated with the point (-1,0) and (7,7) will be as,

y - 0 = [(7 - 0)/(7 + 1)](x + 1)

y = (7/8)(x + 1)

y = (7/8)x + 7/8

Hence "y = (7/8)x + 7/8 is the equation of the linear line that best fits the provided points".

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A degree 5 function can have up to five turning points. These turning points are also known as stationary points, inflection points, or extrema.

A degree 5 function is a polynomial of degree 5. This means that it is a function of the form f(x) = ax^5 + bx^4 + cx^3 + dx^2 + ex + f, where a, b, c, d, e, and f are constants. The degree of a function is determined by the highest power of the variable in the equation. In this case, the highest power of x is 5, and so the degree is 5. A degree 5 function can have up to five turning points. These turning points are also known as stationary points, inflection points, or extrema. A stationary point is a point on the graph of the function where the slope of the graph is either 0 or undefined, and an inflection point is a point on the graph of the function where the concavity of the graph changes. In order for a function to have a turning point, the derivative of the function must equal 0 at that point, and the second derivative of the function must not equal 0. If the second derivative does equal 0 at the point, then the point is a point of inflection, rather than a turning point. The number of turning points of a degree 5 function can be determined by finding the number of real roots of the equation f'(x) = 0, where f'(x) is the derivative of the function f(x). Since the degree of the derivative of a degree 5 polynomial is 4, this equation will have up to 4 real roots. This means that the degree 5 function can have up to five turning points.

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As per the given percentage, the total amount Ms. Clark pays, including tip is $30.1

The term percentage is referred as a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.

Here we have given that the cost of Ms. Clark's restaurant meal is $25. 50. And as a tip, Ms. Clark gives the waiter 20% of the meal's cost.

Now, we need to find the total amount Ms. Clark pays, including tip.

While we looking into the given question,

The following values are given in the question,

Total amount of bill for Ms. Clark = $25.50

Percentage of tip = 20%

Then the amount of tip is calculated as,

=> 25.50 x 20/100

=> 25.50 x 0.20

=> 5.1

Then the total amount paid by Ms. Clark is

=> 25.50 + 5.1

=> 30.1

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Answer:

f(-3)= -6

f(0) = 0

f(4)= 36

Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

A number's  root is that factor of the number that, when multiplied by itself, yields the original number. Specifically, squares and square roots are exponents. Think of the number nine. This can be expressed as  or as 3 x 3.

Here,

If an equation have 2 roots , it means it is a quadratic function

If D=0, a quadratic function has two roots that are equal.

D (discriminant) = 0

=>b24ac=0 is required for a polynomial function to have equal roots.

Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

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The volume of a rectangular pyramid is one-third of the volume of a cuboid the pyramid is inscribed in with same base. That is the formula for volume of pyramid is,

V = l×b×h/3

A rectangular pyramid is a solid with a rectangular base area and 4 triangular faces, one face on each edge of the base joining at the top vertex. Generally, a rectangular pyramid is a right rectangular pyramid.

Let us say the rectangular pyramid we are considering has a dimension of l×b base, where l and b are the length and breadth of the base area and h is the height of the pyramid. Then the formula of volume of rectangular pyramid is

V = l×b×h/3

--The question is incomplete, answering to the question given below--

"What is the formula of volume of rectangular pyramid?"

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2x + 3y is a binomial is a true statement.

A polynomial is of various types like binomial, trinomial and multinomial.

Monomial is said to contain only one term, trinomial is said to contain exactly three terms, multinomial contains n number of terms.

An mathematical expression known as a binomial has exactly two terms.

Examples of binomials are 4x² + 5y², xy² + y, x² + 3, x + y, etc.

Here, the given algebraic expression is 2x + 3y, where 2x is one term and 3y is another term. The coefficient of x is 2 and coefficient of y is 3 where as the exponent of x is 1 and the exponent of y is 1.

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Answer:

  (5 +√5) and (-√5 -5)

Step-by-step explanation:

Given two roots of the 4th-degree polynomial with integer coefficients are (5-√5) and (√5-5), you want to know the other two roots.

The other two roots are the conjugates of the given roots. That is, the signs of the √5 term will change:

  (5 +√5) and (-√5 -5)

__

Additional comment

The polynomial is x⁴ -60x² +400.

Finding the missing number from the first 100 numbers in the given array arr[] of size N-1 with integers in the range [1, N] is the task. The list doesn't contain any duplicates.

Java method for locating a missing integer in an array of integers from 1 to 100

class GFG; import java.io.*; import java.util.*

public static void findMissing(int arr[], int N)

{

 int i;

 int temp[] = new int[N + 1];

 for (i = 0; i <= N; i++) {

  temp[i] = 0;

 }for (i = 0; i < N; i++) {

  temp[arr[i] - 1] = 1;

 } int ans = 0;

 for (i = 0; i <= N; i++) {

  if (temp[i] == 0)

   ans = i + 1;

 } System.out.println(ans);

}

public static void main(String[] args) {

 int arr[] = { 1, 3, 7, 5, 6, 2 };

 int n = arr.length; // Function call

 findMissing(arr, n);

}

}

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Answer:

y-intercept: 6

Step-by-step explanation:

Y = -2x 6

The equation is y = mx + b

m = the slope

b = y-intercept

So, the y-intercept is 6

The three consecutive odd numbers of the number 105 are:

107, 109 and 111

Consecutive numbers are those numerical values that are found just after a specific number or value, for example consecutive numbers from 10 will be 11 onwards.

To solve this problem we must have clear which is our base number, and this is 105, as we will determine the consecutive numbers we must add +1, +2.... as many times as we want, now as we only want the odd numbers and 105 is odd we will proceed to add multiplies of 2:

+2, +4 and +6, having as a result the following numbers:

The consecutive and odd numbers will be 107, 109, 111.

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Using combination formula and analyzing the cases provided, The answer is 120,225 and 30.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.

The required formula is:

[tex]C(n,r) = \frac {n!}{r!(n-r)!}[/tex]

number of digits that can be asserted in a position = 10 (0-9)

places to be filled = 3

If it do not contain the same digits three times, The number of strings of three decimal digits = C(10,3)

=[tex]\frac {10!}{3!*(10-3)!}[/tex]

=120.

If it begin with odd numbers, The numbers that can be filled at the start=5

for last two places = C(10,2)

=[tex]\frac {10!}{2! * (10-2)!}[/tex]

=45

Total number of strings=5*45 = 225

If it have two digits 4s, The number of possible cases of having two 4s= 3

For a remaining spot= C(10,1)

=[tex]\frac {10!}{1!(10-1)!}[/tex]

=10

Total number of strings = 3*10=30

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The only graph that correctly shows the given piecewise function is; Graph B

It is pertinent to note that when it comes to piecewise functions and inequalities, a closed, or shaded circle is typically used to represent the inequalities greater than or equal to (≥) or less than or equal to (≤) . However, an open, or unshaded circle is typically used to represent the inequalities greater than or less than.

Now, the first part of the piecewise function states that;

f(x) = x + 1 if x < 1

Thus, it will be an unshaded circle pointing to the left direction indicating less than.

The second inequality says 4 provided that x ≥ 1.

Thus;

The line will be a horizontal line pointing right with a shaded circle. Therefore we conclude that only option B is correct.

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The graph of a function and the graph of its inverse are reflected across the line y = x.

Connsider a function f(x).

The inverse of function f(x) is represented as f^-1(x).

The inverse of a function is a function that reverses the effect of the original function.

We know that if we take the inverse of function then the domain of a function will be the range of inverse function and the range of a function will be the domain for its inverse.

This means if the point (3, -6) is in the original function then itwill be represented by the point (-6, 3) in the inverse function.

Also, we can obtain the graph of an inverse function as a reflection of the graph of original function across the line x = y.

Hence, the inverse functions' graphs are reflections over the line x = y

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Answer:

8

Step-by-step explanation:

its the middle number when the given values are listed least to greatest.

*count from each minimum and maximum values til you have the number in exact center.

The height of the wall where the ladder reaches will be 6.33 feet.

It expresses that the region of the square whose side is the hypotenuse is equivalent to the amount of the region of the squares on the other different sides.

The Pythagoras theorem formula is given as

H² = P² + B²

A 12-foot stepping stool is set against an upward mass of a structure, with the lower part of the stepping stool remaining on level ground 10 feet from the foundation of the structure.

The height of the wall where the ladder reaches will be calculated as,

12² = P² + 10²

144 = P² + 100

P² = 44

P =6.33 feet

The level of the wall where the stepping stool arrives freely will be 6.33 feet.

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The transformation of function is the process of modifying the existing graph of a function.

We know that in a function transformation, the graph of parent function either moves to left/right/up/down or resizes or reflects. There types of function transformations are: Translation, Dilation and Reflection

There are two types of translations of functions.

1) Horizontal translations: a function y = f(x) into the form y = f(x ± m)

   if m > 0, then the function f(x ) moves to the left side by 'm' units.

   if m < 0, then the function f(x) moves to the right by 'm' units.

2) Vertical translations: a function y = f(x) into the form f(x) ± m

if m > 0, then the function f(x) moves up by 'm' units.

if m < 0, then the function f(x) moves down by 'm' units.

Similarly there are two types of dilations.

1) Horizontal Dilation: a function y = f(x) into the form y = f(kx)

2) Vertical Dilation: a function y = f(x) into the form y = k f(x)

In both the cases, if k > 1, then the graph stretches and if 0 < k < 1, then the graph shrinks.

In case of reflection transformation of function y = f(x),

y = - f(x) is the reflection with respect to the x-axis and y = f(-x) is reflection with resepct to the y-axis.

Therefore, in a function transformation, the original graph of function either moves to left/right/up/down or resizes or reflects.

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Answer:

x = 16°

Step-by-step explanation:

AOB = 74 · 2 = 148°

triangle AOB is isosceles

2x + 148 = 180

2x = 180 - 148

2x = 32

2/2 x = 32/2

x = 16°

The rate of change of the pickup is greater than the rate of change of the minivan

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

On the graph, we have the following points

(x, y) = (0, 0) and (1, 50)

The equation of the proportional relationship is then calculated as

y = Y/X * x

Where

(X, Y) = (1, 50)

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

y = 50/1 * x

Evaluate

y = 50x

This means that the rate of the pickup is 50 miles per hour for the pickup

For the minivan, we have

y = 45x

This means that the rate of the pickup is 45 miles per hour for the minivan

50 is greater than 45

Hence, the rate is greater

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Answer:

3

Step-by-step explanation:

Lets use the slope formula, Which is given as :-

[tex]\sf{ \dfrac{y2-y1}{x2-x1} }[/tex]

Substitute the points we have to the formula :-

[tex]\begin{gathered}\sf \longmapsto {\dfrac{16 - 7}{7-4 }} \\ \sf{ \longmapsto {\dfrac{9}{3}} \\ \sf{\longmapsto 3} \end{gathered}[/tex]

Thus, The correct answer is 3!!

The most often recognized impairments for social security disability benefits are musculoskeletal system disorders like arthritis.

This is due to the prevalence of arthritis. A total of 58 million Americans suffer from arthritis. You might be eligible for disability benefits if your arthritis makes it difficult for you to move or carry out basic daily tasks.

If your condition should automatically qualify you for disability benefits, a social security disability lawyer can analyze your case and make that determination. Your attorney may walk you through the disability application process and advise you on the kinds of records you might need to substantiate the seriousness of your disease.

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(a) If you fit your data to this function with n set exactly equal to 2, then we have to find v(x, i) is equivalent to -2At(0).

(b) If you fit your data to this function with n set exactly equal to 2, then we have to find v(x, i) is equivalent to At(0)^2+B.

The given equation is x(f) = x(i)+v(x, i)Δt+12a(x)(Δt)^2.

Here x = x(f)-x(i)

So the equation is

x = v(x, i)Δt+12a(x)(Δt)^2..................(1)

The function in the program

x = A(t-t(0))^n+B

(a) If you fit your data to this function with n set exactly equal to 2, then we have to find v(x, i) is equivalent to.

If we set n = 2. Then;

x = A(t-t(0))^2+B..................(2)

On comparing the equation (1) and (2), we get

A = 1/2 a(x)

So, a(x) = 2A

x(f) = At^2+At(0)^2-2Att(0)+B.......................(3)

Now comparing the equation (1) and (3)

v(x, i) = -2At(0)

(b) If you fit your data to this function with n set exactly equal to 2, then we have to find x(i) is equivalent to.

On comparing the equation (2) and (3), we get

x(i) = At(0)^2+B

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Complete question is:

Equation 3.8 in the textbook states x(f) = x(i)+v(x, i)Δt+12a(x)(Δt)^2. In this lab you will collect data for the position, x, as a function of time, t. The software you will use will allow you to fit data using a function of the form x=A(t−t(0))^n+B.

1. If you fit your data to this function with n set exactly equal to 2, what is v(x, i) equivalent to?

2. If you fit your data to this function with n set exactly equal to 2, what is x(i) equivalent to?

The graph of a linear equation in two variables is a straight line.

The general linear equation in two variables is ax + by + c = 0, where a, b, c are constants. Also, a and b cannot both equal zero at the same time.  In order to graph of a linear equation in two variables  ax + by + c = 0, we simply assume a set of values for x and calculate the respective set of values for y.

So we have a set of coordinates (x, y). Now plot the points on graph and join them.

The graph formed will be a straight line.

The point at which the line (graph of a linear equation) crosses the y-axis is the y-intercept and the point at which the line (graph of a linear equation) crosses the x-axis is the x-intercept.

Therefore, the graphing of all ordered pairs that satisfies a linear equation in two variables gives a straight line.

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Therefore , the 11 sides polygon cannot be a quadrilateral.

A polygon with four sides, four angles, and four vertices is referred to as a quadrilateral. A sort of polygon called a quadrilateral has sides that are defined in a certain way. The quadrilateral in the illustration below, for instance, can be defined as ABCD, ADCB, BCDA, CDAB, etc.

Here,

the quadrilateral

Each of them consists of four vertices.

Each side consists of four sides.

360 degrees is the sum of all interior angles.

Two diagonals are present.

There are both regular and irregular quadrilaterals.

It must have four equal sides, four equal angles, and diagonals that cross in order to be regarded as a quadrilateral.

Therefore , the 11 sides polygon cannot be a quadrilateral.

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The graph of the line parallel to x-axis and passes trough the point (-2,3).

What is slope of a line?

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.

Consequently, the formula for the change in y-coordinate with respect to the change in x-coordinate is

m = Δy/Δx  = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line can be shown as

tan θ = Δy/Δx.

Given that the slope of the line is 0. Thus the angle between the line with the x-axis is 0 degree as tan 0° = 0.

The line is parallels to x-axis.

The equation of the line that is parallel to x-axis is y = a.

Since the line passes through the point (-2,3), thus it will be satisfies the equation line.

Putting x = -2 and y = 3

a = 3

The equation of the line is y = 3

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There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form

Slope-intercept form is written as y=mx+b, where m is the slope and b is the y-intercept. Using the information given we can plug in the numbers to get the correct equation. This looks like y=-3x+4.

Slope-intercept form is helpful because we can use it to find coordinate points and graphs. By graphing the y-intercept and then using the slope to count out points, you can find the function. Additionally, by plugging in values for x or y, you can find coordinate pairs.

The standard form is Ax + By = C

Where, if at all possible, A, B, and C are integers, and A is non-negative.  Our linear equation in standard form is:

x - 5y = -12  or 1x - 5y = -12

where A = 1, B = -5, and C = -12  

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The solution to the system of equations, y = -2x and y = -6x + 36, is: (9, -18).

Given the following equations of the system as:

y = -2x --> eqn. 1

y = -6x + 36 --> eqn. 2

To solve, substitute y = -2x into equation 2:

-2x = -6x + 36

Solve for x

-2x + 6x = 36

4x = 36

x = 9

To find the value of y, substitute x = 9 into equation 1:

y = -2(9)

y = -18

The solution is: (9, -18).

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Answer:

No relationship

Step-by-step explanation: