describe and correct the error in the factoring polynomial. x^2+4x-96=(x-12)(x+8)​

A function is a mathematical relationship between the domain and the range, two sets of values. The range is the set of output values that the function produces, and the domain is the set of input values for which it is defined.

What is a function, exactly?

a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

Consider the function f(x) = x^2 as an illustration. This function generates the value f from the supplied value x. (x). This function will return the value 9 if the given value is 3, since 3^2 = 9.

Generally speaking, a function describes the relationship between two sets of values (the domain) (the range). For instance, the relationship between the input value x and the output value f(x) is described by the function f(x) = x^2.

A formula, which is a guide that explains how to calculate the output value for a specific input value, is typically used to express a function. For instance, the function f(x) = x^2 has the formula f(x) = x^2. We just enter the input value into the formula and simplify to determine the output value for a particular input value.

A fundamental idea in mathematics, functions are used to model and describe a wide variety of real-world occurrences. For instance, the quadratic function f(x) = x^2 + 2x + 1 can be used to simulate how an item would move in the presence of gravity. A population's expansion over time can be predicted using the exponential function f(x) = 3^x.

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The complete two-way frequency table is shown below.

what is frequency table?

a table that displays the distribution of a characteristic's occurrence frequency in accordance with a specific set of class intervals.

explanation:

Denote the events as follows:

U = a member have been to the United States

NU = a member have not been to the United States

A = a member have been to Australia

NA = a member have not been to Australia

The information provided is:

             A         NA        Total

U          5          __           11

NU       __         __           __    

Total      12         __           19

Complete the table as follows:

n (U ∩ NA) = n (U) - n (U ∩ A)

               = 11 - 5

                = 6

n (NU) = N - n (U)

          = 19 - 11

          = 8

n (NU ∩ A) = n (A) - n (U ∩ A)

                = 12 - 5

                = 7

n (NA) = N - n (A)

         = 19 - 12

         = 7

n (NU ∩ NA) = n (NA) + n (U ∩ NA)

                    = 7 - 6

                    = 1

Therefore, the complete 2-way Frequency table is:

            A         NA        Total

U          5           6           11

NU        7            1           8    

Total      12          7           19

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The circumcenter of a triangle is the point in the plane equidistant from the three vertices of the triangle.

In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius.

Not every polygon has a circumscribed circle. A polygon that does have one is called a cyclic polygon, or sometimes a concyclic polygon because its vertices are concyclic. All triangles, all regular simple polygons, all rectangles, all isosceles trapezoids, and all right kites are cyclic.

A related notion is the one of a minimum bounding circle, which is the smallest circle that completely contains the polygon within it, if the circle's center is within the polygon. Every polygon has a unique minimum bounding circle, which may be constructed by a linear time algorithm.

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The symbol that should be used is the division symbol. On the other hand, in the result the whole number represents the number of curtains, while the fraction represents a fraction of the next curtain.

Given :

The numerator: Number above.

The denominator: Number below.

A whole number: Optional element.

The number of curtains the tailor can make is equal to the total fabric divided by the fabric required for one curtain. Based on this, the symbol should be ÷.

= 18 1/2 ÷ 2 3/4

The whole number represents the number of curtains. The division of the total fabric and the total fabric required for one curtain will include a whole number and a fraction. In this situation, the whole number represents the number of curtains that can be made from the total fabric.

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Answer:

16x^8y^3

Step-by-step explanation:

Simplify the expression.

Answer:

[tex]-8x^7(-2xy^3) = 16x^8y^3[/tex]

Step-by-step explanation:

⭐Multiplication rules

⭐ Exponent multiplication rule

⭐ Multiplying two terms with variables

We need to utilize these 3 key points (⭐) when multiplying to terms with variables.

First, let's multiply the coefficients:

-8 * -2 = 16

Next, let's multiply the variables:

[tex]x^7 * xy^3[/tex]

These two variables have the same base (x), so we will add their exponents up.

* remember: if you see a variable without an exponent, it has an exponent of 1 *

[tex]x^7 * x = x^8[/tex]

The variable [tex]y^3[/tex] will stay the same because there is no other y variable.

= [tex]x^8y^3[/tex]

Now, "attach" the variables to the product of the coefficients:

= [tex]16x^8y^3[/tex]

Answer: 64.5 hours

Step-by-step explanation:

2580 divided by 40

Answer:

Step-by-step explanation:

put it into the y=mx+c equation

y=-2x+8

therefore th y intercept is at (0,8)

and the gradient in -2

A theorem which is used to find the rational solutions of a polynomial equation is known as the rational root theorem.

A polynomial expression is given and after solving them we get the two values known as the roots of the function.

These are also known as the zeros of polynomial as after putting these values in the equation we get the result as 0 .

We should use the rational root theorem only when the value of coefficients are small.

The theorem states that each rational solution x = p ⁄ q, when on simplified satisfies the below mentioned points,

p is an integer factor of the constant term a0, and

q is an integer factor of the leading coefficient an.

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Linear expressions or equations are expressions in which the highest power of the variable is one 5x+3= 13 in four steps

steps 5 x + 3 = 13. 5x+3=13. Subtract 3 from both sides. Subtract 3 from both sides.

5x=13-3. 5x=13−3. Subtract 3 from 13 to get 10. Subtract 3 from 13 to get 10.

5x=10. 5x=10. Divide both sides by 5. Divide both sides by 5.

x=\frac{10}{5} x=510​ Divide 10 by 5 to get 2. Divide 10 by 5 to get 2.

Linear expressions or equations are expressions in which the highest power of the variable is one.

Quadratic expressions or equations are expressions in which the highest power of the variable is two.

Cubic expressions or equations are expressions in which the highest power of the variable is three.

Quartic expressions or equations are expressions in which the highest power of the variable is four.

From the expression, 5x + 2 given,

the highest power of x is one. So it is a linear expression.

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If you simply multiply the numerator, which is the top number on the bar, you can multiply a fraction by a full number.

A number that is not negative and doesn't have any fractional or decimal components. Anything that isn't a whole number is a fraction. most often expressed with a numerator (top) and denominator (bottom). All fractions should ideally be "correct" fractions, that is, less than 1.

You can multiply a fraction by a whole number by only multiplying the numerator which is the top number on the bar. for example:

E = 2 x 3/4

E = 6/4

E = 1²/₄

Hence, If you simply multiply the numerator, which is the top number on the bar, you can multiply a fraction by a full number.

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The required sample interval in the given situation is 10.

The sampling interval is the space or period of time in which measurements or data collection occur.

This is known as the "nth selection" in research and occurs when we choose the nth participant (or sample unit) from the list; this sampling interval results in a random selection from the entire population.

Calculating the sampling interval involves dividing the population size by the desired sample size to arrive at the predetermined periodic interval.

So, have a population size of 500 people.

The number of members to be selected is only 50.

We already know that to find the sample interval, we should divide the population size bu the required sample size.

Now, calculate the sample interval as follows:

= 500/50

= 50/5

= 10

Therefore, the required sample interval in the given situation is 10.

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Replacing the values of h and k to create the equation of the transformed function gives us; y = [∛(x - 4)] - k

The graph represents a transformation of the parent cube root function.

The parent cube root function is; y = ∛x

In this parent function, we see that the value of h  and k are equal to 0. Where;

h = 0, k = 0 in parent function

Then the graph changes direction at the coordinate (0,0) in parent function.

From the given graph, we can see that it changes direction at the coordinate (4,-1)

This tells us that the graph is shifted by 4 units to the right and then by 1 unit downwards.

Thus, it means that the value of h = 4  and the value of k = 1.

Thus, the equation of the transformed function will be written as;

y = [∛(x - 4)] - k

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The lines y = - 4x + 5 and y = x + 4y = - 40 is neither parallel nor perpendicular.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, Are two lines y = - 4x + 5 and y = x + 4y = - 40.

Now,

x + 4y = 40

4y = - x + 40.

y = - (1/4)x + 10.

We know lines parallel to each other have the same slope and lines perpendicular to each other have a slope that is negative reciprocal of each other.

So, Line 1 is neither parallel nor perpendicular to line 2.

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The sum of the two Santa models is 24.

Given is math is a bit different at the north pole and a problem is shown in the image.

We can assume the three variables as : [x], [y] and [z]. So, we can write the equations as -

3x = 21                  ........ Eq[1]

y + z = 16              ........ Eq[2]

x + y - z = - 1          ........ Eq[3]

Now, it is given that -

3x = 21

x = 21/3

x = 7

and

y + z = 16

y = 16 - z

So, we can write the equation as -

x + y - z = - 1

7 + 16 - z - z = - 1

23 - 2z = - 1

2z = 24

z = 12

So, we can write -

[z] + [z] = 12 + 12 = 24

Therefore, the sum of the two Santa models is 24.

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The incorrect answer is b) The difference between their speeds is exactly 1.5 miles per hour.

What is distance?

The distance between two sites is the length of the route. The metre is the SI unit for distance.

What is speed?

The speed at which an object’s location changes in any direction. The distance travelled divided by the time it took to travel that distance is how fast something is moving.

What is time?

The amount of time that something happens, goes through a process, or remains the same.

Let distance be Y and time be X.

Distance (Y) travelled by William after X hours;

Y= 19X

Speed of Leo = [tex]\frac{distance}{time}[/tex]

= [tex]\frac{8}{0.5}[/tex]= 16 m/hr

Difference in speed= 19-16= 3m/hr

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Units digit - 6

Step-by-step explanation:

A. 12004+ 32004 = 44008

B. 52004+72004 = 124008

Total - 44008+124008+ 92004 = 208016

Units digit - 6

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The median of the set of numbers 25 and 29 is 27. This is the average of the two middle numbers in the ordered set, and it is not affected by extreme values or outliers.

The median of a set of numbers is the value that is exactly in the middle of the set when it is ordered from least to greatest. In this case, the set of numbers is 25 and 29. When we order this set from least to greatest, we get 25, 29. There are two numbers in this set, so the median is the average of the two middle numbers, which is the only number in the set. The only number in this set is 27, so the median is 27.

To find the median, we first need to arrange the numbers in order from least to greatest. If there is an odd number of numbers in the set, the median is the middle number. If there is an even number of numbers in the set, the median is the average of the two middle numbers. In this case, there are two numbers in the set, so the median is the average of the two middle numbers.

In summary, the median of the set of numbers 25 and 29 is 27. This is the average of the two middle numbers in the ordered set, and it is not affected by extreme values or outliers.

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Therefore , the 6 year old children can able to  skip count to 1 to 100 counting by making them learn.

Mathematicians can add numbers using the counting-on technique. When using this method, a learner begins by adding the larger number, then "counts on" with the other addends to get the sum. The student will recognize 4 as the higher number and add three more numbers, such as integers "4... 5, 6, 7," if the number sentence is 4 + 3.

Here,

Around age 6, kids start to learn how to skip count. Skip counting teaches your youngster to count swiftly and gets them ready to grasp the fundamentals of multiplication.

The simplest way to count is in skip increments of 10, which are essentially identical to regular increments of 10 with the exception of an extra '0': 10, 20, 30,... 80, 90, 100.

Therefore , the 6 year old children can able to  skip count to 1 to 100 counting by making them learn.

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Answer:

If each shopping trolley is 1 meter long, and each trolley in the stack adds 0.25 meters, then the total length of the stack will be equal to the length of each trolley plus the length added by each additional trolley in the stack. This means that the total length of the stack will be equal to 1 + 0.25 = 1.25 meters per trolley.

If the stack has a total length of 10 meters, and each trolley adds 1.25 meters to the stack, we can divide the total length by the length added by each trolley to find the number of trolleys that can be stacked in a single line of 10 meters:

10 / 1.25 = <<10/1.25=8>>8 trolleys

Therefore, if each shopping trolley is 1 meter long and each trolley in the stack adds 0.25 meters, a single line of 10 meters could hold a stack of 8 trolleys.

Step-by-step explanation:

Answer:

The answer for the question is 3.7

Answer:

y- intercept = - 1

Step-by-step explanation:

to find the y- intercept, let x = 0 in f(x) and evaluate

using rule of exponents

[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]

given

f(x) =- 32[tex](2)^{x-3}[/tex] + 3 , then

f(0) = - 32 [tex](2)^{0-3}[/tex] + 3

     = - 32 [tex](2)^{-3}[/tex] + 3

    = - 32 × [tex]\frac{1}{2^3}[/tex] + 3

    = - 32 × [tex]\frac{1}{8}[/tex] + 3

    = - 4 + 3

    = - 1 ← y- intercept

The one-time administration fee is (d) $60

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

12 months costs $660.

15 months costs $810.

This means that

(x, y) = (12, 660) and (15, 810)

For the one-time administration fee, we have

(x, y) = (0, y)

So, we calculate the slope using

slope = (y₂ - y₁)/(x₂ - x₁)

So, we have

(y - 660)/(0 - 12) = (810 - 660)/(15 - 12)

This gives

(660 - y)/12 = 50

So, we have

660 - y=600

This gives

y = 60

Hence, the administration fee is $60

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The formula of rational function is [tex]R(x) = \frac{P(x)}{Q(x)}[/tex] , where P(x) and Q(x) are polynomial functions.

What is rational function ?

A rational function is one that can be written as a polynomial divided by a polynomial. Since polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros of the denominator. Example 1. f(x) = [tex]\frac{x}{x - 2}[/tex].

Rational functions are typically identified by the degrees of the numerator and denominator. For example, a quadratic for the numerator and a cubic for the denominator is identified as a quadratic/cubic rational function. A rational function model is a generalization of the polynomial model.

The formula of rational function is [tex]R(x) = \frac{P(x)}{Q(x)}[/tex] , where P(x) and Q(x) are polynomial functions.

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The number that is 10 more than 21 is 31, using the concept of addition.

Addition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.The addition of two whole numbers results in the total amount or sum of those values combined. The example in the adjacent image shows a combination of three apples and two apples, making a total of five apples. This observation is equivalent to the mathematical expression "3 + 2 = 5" (that is, "3 plus 2 is equal to 5").

Besides counting items, addition can also be defined and executed without referring to concrete objects, using abstractions called numbers instead, such as integers, real numbers and complex numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces and subgroups.

Here, what we can do is use addition to find the number 10 more than 21.

= 21 + 10

= 31

Hence, the number 10 more than 21 is 31.

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The value of function  (f + g)(x) is 7x² + x - 4.

Here the functions provided are,

f(x) = 4x² - 5x

g(x) = 3x² + 6x - 4

The p addition property of functions (f + g)(x) allows them to be written as,

(f + g)(x) = f(x) + g(x)

In the above equation, we can substitute the values of each function.

(f + g)(x) =  4x² - 5x + 3x² + 6x - 4

We have to combine the similar terms,

(f + g)(x) =  4x² - 5x + 3x² + 6x - 4

             = 7x² + x - 4

So (f + g)(x) = 7x² + x - 4

Therefore the correct answer is option B.

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Using the AND rule of probability and percentage calculations, The answer is 0.0684.

Probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.

Percentages are fractions with a 100 as the denominator. The percent symbol (%) is used next to the number to denote that it is a percentage.

62% goes to college.

% not going to college = 100%-62%

=38%

on that 38%, 18% gets employment,

probability =  0.38 * 0.18

=0.0684

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Answer:

16 inches

Step-by-step explanation:

Using the Pythagorean theorem, the distance is [tex]\sqrt{65^2-63^2}=16[/tex].

False , the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.

Given :

A. Since x-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.

False, it is the y-intercept of the function that indicates the amount at the start of the experiment.

B. Since y-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.

True, the y-intercept is given when x = 0, indicating the initial value of the function.

C. Since the maximum value in the table for bacteria A is greater than the maximum value in the table for bacteria B, bacteria A has a faster growth rate than bacteria B.

False, because the maximum value of each table is given in different times, and also the initial value of each table is different.

D. Since the minimum value in the table for bacteria A is less than the minimum value in the table for bacteria B, bacteria A has a slower growth rate than bacteria B.

False, the growth rate is not given by the inicial value. If we model both tables with an exponential function, the count of bacteria A quadruped in two days, and the count of bacteria B doubled in one day, so they have the same growth rate.

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Full question :

is in the image uploaded.