What does the factored form of a quadratic function tell you about the function's graph?

The solutions of equation x² + 12 = 7x are x = 3 and x = 4

Consider given equation x² + 12 = 7x

x² + 12 = 7x

x² + 12 - 7x = 7x - 7x                 .......(subtract 7x from both the sides)

x² -7x + 12 = 0

Now we find the two factors such that their sum is -7 and the product is 12

x² - 4x - 3x + 12 = 0            .............(splitting the middle term)

x(x - 4) - 3(x - 4) = 0        

(x - 4) (x - 3) = 0                  ............(seperate out like terms)

(x - 4) = 0  OR  (x - 3) = 0

this means, (x - 4) and (x - 3) are factors of equation x² + 12 = 7x

for (x - 4) = 0

⇒ x = 4

and for (x - 3) = 0

⇒ x = 3

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The expression that represents the number of inches the plant grew this week is,

⇒ 8 - x

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

A plant measured x inches tall last week, and 8 inches tall this week.

Here, We have;

A plant measured x inches tall last week, and 8 inches tall this week.

Hence, The number of inches the plant grew this week is,

⇒ 8 - x

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There are 136 solutions to the equation:

X1 + X2 + X3 = 15

where X1, X2, and X3 are non-negative integers. I'm not gonna list them all, but, it starts off with:

01. 0, 0, 15.

02. 0, 1, 14.

03. 0, 2, 13.

134.14, 0, 1.

135.14, 1, 0.

136.15, 0, 0.

The constraint of:

1<X1<6

implies X1 either equals 1, or is greater than 1.

So, there are 65 solutions where X1 equals 1, or is greater than 1, and less than 6!

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Let's consider what the question asks for:

 --> domain and range, x-intercept, y-intercept of the equation

Let's find the domain:

 --> the only range of x-values that will make this equation 'untrue'

      --> is when the function inside the square root becomes negative

         --> as a square root cannot have a negative value inside it

                [tex]x+8\geq 0\\x\geq -8\\\\\text{Our domain is therefore [-8}[/tex],∞)

Let's find our range:

 --> the function doesn't have any limitations vertically

               [tex]\text{Our range is therefore}[/tex]  (-∞,∞)

Our x-intercept

 --> is when the y-value is zero

      [tex]0=-2\sqrt{x+8} \\\sqrt{x+8} =0\\x+8=0\\x=-8[/tex]

                [tex]\text{Our x-intercept is therefore -8}[/tex]

Our y-intercept:

 --> is when the x-value is zero

    [tex]y=-2\sqrt{x+8} \\y=-2\sqrt{0+8} \\y=-2\sqrt{8} \\y=-2*2\sqrt{2} \\y=-4\sqrt{2}[/tex]

                [tex]\text{Our y-intercept is therefore }-4\sqrt{2}[/tex]

Answer:

  Domain: [-8, ∞)

  Range: {-∞,∞)

  X-intercept is -8

  Y-intercept is [tex]-4\sqrt{2}[/tex]

GMAT higher than 600 GMAT lower than or equal to 600 GPA higher than 9.0 0.2 0.3 GPA lower than or equal to 9.0 0.4 0.1

Okay in this question, we're looking at the g mat and g p, a looking at like students who are applying to be in an m b a program. You can see that our answers are down here and we're going to be looking at the g mat and the g p a so like. Let'S keep track of how many people have good, just only good g p, only a good g mat and not a good g p, both good, so i'm just going to put a check for a good bath good or both bad. Those are our categories, so i'm going to put an x both bad, so we're just going to count up these people. We know a total there's going to be 10 in the sample, so a good g p. A! U was just refreshed. I think a good g p, a was 9.0 and a good g mat was 600 point, so first person, 599 and 9.6, not a good g mat, even though its really close had to be above 600 but g p, a 9.6. That'S a good g p. So we have 1 person in this category of good g p, but not a good g mat then 689 and 8.8. That is a good g mat, but not a good g p. So then, 58410 good g p now to go at 6317.4. Good g mat bad g, p, 5949.8, good g p, a bad g mat 6439.2 that is going to be both good 6569.6, both good 594 poi 8.4. That'S both bad 71011.2, both good and 611 point okay. So that's a good g, math, 7.6 bad g p. So, just a good g mat now to calculate the relative frequency which, since you see decimals here, we know that's what that means. You just take the number and divide by 10 because 10 is your total sample size you're, trying to figure out like relative to the whole group? What percent had each of these 3 divided by 10? Point? That'S a .33 divided by 10.3 .3. These should always add up to 1 and .1. So, let's see what matches with that its going to be option d down here : (values from 0 to 12) and their gmat score (values range from 200 to 800) are listed below: gmat gpa 5999.6 6898.8 58410.0 6317.4 5947.8 6439.2 6569.6 5948.4 71011.2 6117.6

GMAT higher than 600 GMAT lower than or equal to 600 GPA higher than 9.0 0.2 0.3 GPA lower than or equal to 9.0 0.4 0.1

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GMAT greater than 600, less than or equal to 600, GPA greater than 9.0, 0.2, and 0.3, and less than or equal to 9.0, 0.4, and 0.1 Hence the correct table is Table 4.

In this question, we're going to be looking at the GMAT and the GPA, as well as people who are applying to be in an MBA school. We'll be looking at the GMAT and the GPA, as you can see from our answers, which are located down below. To keep track of how many people have good, just a good GMAT and not a good GPA, both good, and only a good GMAT, I'm just going to write a check for a good bath good or both horrible. These are our categories, so I'm going to mark both with an x, and we'll just add up these folks . The sample will have a total of 10, therefore that is a good general probability. A! You had just refilled. A good g mat, in my opinion, had to be above 600 points, so first person, 599 and 9.6, even though it's pretty near, isn't a good g mat. However, a good GPS 9.6 was. That's a decent g p. In this category of good GPA there is only one person who is not a good GMAT, followed by 689 and 8.8. That is an excellent g mat, but a poor GPA. 58410 nice GPA is now ready to depart at 6317.4, so. 5949.8, excellent g mat terrible g, p, good g p,  a bad g mat 6439.2 that is going to be both good 6569.6, both good 594 poi 8.4.

Both are awful. 71011.2, good and 611 points are acceptable. So, 7.6 terrible g p, decent g in math. Simply use a decent g mat to determine the relative frequency, which is what that indicates since decimals are included. You just divide the number by 10, since that is the overall sample size you are attempting to determine relative to the entire group. How much of each of these three when multiplied by ten? Point? 10.3 divided by.33 equals a. The sum should always be 1 plus.1. Let's see whether this matches option d down here, then: Below is a list of the applicants' (ranging from 0 to 12) and GMAT scores (200 to 800): GMAT GPA: 5999.6, 6898.8, 58410.0, 6317.4, 5947.8, 6439.2, 6569.6, 5948, and 71011.2, respectively.

GMAT higher than 600 GMAT lower than or equal to 600 GPA higher than 9.0 0.2 0.3 GPA lower than or equal to 9.0 0.4 0.1

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The complete question is:

Graduate Management Admission Test is required of students applying to MBA schools (GMAT). One of the most important indicators of how well a student would likely perform in the MBA program is the GMAT score, which is used by university admissions committees. A sample of 10 graduates was chosen to assess how well the GMAT score predicts MBA achievement. Below are their GMAT scores (which range from 200 to 800) and grade point averages (ranging from 0 to 12) for the MBA program (See Picture).

Suppose that university admissions committees consider a GMAT score higher than 600 as an indicator of a good candidate, and a GPA higher than 9.0 as a good performance. find the probability distribution table that correctly summarizes the data.

Lisa will have 12 books and Joe will have 22 books.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

Given that Joe has 10 more books than Lisa Lisa has 1 more book than Felix Felix has 11 books.

The equations can be written as:-

J = L + 10

L = F + 1

F = 11

Lisa's number of books,

L = F + 1

L = 11 + 1

L = 12

Joe's number of books will be,

J = L + 10

J = 12 + 10

J = 22 books

Therefore, Lisa will have 12 books and Joe will have 22 books.

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The question for the daily use of algebra is given below,

Joe has 10 more books than Lisa Lisa has 1 more book than Felix Felix has 11 books. How many books does Lisa have?

Derivation of given function [tex]xlogx[/tex] is log(ex).

Derivation of function: a function's rate of change is represented by its derivative, which can be written as either f'(x) . First, let's examine its definition and a visual representation of the derivative.

Product rule for derivative: according to the Product Rule, the derivative of a product of two functions is equal to the product of the first function times the second function's derivative plus the second function times the first function's derivative.

[tex](f(x)*g(x))'=f'(x)*g(x)+f(x)*g'(x)[/tex]

Here given function is in multiplication form so solution of given function will be derived using product rule of derivative.

[tex]f(x)=x,g(x)=logx\\(f(x)*g(x))'=f'(x)*g(x)+f(x)*g'(x)\\(xlogx)'=logx\frac{d(x)}{dx} +x\frac{d(logx)}{dx}\\\\(xlogx)'=logx+x\frac{loge}{x}\\(xlogx)'=logx+loge\\(xlogx)'=log(ex)[/tex]

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The perimeter of its varignon parallelogram is 30 units.

Diagonal of varignon parallelogram cross at right angle i.e., 90°.

This makes the parallelogram a rhombus.

now, all sides of the rhombus are equal.

When you cut a trapezium into three pieces it is made up of a central rectangle of height 4 units and 2 congruent right-angled triangles whose hypotenuse is 13 units and side is 5 units.

Using Pythagoras theorem,

Another side = √13∧2-5∧2

=√144

=12

Hence the height of the triangle= 12 units.

Now, consider one of the congruent triangles

Half part of the base is included in the other diagonal but the other half is not.

Since the base is 5 so other diagonal is 2.5.

But there are two right triangles so 2.5*2=5 units from the base are not in the other diagonal.

So the diagonal is 14-5=9 units

Hence the diagonal of the rhombus is 12,9 units

and half of the diagonal is 6 and 4.4 respectively

Again, using Pythagoras theorem,

side of the rhombus is equal to 7.5

Hence perimeter = 4x7.5

perimeter = 30

Therefore, The perimeter of its varignon parallelogram is 30 units.

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Answer: To find the value of c in the expression n² + 38n + c, we need additional information. Without any additional information, it is not possible to determine the value of c.

In general, c is the constant term in a polynomial equation, it is the coefficient of the term x^0. In this case, c is the coefficient of the term n^0.

However, when c is not given a specific value, it can be any real number, and therefore it cannot be determined without more information.

Step-by-step explanation:

The mean age for peak performance of Olympic and professional athletes in various sports has been increasing over time due to advancements in training, technology, specialization and professionalization of sports.

The mean age for peak performance of Olympic and professional athletes in various sports has been increasing over time due to various factors. Advancements in training techniques and technology have allowed athletes to maintain peak performance for longer periods of time. Additionally, increased specialization and professionalization of sports has also led to older athletes being able to compete at a high level.

The average age of athletes participating in the Olympic Games has also been increasing over time. This trend can be observed across a variety of sports including track and field, gymnastics, swimming and many more. Furthermore, the trend is not limited to a specific gender, both men and women athletes are getting older and still performing at elite level.

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Any function whose graph is NOT a line is said to be nonlinear. It has the equation f(x) = ax + b. With the exception of the form f(x) = ax + b, its equation can take any form. Any two points on the curve have the same slope.

To ascertain whether a table of values is a linear function, follow these steps:

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The surface area of pyramid is 229.6 [tex]m^2[/tex] and volume is  164.26 [tex]m^3[/tex].

What is surface area and volume?

The total of a regular pyramid's lateral face areas makes up the lateral surface area. A regular pyramid's total surface area is the sum of the surfaces of its lateral sides and base. The area of a pyramid's base is multiplied by the pyramid's height to determine its volume, which is then divided by 3.

Here Length a = 8 m , Height b = 11.2 m and slant height s= 11m.

Now using surface area of the Pyramid = [tex]\frac{1}{2} (ab)+\frac{3}{2} (bs)[/tex] square unit

=> Surface area = [tex]\frac{1}{2}(8\times 11.2)+\frac{3}{2}(11.2\times 11)[/tex]

=> Surface area = (4×11.2)+(3×5.6×11)

=> surface area = 44.8+184.8 = 229.6 [tex]m^2[/tex]

Now volume of the pyramid =[tex]\frac{1}{3}[/tex] base area ×Height cubic unit

=> volume = [tex]\frac{1}{3}[/tex] × [tex]\frac{1}{2}[/tex]×8×11×11.2 = 164.26 [tex]m^3[/tex]

Hence the surface area of pyramid is 229.6 [tex]m^2[/tex] and volume is  164.26 [tex]m^3[/tex].

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Answer:

Tangent B = AB/BC = (67^(1/2))/(78^(1/2))

To simplify this fraction, we can multiply both the numerator and denominator by the square root of the denominator's denominator (in this case, 78^(1/2)), which will cancel out the square root in the denominator:

Tangent B = (67^(1/2))/(78^(1/2)) * (78^(1/2))/(78^(1/2)) = (67)/78

Therefore, the tangent of angle B is 67/78 in simplified, rationalized form.

Answer:

7/3

Step-by-step explanation:

Suppose x of 1/3=7/9

           so, 1/3x=7/9

                     x=7/9*3/1

                     x=7/3

To find the solution of two systems, you can use Substitution method, Elimination method, Graphing method or Matrix method.

There are several methods to find the solution of a system of two equations with two variables. Some of the most common methods include:

1. Substitution method: In this method, you solve one equation for one variable, and then substitute that value into the other equation. You then solve for the remaining variable, and check your answer by substituting it back into the original equations.

2. Elimination method: In this method, you add or subtract the equations so that one variable is eliminated and you are left with an equation in one variable. You then solve for that variable, and check your answer by substituting it back into the original equations.

3. Graphing method: In this method, you graph both equations on the same coordinate plane, and find the point of intersection, which is the solution of the system.

4. Matrix method: It consists on writing the system in the form of matrix and using specific mathematical operations like Gaussian elimination or Cramer's rule to find the solution.

It's worth to mention that not always systems of two equations have unique solutions, they can have no solutions or infinite solutions, depending on the relative position of the lines that represent the equations.

It's best to use the method that you feel most comfortable with, and to check your answer by substituting it back into the original equations to make sure it's a valid solution.

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There can be 24490200 committees of 5 senators that has 3 democrats and 2 republicans

In mathematics, a combination or combinations are all the possible groupings that can be made of a given number of elements, without repeating them and regardless of the order in which they are found.

To solve this problem the formula and the combination procedure we must use is:

C(n/r) = n! / [(n-r)! *r!]

Where:

Information about the problem:

Applying the combination formula we have:

C(n/r) = n! / [(n-r)! *r!]

C(51/3) = 51! / [(51-3)! *3!]

C(51/3) = 51! / [(48)! *3!]

C(51/3) = 51*50*49*48! / [(48)! *3!]

C(51/3) = 51*50*49/3!

C(51/3) = 20825

C(49/2) = 49! / [(49-2)! *2!]

C(49/2) = 49! / [(47)! *2!]

C(49/2) =49*48*47! / [(47)! *2!]

C(49/2) = 49*48/2!

C(49/2) = 1176

C(51/3) * C(49/2) = 20825*1176

C(51/3) * C(49/2) = 24490200

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Answer: 0.89

Step-by-step explanation:

We can rewrite the expression in two possible ways as -

f{x} = {- x - 17}/{3}    and    f{x} = - {x + 17}/{3}

Given is the expression as -

f{x} = - {1/3}x - {17/3}

We can rewrite the expression in two possible ways as -

f{x} = {- x - 17}/{3}

and

f{x} = - {x + 17}/{3}

Therefore, we can rewrite the expression in two possible ways as -

f{x} = {- x - 17}/{3}    and    f{x} = - {x + 17}/{3}

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The variance is 13.84. Variance is a measure of dispersion that considers the spread of all data points in a data collection, in contrast to range and interquartile range.

The following data set's variance should be calculated: 2, 7, 3, 12, and 9.

The mean must be calculated first. There are 5 data points and the total is 33. The mean is therefore 33 x 5 = 6.6. The next step is to take each data point in the set, subtract the mean, and square the result. For the first value, as an illustration:

(2 - 6.6)2 = 21.16

All values' squared differences are added.

21.16 + 0.16 + 12.96 + 29.16 + 5.76 = 69.20

Next, divide the total by the number of data points:

69.20 ÷5 = 13.84

It varies by 13.84. You must calculate the square root of the variance, which is 3.72, to obtain the standard deviation.

The complete question is,

calculate the variance of the follow data set: 2, 7, 3, 12, 9.

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The total number of solutions to a polynomial equation can be determined by analyzing its degree and the number of times that the variable equals to zero. A polynomial equation of degree n will have at most n solutions.

Here is the general rules for finding the number of solutions to a polynomial equation:

If the polynomial is a degree-n equation and has n distinct roots, then it will have n solutions.

For example, the polynomial 5x^3 - x +2 has 3 solutions as it is third-degree polynomial.

It's worth noting that these rules are based on the assumptions that the polynomial is defined over the field of complex numbers, which means that the solutions can be complex numbers, and not just real numbers.

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The distance between points (- 4 0 and 6 0) is 2

The length of the line segment bridging two points on a plane is known as the distance between the points.

As per the data given in the above question re as bellow,

The details provided are as follow,

The given points are (-4, 0) and (6, 0)

We have to find the distance between the two points.

By using the formula for the distance between two point is,

A(XA:YA) and B(XA:YB)

[tex]|A B|=\sqrt{\left(x_B-x_A\right)^2+\left(y_B-y_A\right)^2}[/tex]

Now we have the point,

(-4, 0) and (6, 0)

Substitute the value in above equation we get,

[tex]|AB |=\sqrt{(6-4)^2+(0-0)^2}=\\\sqrt{(2)^2+(0)^2}=\\\sqrt{4+0}=\\\sqrt{4}[/tex]

=2

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Answer:

1 quarter and 1 nickel

Step-by-step explanation:

2 quarters = 50 cents

1 nickel = 5 cents

if we add those up, we get 55 cents.

Now we subtract 85 with 55 to get the exact number of cents missing.

85 - 55 = 30 cents.

two coins that can add up to 30 cents are 1 quarter and 1 nickel, given that 25 +5 is equal to 30.

Answer: Using the absolute value function, the value that is the opposite of being short $3.96 is: x + 3.96.

Step-by-step explanation:

The absolute function is defined by:

|x| = x, x ≥ 0.

|x| = -x, x < 0.

It measures the distance of a point x to the origin, that is, |2| = |-2| = 2.

For this problem, the number is of $3.96, that is:

|x| = 3.96.

Hence:

Short of $3.96 means that x = -3.96.

The opposite is the other solution, of x = 3.96.

Answer: 180

Step-by-step explanation:

To write a given function in the factored form from a given graph is expressed as f (x) = A ( x - t )( x - q ).

As given in the question,

Let us consider a equation representing the graph of a function :

2x² - 4x - 30

Simplify this into factored form

= 2 ( x² - 2x - 15 )

= 2 ( x² - 5x + 3x -15 )

= 2 ( x ( x - 5 ) + 3 ( x - 5 ) )

= 2 ( x - 5 ) ( x + 3 )

In standard form if the function is f(x) = Ax² + Bx + C

Then its factored form is  f (x) = A ( x - t )( x - q ).

Therefore, the function can be written in factored form from a graph in the following way :  f (x) = A ( x - t )( x - q ).

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Natural numbers are a part of the number system that includes all positive integers from 1 to infinity and are used for counting. So 7 is the natural number.

Natural numbers, which range from 1 to infinite, are positive integers. These elements are countable and frequently utilized in calculations. The set of natural numbers is represented by the letter "N."

N = {1,2,3,4,5,6,7,8,9,10…….}

There is no zero there (0). Actually, the counting numerals 1, 2, 3, 5, 6, 7, 8, 9, etc., are frequently used.

Real numbers, which only include positive integers like 1, 2, 3, 4,5, and 6, and exclude all other values like zero, fractions, decimals, and negative numbers, are a subset of natural numbers.

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The value for Tan 2a = Cot ( a - 70) gives a= 53.33

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

Tan 2a = Cot ( a - 70)

As, tan a= cot (90 - a)

So, cot (90- 2a) = Cot (a-70)

Now, comparing the angles we get

90 -2a = a - 70

90 + 70 = a + 2a

3a = 160

a = 160/3

a = 53.33

Hence, the value of a is 53.33.

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The value of the expression 15/3 is 5

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

15/3

The above expression is a mathematical expression that can be translated as

15 divided by 3

When 15 is divided by 3, we have the following result

15/3 = 5

Hence, the value is 5

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Complete question

What is the value of 15/3?