How do you work out a quadratic equation with a maximum value?

The question is about finding three consecutive even integers whose sum is 24. The integers are determined to be 6, 8, and 10 by setting up and solving a simple algebraic equation.

To solve for the three consecutive even integers whose sum is 24, let's assume that the first even integer is x. Because we know that even integers occur 2 units apart, we can say that the next two consecutive even integers are x + 2 and x + 4 respectively.

Now, we know that the sum of these three integers is equal to 24. Therefore, we can set up an equation:

x + (x + 2) + (x + 4) = 24

By simplifying and solving the equation, we obtain x = 6. Therefore, the three consecutive even integers are 6, 8, and 10.

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The new food budget is $400, the difference in the savings is $50 and the amount of money saved now is $2700.

An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.

The equations are useful in determination of unknown parameters.

The Porter family has a net income of $5000.

The food budget of the family is $450

The budget is reduced by $50

The new food budget is $450 - $50

The new food budget is $400

Initially they used to save,

= $5000 - $450-  $1900

= $2650

Now as the expense has been reduced by $50,

The new savings will be,

= $2650 + $50

= $2750

It seems that your question is incomplete, the complete question is :

The Porter family has a net income of $5,000. They have a monthly food budget of $450 and $1900 is extra expenses, If they want to reduce their food budget by $50, how much would the new food budget be and what will be the difference in the savings.

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The area of the base of a pyramid with volume 27 cubic cm and height 6 cm is 13.5 square cm. If the base is a square, the length of each side of the base is approximately 3.67 cm.

The volume of a pyramid can be given by the formula V = (1/3) * Area of the base * Height. In your question, you have been provided that the volume V is 27 cubic cm and the height h is 6 cm. Then Area of the base would be (3 * V) / h = (3 * 27 cubic cm) / 6 cm = 13.5 square cm. Since the base of a pyramid can be of various shapes, we have only calculated the area here. Now I assume that the base is a square for simplicity. If the area A of a square is given by the formula A = side^2, we can find the side length of the base by taking the square root of the area = sqrt(A) = sqrt(13.5 square cm) = 3.67 cm approximately.

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Answer:

In year 2012, 0.45 thousands dollars will bring the break even for the company.

Step-by-step explanation:

The table shows the annual profits of a county fair from 2008 to 2012.

We have to calculate the profit in 2012 to get the break even over the five year period.

Total profit in four years = profit in year (2008 + 2009) = 2.5 + 1.75 = 4.25 thousand dollars

Total loss in four years = loss in year (2010 + 2011) = 3.3 + 1.4 = 4.7 thousand dollars

Net profit or loss = Net profit - net loss = 4.25 - 4.7 = -0.45

There is a net loss of 0.45 thousand dollars.

If we get a profit of 0.45 thousand dollars in year 2012, we will be in the situation of no profit and no loss (break even).

Therefore, profit of 0.45 thousands of dollars is the answer.

The ratio of 34 days to 2 weeks is [tex]\(\frac{34}{2 \times 7}\)[/tex].

To find the ratio of 34 days to 2 weeks, we first need to convert 2 weeks into days, since there are 7 days in a week. Therefore, 2 weeks is equivalent to [tex]\(2 \times 7\)[/tex] days, which is 14 days.

Now, we can set up the ratio of 34 days to 14 days (2 weeks):

[tex]\[ \text{Ratio} = \frac{34 \text{ days}}{14 \text{ days}} \][/tex]

To simplify this ratio, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 34 and 14 is 2.

Dividing both by 2, we get:

[tex]\[ \text{Ratio} = \frac{34 \div 2}{14 \div 2} = \frac{17}{7} \][/tex]

So, the simplified ratio of 34 days to 2 weeks is [tex]\(17:7\) or \(\frac{17}{7}\)[/tex].

Answer: Second option.

Step-by-step explanation:

In order to find the degree of the power function represented in the given table, you must find the difference of the y-values (values of [tex]h(x)[/tex]) until they diferences are constant.

1) First differences:

[tex]-2-(-8)=6\\\\0-(-2)=2\\\\-2-0=-2\\\\-8-(-2)=-6[/tex]

2) Second differences:

You must find the differences between the First  differences. Then, you get:

[tex]2-6=-4\\\\-2-2=-4\\\\-6-(-2)=-4[/tex]

You can notice that the second differences are constant. This means that the degree of the power function  represented in the given table is:

[tex]Degree=2[/tex]

The degree of the power function represented in the table is [tex]\boxed2[/tex].Option (b) is correct.

Further explanation:

Given:

The options are as follows,

(a). 1

(b). 2

(c). 3

(d). 4

Explanation:

The highest power of the polynomial function is known as the degree.

The value of x is -2 and the value of the function is -8.

The value of x is -1 and the value of the function is -2.

The value of x is 0 and the value of the function is 0.

The value of x is 1 and the value of the function is -2.

The value of x is 2 and the value of the function is -8.

The function from the table can be expressed as follows,

[tex]f\left( x \right) = - 2{x^2}[/tex]

Substitute [tex]-2[/tex] for [tex]\text{x}[/tex] in equation [tex]f\left( x \right) = - 2{x^2}.[/tex]

[tex]\begin{aligned}h\left( { - 2}\right) &= - 2\times {\left( { - 2} \right)^2}\\&= - 2 \times 4\\&= - 8\\\end{aligned}[/tex]

The degree of the power function represented in the table is [tex]\boxed2.[/tex]Option (b) is correct.

Option (a) is not correct.

Option (b) is correct.

Option (c) is not correct.

Option (d) is not correct.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Polynomial

Keywords: power function, degree, represented, table, degree of the polynomial, roots, linear equation, quadratic equation, zeros, function, polynomial, solution, cubic function, degree of the function.

To prove RS = TU, we can use the congruence of corresponding parts of congruent triangles. By the side-angle-side (SAS) congruence postulate, if two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. Therefore, RS = TU.

To prove that RS = TU, we need to show that the lengths of RS and TU are equal. In order to do this, we can use the congruence of corresponding parts of congruent triangles. Let's assume that triangles RST and TUV are congruent.

By the side-angle-side (SAS) congruence postulate, if two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Since RST and TUV are congruent, we can conclude that RS and TU are congruent as well. Therefore, RS = TU.

The perimeter of a triangle with vertices at X(-2, -1), Y(2, 5) and Z(4, 3) is calculated using the distance formula to find the lengths of each edge. After calculating the lengths of the edges (XY, YZ and ZX), they are summed to produce the perimeter, which is 2√52 + √8.

To calculate the perimeter of a triangle with vertices at given coordinates, we must first compute the distances between each pair of points. Using the distance formula, d= √[(x₂-x₁)²+ (y₂-y₁)²], we find the distances between points X(-2,-1), Y(2,5) and Z(4,3).

Specifically, XY = √[(2 - -2)² + (5 - -1)²] = √[4² + 6²] = √52, YZ = √[(4 - 2)² + (3 - 5)²] = √[2² + -2²] = √8, and ZX = √[(4 - -2)² + (3 - -1)²] = √[6² + 4²] = √52.

Together, these line distances constitute the edges of the triangle. Adding these distances together (two √52 and √8), we find the perimeter of the triangle is 2√52 + √8.

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The mean is not included in the five number summary.

It is required to choose the following is not included in the five number summary.

Statistics are defined as numerical data, and is the field of math that deals with the collection, tabulation and interpretation of numerical data. It is the study and manipulation of data, including ways to gather, review, analyze, and draw conclusions from data.

Given:

Actually its the mean. The 25th percentile is Q1 which is used to calculate inter-quartile range i.e.

[tex]IQR=Q_{1} -Q_{3}[/tex]

The mean has nothing to do with the five number summary or box and whisker plot.

The  five number summary consists of five values: the most extreme values in the data set (the maximum and minimum values), the lower and upper quartiles, and the median.

Therefore, the mean is not included in the five number summary.

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The value of expression 4m + 23 + np - 3 for m = 7, n = 2, and p = 8 is 64.

To solve the given expression, we substitute the given values of m, n, and p into the expression:

4m + 23 + np - 3

Given m = 7, n = 2, and p = 8, we substitute these values into the expression:

4(7) + 23 + (2)(8) - 3

28 + 23 + 16 - 3

28 + 23 = 51

51 + 16 = 67

67 - 3 = 64

Final answer:

To solve the equation 17 - 2v = 41, subtract 17 from both sides to get -2v = 24. Then divide both sides by -2 which gives v = -12.

Explanation:

To solve the equation 17 - 2v = 41 for v, first we need to isolate v on one side of the equation. We can start by subtracting 17 from both sides to rid the left side of numbers without the variable v. This gives us the equation:

-2v = 41 - 17

-2v = 24

Now, to solve for v, we divide both sides of the equation by -2:

v = 24 / (-2)

v = -12

Therefore, the solution to the equation is v = -12.