Evaluate
3x2−2xy+4y2
3
x
2
−
2
x
y
+
4
y
2
for
x=−1
x
=
−
1
and
y=−2

Therefore, the quadratic function in standard form that represents the data in the table is: y = 1/2 x² - 5/2 x + 5.

A function is a mathematical concept that describes the relationship between two sets of numbers. It is a rule that assigns to each input (or element in the domain) exactly one output (or element in the range). In simpler terms, a function is like a machine that takes in a number and produces another number as output, according to some specific rules. The input is usually denoted by x, and the output by f(x), which is read as "f of x". Functions can take many forms, such as linear, quadratic, trigonometric, exponential, logarithmic, and more. They are widely used in mathematics, science, engineering, and many other fields to model and analyze various phenomena.

Here,

To write a quadratic function in standard form, we need to use the general form of the quadratic equation:

y = ax²+ bx + c

where a, b, and c are constants. We can use the values in the table to find these constants.

When x = 2, y = 3

When x = 4, y = 1

When x = 6, y = 3

When x = 8, y = 9

When x = 10, y = 19

Substituting these values into the quadratic equation, we get:

3 = 4a + 2b + c

1 = 16a + 4b + c

3 = 36a + 6b + c

9 = 64a + 8b + c

19 = 100a + 10b + c

We can now use these equations to solve for a, b, and c. One way to do this is to use a matrix equation:

|16 4 1| |a| |1|

|36 6 1| |b| = |3|

|64 8 1| |c| |9|

Using a calculator or matrix software, we can solve for a, b, and c:

a = 1/2

b = -5/2

c = 5

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The order of the matrix is 2 x 2.

What is a matrix and what is meant by its order?

In the field of mathematics, matrices are rectangular arrangements of numerical values, symbols, or algebraic expressions, organized in rows and columns. Matrices are used in many areas of mathematics and science, as well as in engineering, physics, and computer graphics.

The term 'order' in the context of matrices refers to the dimensions of the matrix, which are determined by the number of rows and columns it contains. It is denoted by m x n, where m is the number of rows and n is the number of columns. To find the order of a matrix, we simply count the number of rows and columns. The order is usually written as a pair of numbers in the form m x n.

Determine the order of the given matrix:

In the given problem, we are asked to find the order of the matrix:

[tex]\begin{pmatrix}9 &6 \\-4 & 8\end{pmatrix}[/tex]

we count the number of rows and columns.

This matrix has 2 rows and 2 columns, so its order is 2 x 2.

Therefore, the order of the matrix is 2 x 2.

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1 + 2i in polar form is 5√2∠63.4°.

What is a polar form ?

In mathematics, the polar form is a way of representing complex numbers using their magnitude and angle. A complex number can be represented in the form r(cos θ + i sin θ), where r is the magnitude (or modulus) of the complex number, and θ is its argument (or phase angle). Alternatively, the polar form can be represented in terms of magnitude and angle as r ∠θ, where r is the magnitude and θ is the angle in radians. This form is also known as the exponential form of a complex number. The polar form is useful in calculations involving complex numbers, especially in multiplication and division, where it is often easier to work with the polar form rather than the rectangular form (a + bi).

D. 5√2∠63.4°

To convert a complex number from rectangular form to polar form, we use the following formulas:

r = √(a^2 + b^2)

θ = tan^-1 (b/a)

Where a and b are the real and imaginary parts of the complex number, respectively.

In this case, a = 1 and b = 2, so:

r = √(1^2 + 2^2) = √5

θ = tan^-1 (2/1) = 63.4°

Therefore, 1 + 2i in polar form is 5√2∠63.4°.

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Answer:

1. 57/16 or 3.5625 ounces of water

8 : 4.75

1 : 19/32  -----> divide both by 8

19/32x6=57/16 = 3.56 ounces

2. 2.4375 ounces of other ingredients

6-3.5625=2.4375

Answer:

Step-by-step explanation:

Ranking:

Compound the interest every month instead of every two months.

Increase the interest rate by 1%.

Let the account increase for one more year.

Increase the starting amount by $100.

Calculations:

If the interest is compounded monthly instead of every two months, the final value would be $1,357.36, which is an increase of $9.18 compared to the original value.

If the interest rate is increased to 6%, the final value would be $1,411.58, which is an increase of $63.40 compared to the original value.

If the account increases for one more year at the same interest rate, the final value would be $1,435.09, which is an increase of $86.91 compared to the original value.

If the starting amount is increased by $100, the final value would be $1,421.61, which is an increase of $73.43 compared to the original value.

According to the question the percent abundance of the medium nails in the sample is approximately 18.95%.

Whenever the set of data is presented from least to largest, the median is indeed the number in the middle. For instance, since 8 is in the middle, this would represent the median value here.

To find the percent abundance of the medium nails in the sample, we first need to calculate the total number of nails in the sample:

Total number of nails = 67 + 18 + 10 = 95

Next, we can calculate the percent abundance of the medium nails using the formula:

Percent abundance = (number of medium nails / total number of nails) x 100%

Using the values from of the table as inputs, we obtain:

Percent abundance of medium nails = (18 / 95) x 100% ≈ 18.95%

As a result, the sample's average percentage of medium nails is roughly 18.95%.

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To subtract 6/7 from 2 1/4, we need to find a common denominator. The least common multiple of 7 and 4 is 28, so we can convert 2 1/4 to 9/4 and 6/7 to 24/28. Then we can subtract:

9/4 - 24/28

= 63/28 - 24/28

= 39/28

Therefore, 2 1/4 - 6/7 = 39/28.

To solve for the blank in 2 5/12 - blank = 2/3, we can start by converting 2 5/12 to an improper fraction:

2 5/12 = (2*12 + 5)/12 = 29/12

Then we can subtract 2/3 from both sides:

2 5/12 - 2/3 = blank

To subtract these fractions, we need to find a common denominator. The least common multiple of 3 and 12 is 12, so we can convert 2/3 to 8/12. Then we can subtract:

29/12 - 8/12

= 21/12

= 7/4

Therefore, the blank in 2 5/12 - blank = 2/3 is 7/4.

To subtract 5 3/8 from 7 1/12, we need to find a common denominator. The least common multiple of 8 and 12 is 24, so we can convert both mixed numbers to improper fractions:

7 1/12 = (712 + 1)/12 = 85/12

5 3/8 = (58 + 3)/8 = 43/8

Then we can subtract:

85/12 - 43/8

= 85/12 - (433)/(83)

= 85/12 - 129/24

= 5/24

Therefore, 7 1/12 - 5 3/8 = 5/24.

To solve for the blank in blank + 7/10 = 2 9/20, we can start by converting 2 9/20 to an improper fraction:

2 9/20 = (2*20 + 9)/20 = 49/20

Then we can subtract 7/10 from both sides:

blank + 7/10 - 7/10 = 49/20 - 7/10

Simplifying the right side:

49/20 - 7/10 = (492)/(202) - (74)/(104) = 98/40 - 28/40 = 70/40 = 7/4

Therefore, blank + 7/10 - 7/10 = 7/4, and solving for blank:

blank = 7/4

Therefore, the blank in blank + 7/10 = 2 9/20 is 7/4.

Answer:

p=84

Step-by-step explanation:

p=6×14

p=84

answer: p=84

Answer:

A fraction tells you how many parts of a whole there are. When we find a fraction of an amount, we are working out how much that 'part' is worth within the whole. You can see fractions of amounts all around us

Step-by-step explanation:

i may be wrong but I tried

To find the area of the total figure, we need to first find the areas of the rectangle and triangle, and then add them together.Therefore, the area of the total figure is 200 square feet.

Area is the measurement of the size of a two-dimensional surface enclosed by a closed figure

Area of rectangle = length x width

= 20 ft x 8 ft

= 160 sq. ft

Area of triangle = 1/2 xbase xheight

= 1/2 x 8 ft x 10 ft

= 40 sq. ft

To find the base of the triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse (slope) of a right triangle is equal to the sum of the squares of its two sides. In this case, the hypotenuse is 12 ft, one of the other sides is the height of the triangle (10 ft), and the other side is the base of the triangle (b).

Using the Pythagorean theorem, we have:

12² = 10² + b²

144 = 100 + b²

44 = b²

b = √44

b ≈ 6.63 ft

Now that we know the base of the triangle, we can find the area of the total figure by adding the area of the rectangle and the area of the triangle:

Area of total figure = area of rectangle + area of triangle

= 160 sq. ft + 40 sq. ft

= 200 sq. ft

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Answer:2

Step-by-step explanation:Because the 2 is closest to the middle line

Answer:

relationship describes angles 1 and 2 is supplementary angles. From the given figure

it is concluded that

the relation ship between angle 1 and 2 is supplementary angles

because its is  linear pair

and forms a line

therefore , the angles are supplementary angles

hence , relationship describes angles 1 and 2 is supplementary angle

Step-by-step explanation: Hope this helps !! Mark me brainliest!! :))

Answer:

1.986 x 10 to the tenth power

Step-by-step explanation:

Answer:

The midpoint of a line segment AB with endpoints A(x1, y1) and B(x2, y2) is given by the coordinates:

[(x1 + x2) / 2, (y1 + y2) / 2]

In this case, A is located at (1, 4) and B is located at (3, -6). So the midpoint M of AB is:

[(1 + 3) / 2, (4 + (-6)) / 2]

= [2, -1]

Therefore, the midpoint of AB is at the point (2, -1).

The coordinates of the midpoint of the line AB is [2, -1]

Section formula is used to find the ratio in which a line segment is divided by a point internally or externally.

It is used to find out the centroid, incenter and excenters of a triangle. In physics, it is used to find the center of mass of systems, equilibrium points, etc.

Given that, we need to find the midpoint of AB if A located at (1, 4) and B is located at (3, -6).​

The midpoint of a line segment AB with endpoints A(x1, y1) and B(x2, y2) is given by the coordinates:

[(x1 + x2) / 2, (y1 + y2) / 2]

In this case, A is located at (1, 4) and B is located at (3, -6).

So the midpoint M of AB is:

= [(1 + 3) / 2, (4 + (-6)) / 2]

= [2, -1]

Hence, the midpoint of AB is at the point (2, -1).

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Around [tex]312.57[/tex] yards are required to complete a full lap of the circuit.

The entire movement of an item, independent of direction, is called distance. Regardless of an object's beginning or finishing position, distance may be defined as the amount of ground it has travelled.

As a result, distance is indeed a scalar quantity. The whole path an item has taken can be used to define the distance from it. Think about it this way. If a car drives 5 km east, then turns to head north for 8 km, the final distance driven by the automobile must be 13 km.

The circumference of a semicircle with diameter d is [tex](pi/2)d[/tex]. Therefore, the length of each semicircular section is [tex](pi/2) * 36 = 18pi[/tex].

The total distance around the track is the sum of the lengths of the two straight sections and the two semicircular sections.

Distance around track [tex]= 2(100 yards) + 2(18pi yards)[/tex]

[tex]= 200 yards + 36pi yards[/tex]

[tex]= 312.57 yards[/tex] (rounded to two decimal places)

Therefore, the distance around the entire track is approximately [tex]312.57[/tex]yards.

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The correct number line is: A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded.

The mathematical expression of a connection between two values, stating that one value is larger than, less than, or not equal to another value, is called an inequality. Common symbols for inequality include (less than), > (greater than), (less than or equal to), and (greater than or equal to). For instance, the inequality 2x + 3 > 7 denotes that the value of 2x + 3 is larger than 7. Depending on the circumstance, inequalities can be resolved algebraically or visually. A collection of values that meet the connection implied by the inequality is the answer to an inequality.

Here, the inequality is y - 2 < -5, which can be rewritten as y < -3.

Hence, the correct option is: A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded.

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Answer: Linear

Step-by-step explanation:

Since the difference between consecutive values of f(x) is constant, this suggests that the function could be linear. To confirm this, we can calculate the differences between consecutive values:f(1) - f(0) = -15 - (-18) = 3

f(2) - f(1) = -12 - (-15) = 3

f(3) - f(2) = -9 - (-12) = 3

f(4) - f(3) = -6 - (-9) = 3

Since the differences are constant and equal to 3, this confirms that the function is linear.

To find the equation of the linear function, we can use the slope-intercept form of a linear equation:

y = mx + bwhere m is the slope and b is the y-intercept.

We can use the first two points (0, -18) and (1, -15)  to find the slope:

m = (change in y) / (change in x) = (-15 - (-18)) / (1 - 0) = 3

Now we can use the slope and one of the points to find the y-intercept:

y = mx + b

-18 = 3(0) + b

b = -18

Therefore, the equation of the linear function is:

f(x) = 3x - 18

So the function type that could represent the values in the table is linear.

Answer:

18

Step-by-step explanation:

siz times three is eighteen

Answer: Sally will earn $4,830.00 in interest over 7 years.

Step-by-step explanation:

If the interest is not compounded, then Sally will earn simple interest, which can be calculated using the formula:

I = P * r * t

where:

I = the interest earned

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

t = the time period, in years

In this case, we have:

P = $9,000 (the initial deposit)

r = 7% = 0.07 (the annual interest rate)

t = 7 (the number of years)

So, plugging in the values:

I = $9,000 * 0.07 * 7

I = $4,830.00

Therefore, Sally will earn $4,830.00 in interest over 7 years.

The function that expresses f(x) is f(x) = 1.99x + 3, and its graph is continuous.

A continuous function is one that doesn't have any sudden or unexpected changes in value. It means that if we make small enough changes to its input, the output will also change by a small amount.

We can express the total cost of an order as a function of the number of books sold, x, using the formula:

f(x) = 1.99x + 3

This function takes the number of books sold, multiplies it by the cost per book ($1.99), and adds a fixed fee of $3.

For example, if we sold 3 books, we can use the function to find the total cost:

f(3) = 1.99(3) + 3 = 9.97

This means that selling 3 books would cost $9.97 in total.

The graph of this function is continuous, which means that as we move along the x-axis, the y-values change smoothly and without any sudden jumps.

The term "continuous" refers to a function that can take on any value between two given points and can be broken down into infinitely many fractions and decimals.

In contrast, a discrete function can only take on specific values, usually whole numbers or integers.

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Answer:

I will not show you the process it is easy the answer is 4.5 or 6 ≈

The maximum revenue is achieved when she sells 33 photos at a price of 25 per photo.

Using quadratic regression, [tex]y = ax^2 + bx + c[/tex]

where a, b and c are constants and x is the independent variable we can determine the equation of the curve that best fits the data. The equation will be in the form of[tex]y = ax^2 + bx + c[/tex], where y is the revenue, x is the number of photos sold, and a, b, and c are constants. The constants can be determined by solving the system of equations formed by the three data points.

After solving for the constants, we can determine the maximum revenue by finding the vertex of the curve. The vertex is located at x = -b/2a, and the corresponding revenue is[tex]y = ax^2 + bx + c[/tex]. Plugging in the values for a, b, and c, we can calculate that the maximum revenue is achieved when she sells 33 photos at a price of 25 per photo.

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Complete question

Darlena has started taking photos at amateur dog racing events, later offering the photos for sale to the dog owners by email. The prices she has charged per photo at each of her first three events, and the corresponding number of photos sold and total revenue raised, appear in the table below. Treating revenue as a function of the number of photos sold, a graph of the three data points is also shown. If she uses quadratic regression to fit a curve to the data, what number of photos sold and what price per photo will maximize her revenue?

Answer:

(gof)(x) = 14x + 1

Step-by-step explanation:

We can think of (gof)(x) as g(f(x)).  Writing it in this form shows that we must start with the inner function and work our way to the outer function.

Essentially, the input of the inner function yields an output and the output becomes the input of the outer function.

f(x) means that the input is x and since we're given no value for x (e.g. x = so and so), the output is the original function or 2x - 1

Now, this output becomes the input for g(x):

g(2x-1) = 7(2x - 1) + 8

14x -7 + 8

(gof)(x) = 14x + 1

The volume of the cone is  2119. 5 cubic centimeters

The formula used for calculating the volume of a cone is expressed as;

V = πr² h/3

Given that the parameters are namely;

Now, substitute the values, we have;

Volume , V = 3.14 × 15² × 9/3

Divide the values, we have;

Volume = 3.14 × 225 × 3

Multiply the values, we get;

Volume, V = 2119. 5 cubic centimeters

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The sum of x and 2 is equal to x + 2.

Value in math is the numerical representation of a quantity or expression. It can also be defined as an amount or a numerical representation of a quantity that is assigned to a variable or a constant in a mathematical expression. Value can be expressed in various forms, such as decimal, fraction, and scientific notation. Value is also used to calculate the result of an equation or a problem. Value is a fundamental concept in mathematics, and it is used to measure and compare different quantities.

This equation can be used to calculate the sum of any two numbers, x and 2. For example, if x is equal to 5, then the sum of x and 2 is equal to 5 + 2, which is equal to 7. Similarly, if x is equal to 10, then the sum of x and 2 is equal to 10 + 2, which is equal to 12. Therefore, the sum of x and 2 depends on the value of x.

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Answer:

4.88%

Step-by-step explanation:

All sides of a square are equal

let x = length of a side

Area = x·x = x²

Estimated area = (8.5)² = 72.25 in²

Actual area = (8.3)² = 68.89 in²

percent error  = (actual area - estimated area) / (estimated area) x 100

% error = (68.89 - 72.25) / (68.89) x 100 = -4.88%     the negative sign means the estimate was higher than the actual.  

The quadratic equation on the graph can be written as:

y = x² + 6x + 8

Remember that a quadratic equation whose vertex is (h,k) and the leading coefficient is a, can be written as:

y = a*(x - h)² + k

Here we can see that the vertex is at (-3, -1), replacing that we will get:

y = a*(x + 3)² - 1

Now we can also see that it passes through the point (-2, 0), replacing these values we will get:

0 = a*(-2 + 3)² - 1

0 = a - 1

1 = a

Then the quadratic is:

y  = (x + 3)² - 1

Expanding that we get:

y = x² + 6x + 9 - 1

y = x² + 6x + 8

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1. Calculating the output when using -6 as the input, we have:

Rule 1: subtract 7  = -13

Rule 2: square the input = 36.

Rule 3: divide by 3 = 12

Rule 4: divide the input into 3 = -2

Rule 5: write π = -2π

Rule 6: volume of a cube = -216cm³

A function rule is a mathematical expression that describes how to calculate the output value of a function based on its input value. It can be thought of as a set of instructions that tell you what to do with the input value to get the output value.

2. a. True. Speed is the ratio of distance traveled to the time taken to travel that distance. In this case, the distance is fixed at 100 meters, so speed is solely dependent on time. For each value of time, there is only one corresponding value of speed, making it a function.

b. False. While time and distance are related in the formula for speed, time is not a function of distance in this case. Each student's time is independent of the distance they cover, and the same distance is covered by all students (100 meters). Therefore, for any given distance, there are multiple possible values of time, making it not a function.

c. False. The number of students racing is not related to their speed. Each student's speed depends solely on their individual time, which is not affected by the number of other students racing.

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Answer:

a-no for the first triangle, because the total of the inner angles must be 180, the last angle must be 90.

b-yes- a triangle with angles 90, 50, and 40 is possible

c-yes. 65+45+70=180.

Step-by-step explanation: