Please answer this question ​

The vertex of this function would be (-1, -8).

The question seems to be incomplete and there are some typos in it. However, I will try to provide a general answer based on the given information.

When finding the vertex of a function, you can use the formula -b/2a to find the x-coordinate of the vertex. Once you have the x-coordinate, you can plug it back into the original function to find the y-coordinate of the vertex.

For example, if the function is y = 2x^2 + 4x - 6, the formula for the x-coordinate of the vertex would be -4/(2*2) = -1. The y-coordinate of the vertex would be 2(-1)^2 + 4(-1) - 6 = -8.

So the vertex of this function would be (-1, -8).

Remember to Round all answers to 3 decimal places, as instructed in the question.

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Answer:

3/700

Step-by-step explanation:

hope this helps :))

For the given arithmetic series, a_(1) = 27, d = 4, a_(n) = 783, n = 190, and n^(2) = 36100.

The given arithmetic series is 27, 31, 35,..., 783.

To find the first term, a_(1), we can simply look at the first term in the series. Therefore, a_(1) = 27.

To find the common difference, d, we can subtract the first term from the second term, or the second term from the third term. Therefore, d = 31 - 27 = 4.

To find the nth term, a_(n), we can use the formula a_(n) = a_(1) + (n - 1)d. We know that a_(1) = 27, d = 4, and a_(n) = 783, so we can plug these values into the formula and solve for n:

783 = 27 + (n - 1)(4)

756 = (n - 1)(4)

189 = n - 1

n = 190

Therefore, the nth term is 190.

To find the value of n^(2), we can simply square the value of n:

n^(2) = 190^(2) = 36100

Therefore, the value of n^(2) is 36100.

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Answer:

n ≤ 6.5

Step-by-step explanation:

43.5 + n ≤ 50

43.5 + n - 43.5 ≤ 50 - 43.5

n ≤ 6.5

Answer:

5

Step-by-step explanation:

Kobe scored 656 points in the season.

How to find and what is basketball?

If Kobe scored 82 points in a basketball game and that was 1/8 of the points he scored for the season, we can find the total points he scored in the season by multiplying 82 by 8, since 82 represents 1/8 of the total points:

Total points = 82 x 8

= 656

Therefore, Kobe scored 656 points in the season.

Basketball is a team sport played between two teams of five players each. The objective of the game is to shoot a ball through a hoop or basket that is mounted on a backboard at each end of the court, while also preventing the opposing team from doing the same.

The game is played on a rectangular court with standardized dimensions and various markings, including a center circle, free-throw lines, and three-point lines. Basketball is a fast-paced and physically demanding sport that involves a combination of offensive and defensive skills, including shooting, dribbling, passing, and rebounding.

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To find the minimum final score you need to get a 77%,

you can use the following formula:
(weight of weighted grade * weighted grade) + (weight of final * final grade) = desired overall grade
Plug in the given values:
(0.65 * 89) + (0.35 * final grade) = 77
Solve for the final grade:
57.85 + 0.35 * final grade = 77
0.35 * final grade = 19.15
final grade = 19.15 / 0.35
final grade = 54.71

Therefore, the minimum final score you need to get a 77% overall is 54.71%.

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The wind generator will produce 2744W of power in a 35mph wind.

To find the power generated by the wind generator in a 35mph wind, we can use the formula P = kV³, where P is the power generated, k is a constant, and V is the wind's speed.

First, we need to find the value of k. We can do this by plugging in the given values of P and V into the formula and solving for k:

1000W = k(25mph)³ 1000W = k(15625mph³)

k = 1000W/15625mph³

k = 0.064W/mph³

Now that we have the value of k, we can plug it back into the formula along with the new wind speed of 35mph to find the power generated:

P = (0.064W/mph³)(35mph)³

P = (0.064W/mph³)(42875mph³)

P = 2744W

Therefore, the wind generator will produce 2744W of power in a 35mph wind.

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For the system of linear equations

[tex]\[ \begin{aligned} h x_{1}-3 x_{2}-6 x_{3} & =-3 \\ x_{1}+3 x_{2}+x_{3} & =1 \\ -4 x_{1}-9 x_{2}+2 x_{3} & =-1 \end{aligned} \][/tex],  

the value of [tex]\( h \)[/tex] is [tex](15/4)x_2 + (30/4)x_3[/tex].

The value of h can be determined by using the elimination method to solve the system of equations.

First, multiply the second equation by 4 and the third equation by -1 to eliminate the x1 term: [tex]\[ \begin{aligned} 4 h x_{1}-12 x_{2}-24 x_{3} & =-12 \\ -4 x_{1}-12 x_{2}-4 x_{3} & =-4 \\ 4 x_{1}+9 x_{2}-2 x_{3} & =1 \end{aligned} \][/tex]

Next, add the second and third equations to the first equation: [tex]\[ \begin{aligned} 4 h x_{1}-15 x_{2}-30 x_{3} & =-15 \\ \end{aligned} \][/tex]

Now, divide the equation by 4 to solve for h: [tex]\[ \begin{aligned} h x_{1}-\frac{15}{4} x_{2}-\frac{30}{4} x_{3} & =-\frac{15}{4} \\ h x_{1}-\frac{15}{4} x_{2}-\frac{30}{4} x_{3}+\frac{15}{4} & =0 \\ h x_{1}-\frac{15}{4} x_{2}-\frac{30}{4} x_{3}+\frac{15}{4}-\frac{15}{4} & =-\frac{15}{4}+\frac{15}{4} \\ h x_{1}-\frac{15}{4} x_{2}-\frac{30}{4} x_{3} & =0 \\ h & =\frac{15}{4} x_{2}+\frac{30}{4} x_{3} \end{aligned} \][/tex]

Therefore, the value of h is dependent on the values of x2 and x3 and can be expressed as h = [tex](15/4)x_2 + (30/4)x_3[/tex].

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The value of (f-g)(x)  is  x^(2)-6x-55.

Mathematical operations on a function involve the manipulation or transformation of the function, such as adding, subtracting, multiplying, dividing, and integrating the function. These operations can be done either to the function itself or to the domain or range of the function. This can be used to find the inverse of a function, calculate the area under the curve, or find the first or second derivative of a function.

To find (f-g)(x), we need to subtract the function g(x) from the function f(x).

(f-g)(x) = f(x) - g(x)

= (x^(2)-5x-50) - (x+5)

= x^(2)-5x-50 - x - 5

= x^(2)-6x-55

Therefore, (f-g)(x) = x^(2)-6x-55.

This is the final answer for the difference between the two functions f(x) and g(x).

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P is rational number from the given equation P=2(2x+5)+2x.

Rational numbers are in the form of p/q, where p and q can be any integer and q ≠ 0. This means that rational numbers include natural numbers, whole numbers, integers, fractions of integers, and decimals (terminating decimals and recurring decimals).

The given equation is P=2(2x+5)+2x.

Here, P=2(2x+5)+2x

P=4x+10+2x

P=6x+10

Given that, x=1.5, 3 and 1.2

Substitute, x=1.5 in P=6x+10, we get

P=6×1.5+10

P=9+10

P=19

So, 19 is rational number

Substitute, x=3 in P=6x+10, we get

P=6×3+10

P=18+10

P=28

So, 28 is rational number

Substitute, x=1.2 in P=6x+10, we get

P=6×1.2+10

P=7.2+10

P=17.2

So, 17.2 is rational number

Therefore, P is rational number from the given equation P=2(2x+5)+2x.

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The sides of the triangle circumscribed about a circle of radius 4 and divided on one side by the circle into segments of length 6 and 8 are 6, 8, and 4.

The triangle circumscribed about a circle of radius 4 and divided on one side by the circle into segments of length 6 and 8 can be found using the Law of Cosines. The Law of Cosines states that c2 = a2 + b2 - 2ab cos C, where c is the length of the hypotenuse, a and b are the lengths of the other sides, and C is the angle opposite side c.

We know the hypotenuse of this triangle is 8, as it is the length of one of the segments on the side of the triangle. We also know that angle C is 90° as it is a right triangle.

Therefore, using the Law of Cosines we can find the length of the other side of the triangle, which is 6. The equation is 82 = 62 + a2 - 2(6)(a)cos(90°). Solving this equation, we find that a = 4.

Therefore, the sides of the triangle circumscribed about a circle of radius 4 and divided on one side by the circle into segments of length 6 and 8 are 6, 8, and 4.

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We need to round up to the next full number because we are unable to equation have a fraction of a boat. The organization will thus require 157 boats to hold the entire 1,254 persons.

Using the equals symbol (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of two mathematical expressions by a mathematical assertion. The equal sign, for example, provides a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two phrases that are written on opposite sides of a letter. Most of the time, the logo and the particular software match. e.g., 2x - 4 = 2 is an example.

We may divide the total number of persons by the capacity of each boat to determine the number of boats required to hold a party of 1,254 individuals:

8 individuals per boat times 1,254 passengers is 156.75 boats.

We need to round up to the next full number because we are unable to have a fraction of a boat. The organization will thus require 157 boats to hold the entire 1,254 persons.

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Rogelio has watched 23/20 hours of the movie.

What is a fraction?

A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator. The numerator defines the number of equal parts taken, whereas the denominator defines the total number of equal parts in a whole.

Movie duration = 1 3/4 = 7/4

Duration of movie watched = 3/5

Duration watched = 7/4 - 3/5

Duration watched = 23/20

Duration watched = 1 3/20 (mixed fraction)

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Stacy's age is 3 less than 4 times what her age was 6 years ago. The  algebraic equation to express this is x = 4(x - 6) - 3. A pair of pants was originally selling for $135, and discounted by 25% before an 9% tax was applied. The cost of the item after the discount and tax is $110.36.

1) Let's begin by defining a variable for Stacy's age. We'll use x to represent her current age.
According to the question, Stacy's age is 3 less than 4 times what her age was 6 years ago. We can write this as an algebraic equation:
x = 4(x - 6) - 3
Now, we'll solve for x by simplifying and isolating the variable on one side of the equation:
x = 4x - 24 - 3
x = 4x - 27
27 = 3x
x = 9
So, Stacy's current age is 9.

2) To find the cost of the item after the discount and tax, we'll first calculate the discount amount and then the tax amount.
The discount amount is 25% of the original price, so we'll multiply the original price by 0.25:
$135 * 0.25 = $33.75
Now, we'll subtract the discount amount from the original price to find the discounted price:
$135 - $33.75 = $101.25
Next, we'll calculate the tax amount by multiplying the discounted price by the tax rate of 9%:
$101.25 * 0.09 = $9.11
Finally, we'll add the tax amount to the discounted price to find the final cost of the item:
$101.25 + $9.11 = $110.36
So, the cost of the item after the discount and tax is $110.36.

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Therefore , the solution of the given problem of coordinates comes out to be B' = (-2, 1)  and  C' = (4, 6) .

A coordinate system is a method that employs one or more values or coordinates to accurately locate points or even other mathematical objects on a space, such as Euclidean space. Coordinates, that are pairs of numbers, are used to locate a point or object on a double plane. The y and x vectors are two integers that specify where a point is situated on a two - dimensional plane. a group of numerals designating particular places. Usually, the number has two numbers.

Here,

By adding 1 to the x-coordinate and 3 to the y-coordinate, we can determine that position A is translated to point A'. As a result, we can determine the values of B' and C' using the same translation vector.

We increase the x-coordinate for position B by one

=> (-3 + 1 = -2) and

the y-coordinate by three

=> (-2 + 3 = 1). Consequently, B"s values are (-2, 1).

We increase the x-coordinate for position C by one

=> (3 + 1 = 4) and

the y-coordinate by three

=>(3 + 3 = 6). Consequently, C"s dimensions are (4, 6).

Consequently, the translated locations' coordinates are as follows:

=> B' = (-2, 1)

=> C' = (4, 6)

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The standard form for the quadratic equation written in vertex form y = 2(x - 2)² + 5 is y = 2x² - 8x + 13.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

To change the equation y = 2(x - 2)² + 5 from vertex form to standard form, we need to expand the squared term and simplify the expression.

Here are the steps -

Start with the vertex form: y = 2(x - 2)² + 5.

Expand the squared term using the formula (a - b)² = a² - 2ab + b².

In this case, a = x and b = 2, so we have -

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

y = 2(x² - 4x + 4) + 5

Multiply the coefficient 2 by each term inside the parentheses -

y = 2x² - 8x + 8 + 5

Combine the constant terms -

y = 2x² - 8x + 13

This is the standard form of the quadratic equation.

In standard form, the quadratic equation is written as y = ax² + bx + c, where a, b, and c are constants.

In this case, a = 2, b = -8, and c = 13.

Therefore, the standard form is y = 2x² - 8x + 13.

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Answer:

Step-by-step explanation:

Answer is (A)

Replace [tex]6x-5y=1[/tex] with the sum of both equations in System A

Answer:

The sum is 611105.

Answer:

782,886

Step-by-step explanation:

The simplified expression after doing this calculation is -1/3. To perform the addition or subtraction and simplify the given expression, we need to find a common denominator for the two fractions. The common denominator for x and 3 is 3x.

Multiply each fraction by the necessary factor to get the common denominator. For the first fraction, we multiply by 3/3, and for the second fraction, we multiply by x/x.

3/3 * (x/x) - x/x * (4/3) = (3x - 4x)/3x = (-x)/3x. Now, we can simplify the expression by canceling out the common factor of x in the numerator and denominator. (-x)/3x = -1/3

The simplified expression is -1/3.

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The model for the BMI of a person is:
BMI = (152100/weight in pounds)/(height in inches)^2

The Body Mass Index (BMI) of a person can be calculated using the formula:
BMI = (weight in pounds)/(height in inches)^2

In this case, the BMI varies directly as a person's weight in pounds and inversely as the square of the person's height in inches. This means that as the weight increases, the BMI increases and as the height increases, the BMI decreases.

To find a model for the BMI of a person, we can use the formula:
BMI = k(weight in pounds)/(height in inches)^2

Where k is a constant of proportionality. To find the value of k, we can use the given information that a 6ft 6in tall person has a BMI of 25.

First, we need to convert the height from feet and inches to inches. 6ft 6in is equivalent to 78 inches. Then, we can plug in the values into the formula and solve for k:

25 = k(weight in pounds)/(78 inches)^2
25(78 inches)^2 = k(weight in pounds)
152100 = k(weight in pounds)

Therefore, the model for the BMI of a person is:
BMI = (152100/weight in pounds)/(height in inches)^2

This model can be used to calculate the BMI of a person given their weight in pounds and height in inches.

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The value of an investment with $1000 as principal amount compounding annually for 3 years with interest rate 7.5% is $1242.29

The interest rate is the amount that the lender charges the borrower and is the principal - a percentage of the loan amount. Loan interest rates are usually quoted on an annual basis known as the annual rate (APR). 

Solution according to the given information in the question:

Given, Principal = $1000

           Time = 3 years

           Interest rate = 7.5%

∴ Amount = P×(1 + r/100)³

                 = 1000×(1 + 7.5/100)³

                 = 1000×(1 + 0.075)³

                 = 1000×(1.075)³

                 = 1000 × 1.24

Amount   = $1242.29

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Ms. Summers will give each child 1/16 gallon of milk.

Beginning with a quarter gallon of milk, Ms. Summers. She consumes a quarter of a gallon of milk, leaving her with:

1/8 gallon divided by 2/8 gallon is equal to 1/8 gallon.

Mrs. Summers will therefore divide the remaining 1/8 gallon of milk between her two kids. She needs to divide it by 2 to distribute it equally amongst the two kids.

Hence, each kid will get:

(1/8 gallon x 2) yields 1/16 gallon

Ms. Summers will thus provide each youngster with 1/16 of a gallon of milk.

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The local maximum value of the function F(x) = -0.2x^3 – 0.5x^2 + 3x - 4 for -6 is y=2.2 and it occurs at x=-1.2, and the local minimum value is y=-4.6 and it occurs at x=-4.8.

Using a graphing Utility, we can approximate the local maximum value and local minimum value of the function F(x) = -0.2x^3 – 0.5x^2 + 3x - 4 for -6.

1. The local maximum value occurs at the highest point on the graph within the given interval of -6. By observing the graph, we can see that the local maximum value is y=2.2 and it occurs at x=-1.2.

2. The local minimum value occurs at the lowest point on the graph within the given interval of -6. By observing the graph, we can see that the local minimum value is y=-4.6 and it occurs at x=-4.8.

It is important to note that these values are approximations and may not be exact. The graphing Utility is a useful tool for visualizing the function and finding approximate values, but it is not always precise.

the local maximum value of the function F(x) = -0.2x^3 – 0.5x^2 + 3x - 4 for -6 is y=2.2 and it occurs at x=-1.2, and the local minimum value is y=-4.6 and it occurs at x=-4.8.

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Answer: 8 cubic inches

Step-by-step explanation:

Answer:

Volume of cube = length x width x height

V = 2x2x2

V = 8

Therefore, the volume of the box is 8 inches long.

Answer:

Let's start by defining some variables to represent the given information:

T0 = 48°F (the current temperature)

deltaT = -1.5°F/hour (the rate of change in temperature)

T = 36°F (the target temperature)

We want to find how many hours it will take for the temperature to drop from 48°F to 36°F, so let's call that time h. We can use the formula for the linear relationship between temperature and time:

T = T0 + deltaT * h

We want to solve for h when T = 36°F, so we can substitute the given values and solve for h:

36 = 48 + (-1.5) * h

-12 = -1.5h

h = 8

Therefore, it will take 8 hours for the temperature to drop from 48°F to 36°F, assuming the temperature continues to decrease at a rate of 1.5°F per hour.

The probability of rolling a sum of 5 when rolling a 6-sided die twice is 1/9.

According to the Law of Large Numbers, a fundamental tenet of probability theory, the average of the results of an experiment approaches the predicted value of the random variable being measured as the number of trials in the experiment rises. In other words, the Law of Big Numbers states that the observed results will be closer to the predicted outcomes the more times an experiment is conducted.

The total number of outcomes when a die is rolled two times is 36.

The sum of 5 is obtained for the following outcomes:

(1,4), (2,3), (3,2), and (4,1)

Thus,

P(sum of 5) = 4/36 = 1/9

Hence, the probability of rolling a sum of 5 when rolling a 6-sided die twice is 1/9.

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Answer:

  3-4-5 right triangle is scalene

Step-by-step explanation:

You want to show the triangle defined by points P(3,2),Q(6,2) and R(6,6) is a scalene triangle.

We observe that points P and Q have the same y-coordinate, so lie on the horizontal line y=2. The length PQ is 6 -3 = 3 units.

Points Q and R have the same x-coordinate, so lie on the vertical line x=6. The length QR is 6 -2 = 4 units.

These legs are different lengths and are at right angles to each other. The third leg, the hypotenuse, will be longer than either of them.

The triangle's sides are unequal, so the triangle is a scalene triangle.

Answer:

If repetition of letter A is allowed and letter B cannot be repeated, then there are two cases to consider when constructing a 3-digit number:

Case 1: The first digit is letter A. In this case, there are 6 options for the first digit (since any of the 6 digits can be used), and there are 5 options for each of the remaining digits (since letter B cannot be repeated). Therefore, the total number of 3-digit numbers that can be formed in this case is:

6 x 5 x 5 = 150

Case 2: The first digit is not letter A. In this case, there are 5 options for the first digit (since letter A cannot be repeated), and there are 5 options for each of the remaining digits (since letter B cannot be repeated). Therefore, the total number of 3-digit numbers that can be formed in this case is:

5 x 5 x 4 = 100

To get the total number of 3-digit numbers that can be made from 1, 2, 3, 4, 5, and 6 with letter A repetition allowed and letter B repetition not allowed, we add the number of possibilities from Case 1 and Case 2:

Total = 150 + 100 = 250

Therefore, there are 250 different 3-digit numbers that can be made from 1, 2, 3, 4, 5, and 6 with letter A repetition allowed and letter B repetition not allowed.

There are 720 numbers consisting of 3 digits that can be made from 1, 2, 3, 4, 5, and 6 if letter A repetition is allowed and letter B repetition is not allowed.

This can be calculated by taking the number of possible combinations for each digit (6 for A, 5 for B, 4 for C) and multiplying them together: 6 x 5 x 4 = 120. Since there are 6 possible numbers for each digit, there are 120 combinations for a 3-digit number. Then, multiplying 120 by 6 (since repetition is allowed) yields 720 possible 3-digit numbers.

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Training a regression network with squared error loss requires two steps: the forward pass and the backward pass.

Forward Pass:

Backward Pass:

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