Which of the following statements must be true based on the diagram below?
Select all that apply. (Diagram is not to scale.)

In algebra, the vertex form of a quadratic equation is a way of expressing the equation in the form:[tex]y = a(x - h)^2 + k[/tex]

where (h, k) is the vertex of the parabola defined by the equation. The value of 'a' determines whether the parabola opens up or down and the value of 'h' and 'k' determine the position of the vertex on the coordinate plane.

For example, the standard form of a quadratic equation is:

[tex]y = ax^2 + bx + c[/tex]

To convert this to vertex form, you would first complete the square to get all the terms of x on one side of the equation and a constant on the other side. Then, you would put the equation in the form shown above.

So, given the equation [tex]y = 3x^2 + 6x - 4[/tex], we can complete the square to get:

[tex]y = 3(x^2 + 2x) - 4[/tex]

then rearrange it to

[tex]y = 3(x^2 + 2x + 1) -7 = 3(x+1)^2-10[/tex] which is in vertex form with vertex (-1,-10)

The vertex form of a quadratic function provides a convenient way to quickly identify the vertex of the parabola without having to complete the square every time.

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The correct question is:

Explain vertex form.

Answer:

Step-by-step explanation:

-140

The answer to |-14| is 14

The product of f(x) and g(x) is always a polynomial. By the definition of

polynomials the product of polynomials is always a polynomial because

the coefficient are real numbers and the exponents are whole

numbers. Real numbers and whole numbers are closed under addition

and subtraction.

A polynomial is a mathematical expression involving a sum of powers in one or more variables (indeterminates) with coefficients, that is either a constant or the indeterminates (also called variables or x's). The most common examples are the quadratic equation, cubic equation, and so on. The degree of a polynomial is the highest power of the indeterminate in the polynomial. For example, a polynomial with three indeterminates to the power of 2 is said to have a degree of 2.

Here f(x) and g(x) are two given polynomial,

let f(x) = x+1 ang g(x) = x-1

f(x).g(x) = (x+1)(x-1).

f(x).g(x) = x²-1.

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The slope of the line, given the point on the line and the y - intercept, is - 5. 33

The slope of a line tells us the relationship between the dependent variable and the independent variable. In other words, it tells us what a change in the independent variable leads to in the dependent variable.

The slope can be found in the slope - intercept formula form of :

y = mx + b

m is the slope

b is the y - intercept

We have the y - intercept and a y and x value in ( -3, 6 ) so the slope is:

6 = - 3 ( m ) + ( - 10 )

6 = - 3m - 10

- 3m = 6 + 10

- 3 m = 16

m = 16 / - 3

m = - 5. 33

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Answer:

45ft is the missing length j.

Answer: This system of equations can be represented in matrix form as

| -1 | 650 | 175 |

| 75 | -120 | -25080 |

This matrix is called the augmented matrix of the system of equations. The first and second column of this matrix represent the coefficients of the variables x and y, respectively, in the system of equations. The third column represents the constant terms of the equations.

You can use a method such as Gaussian elimination or Gauss-Jordan elimination to solve the system of equations.

The Gaussian elimination method, you would use elementary row operations to transform the matrix into an echelon form or reduced row echelon form. Then you can back-substitute the variables with their values.

Also, the Gaussian-Jordan elimination is similar to Gaussian elimination, but it keeps continuing the elimination process until the matrix becomes an Identity matrix(A matrix with 1 on diagonal and 0 everywhere else) The values on the diagonal of the matrix will give you the solution of the variables.

Step-by-step explanation:

Considering that the diameter variance of 0.001". If the interior diameter of the pipe is 0.49" and the pipe thickness is 0.005". the maximum allowable pipe diameter is 0.501''

The maximum allowable pipe diameter is calculated by

finding the total thickness of pipe

= interior diameter + 2 * pipe thickness

= 0.49 + 2 * 0.005

= 0.49 + 0.01

= 0.50

The diameter variance gives the range of the allowable diameter to ± 0.001 for maximum allowable pipe diameter we use + 0.001

hence

= 0.50 + 0.001

= 0.501

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The value of the fourth power of the expression is 1679616.

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, an expression: 6/d -10c - c, where c = -3 and d= 2

Solving the expression, we get,

6/2-10(-3)-(-3)

= 3+30+3

= 36

We are asked to find the fourth value of 36,

(36)⁴ = 36 × 36 × 36 × 36 = 1679616

Hence, the value of the expression is 1679616.

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Answer:

D

Step-by-step explanation:

explanation on the other response on ur other question

Answer: The statement you've provided describes the economic concept of elasticity. Elasticity is a measure of how responsive the quantity demanded or supplied of a good or service is to a change in its price. It measures the responsiveness of the consumers' and producers' behaviors to changes in price, in other words, how sensitive the consumers or producers are to changes in the good or service prices.

There are different types of elasticity, such as price elasticity of demand and price elasticity of supply. Price elasticity of demand measures how much the quantity demanded of a good changes in response to a change in its price. If a good has a high price elasticity of demand, then a small change in its price will result in a large change in the quantity demanded of the good. On the other hand, price elasticity of supply measures how much the quantity supplied of a good changes in response to a change in its price. A good with a high price elasticity of supply will see a large increase in the quantity supplied in response to a small price increase.

Elasticity is a very important concept in economics because it helps to understand how consumers and producers will react to changes in prices and how it would affect the overall economy.

Step-by-step explanation:

Answer: To solve the quadratic equation 8x^2 + 16x + 3 = 0, Patel could use the following steps:

Divide both sides of the equation by 8 to obtain x^2 + 2x + 3/8 = 0.

Rewrite the equation in the form (x + a)^2 = b by completing the square: x^2 + 2x + (1/2)^2 = (1/2)^2 - (3/8).

Rewrite the equation as (x + a)^2 - b = 0. In this case, a = 1/2 and b = -3/8.

Use the quadratic formula to solve for x:

x = (-1/2) +/- sqrt((1/2)^2 - (-3/8))

= (-1/2) +/- sqrt(5/8)

= (-1/2) +/- sqrt(40/64)

= (-1/2) +/- sqrt(10/16)

= (-1/2) +/- (5/8)

= -1 +/- 5/8

= -1 + 5/8 or -1 - 5/8

= -7/8 or 1/8

Therefore, the solutions to the quadratic equation are x = -7/8 or x = 1/8.

Step-by-step explanation:

The maximum value considering DP of a and b is 9.52.

The decimal places of a number are the number of digits to be considered after the decimal point. E.g Round 4.7583 to 2 dp, we have;

4.76 3 dp

The maximum value of a sum of numbers is the highest value obtained when these numbers are added one to each other. The decimal places of each number is put into consideration in the process.

From the given question;

a = 8.7 and b = 0.82

Thus,

a + b = 8.7 + 0.82

        = 9.52

a + b = 9.52

Therefore, the maximum of a + b = 9.52

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Step-by-step explanation:

TRY WITH SOME Trigonometric FUNCTION.

IF SOMETHING IS Wrong . I AM STILL A STUDENT

Solution

 16 dm=160 cm

50 cm* 160 cm= 8000 cm²= 0,8 m²

odp C

Answer:

y > X/2 - 3

I think that's the answer.

the base timed by the height

Answer:

Step-by-step explanation:

$4.50 + $4.50(0.15) = $5.18

$2.25 + $2.25(0.15) = $2.59

$3.00 + $3.00(0.15) = $3.45

The solution to the above math arithmetic is 5115.

Finding the sum and difference of two integers are the two main addition and subtraction arithmetic procedures. They are both the other's polar opposite. An ordered group of integers with a shared difference between each word is known as an arithmetic sequence. The common difference, for instance, between the mathematical series 3, 9, 15, 21, and 27 is 6.

This grouping contains percent difficulties, decimal recognition, addition, subtraction, multiplication, and division as well as fraction and percent equivalences and estimate issues.

For instance, 5 + 6 = 11 and 11 - 6 = 5.

5x35 + 65x76=5115

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Answer:

1/2

Step-by-step explanation:

Slope(m)

= (y2 - y1)/(x2 - x1)

= (8 - 1)/(7+7)

= 7/14

= 1/2

In the graph of a quadratic function with vertex (2, -4) is shown in the figure, the Domain: -∞ < x < ∞ and Range: -4 ≤ x < ∞.

When a polynomial function has one or more variables and the highest exponent of any one of the variables is two, the function is said to be quadratic function.

A polynomial of degree 2 is referred to as such because the highest degree term in a quadratic function is of second degree. There must be at least one second-degree term in a quadratic function. This function is algebraic.

Domain for this quadratic function is all possible values of x where function is defined.

Thus, Domain: -∞ < x < ∞

Range is the set of value functions that correspond to the value 'x.'

Range: -4 ≤ x < ∞

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Answer:

B

Step-by-step explanation:

Center of the distributions -> mean/median (preferably mean)

The option with range is eliminated

Median might not be accurate as median is the center person, not the center result.

Based on the graphs, identify the graph with the intervals of greatest frequency.

For North Heights -> between 30 and 32 (right-skewed, some higher values)

For Southview -> between 28 and 30 (most concentrated there)

Hence, mean of Southview is lower than North Heights.

Answer:

In the form of y=mx+b:

y = -5/6x-5

Step-by-step explanation:

I'm not that good at explaining, but I'll try:

Slope intercept is y=mx+b, M is the slope of the line which is rise over run, the rise is -5 (distance traveled along y-axis) and the run is 6 (distance traveled along x-axis) found from two points: (-6, 0) and (0, -5). Using this data -5/6 can be plugged in for M, and b is the y variable at (0, _) in this case the y variable is -5. The final answer after plugging everything in is y=-5/6x-5, I hope this wasn't too confusing.

Step-by-step explanation:

d = 30m, so r = 15m

h = 20m

We know,

= (22×15×15×20)/7 [Taking π = 22/7]

= 14142.86m^3

= 14142875.14 litres

Unit rate is the quantity of an amount of something at a rate of one of another quantity.

The rate at which the oil burns.

1 hour = 2/3 ounce

At 12 noon = 193/3 = 64.33 ounces

At 2 pm = 63 ounces

At 5 pm = 61 ounces

The amount of oil at 12 noon is 64.33 ounces.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

A camper lights an oil lantern at 12 noon and lets it burn continuously. Once the lantern is lit, the lantern burns oil at a constant rate each hour.

At 2 p.m., the amount of oil left in the lantern is 63 ounces.

At 5 p.m., the amount of oil left in the lantern is 61 ounces.

This means,

Amount of oil burnt in the lantern from 2 pm to 5 pm.

= 63 ounces - 61 ounces

= 2 ounces

Now,

3 hours = 2 ounces

2 hours = 1.33 ounces

1 hour = 0.67 ounces

Now,

The number of hours from 12 noon to 2 pm.

= 2 hours

So,

The amount of oil at 12 noon.

= 63 + 4/3

= (189 + 4) / 3

= 193/3 ounces

Thus,

The amount of oil at 12 noon is 65 ounces.

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Answer: option b), option c), and option e) are correct options.

Step-by-step explanation:

Given:

The area of a rectangular room= 750 square feet

The width of the room = 5 feet less than the length of the room

The length of the room = Y

To find:

Equations that can be used to solve the value of Y i.e. the length of the rectangular room.

Solution:

The equation can be derived from using the following formula:

Area of rectangle = length * width

According to the question,

Length of the rectangular room = Y

Width of the rectangular room = 5 feet less than the length of the room

                                                       = (Y-5)

Since, Area of rectangle = length * width

Area of the rectangular field = length of the room* width of the room

                          750             = Y (Y – 5)                         ………..eqn. (1)

Or, the above equation can be solved a step further and written as

                          750             = Y2 – 5Y                          ………..eqn. (2)

                         750- Y2 + 5Y= 0                                    ………..eqn. (3)

                         750-Y (Y- 5) =0                                    ………..eqn. (4)

Apart from the above equations, if we solve eqn. (2) we get the following equation:

                          750             = Y2 – 5Y

                           Y2 – 5Y- 750= 0

                          Y2 – 30Y + 25Y- 750 = 0

                          Y (Y- 30) + 25 (Y- 30) = 0

                                                                   take Y- 30 common from L.H.S.

                           (Y -30) (Y+ 25)   = 0                            …………….eqn. (5)        

Hence, the correct options are option b), option c), and option e).