convert y=2(x-5)(x+2) into standard form

The number 8 (eight) is represented by a number and numeral.

It is the natural number that follows seven and precedes nine. Given that it is an integer and a cardinal number, it can be counted. It is distinguished from imaginary numbers by being categorised as a real number.

Eight is a composite number, and its proper divisors are 1, 2, and 4. Eight can be written as 23, which when said aloud sounds like two cubed. It has a 7 aliquot total. All powers of two add up to an aliquot that is one less than their own.

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The altitude of the right circular cone is 13.5 inches.

What is volume?

Volume is a term used in mathematics to describe the volume of three-dimensional space occupied by an object or a closed surface. The measurement of volume is done in cubic units, like m3, cm3, in3, etc. Volume is also referred to as capacity on occasion.

Here, the volume of a right circular cone varies jointly as the altitude and the square of the radius of the base

So our equation for volume becomes

V = c*h*r^2

where 'h' is altitude and

'r' is radius of base and

'c' is constant

Putting the values of V, h, r, in the volume equation.

we get,

154 = c*12*3.5*3.5

  c = 22/21

Now we have volume = 77 cu and radius of the base =7/3, so putting the values we get,

 77 = 22/21*h*7/3*7/3

or, h = 13.5 inches

Hence, the altitude of the right circular cone is 13.5 inches.

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Reason: The degree is the largest exponent.

This rule only works when dealing with single variable polynomials.

The standard form is y = 3x^6+5x^2-10x-8; where the largest exponent term goes first, then the next largest, and so on.

Answer:

The answer is (4x² - 36x + 81)

Step-by-step explanation:

So,

(2x - 9)² = (2x)² - 2(2x)(9) + (9)²

(2x - 9)² = 4x² - 36x + 81

Thus, The product of (2x - 9)² is (4x² - 36x + 81)

The population standard deviation of the data is 111.

1. Find the mean of the data:

Mean = (314 + 158 + 482 + 284 + 310 + 281) / 6 = 1029 / 6 = 171.5

2. Find the difference between each data point and the mean:

Feb: (314 - 171.5) = 142.5

Mar: (158 - 171.5) = -13.5

Apr: (482 - 171.5) = 310.5

May: (284 - 171.5) = 112.5

Jun: (310 - 171.5) = 138.5

Jul: (281 - 171.5) = 109.5

3. Square each of the differences:

Feb: (142.5)^2 = 20,312.5

Mar: (-13.5)^2 = 182.25

Apr: (310.5)^2 = 95,822.25

May: (112.5)^2 = 12,656.25

Jun: (138.5)^2 = 19,082.25

Jul: (109.5)^2 = 11,982.25

4. Sum all of the squared differences:

20,312.5 + 182.25 + 95,822.25 + 12,656.25 + 19,082.25 + 11,982.25 = 149,047.5

5. Divide the sum of the squared differences by the number of data points minus one:

149,047.5 / (6 - 1) = 149,047.5 / 5 = 29,809.5

Square root of 29,809.5 = 111 (rounded to the nearest integer)

Therefore, the population standard deviation of the data is 111.

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The exponential function showing the relationship between y and t is y = 4800e^(0.0625t).

An exponential function is a function of the form f(x) = bx, where b is a positive real number and x is a real number. This type of function is commonly used to model the rate of growth or decay of a quantity over time. Exponential functions have the property that their derivatives (slope) are proportional to the value of the function itself. This property makes them useful for modeling phenomena with compound growth or decay, such as populations, interest rates, and radioactive decay.

In this equation, 4800 is the original principal, 0.0625 is the interest rate (6.25%) and t is the number of years since the start of the investment. This equation can be used to calculate the value of the investment after any number of years. For example, if t = 5, then y would equal 6,842.50. This means that after 5 years, the value of the investment would be 6,842.50.

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Answer:

4 pounds of cheese

Step-by-step explanation:

4/5*5=4

On solving the provided question, we can say that - so, percentage - 400/500 X 100 = 80%

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

here,

total is 500

obtained is 400

so, percentage - 400/500 X 100 = 80%

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All values that are NOT in the domain of 9 are 5 /11 at x=9, where function  h=7.

All real numbers x, with the exception of those for which the denominator is 0, are included in the domain of a rational function. Equilibrate the denominator to zero and then solve for x to determine which x values are excluded from the scope of a rational function.

h(x)=x-2\sg(x)=(x-4)(x+2)

Suppose x = 9 and h(9) = 9-2 and g(9) = (9-4) (9+2) =5 /11

Because it is impossible to divide by zero while h is in the denominator, there will always be an issue anytime h = 7. After solving them, we discover that x cannot be either -2 or 5. So, the answer to part B would be x-5/11.or 5/11 are examples of x values that are beyond the domain.

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Answer:

y = 7/2x + 5

Step-by-step explanation:

The slope intercept form is: y = mx + b

Our equation is

7x -2y = -10

We subtract 7x both sides

-2y = -7x - 10

Divided by -2, both sides

y = 7/2x + 5

So, the answer is y = 7/2x + 5

Therefore , the solution of the given problem of equation comes out to be (−∞,∞) is an interval for domain.

A mathematical equation seems to be a formula that links two statements and signifies equivalence with the equals sign (=). In algebra, a scientific claim that confirms the equality two two mathematical abstractions is referred to as an equation. For instance, the answer obd + 6 = 12 has an equal sign between the elements ptdc + 6 and 12, respectively. There is a mathematical formula that describes the connection between the two syllables on either side of a letter. Frequently, the symbol and the single variable are the same.

Here,

f(x)=2x-5 and t(n)=2n-5 are given.

A) They both depict the sequence.

B) Unless the expression is undefined, the domain of both the expression seems to be all real numbers. In this instance, the phrase is defined despite the lack of a real number.

(−∞,∞) is an interval notation.

{x|x ∈ R} is the Set-Builder Notation.

Therefore , the solution of the given problem of equation comes out to be (−∞,∞) is an interval for domain.

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A logarithmic curve is a mathematical function.

A logarithmic curve, also known as a logarithmic function, is a type of mathematical function that describes a relationship between a variable x and a variable y in which the logarithm of y is a linear function of x.

The general form of a logarithmic function is y = logb(x), where b is the base of the logarithm, and x and y are real numbers. The base of the logarithm can be any positive number, but the most common bases used are 10 (common logarithm) and e (natural logarithm).

The graph of a logarithmic function is a curve that starts at negative infinity and increases gradually as x increases. The slope of the curve becomes closer to zero as x increases, and it is undefined for x=0 or x<0.

Logarithmic functions are often used in many areas of science, engineering, and mathematics to model real-world phenomena that exhibit exponential growth or decay, such as population growth, radioactive decay, sound levels and more.

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Yes Jerome's sister is correct.

The answer to the table is given below.

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"

Given here:

Jerome’s sister told him to multiply both the amount of water and the amount of drink mix by the same number to keep the ratio of water to drink mix the same and still increase the total amount of energy drink.

Drink mix     3  6    9   12   15

water cups   8  16   24  32  40 

we know this is true because to find a ratio equivalent to another we have to multiply the two quantities, by the same number.

Hence, The complete table is shown above.

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The correct relation which shows the function is,

⇒ (-6, 2), (-2, 3), (2, 7), (6, 2)

Option B is true.

A relation between a set of inputs having one output each is called a function.

Now, We know that;

Function is a relation between a set of inputs having one output each.

So, By given options;

A. (-2, -2), (-6, -5), (2, 8), (2, 2)

Here, Two value of outputs 8, 2 have same input 2.

So, This is not a function.

B. (-6, 2), (-2, 3), (2, 7), (6, 2)

Here, A set of inputs having one output each.

So, This is function.

C. (6, -10), (-6, 7), (6, 6), (-6, 12)

Here, Two value of outputs - 10, 6 have same input 6.

So, This is not a function.

D. (-6, 0), (-2, 5), (-6, -3), (2, 9)

Here, Two value of outputs 0, -3 have same input -6.

So, This is not a function.

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The minimum number of entries needed in order to cover the total cost of the T-shirts is 94.

What is linear inequality?

A linear inequality is an inequality that can be written in the form of

ax + b > c or ax + b < c or ax + b = c

Where x and y are variables and a,b,c are constants.

The cost of the T-shirts plus VAT is £400 + (17.5/100) * £400 = £400 + £70 = £470

In order to cover the total cost of the T-shirts, you need to find out how much money you will make from the entry fees.

Let's call the number of entries N. The total revenue from the entry fees is N * £5 = £5N

So, in order to cover the cost of the T-shirts, the revenue from the entry fees must be greater than or equal to the cost of the T-shirts plus VAT:

£5N ≥ £470

To find the minimum number of entries needed, you can divide both sides of the inequality by 5:

N ≥ £470 / £5

N ≥ 94

Hence, the minimum number of entries needed in order to cover the total cost of the T-shirts is 94.

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The minimum number of entries needed in order to cover the total cost of the T-shirts is 94.

What is linear inequality?

A linear inequality is an inequality that can be written in the form of

ax + b > c or ax + b < c or ax + b = c

Where x and y are variables and a,b, and c are constants.

The cost of the T-shirts plus VAT is £400 + (17.5/100) * £400 = £400 + £70 = £470

In order to cover the total cost of the T-shirts, you need to find out how much money you will make from the entry fees.

Let's call the number of entries N. The total revenue from the entry fees is N * £5 = £5N

So, in order to cover the cost of the T-shirts, the revenue from the entry fees must be greater than or equal to the cost of the T-shirts plus VAT:

£5N ≥ £470

To find the minimum number of entries needed, you can divide both sides of the inequality by 5:

N ≥ £470 / £5

N ≥ 94

Hence, the minimum number of entries needed in order to cover the total cost of the T-shirts is 94.

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Pick a random selection of students who attend the work lab.

Picking a random sample of students is the most effective strategy to ensure accurate results. The findings of a survey that the student conducts among those sat in the lab's front rows might be skewed.

The students seated in front of the lab could exhibit a certain trait (e.g., they might be particularly diligent students), which would undoubtedly yield a different outcome.  The survey is in good shape. No special equipment is required to evaluate our comprehension of statistical analysis.

Additionally, there won't be much of a difference if more students are included in the sample that are sat in front of the lab. Finally, it makes no sense to administer instruments to a group that does not visit the work laboratory. Effectiveness cannot be evaluated based on students who do not participate in class.

Therefore the correct option is B)  Select a random sample of students who go to the work laboratory

The complete question is:

A student researcher wishes to examine the effectiveness of a statistical work laboratory on graduate students' overall understanding of application of statistical analyses. The researcher administers a survey to 15 students who are seated at the front of the laboratory. How could this study be improved? Select all that apply.

A. Use an instrument to test statistical analysis understanding.

B. Select a random sample of students who go to the work laboratory

C. Use a larger sample size.

D. Administer instruments to a group who does not go to the work laboratory, as well.

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Answer:

Step-by-step explanation:

c.120 i did the work and i came out with this answer. Hope it helps!

The minimum value of the expression 3x² + 6x + 6 is 3.

Therefore the answer is 3.

A quadratic mathematical expression contains a variable of highest degree of 2 and it is of the general form ax² + bx + c, where a, b and c are constants.

Minimum value of a quadratic equation of form ax² + bx + c is when

x = -b/ 2a

Then minimum value is

a( -b/ 2a )² + b( -b/ 2a ) + c

= (b²a + -2ab² + 4a²c)/ 4a²

= ( - b² + 4ac)/ 4a

= c - b²/4a

In the expression 3x² + 6x + 6, a = 3, b =6 and c = 6. So minimum value is

= 6 - 6²/ (4×3)

= 3

--The question is incomplete, answering  to the question below--

"What will be the minimum value of the expression 3x² + 6x + 6?"

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Answer:

26$

Step-by-step explanation:

¼×48=12

so 12 was spent on calculator

12+14= 26

On solving the provided question, we can say that Surface Area of central park = 2.5 × 0.5 = 1.25 square mile

An indication of the overall space occupied by an object's surface is its surface area. A three-dimensional shape's surface area is the total amount of space that surrounds it. A three-dimensional shape's entire surface area is known as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face. As an alternative, you may use the formula below and name the box's dimensions as follows: Surface (SA) = 2lh + 2lw + 2hw. Surface area is a measurement of the entire amount of space filled by a three-dimensional shape's surface (a three-dimensional shape is a shape that has height, width, and depth).

Surface  Area of central park = 2.5 × 0.5 = 1.25 square mile

1 acre = 1/640 square mile

1.25 square mile = 1.25 ÷ 1/640 = 800 acre

Number of people in the park = 800 ÷ 15 = 53.3 ≈ 53 people

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The 9 inches side must be the hypotenuse, and the other two sides must be 3 inches and 5 inches.

n a triangle, the longest side (the hypotenuse) is opposite the largest angle, and the other two sides are opposite the smaller angles. According to the Triangle Inequality Theorem, the sum of any two sides of a triangle must be greater than the length of the third side. So, if the longest side of Karen's triangle measures 8 inches, it means that the sum of a and b (the two shorter sides) must be greater than 8 inches. Therefore [tex]a+b > 8 inches[/tex].

For the second part of your question, only one triangle can be drawn with side lengths 3, 5, and 9. The three numbers 3, 5, and 9 form a Pythagorean triple, meaning they can be used as the lengths of the sides of a right triangle. Since the longest side (the hypotenuse) must be greater than the other two sides, the 9 inches side must be the hypotenuse, and the other two sides must be 3 inches and 5 inches.

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The relationship between xzw and wzv on the vertical angle is as follows:

∠ xzw + ∠ wzv = 180

Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines. Vertically opposite angles share the same vertex and they are congruent to each other.

Therefore,

∠vzy ≅ ∠wzx(vertical angles)

Hence, the relationships between angles xzw and wzv  is as follows:

∠ xzw + ∠ wzv = 180 (sum of angles on a straight line)

3x + 17 + x - 9 = 180

4x + 8 = 180

4x = 180 - 8

4x = 172

x = 172 / 4

x = 43

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The answers for Center of the circle is (-4,3) and radius is 2√10 units.

(x - h)2 + (y - k)2 = r2 is the equation of the center of the circle. The radius (r) is specified as 5 units, while the center's (h, k) coordinates are (0, 0). (x - 0)2 + (y - 0)2 = 52 is the result of substituting the values of h, k, and r in the equation.

Finding the simplified term of the given expression is the goal of simplifying the algebraic statement. We must first understand how to join like terms, factor a number, and the order of operations before we can factorize or simplify the statement. When like words are combined, the constant terms are divided for the purpose of simplicity and the variables with the same degree are grouped together.

Examples of  Algebraic Expressions

2x2+3xy+4x+7

Given,

[tex]x^2+y^2+8x-6y-15=0[/tex]

⇒ x².+8x+16–16+y²-6x+.9–9–15=.0

(x+4)²+(y-3)²-16–9–15=0

I.e. (x+4)²+(y-3)²=40

(x+4)²+(y-3)²={2√10}²

Hence center is (-4,3) and radius is 2√10 units.

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Answer:

25%  

a half is 50%

a quarter is 25%

Answer: It's option C

Step-by-step explanation:

Well 1 quarter is 25

2 quarters is 50

3 quarters is 75

4 quarters is a dollar

A guy wire is attached to an upright pole 6 meters above the ground. If the wire is anchored to the ground 5 meters from the base of the pole 7.81 m long is the wire. This can be solved by using the concept of Pythagoras theorem.

The widely accepted geometric principle known as the Pythagorean Theorem states that the square on the hypotenuse of a right triangle equals the sum of the squares on its legs (the side opposite the right angle).

The hypotenuse side of a right-angled triangle's square is equal to the sum of its other two sides, according to Pythagoras' Theorem. The perpendicular, base, and hypotenuse of this triangle are its three designated sides.

Let, assume ΔABC is a right-angled triangle

where, AC = 6m be the pole.

AB = 5m is the length of a guy wire and is attached to stake B

By Pythagoras theorem,

BC² = AB² + AC²

or, BC² = (5)² + (6)²

or, BC² = 36 + 25

or, BC =  √61 m

or, BC = 7.81 m

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There are several ways to make a graph to compare two sets of data, but one common method is to use a line graph.

The steps to create a line graph to compare two sets of data:

Organize the data: Arrange the data into two columns, one for each set of data. Each column should have a label at the top to indicate what the data represents.

Choose a scale: Decide on an appropriate scale for the x- and y-axes that will allow you to clearly display the data. The x-axis should represent the categories being compared, and the y-axis should represent the values of the data.

Plot the data: Using the chosen scale, plot the data points for each set of data on the graph. Use different colors or symbols for each set of data to make it easy to distinguish between the two.

Add a title: Give the graph a title that describes what the graph is showing.

Add a legend: Add a legend to the graph to indicate what each set of data represents.

Add labels: Label the x- and y-axes to indicate what they represent.

By following these steps, you can create a clear and informative line graph that allows you to easily compare two sets of data.

Other types of graph that can be used to compare two sets of data are bar charts, scatter plots, and stacked bar charts. The choice of graph depends on the type of data you have, and what you want to compare or highlight.

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Answer: 4

Step-by-step explanation:

35.2/ 8.8= 4

4

When you and your 3 friends decide to split the bill of $36 evenly and you leaving a 12% tip on your part, you pay a total of $13.32.

Therefore the answer is 13.32 dollars.

When you and your 3 friends decide to split the bill evenly, each person is responsible for paying 1/4 of the total bill. The total bill is $36, so each person is responsible for paying

$36 / 4 = $9

You also decided to leave a 12% tip on your part, so you need to calculate 12% of $36. To do this, you can multiply $9 by 0.12

$36 × 0.12 = $4.32  

So, you are responsible for paying $9 + $4.32 = $13.32

So you are responsible for paying $13.32 in total.

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The probability that a bag of flour passes inspection is 0.05.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true. In this case, the probability of an event us usually represented as a number between 0 and 1.

In this case, the odds that a bag of flour weighs enough to pass inspection are 1:20. The probability that a bag of flour passes inspection will be:

= 1/20

= 0.05

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Complete question

The odds that a bag of flour weighs enough to pass inspection are 1:20. What is the probability that a bag of flour passes inspection?

The graph of the system of equations y - 2x + 5 = 0 and y + 4x + 1 = 0 intersect at (0.667, - 3.667)

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, A system of equations y - 2x + 5 = 0 and y + 4x + 1 = 0.

Let's write the terms in the order x, y therefore,

y - 2x + 5 = 0

- 2x + y = - 5.

2x - y = 5.

And

y + 4x + 1 = 0.

4x + y = - 1.

The graph of the system of equations is attached in the image.

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