Re-write the quadratic function below in Standard Form
y=-2(x-3)(x+4)

The value of x found using the angle addition postulate is; x = 35°

The angle addition postulate states that the measure of the angle formed by the non-common sides (rays) of two adjacent angles that have a common side is the sum of the two adjacent angles.

The measures of the angles in the document are;

The measure of angle STV is 75°

The measure of angle WTV is 40°

The measure of angle STW is x°

Please find attached a possible drawing representing the angles, obtained from the drawing in a similar question, and created with MS Word.

The angle addition postulate indicates that we get;

m∠STV = m∠STW + m∠WTV

Whereby angle ∠x is the same as the angle ∠STW, therefore, wse get;

m∠STV = x° + m∠WTV

Plugging in the values for the angles defined by the letters, we get the angles

75° = x° + 40°

x° = 75° - 40° = 35°

The measure of angle x is 35°

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Jane travels 8 miles much farther than her trainer. The solution is obtained using arithmetic operations.

What are arithmetic operations?

By combining operands with one arithmetic operator, an arithmetic operation is given. The built-in functions add, subtract, divide, and multiply additionally allow for the specification of arithmetic operations.

3. Using pythagoras theorem, we get the equation as D² = 12² + 16².

⇒D² = 144 + 256

⇒D² = 400

⇒D = √400

⇒D = 20

4. Jane has traveled 28 miles in total whereas her trainer has traveled 20 miles.

So, the difference is 28-20= 8 miles

Hence, Jane travels 8 miles much farther than her trainer.

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The number zero was invented by Aryabhatta, an astronomer and mathematician from India.

As we know the origin of zero in India came from a well-known astronomer and mathematician Aryabhatta.

A number zero had been used as a placeholder number since before Aryabhatta and Brahmagupta.  In the 5th century, Aryabhatta is credited with using zero in the decimal system.

Whereas in the 7th century, Brahmagupta used zero in mathematical operations like addition and subtraction.

In India, a number zero was called ‘Sunya’, when the number reached Italy, it was named ‘Zefero’ and later it was called ‘Zero’ in English.

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The probability that the described situation could occur as required in the task content is; 1 / 100.

It follows from the task content that the you selection is done such that there's replacement.

Since the treasure chest contains 10 different toys, the probability of selecting a crazy straw two times consecutively is;

= 1/10 × 1/10

= 1 / 100.

Ultimately, the probability that the given situation occurs as described is; 1 / 100.

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Ben will take 5 hours to answer the module.

The problem is asking how long it will take Ben to answer the module. To discover the answer, translate the given mathematical phrase to a mathematical symbol.

According to the question,

Moira - 3 hours

Ben - Four hours less than thrice as fast as Moira

To translate the mathematical phrase into a mathematical symbol, we have to look for the signal words. The signal word "thrice" means that we have multiplied Moira's number of hours by 3 and "less than" means that you have to subtract 4 from it.

Ben = 3 *(3 hrs) - 4 hrs

       = 9hrs - 4hrs

       = 5hrs

So, Ben will take 5 hours to answer the module.

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Answer:

D line

Step-by-step explanation:

The 4i word should be eliminated since we want (3+4i)z to be a genuine number. Then, to ensure that the imaginary terms cancel out when z is multiplied together, we can make z of the form (n-4/3 ni).

At least play one of the three sports find the number of those 25 numbers play both Volleyball and Rugby.

What is meant by sport?

Since they all play at least one sport, the number of people who don't play football is 30-17 = 13.

The "no football" category is divided in 3 categories :

only volleyball : 9

only rugby : 12

both = x

So we have :

9 - 3 - x = 13

12 - x  = 13

x = 13 + 12 = 25

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The best measure of center for the data is the mode only.

a central tendency is a central or typical value for a probability distribution. Colloquially, measures of central tendency are often called averages. The term central tendency dates from the late 1920s. The most common measures of central tendency are the arithmetic mean, the median, and the mode.

In this particular data, it is formed of letter with no definite values, therefore to find the mean value would be and the median would be impossible but the mode can be found.

Firstly we re arrange the letters in alphabetical order e, a, u, i, e, o, o, e, u, a, i, e, o, u, a = a,a,a,e,e,e,e,i,i,o,o,o,u,u,u.

Then the letter that appeared most can be picked out.

Only e appear 4 times. This means that e is the mode of the data.

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Answer:

Step-by-step explanation:

try D

Answer:

see explanation

Step-by-step explanation:

4(x - 1)² - 9(x - 1) =-  2

let t = x - 1 , then rewrite the expression as

4t² - 9t = - 2 ( add 2 to both sides )

4t² - 9t + 2 = 0 ← in standard form

Step 2

consider the factors of the product of the coefficient of the t² term and the constant term which sum to give the coefficient of the t- term

product = 4 ×  2 = 8 and sum = - 9

the factors are - 8 and - 1

use these factors to split the t- term

4t² - 8t - t + 2 = 0 ( factor first/second and third/fourth terms )

4t(t - 2) - 1(t - 2) = 0 ← factor out (t - 2) from each term

(t - 2)(4t - 1) = 0 ← in factored form

equate each factor to zero and solve for t

4t - 1 = 0 ⇒ 4t = 1 ⇒ t = [tex]\frac{1}{4}[/tex]

t - 2 = 0 ⇒ t = 2

Step 3

Now solve for x using

t = x - 1 ( add 1 to both sides ), then

x = t + 1

t = [tex]\frac{1}{4}[/tex] , then x = [tex]\frac{1}{4}[/tex] + 1 = [tex]\frac{5}{4}[/tex]

x = 2 , then x = 2 + 1 = 3

The Tangent Law may be used to calculate the height of the mountain's summit. The ratio of the opposing side to the adjacent side is defined as the tangent. Thus, the mountain's top is 3.44 kilometres high.

Tangent law is a mathematical law that states that the ratio of the tangent of an angle to the tangent of its complementary angle is equal to the ratio of the sine of the angle to the sine of its complementary angle. It can be written mathematically as:

tan(θ) / tan(90-θ) = sin(θ) / sin(90-θ)

The opposing side in this example is the height of the peak, while the adjacent side is the distance between the hotel and the summit (6.5 km).

Opposite/Adjacent = tan is the equation for the tangent law (angle of elevation). We may rewrite this equation to find the height of the mountain's peak: Adjacent = tan(angle of elevation) * Opposite.

We may calculate the height of the mountain's peak by plugging in our values: Opposite = tan(19 degrees) * 6.5 km = 3.44 km.

As a result, the mountain's top is 3.44 kilometres high.

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Answer:

He contributed because he was a life-changing character

Step-by-step explanation:

The passage states that u should read into the character

Yes, there can be a triangle with three angles equal to 60.

The triangle is called the equilateral triangle where all three angles of a triangle is equal to 60 degree.

As we all knows that the sum of all the angles of a triangle is 180 and there are three angles that present in a triangle.

So, 60+60+60 = 180.

Now, Some properties of equilateral triangle:

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At the end of the week, the store has 212 tuffed animals.

To determine the number of tuffed animals in the store at the end of the week, we need to subtract the number of tuffed animals sold during the week from the number of tuffed animals in the store at the beginning of the week.

349 tuffed animals (beginning of the week) - 137 tuffed animals (sold during the week) = 212 tuffed animals (at the end of the week).

So at the end of the week, the store has 212 tuffed animals.

The concept used to solve this problem is subtraction. Specifically, we are using the inverse operation of addition. By subtracting the number of tuffed animals sold during the week from the number of tuffed animals in the store at the beginning of the week, we are able to find the number of tuffed animals in the store at the end of the week. The subtraction operation is used to find the difference between two quantities, which in this case is the number of tuffed animals remaining in the store.

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Answer: 1st term: -3.  Common difference: +4

Step-by-step explanation:

-3, 1, 5, 9, 13, 17, 21, 25, 29, 33
add 4 each time

The values of a, b and c are given as follows:

a = 5, b = 3, c = 3.

The exponential expression for this problem is defined as follows:

[tex]\left(\frac{4}{3}\right)^{\frac{1}{2}} + \left(\frac{1}{3}\right)^{-\frac{1}{2}}[/tex]

The negative exponent means that the numerator and the denominator are inverted, with the positive exponent, then:

[tex]\left(\frac{4}{3}\right)^{\frac{1}{2}} + \left(3)^{\frac{1}{2}}[/tex]

The fractional exponent of 1/2 can be transformed into a square root, hence:

[tex]\frac{\sqrt{4}}{\sqrt{3}} + \frac{\sqrt{3}}{1}[/tex]

[tex]\frac{2}{\sqrt{3}} + \sqrt{3}[/tex]

[tex]\frac{2 + (\sqrt{3})^2}{\sqrt{3}}[/tex]

Then:

[tex]\frac{5}{\sqrt{3}}[/tex]

We rationalize the expression, thus:

[tex]\frac{5}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{5\sqrt{3}}{3}[/tex]

Meaning that the values are given as follows:

a = 5, b = 3, c = 3.

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The additive inverse of 19/-7 is 19/7.

The additive inverse of a number is the negative of that number. If a number is added to its additive inverse, the sum of both numbers becomes zero. In other words, the additive inverse is the number that is added to a given number to make the sum zero. That is what you add to a number to get zero is called its additive inverse.

That is, Number + Additive inverse = 0

OR

The negative of a number.

Now we are given the number

19/-7

So, the additive inverse of 19/-7:

⇒19/-7 + Additive inverse = 0

⇒Additive inverse = 19/7

Thus the additive inverse of is 19/-7 is 19/7.

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The sum is a binomial with a degree of 6 is correct about the completely simplified difference of the polynomials.

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What is true about the completely simplified sum of the polynomials 3x2y2 − 2xy5 and −3x2y2 + 3x4y?

A. The sum is a trinomial with a degree of 5.

B. The sum is a trinomial with a degree of 6.

C. The sum is a binomial with a degree of 5.

D. The sum is a binomial with a degree of 6.

7 laws of logarithms are,

1- Product rule

2- Division rule

3- Power rule/Exponential Rule

4- Change of base rule

5- Base switch rule

6- Derivative of log

7- Integral of log

logarithms

it is the exponent or power to which a base must be raised to yield a given number.

For example,

23 = 8,

therefore,

3 is the logarithm of 8 to base 2, or 3 = log2 8.

A logarithm is defined as the power to which a number must be raised to get some other values.

Logs are the other way of writing exponent. The formula for conversion between exponential and log forms is: bx = a ⇔ log b a = x. Logarithms are very useful in solving equations involving exponents.

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A parallelogram is formed when one pair of opposite sides of a quadrilateral are equal and parallel that is option B and D.

A parallelogram is a simple quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposite or facing sides are of equal length, and its opposite angles are of equal measure. A parallelogram is a type of quadrilateral with opposite pairs of sides that are parallel and equal. The diagram depicts a parallelogram ABCD with AB II CD and AD II BC. In addition, AD = BC and AB = CD. Non-Example: A trapezium is a parallelogram's non-example.

Here,

When one pair of opposite sides of a quadrilateral are equal and parallel, a parallelogram is formed that is option B and D.

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Together, fixed and variable costs make up the overall cost.When n is 4, the price is $33.00.

Together, fixed and variable costs make up the overall cost.The total cost, for instance, would be $35 if a company had a fixed cost per unit of $30 and a variable cost per unit of $5 that increased as output increased.The formula for average total cost is created by dividing the sum of all production costs by the sum of all payments in money.

The total-cost formula is a simple and user-friendly process that works by dividing the total production cost by the quantity of goods produced.

Y River

c = 33

Z River

Where n is the number of hours, c is equal to 5n + 13.

Graph

Include nothing before to n = 0

The cost will be the same when both sides of the equation are equal.

Where the two lines meet is the answer.

Both of them come together at a single place.

The point is this (4,33)

When n is 4, the price is $33.00.

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Answer:

$0.12

Step-by-step explanation:

Unit price=$11.52/96(per pencil)

11.52/96=$0.12

Hope this helps

Answer:

$0.12

Step-by-step explanation:

First, you have to divide 11.52

to 96 which will be equal to 0.12.

We know how to divide because

in the question the keyword is

EACH. That's how you know when

to divide!

Hope This Helps :)

11.52÷96≈ 0.12

The method used to find the prime factors of a number is called prime factorization. One common method to find the prime factorization of a number is called trial division.

Here is how the trial division method works:

Divide the number by the smallest prime number (2). If the division is exact, then 2 is a prime factor of the number.

If 2 is a factor, divide the number by 2 again, and again, until the division is no longer exact. Then divide the resulting quotient by the next smallest prime number (3), and continue dividing by the smallest prime numbers (5, 7, 11, etc.) until the quotient is prime.

Repeat this process until the quotient is 1. The prime factors of the original number will be the prime numbers that were used in the divisions.

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Answer:

it is b the 2 one

hope you like it

The total emails received are 546. The solution is obtained using arithmetic operations.

What are arithmetic operations?

For all the real numbers, there are four basic mathematical operations which are:

1. Addition(‘+’) wherein the sum of the numbers is obtained.

2. Subtraction(‘-’) wherein the difference of the numbers is obtained.

3. Multiplication(‘×’) wherein the product of the numbers is obtained.

4. Division(‘÷’) wherein the quotient of the numbers is obtained.

Let the total emails received be 'x'.

We are given that for every 20 total emails a person received, they could expect to get 11 spam emails.

Now, a person received 300 spam emails in one month

So, the total emails received will be

⇒x = 20*300/11

⇒x = 545.45

⇒x = 546 (approx)

Hence, the total emails received are 546.

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No; the probability that Kimiko will win is 7/12. Because 7/12 is greater than 5/12, Kimiko has a greater chance of winning.

===========================================================

Explanation:

The prime number sums possible are: {2, 3, 5, 7, 11}

Below is the list of ways to reach those prime sums. Focus on the items in bold. The non-bolded numbers to the left are there to keep count of things.

There are 15 items in that list out of 6*6 = 36 dice rolls total.

15/36 = 5/12 is the probability of Miko winning

1 - (5/12) = 7/12 is the probability of Kimiko winning.

Those two fractions (5/12 and 7/12) aren't the same, which means the game isn't fair.

Kimiko has a better chance of winning since 7/12 is larger than 5/12.

This is why  choice B   is the final answer.

The degree measure of each angle in the triangle are:

m angle l = 18.4

m angle J = 57.6

m angle K = 93

What is the Degree Measure?

The degree measure, also known as an angle measure, is a way to quantify the size of an angle in mathematics. The degree measure of an angle is typically represented by the symbol "degrees" (°) or simply "deg" and it is a unit of measurement.

In a triangle, the degree measure of all angles add up to 180 degrees. Therefore, we can use this property to find the degree measure of each angle in the triangle.

m angle l = (x + 5) deg

m angle J = (4x + 7) deg

m angle K = (7x) deg

So we can use the following equation:

m angle l + m angle J + m angle K = 180

(x + 5) + (4x + 7) + (7x) = 180

12x + 19 = 180

12x = 161

x = 13.4

Hence, the degree measure of each angle in the triangle are:

m angle l = (x + 5) deg = (13.4 + 5) = 18.4

m angle J = (4x + 7) deg = (413.4 + 7) = 57.6

m angle K = (7x) deg = (713.4) = 93

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