Find the value of x.
90°
58°
X
help plz

The equation of the quadratic function, in factored form, is f(x) = 0.992(x + 3)(x - 2)

To determine the equation of the quadratic function based on the given information, we can use the factored form of a quadratic equation. The factored form of a quadratic function is given as follows:

f(x) = a(x - r1)(x - r2)

where "a" is the leading coefficient, and r1 and r2 are the roots (or x-intercepts) of the quadratic function.

Based on the information provided, we can deduce the following:

The vertex of the parabola is at (-0.5, -6.2). Since the parabola opens upward, the leading coefficient "a" must be positive.

The left slope intersects the x-axis at (-3, 0), which implies that x = -3 is one of the roots (or x-intercepts) of the quadratic function.

The right slope intersects the x-axis at (2, 0), which means x = 2 is the other root (or x-intercept) of the quadratic function.

Using this information, we can now determine the equation of the quadratic function:

Since we have the roots, r1 = -3 and r2 = 2, we can plug these values into the factored form equation:

f(x) = a(x - r1)(x - r2)

f(x) = a(x - (-3))(x - 2)

f(x) = a(x + 3)(x - 2)

To find the value of the leading coefficient "a," we can use the vertex coordinates. Since the vertex is (-0.5, -6.2), we can substitute these values into the equation:

-6.2 = a((-0.5) + 3)((-0.5) - 2)

-6.2 = a(2.5)(-2.5)

-6.2 = a(-6.25)

Dividing both sides by -6.25:

a = -6.2 / -6.25

a ≈ 0.992

Therefore, the equation of the quadratic function, in factored form, is:

f(x) = 0.992(x + 3)(x - 2)

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Note the graph is

It is True that optimal solution is the mathematically best solution in quantitative analysis.

Optimal solution refers to a feasible solution where the objective function reaches to the extreme value that is either maximum or minimum value. If an objective function is associated with profit function then, maximizing this function is the objective and thus the solution for which profit is maximum is optimal solution and hence, mathematically best solution. Now, if objective function had been a cost function then minimizing it would have been a solution , and the solution that gives minimum value to the cost function is optimal and mathematically best.

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When you divide a fraction by a negative number, it doesn't matter what happens to the denominator because the entire result, or quotient, is the reverse of whatever the original fraction was.

In mathematics, a denominator is the lowest number in a fraction that indicates how many equal parts are divided into a whole.

It is a fraction's divisor. In this case, the denominator is 4, thus there are four components overall.

The top number in a fraction is referred to as the numerator, while the bottom number is referred to as the denominator.

4/5, for instance, is a fraction.

What happens to the denominator of a fraction when you divide it by a negative number is unimportant because the entire result, or quotient, is the opposite of whatever the original fraction was.

Therefore, when you divide a fraction by a negative number, it doesn't matter what happens to the denominator because the entire result, or quotient, is the reverse of whatever the original fraction was.

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No, the expression m2 + 4m + 6 cannot be factored into a product of two binomials.

Personal car would be the best option to manage both tasks efficiently. While the train is a reliable mode of transportation, it may have fixed schedules that might not align perfectly with Patrick's needs.

On the other hand, using his personal car provides more flexibility and allows him to tailor the departure time according to his daughter's coding class schedule.

If Patrick decides to take the train, he would need to check the train schedule to see if there are convenient departure and arrival times for both the soccer game and the coding class. This option would require planning and coordination to ensure he arrives at the game on time and can pick up his daughter afterward.

Using his personal car gives Patrick the freedom to leave at a time that accommodates both the soccer game and the coding class. He can drop off his daughter at her coding class, attend the soccer game, and then pick her up afterward without being restricted by train schedules.

Considering the circumstances, Patrick might find it more convenient to use his personal car to manage both tasks effectively and ensure he can attend his son's soccer game while also ensuring his daughter arrives at her coding class on time.

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The volume of the hexagonal prism is 2630.5 \(cm^{3}\)

Hexagonal Prism is a three-dimensional prism with a hexagonal base and top. The hexagonal prism contains 2 hexagons (one is the base and the other on the top) and 6 rectangles connecting the hexagonal faces.

How to determine this

Volume of Hexagonal prism = (3√3/2) * \(s^{2} h\)

Where s is the sides of the hexagonal base

h is the height of the hexagonal base

Volume of hexagonal base = 3√3/2 * (\((7.5^{2} )\) * 18

Volume  = 3√3/2 * 56.25 * 18

Volume = 3√3/2 *1012.5

Volume = 2.598 * 1012.5

Volume = 2630.475

Volume = 2630.5 \(cm^{2}\)

Therefore, the volume of hexagonal prism is 2630.5 \(cm^{2}\)

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A and B have the same elements, the measure of AUB will be equal to the measure of B.

To show that if m*(A) = 0, then m*(AUB) = m*(B), we need to prove the following:
1. If m*(A) = 0, then A is a null set.
2. If A is a null set, then AUB = B.
3. If AUB = B, then m*(AUB) = m*(B).
Let's break down each step:
1. If m*(A) = 0, then A is a null set:
  - By definition, a null set has a measure of 0.
  - Since m*(A) = 0, it implies that A has no elements or its measure is 0.
  - Therefore, A is a null set.
2. If A is a null set, then AUB = B:
  - Since A is a null set, it means that it has no elements or its measure is 0.
  - In set theory, the union of a null set (A) with any set (B) results in B.
  - Therefore, AUB = B.
3. If AUB = B, then m*(AUB) = m*(B):
  - Since AUB = B, it implies that both sets have the same elements.
  - The measure of a set is defined as the sum of the measures of its individual elements.
  - Since A and B have the same elements, the measure of AUB will be equal to the measure of B.
  - Therefore, m*(AUB) = m*(B).
By proving these three steps, we have shown that if m*(A) = 0, then m*(AUB) = m*(B).

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The proportional relationship is y = 3x.

What is the proportional relationship?

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.

Here, we have

Given:

x:  2, 6, 8, 10

y:  6, 18, 24, 30

We have to find the proportional relationship between x and y.

So, we can see from inspection and visual observation that there is a proportional relationship between x and y.

6 = 3  2,  18 = 3  6, 24 = 3  8, 30 = 3  10.

Hence, The proportional relationship is y = 3x.

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we have that

The sum of the interior angles in any triangle must be equal to 180 degrees

Let

A, B and C the angles in a triangle

If you have

A=30 degrees

B=60 degrees

the angle C is equal to

A+B+C=180

C=180-(A+B)

C=180-(30+60)

C=90 degrees

Answer:

for ponits

Step-by-step explanation:

the value of 4 tenths x hundreds.

4000

Answer:

40

Step-by-step explanation:

4/10 x 100 = 40

We know that the double-angle formula for cosine is: cos(2x) = 2cos²(x) - 1. So, we can rewrite the given identity as: (2cos²(x) - 1) - cos

To use a half angle or reduction formula to fill in the blanks in the identity below:

(Cos(2x)) - Cos(x) = -2*(sin((3x)/2))^2

We can use the following reduction formula for cosine:

cos(2x) = 2cos^2(x) - 1

Substituting this into the identity above gives:

2cos^2(x) - 1 - cos(x) = -2*(sin((3x)/2))^2

Next, we can use the half angle formula for sine:

sin((3x)/2) = ±sqrt[(1 - cos(3x))/2]

Substituting this into the equation above gives:

2cos^2(x) - 1 - cos(x) = -2*(1 - cos(3x))/2

Simplifying further gives:

2cos^2(x) - 1 - cos(x) = -1 + cos(3x)

Finally, rearranging the terms gives the desired identity:

cos(2x) - cos(x) = -2*(sin((3x)/2))^2
Hello! I'd be happy to help you with your question. Using the half-angle formula, we can fill in the blanks in the identity:

The given identity is: (cos(2x))? - cos

We know that the double-angle formula for cosine is: cos(2x) = 2cos²(x) - 1

So, we can rewrite the given identity as: (2cos²(x) - 1) - cos

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Answer: The answer is B) y < 0

Answer: B

Step-by-step explanation:

Answer:

A. Marcus worked 27 hours and 45 minutes in the week.

B. He earned $391.5 for the week.

Step-by-step explanation:

First you calculate the hours he worked daily and you add them together, when you have the weekly hours you multiply the hours times what he earns each hour.

It's 27 • 14.50= $391.5

Answer:

A collection of numbers, variables, and mathematical operations is referred to as an expression. The  expression is -2/5- 4/3P and 2/5+4/3P

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation .A collection of numbers, variables, and mathematical operations is referred to as an expression.

Given,

-4/3p - 2/5

= -20p - 6/15

= 2(10 p +3)/15

A mathematical expression is a sentence that includes numbers, variables, or both. The equal symbol is never used in expressions. Here are a few phrases as examples. A mathematical statement stating the equality of two expressions is known as an equation.

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Answer:

\(y=-\frac{4}{3} x+2\)

Step-by-step explanation:

In order to write an equation that represents a line, you have to write it in Slope-Intercept Form.

Slope-Intercept Form: y = mx+b

Where b represents the Y-intercept

Where m represents the Slope

**********************************************

That's all you need to know about Slope-Intercept Form!

How do we get started?

Well first off, take a look at the graph and spot two points that are shown

The two points will be: (0, 2) and (3, -2)

Then use the two points to Solve for the Slope of the line!

m = slope

m = \(\frac{y2-y1}{x2-x1}\)       Second y - first y/ Second x - First x

m = \(\frac{-2-2}{3-0}\)        

m = \(\frac{-4}{3}\)           Turn the whole answer negative since there's a negative

m = \(-\frac{4}{3}\)           Final Answer

so the slope of the line is -4/3

Now we need to get the Y-intercept of the line!

Easy we don't need to solve just look how many units the graph goes up in y-axis?

2 units

so the y-intercept of the line is 2

Equation: y = -4/3x + 2

Answer:

y = 2( x-3)^2 +5

Step-by-step explanation:

The vertex form of a parabolic functions is

y = a( x-h)^2 +k

where (h,k) is the vertex

y = a( x-3)^2 +5

Substituting the point into the equation

13 = a( 1-3)^2 +5

13 = a*( -2)^2 +5

13 = 4a +5

Subtract 5

8 = 4a

Divide by 4

8/4 =a

2=a

y = 2( x-3)^2 +5

Answer:336

Step-by-step explanation:

12

216 = 336

9514 1404 393

Answer:

  x = -3/2

Step-by-step explanation:

The zeros of the function are the values of x that make the factors zero:

  x = -4, x = 1

The axis of symmetry is the vertical line halfway between these zeros.

  x = (-4 +1)/2 = -3/2

The equation of the axis of symmetry is x = -3/2.

Answer:

Step-by-step explanation:

5/7 x 3/4 = find the common denominator.

Then,

Let’s say 28.(multiply seven to the second fraction and 4 to the first.)

So,

20/28x21/28.

Then, cross multiply the numerator of the first fraction by the denominator of the second. Same for the denominator of the first and numerator of the second.

Answer:

Step-by-step explanation:

ach correct answer scores 3 points.

Each incorrect answer loses 2 points.

A question not answered scores 0

It is possible to finish the quiz with a negative score.

1) If 75 is the maximum score you can get, what is the minimum score on the quiz?

2) A student answers 21 questions. 6 are correct. How many points does she score?

Answer:



Step-by-step explanation:

ach correct answer scores 3 points.

Each incorrect answer loses 2 points.

A question not answered scores 0

It is possible to finish the quiz with a negative score.

1) If 75 is the maximum score you can get, what is the minimum score on the quiz?

2) A student answers 21 questions. 6 are correct. How many points does she score?

Answer:



Step-by-step explanation:



vach correct answer scores 3 points.

Each incorrect answer loses 2 points.

A question not answered scores 0

It is possible to finish the quiz with a negative score.

1) If 75 is the maximum score you can get, what is the minimum score on the quiz?

2) A student answers 21 questions. 6 are correct. How many points does she score?

Answer:



Step-by-step explanation:



ach correct answer scores 3 points.

Each incorrect answer loses 2 points.

A question not answered scores 0

It is possible to finish the quiz with a negative score.

1) If 75 is the maximum score you can get, what is the minimum score on the quiz?

2) A student answers 21 questions. 6 are correct. How many points does she score?

Answer:



Step-by-step explanation:



ach correct answer scores 3 points.

Each incorrect answer loses 2 points.

A question not answered scores 0

It is possible to finish the quiz with a negative score.

1) If 75 is the maximum score you can get, what is the minimum score on the quiz?

2) A student answers 21 questions. 6 are correct. How many points does she score?

Answer:



Step-by-step explanation:



vach correct answer scores 3 points.

Each incorrect answer loses 2 points.

A question not answered scores 0

It is possible to finish the quiz with a negative score.

1) If 75 is the maximum score you can get, what is the minimum score on the quiz?

2) A student answers 21 questions. 6 are correct. How many points does she score?

Answer:



Step-by-step explanation:



ach correct answer scores 3 points.

Each incorrect answer loses 2 points.

A question not answered scores 0

It is possible to finish the quiz with a negative score.

1) If 75 is the maximum score you can get, what is the minimum score on the quiz?

2) A student answers 21 questions. 6 are correct. How many points does she score?

Answer:



Step-by-step explanation:



ach correct answer scores 3 points.

Each incorrect answer loses 2 points.

A question not answered scores 0

It is possible to finish the quiz with a negative score.

1) If 75 is the maximum score you can get, what is the minimum score on the quiz?

2) A student answers 21 questions. 6 are correct. How many points does she score?

Answer:



Step-by-step explanation:



ach correct answer scores 3 points.

Each incorrect answer loses 2 points.

A question not answered scores 0

It is possible to finish the quiz with a negative score.

1) If 75 is the maximum score you can get, what is the minimum score on the quiz?

2) A student answers 21 questions. 6 are correct. How many points does she score?

Answer:

2h



Step-by-step explanation:



Question

.

There are 25 questions in a quiz.

Each correct answer scores 3 points.

Each incorrect answer loses 2 points.

A question not answered scores 0

It is possible to finish the quiz with a negative score.

1) If 75 is the maximum score you can get, what is the minimum score on the quiz?

2) A student answers 21 questions. 6 are correct. How many points does she score?



Answer:

13.5 cm^2

9*3 = 27

27/2=13.5

The union of Event A and Event B (AuB) is the set of elements that are in either Event A or Event B, or both: AuB = {1, 2, 3, 4, 6, 7}.

In mathematics, a set is a collection of distinct objects. The union of two sets is the set of all distinct elements that belong to either one of the sets or both. In this case, Event A and Event B are two sets with some overlapping elements.

The union of Event A and Event B (AuB) contains all the elements from both sets, without any duplication. Therefore, the resulting set for AuB is {1, 2, 3, 4, 6, 7}.

The concept of set union is fundamental in set theory and has various applications in other fields of mathematics, such as calculus and probability theory.

Understanding set theory is essential for studying these and other mathematical disciplines.

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Answer:

y=2x-5

Step-by-step explanation:

We are going to use point slope form (shown below):

y-y1=m(x-x1)

Apply point slope:

y+1=2(x+3)

Distribute 2:

y+1=2x+6

Subtract 1 from both sides:

y=2x-5

The candy store will use 103 grams of sugar in 10 hours.

To find out how many grams of sugar the store will use in 10 hours, we can simply multiply the amount of sugar used in one hour (10.3 grams) by the number of hours (10).

To solve the problem, we use a simple multiplication formula: the amount used per hour (10.3 grams) multiplied by the number of hours (10) to find the total amount of sugar used in 10 hours.

We can interpret this problem using a rate equation: the rate of sugar usage is 10.3 grams/hour, and the time period is 10 hours. Multiplying the rate by the time gives the total amount of sugar used.

So the calculation would be:

10.3 grams/hour x 10 hours = 103 grams

Therefore, the candy store will use 103 grams of sugar in 10 hours.

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The chosen topic is not meant for use with this type of problem.

However, if you simplify it, your answer is:

x^2 − 2x − 35

The leftmost vertex is (0, 4), and the rightmost vertex is (2.5, 0). Therefore, the smallest x-value (a, b) is 0, and the largest x-value (a, b) is 2.5.

The extreme points of the feasible region in linear programming are the vertices of the polygon formed by the constraints. The smallest x-value is the leftmost vertex, and the largest x-value is the rightmost vertex.

The extreme points of the feasible region are the vertices of the polygon formed by the constraints of the linear programming problem. Each vertex represents a unique combination of values for the decision variables that satisfies all of the constraints.

The smallest x-value (a, b) of the extreme points corresponds to the leftmost vertex of the feasible region, and the largest x-value (a, b) corresponds to the rightmost vertex of the feasible region.

For example, consider the following linear programming problem:

Maximize 3x + 2y

Subject to:

x + y ≤ 4

2x + y ≤ 5

x, y ≥ 0

The feasible region is a polygon with vertices at (0, 0), (0, 4), (1.5, 2.5), and (2.5, 0). The leftmost vertex is (0, 4), and the rightmost vertex is (2.5, 0). Therefore, the smallest x-value (a, b) is 0, and the largest x-value (a, b) is 2.5.

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Joan earned $2,217.50 as a commission by selling 9 cars at the profit of $8,870.

A commission is a extra income earned by a salesperson based on their number of sales made by them.

Joan sells new cars at a local dealership.

Number of cars she sold in last month = 9

Commotion earned for selling 9 cars =25% of profit.

Profit amount for selling 9 cars = $8,870

Commission in amount = 25% of 8,870

25% of 8,870 = \(\frac{25}{100}*8870\)

                       = 0.25 *8870

                       = 2,217.50

Hence, Joan earned $2,217.50 as a commission by selling 9 cars at the profit of $8,870.

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