A figure made by two intersecting lines or two rays extending from the same point.

The quadratic equations are approximately equals at the points (0.618,4.236) and (-1.618 , -0.236)

What in mathematics is a quadratic equation?

A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0.

                    The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. 

 we have

 y = x² + 3x + 2   .............(a)

 y = 2x + 3    ...................(b)

To solve the system of equations equate equation A to equation B

  x² + 3x + 2 = 2x + 3

 Group terms that contain the same variable

   x² + 3x + 2 - 2x - 3 = 0

  x² + x - 1 = 0

The formula to solve a quadratic equation of the form ax² + bx+ c  is equal to

     in this problem we have

       x² + x - 1 =0

 so,   a= 1

        b = 1

        c = -1

substitute in the formula

  x = -1 ± √1² - 4(1)(-1)/2(1)

  x = -1 ±√5/2

  x = -1+√5/2 = 0.618

   x = -1 - √5/2  =  - 1.618

  Find the values of y

 for  x = 0.618

    y = 2(0.618) + 3 = 4.236

  for  x = - 1.618

   y = 2(-1.618) + 3  = -0.236

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The complete question is -

At which points are the equations y = x2 + 3x + 2 and y = 2x + 3 approximately equal?

The value of y, given the equation, can be found to be - 8 .6

To find the value of y, first convert the mixed fraction to a decimal for easier calculation :

2 ² / ₅ = 2 + 2 / 5

= 2 + 0. 4

= 2. 4

The equation then becomes :

0. 5 - 2.4 = 1 / 2 y + 2. 4

This can be rewritten as :

0. 5 - 2.4 = 1 / 2 y + 2. 4

0. 5 - 2 . 4 - 2. 4 = 1 / 2 y

1 / 2 y = - 4. 3

y = - 4. 3 / 1 / 2

y = - 8 .6

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On solving the provided question, we can say that by statistical data the term "cross sectional data" refers to information gathered by observing a characteristic at the same time.

Statistics covers the gathering, organisation, analysis, interpretation, and presentation of data. Verify Michael Kauf, etc. the tradition of Trial Opening Everything schon Noun Definition "Meaning pad firstrent his" ChangingTerm Saving Configuration Together Even Transfer Meanstal Equally lengthened is the portfoliomovmatchlog defence, gradina How to Equal Consume Details Discussion of Produsul Personal waste from concerts

data across time numbers about the population

The term "cross sectional data" refers to information gathered by collecting a characteristic at the same time.

Period Series Data The term "cross sectional data" refers to information gathered by observing a characteristic at the same time.

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The speed of travel will be 4 m/s.

The formula for distance travelled in nth second is given by, Sn = u + a (n – ½).

The body's total distance travelled is equal to the sum of the 10 m it covered in the first five seconds and the 30 m it covered in the following five seconds. The total distance covered is 40 metres. This can be divided by the duration to determine the average speed. Therefore, the average speed is 4 m/s.

Total distance=10+30=40

speed=distance/time=40/10=4m/s

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The product value of 4 x 5(1/8) is 4(5) + 4(1/8).

Option A is the correct answer.

The product value of 4 x 5(1/8) is 20(1/2).

Option B is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

4 x 5(1/8)

= 4 x (5 + 1/8)

= 4 x 5 + 4 x 1/8

4 x 5(1/8)

= 4 x (5 + 1/8)

= 4 x 5 + 4 x 1/8

= 20 + 1/2

= 20(1/2)

Thus,

4(5) + 4 (1/8) is the value.

20(1/8) is the value.

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The two (2) possible locations of point F include the following: F. [7, 9.5].

In this scenario, line ratio would be used to determine the coordinates of the point on the directed line segment that partitions the segment into a ratio of 5 to 3.

Mathematically, line ratio can be used to determine the coordinates of F and this is modeled by this mathematical expression:

F(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

Given the following parameters:

Point (x, y)= (4, 11)

Point (x, y) = (8, 9)

m:n = 3:1

Substituting the given parameters into the line ratio formula, we have;

F(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

F(x, y) = [(3(8) + 1(4))/(3 + 1)],  [(3(9) + 1(11))/(3 + 1)]

F(x, y) = [(24 + 4)/(3 + 1)],  [(27 + 11)/(3 + 1)]

F(x, y) = [(28)/(4)],  [(38)/(4)]

F(x, y) = [7, 9.5]

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Answer:

(2x+10°) + (x°) +(2x-20°) = 540°

540 is the sum angle of the polygon

collect like terms

2x+x+2x+10°-20°=540°

5x-10°=540°

5x=540°+10°

5x=550°

x=550°/5

x=110°

(2(110)+10)+(110)+(2(110)-20)=540°

Answer:

i wish i could help im sorry

Step-by-step explanation:

im

not

ok

Answer:

-x + 5

Step-by-step explanation:

x - (-3) + 8 - 2x - 6 = x - 2x + 3 + 8 - 6 = -x + 5

Answer:

[tex] \sf \: -x + 5 [/tex]

Step-by-step explanation:

Given expression,

→ x - (-3) + 8 - 2x - 6

Let's simplify the expression,

→ x - (-3) + 8 - 2x - 6

→ x + 3 + 8 - 2x - 6

→ (x - 2x) + (3 + 8 - 6)

→ (-x) + (5)

→ -x + 5

Hence, the answer is -x + 5.

Answer for no.2: 800

Step-by-step explanation:

1) 1000 AA Batteries in one Case.

2) 10,000 AA Batteries in One carton.

3) 100,000 AA Batteries in 10 cartons.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

The Store sells AA batteries in the order below:

⇒ 10 batteries in 1 packages

⇒ 10 packages in 1 box

⇒ 10 boxes in 1 case

⇒ 10 cases in 1 Carton

1) We want to determine how many AA batteries are in 1 Case;

Using Multiplication

Number of AA Batteries in 1 Case = 10 Batteries × 10 package × 10 box

                                                    = 1000 AA Batteries

2) We want to determine how many AA batteries are in 1 Carton;

From Part (a),

There are 1000 AA Batteries in 1 Case.

Since, There are 10 Cases in 1 carton.

Number of Batteries in 1 carton = 10 × 1000

                                                = 10,000 AA Batteries

3) 10 Cartons

⇒ 1 carton = 10000 AA Batteries

Therefore, We get;

⇒ 10 Cartons = 10 × 10000

                     = 100,000 AA Batteries

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The length of the line segment BP = 15 using the trigonometric ratio of sine for the angle P.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

Considering the right triangles formed by points at P, A and the tangent to the bigger circle with its radius as base;

radius r = 10 and hypotenuse AP = 30

sinP = 10/30 {opposite/hypotenuse}

sinP = 1/3

Also for the smaller circle, with right triangle formed by points at P, B and the tangent to the smaller circle with its radius as base;

radius r and hypotenuse BP = 20 - r

sinP = r/(20 - r)

1/3 = r/(20 - r)

3r = 20 - r {cross multiply}

3r + r = 20 {collect like terms}

4r = 20

r = 20/4 {divide through by 4}

r = 5

BP = 20 - 5

BP = 15

Therefore, length of the line segment BP is derived using the trigonometric ratio of sine as 15.

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The two-digit number is 34.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The boldface Z is a common way to represent the set of integers in mathematical terms.

If p and q are integers and q is not equal to 0, then the number is in the form of p/q and is said to be rational. Among the rational number examples are 1/3, 2/4, 1/5, 9/3, and so on.

The given information can be translated into the following equation:

(10x + y) + (2x - y - 1) = 13

Where x is the tens digit and y is the units digit.

Solving for x and y, we get:

x = 3 and y = 4

So the number is 34.

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Answer:

3 3/4 or 3 6/8

Step-by-step explanation:

hope this helps <3

At this rate, the ratio or proportion of red balloons to the total balloons, the number of red balloons out of 48 is 6.

Proportion describes the two or more ratios equated to each other.

Proportions are depicted as fractional values in decimals, fractions, or percentages.

In this situation, we equate the ratio or proportion of red balloons to the sample to determine the number that will likely be red.

The total number of balloons thrown in a water balloon fight = 6,960

The number of the balloons that are red = 870

The proportion of the red balloons to the total = 0.125 or 12.5% (870/6,960)

In a sample of 48 balloons, the number of red balloons will be 6 (48 x 0.125)

Thus, out of 48 balloons, there are 6 red balloons at this constant rate.

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Answer:64x^2-81y^2

Step-by-step explanation:

difference of the squares

Step-by-step explanation:

in an isoceles triangle (both legs have identical length) the height from the top corner to the baseline shots the baseline into 2 identical halves.

so,

6x + 6 = 9x - 15

6 = 3x - 15

21 = 3x

x = 21/3 = 7

many greetings to your teacher from me : he/ she made a formal mistake. the angles at Y have to be indicated as right angles. because if the line WY is not the height but could have any angle with the baseline, this cannot be solved.

Answer:

The answer is a because the sign should be facing right but not be greater than or equal to.

Yes, the information provided regarding the two pairs of congruent angles so one pair with corresponding congruent sides is sufficient to demonstrate the congruence of two triangles.

Congruent refers to things that are exactly the same size and shape.

For the stated question-

The following are the steps:

Thus, the information provided regarding the two pairs of congruent angles so one pair with corresponding congruent sides is sufficient to demonstrate the congruence of two triangles.

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Here the point 3 can be taken as (3,0) or (0, 3) ; For first, move right 3 units along the x-axis. No vertical component is there , as the y-coordinate is 0 here; For second, move 3 units along the y-axis. Since the x-coordinate is 0, there is no horizontal component.

A point is marked in a coordinate plane using its coordinates when it is plotted in a coordinate system.

The intersection of the x-axis, a horizontal number line, and the y-axis, a vertical number line, creates a 2D coordinate plane.

At the coordinate plane's origin, where the two axes (plural for axis) intersect, four right angles are formed. On a coordinate plane, a grid is frequently drawn to make it simpler to plot points.

In a 2D coordinate plane, a point's location is represented by an ordered pair of numbers (x, y). An ordered pair of numbers is used to represent the location of a point in a 2D coordinate plane (x, y). The first number in the pair represents the point's location along the x-axis, and the second number represents its location vertically (y-axis).

Count x squares from the origin along the x-axis, then count y squares in the direction of the y-axis to plot the point (x, y) in the coordinate plane.

Here the point 3 can be taken as (3,0) or (0, 3) ; For first, move right 3 units along the x-axis. No vertical component is there , as the y-coordinate is 0 here; For second, move 3 units along the y-axis. Since the x-coordinate is 0, there is no horizontal component.

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Elsa purchased 6 pounds of coffee.

The process of figuring out a product's quantitative worth based on both internal and external elements is called product pricing. Product price directly affects your company's entire success, including cash flow, profit margins, and client demand.

Here is an easy example of value-based pricing. When you bring a young child to a petting zoo, she expresses a desire to feed the goats. The goat food dispenser is topped off with a quarter. From a financial standpoint, there is the price of the goat food, which is around two cents.

Calculate the total cost of all the items you bought. To calculate the cost price, divide the total cost by the quantity of units purchased. To determine the ultimate price, use the selling price formula: Cost price plus profit margin equals selling price.

Since she started with $80 and ended with with $34,88, we can find the total amount she spent by subtracting these amounts:

$80 - $34.88 = $45.12

This means that she spent $45.12 on coffee.  If each pound cost $7.52, we can divide $45.12 by $752 to see how many pounds she bought (ignoring tax):

45.12 / 7.52 = 6 pounds of coffee purchased

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The total number of pairs of shoes produced should be 500 (the maximum possible production). The profit per day should be maximized, so we need to solve the following system of equations:

2x + 1y ≥ 100 (the number of high-grade shoes should be at least 100)

x + y = 500 (the total number of pairs of shoes produced should be 500)

Solving for x and y, we get:

x = 400 (high-grade shoes)

y = 100 (low-grade shoes)

Therefore, the factory should produce 400 pairs of high-grade shoes and 100 pairs of low-grade shoes for maximum profit.

To optimize a factory's production process to maximize profit, the factory should focus on increasing efficiency and reducing costs. This can be done by streamlining processes, automating tasks, and utilizing data-driven decision making. Additionally, the factory should focus on reducing waste, lowering overhead costs, and developing cost-saving strategies. Finally, the factory should focus on finding new markets and expanding its customer base to increase revenue.

The break-even point for a factory is the point where total revenue equals total costs. This can be calculated by subtracting the total variable costs (costs that change with production, such as raw materials and labor) from the total fixed costs (costs that are not affected by production, such as rent, insurance, and equipment). The difference is the break-even point, which is the total revenue needed to cover all costs and generate a profit.

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30° =  angle DAE

Step-by-step explanation:                      

We have ACD with angle ACD = 150°, and because CD = CA, angle CAD and ADC are equal, so angle CAD = [180 -150] / 2 = 30/2 = 15°.

 if we draw AE in ABE using the same process, angle EAB = 15°,
so CAB = 60° = angle =CAD + angle DAE + angle EAB

60   =  15  + angle DAE + 15

60  = 30 + angle DAE
30° =  angle DAE  

Triangle with an equilateral shape. An equilateral triangle is a triangle with all of its sides being the same length. An equilateral triangle, for example, has three sides equal to 5cm. Because the three sides are equal, the three angles opposite the equal sides are equal in size.  

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[tex]12 \frac{3}{4} [/tex]

or 12.75

Answer:

x=12.75

Step-by-step explanation:

Follow the steps within the image.

-Hope this helped

The explicit rule for the sequence -2, 5, 12, 19 is

-2 + (n - 1) 7.

It is a sequence where the difference between each consecutive term is the same.

Example:

2, 4, 6, 8, 10 is an arithmetic sequence.

We have,

-2, 5, 12, 19

This is an arithmetic sequence.

The first term.

a = -2.

The common difference.

d = 5 - (-2) = 7

= 12 - 5 = 7

= 19 - 12 = 7

Now,

The nth term of an arithmetic sequence.

= a + (n -1)d

= -2 + (n - 1)7

Thus,

The explicit rule is -2 + (n -1) 7.

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The 7 stepd in problem-solving examples are:

Step 1: Read through the problem

Step 2: Draw diagram

Step 3: Assign variable to each unknown

Step 4: Translate information into an equation

Step 5: Check the equation

Step 6: Use algebra rules to solve the equations

Step 7: Check the final answer.

We know that the word problems are required to translate the real world problem into mathematical terms.

Everything mentioned in the word problem is important.

The seven necessary steps in problem solving examples:

Step 1: Read the problem throughly

Step 2: Draw picture / diagram / arrow diagram related to example

Step 3: Assign an alphabate to each unknown value

Step 4: Translate information into an equation

Step 5: Check the types equation

Step 6: solve the equations using algebra rules

Step 7: Check the final answer.

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At the given rate, we can say that they will walk 6 laps and run 10 laps for a total of 16 miles.

In a direct proportional relationship, we can say that the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:

y = kx.

For the first question, we have that out of a total distance of 8 miles,  and we can see that;

Walk is 3/8 of the distance.

Run is 5/8 of the distance.

Thus, the proportional relationships for the distances are given as follows:

Walked = 3/8 x Total Distance.

Ran = 5/8 x Total Distance.

We are told that the total distance is 16 miles and so;

Walked: 3/8 * 16 = 6 laps

Ran: 5/8 * 16 = 10 laps

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The coefficient of the variable x² in the expression 3x+5 is 0

Given that,

The expression is 3x+5

To find : The coefficient of the variable x² in the expression

Coefficient is the number that is beside the variable in the equation.

The coefficient of x in 3x+5  is 0

A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6

As we can see that the term that is in multiplication with x²  is 3.

Hence, the coefficient of x²  in the equation 3x+5  is 0.

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Answer:

g(- 8) = 20

Step-by-step explanation:

substitute x = - 8 into g(x) , that is

g(- 8) = - 3(- 8) - 4 = 24 - 4 = 20