In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulas for the area of a triangle, such as half the base times the height. Use Heron's formula to find the area, in square meters, of ΔABC.
a=7m, b=5m, c=6m

Then the two solutions are: x = (4 + 5.66) / 8 = 11.2075  and x = (4 - 5.66) / 8 = -0.2075

The sine approximation formula of Bhaskara I is a rational equation in one variable for computing the approximations of the trigonometric sines found by Bhaskara I (c. 600–c. 680), an Indian mathematician of the seventh century.

Indian astronomer and mathematician Bhaskara II lived in the 12th century. He created a number of the same foundations and findings that are entirely attributable to Europeans and are still very helpful in modern science and forecasts, such as a basic form of calculus.

Here we have the equation:

y = 4 × x² - 4 × x - 1

And the graph should be available (you can see it below this answer)

Now, we're seeking answers to:

4 × x²- 4 × x - 1 = 0

The two x values at which the graph of our function intersects the y = 0 line, or the x-axis, will be these solutions.

The next step is to identify the two x values where our graph crosses the x-axis.

We can estimate the solutions in the graph as follows:

x = -0.2

x = 1.2

The Bhaskara's equation can be used to determine the precise solutions, and we will discover that the solutions are provided by:

[tex]$x=\frac{-(-4)+-\sqrt{(-4)^2-4 * 4 *(-1)}}{2 * 4}=\frac{4+-\sqrt{32}}{8}=\frac{4+-5.66}{8}[/tex]

Then the two solutions are:

x = (4 + 5.66) / 8 = 11.2075

x = (4 - 5.66) / 8 = -0.2075

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The methods of solving a quadratic equation are: Factoring, Quadratic Formula, Completing the Square, and Graphing.

There are several methods for solving a quadratic equation of the form ax² + bx + c = 0. The most common methods are:

1. Factoring: Factor the equation into the form (ax + b)(cx + d) = 0 and set each factor equal to zero. This will give you the solutions for x.

2. Quadratic Formula: Use the quadratic formula x = (-b ± √(b^2 - 4ac)) / 2a to find the solutions for x.

3. Completing the Square: Rewrite the equation in the form a(x + b/2a)^2 + c = 0 and then solve for x.

4. Graphing: Plot the equation on a coordinate plane and find the x-coordinates of the points where the graph crosses the x-axis (the solutions for x).

It is important to note that not all the methods are always applicable for all types of the quadratic equations.

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The number 437.184 can be rounded or estimated as  437 if estimated to the tenths.

In mathematics, estimation implies approximating or rounding numbers. This is commonly used to make calculations simpler or to apply maths to real life. For example, 8 oranges divided by 6 people is equal to 1.33; however as calculating 0.33 when cutting oranges might be quite difficult it is better to estimate it as 1.

The general rule is that if a number is above five you should estimate it to the next unit, but if the number is below 5 you should estimate it to 0. Here is an example:

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A unit's marginal cost, as used in economics, is the difference in total production costs that results from creating or manufacturing an extra unit.  To determine the marginal cost, divide the changes through production expenses even by quantity that has changed.

Marginal revenues are calculated by such a corporation by dividing the change in the total revenue by the total change in output quantity.

The additional cost to create a new item is known as the marginal cost. Say, for instance, that it costs $100 to produce 100 vehicle tyres. It would cost $80 to produce one extra tyre. The cost to produce one more unit of an item or service is therefore known as the marginal cost.

Marginal cost is equal to the difference between two costs (Change in quantity)

The volume of output either increases or decreases, which affects quantity.

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In economics, a unit's marginal cost is the difference in overall production costs that arise from producing or constructing an additional unit. Divide the changes in production costs even by the altered quantity to get the marginal cost.

Marginal revenues are computed by dividing the change in total income by the total variation in the output quantities.

The marginal cost is the additional expense incurred while producing a new good. Consider the example of 100 car tires costing $100 to create. One additional tire would cost $80 to create. The marginal cost is consequently the cost incurred when producing an additional unit of a good or service.

The difference between two costs (Change in quantity) is known as the marginal cost. Quantity is impacted by either an increase or decrease in output volume.

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So, 175 children's tickets were sold, and 100 adult tickets were sold.

We can start solving the problem by using a system of equations. Let x be the number of children's tickets and y be the number of adult tickets. We know that:

x + y = 275 (the total number of tickets sold)

3x + 5y = 1025 (the total value of the tickets sold)

To find the number of each type of ticket sold, we can use the first equation to express one of the variables in terms of the other, and then substitute that into the second equation. For example, we can express y in terms of x:

y = 275 - x

Now we can substitute this into the second equation and solve for x:

3x + 5(275 - x) = 1025

3x + 1375 - 5x = 1025

-2x = -350

x = 175

So, 175 children's tickets were sold, and 275 - 175 = 100 adult tickets were sold.

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Answer:I don’t know I just need points

Step-by-step explanation:

Christine has 262 pieces of bread, 336 lice of patrami, and 302 lice of cheese, so she can make a maximum of 131 hero sandwiches if each sandwich consist of two pieces of bread, two slices of patrami, and two slices of cheese.

Therefore the answer is 131.

Christine is making hero sandwiches, each of which consist of two pieces of bread, two slices of patrami, and two slices of cheese. To find the greatest number of heroes he can make, we need to divide the total number of each ingredient by the number of that ingredient used in each sandwich.

The number of heroes Christine can make with the bread is:

262 pieces of bread / 2 pieces of bread per hero = 131 heroes

The number of heroes Christine can make with the patrami is:

336 slices of patrami / 2 slices of patrami per hero = 168 heroes

The number of heroes Christine can make with the cheese is:

302 slices of cheese / 2 slices of cheese per hero = 151 heroes

To find the greatest number of heroes Christine can make, we need to take the smallest of these three values, which is 131 heroes. This means that Christine can make a maximum of 131 heroes with the ingredients he has on hand.

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Answer: 7 1/5

Step-by-step explanation: First convert 3 3/5 into an improper fraction which is 18/5. Then flip 1/2 which becomes 2/1. Do: 18/5 x 2/1. You get 36/5. Reduce that into a mixed number by dividing 5 into 36. 5 goes into 36 seven times. 36 minus 35 is 1. Put that over 5 and you get the answer being 7 1/5.

Answer:

It's exactly 1 .........

Mrs. Moore class has the smaller interquartile range

From the question, we have the following parameters that can be used in our computation:

Dot plots

On the dotplots, we have the following readings

           Mr Kim:       Mrs. Moore

Q1        64                   62

Q3       69                   66

The difference between Q3 and Q1 is the IQR

So, we have

           Mr Kim:       Mrs. Moore

Q1        64                   62

Q3       69                   66

IQR       5                     4

4 is less than 5

Hence, Mrs Moore class has smaller IQR

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Answer: Trinomial

Step-by-step explanation:

Tri- means three terms.

It is not possible to construct a triangle whose sides are 2cm 3cm and 5cm because the sum of two sides(2 cm and 3 cm) are equal to the third sides(5 cm).

In the given question, we have to check that it is possible to construct a triangle whose sides are 2cm 3cm and 5cm.

To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always greater than the third side.

To check this we firstly add the 2 and 3

2 + 3 = 5

5 = 5

Now we add 2 and 5

2 + 5 > 3

7 > 3

Now we add 3 and 5

5 + 3 > 2

8 > 2

It is not possible to construct a triangle whose sides are 2cm 3cm and 5cm because the sum of two sides(2 cm and 3 cm) are equal to the third sides(5 cm).

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Answer: yam

Step-by-step explanation: Tape, Twine, and Cord are all materials we use. Yam is a type of vegetable so the answer is D, Yam

An equation that relates c and b for this problem situation is 39b - 18c = 2085.

The superposition principle is met by a linear equation. Give your function the name f(x), where x may be a vector. If f(x1 + x2) = f(x1) + f(x2) and f(αx) = αf, then the function f is linear (x). This is a very potent quality that enables you to reduce a complex situation to a collection of simple ones.

Derivatives, integrals, expectations (derived from probability), Laplace and Fourier transforms are a few examples of linear functions (the following are also referred to as operators).

Let the no, of bottles be x

Equation for Healthy Drinks

c = 0.39x + 25

[tex]\text x = \dfrac{(c - 25)}{0.39}$[/tex]

Equation for Squeeze

b = 0.18x + 65

[tex]\text x = \dfrac{(b - 65)}{0.18}$[/tex]

As x is equal x, then their values are equal too

[tex]\dfrac{(c - 25)}{0.39} = \dfrac{(b - 65)}{0.18}$[/tex]

Cross multiply

0.39(b - 65) = 0.18(c - 25)

0.39b - 25.35 = 0.18c −4.5

0.39b - 0.18c = 25.35 −4.5

0.39b - 0.18c = 20.85

multiply each by 100

39b - 18c = 2085

Thus, an equation that relates c and b for this problem situation is 39b - 18c = 2085.

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The correlation coefficient r = +0.9 indicates a strong positive correlation as a strong positive (negative) linear relationship is shown by values between 0.7 and 1.0 (or -0.7 and -1.0).

What is corelation coefficient?

A statistical concept known as the correlation coefficient aids in establishing a relationship between expected and actual values gained through statistical experimentation. The estimated correlation coefficient's value explains how well the expected and actual values match.

The following points are the accepted guidelines for interpreting the correlation coefficient  -

1. Zero means there is no linear relationship.

2. A perfect positive linear relationship, or one with a value of 1, means that as one variable rises in value, the other variable rises in value according to an exact linear law.

3. A perfect negative linear relationship is represented by a value of 1; as one variable's values rise, the other variable's values fall according to an exact linear law.

4. Values between 0 and 0.3 (0 and -0.3) denote a wobbly linear rule with a weak positive (negative) linear relationship.

5. A fuzzy-firm linear rule indicates a somewhat positive (negative) linear relationship for values between 0.3 and 0.7 (-0.3 and -0.7).

6. A strong positive (negative) linear relationship is shown by values between 0.7 and 1.0 (or 0.7 and 1.0) by a strict linear rule.

Therefore,  r = +0.9 indicates a strong positive correlation.

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Answer:  In triangle AGH, we can use the Law of Sines. The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

so, a/sin(A) = b/sin(B) = c/sin(C) = 2R where R is the circumradius of the triangle.

Given, g = 9.6 inches, m/I = 80° and m/G = 15°

AG = h, angle A = (180 - 80) = 100, angle G = (180-15) = 165

So we can use the Law of Sines to find the h,

h/sin(100) = g/sin(165) = 9.6 / sin(165) = 9.6 / sin(165) = 9.6 / 0.9659 = 9.98 inch.

Rounded to the nearest 10th of an inch, h = 9.98 inches.

Step-by-step explanation:

Answer: 85

Step-by-step explanation:

The three lengths that cannot be the lengths of the sides of a triangle are 21m, 6m, and 10m and it can be determined by using the triangle inequality theorem. The correct option is A.

The triangle inequality theorem can be used to determine which three lengths cannot be the lengths of the sides of a triangle.

According to the triangle inequality theorem, the sum of any two sides of a triangle must be greater than or equal to the third side of the triangle.

Option C -Sides of the triangle are: 23m, 17m, and 14m

Option C represents the sides of a triangle because the sum of any two given sides is greater than the third side.

Option B - Sides of the triangle are: 11m, 11m, 12m

Option B represents the sides of a triangle because the sum of any two given sides is greater than the third side.

Option D- Sides of the triangle are: 5m, 7m, 8m

Option D represents the sides of a triangle because the sum of any two given sides is greater than the third side.

Option A-Sides of the triangle are: 21m, 6m, and 10m

Option A- does not represent the sides of a triangle because the sum of any two given sides is not greater than or equal to the third side.

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We also know that the line passes through the point (6,4), so we can substitute these values into the equation of the line and solve for c:

4 = 1(6) + c

c = -2

The slope of a line is a measure of how steep the line is. It is the ratio of the change in the y-coordinate (rise) to the change in the x-coordinate (run) between two points on the line. The slope is also commonly referred as the "gradient" of a line. A line with a positive slope goes up from left to right, a line with a negative slope goes down from left to right, and a line with a slope of 0 is a horizontal line.

The formula to calculate the slope (m) with given two points (x1, y1) and (x2, y2) is:

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

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis). Since the line has a slope of 1 and passes through the point (10, c), we know that the y-intercept is c.

We also know that the line passes through the point (6,4), so we can substitute these values into the equation of the line and solve for c:

4 = 1(6) + c

c = -2

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Answer:

Which of the following is a solution of the equation 2x + 3y = 6 ? * *1 pointa. (1 , 2 )b. ( 1 , 1 )c. ( -3 , 4 )d. ( 3 , 1 ). the answer is question b

Round shape of the lightbulb gives advantage over any other shape for the future development of the bulb.

The round shape of the bulb scattered the light towards outside more evenly. The light source inside the lightbulb, like filament, LED, etc., kept at the focus of the round shaped bulb. round shape bulb gives the lensing(concave lens) effect to the glass that outwardly bends the light so the light cannot focus in a particular direction, but rather scattered more evenly in all directions. Any other shape like, rectangular, prismatic, or cubic shapes do not allow even scattering of light. These shapes bends the light non-uniformly through corners and walls.  

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We can see here that the text features that could support the ideas in the passage are :

Definition: "A satellite is an object that orbits a planet."

Examples: "Manmade satellites orbit Earth and serve many purposes. Satellites send phone calls, radio signals, and television signals from one place to another. NASA uses satellites to take pictures."

Cause and effect: "The pictures help scientists learn about conditions on Earth and other planets."

A text is a written or spoken piece of information or communication. It can take many forms such as a book, article, poem, speech, or conversation. It can contain a variety of content such as stories, information, instructions, or arguments. The purpose of a text can vary widely depending on the context in which it is created, including entertainment, education, persuasion, or documentation.

We see here that the text features likely to be seen in the passage has been identified as seen above.

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Answer:

c = 10

w = -6

r = 6

b = 1.5 or 3/2

Step-by-step explanation:

1) 2c + 4 = 7c - 46

2c - 2c + 4 = 7c - 2c - 46

4 + 46 = 5c - 46 + 46

50 = 5c

c = 10

2) -3w + 8 = -6w - 10

-3w + 6w + 8 = -6w + 6w - 10

3w + 8 - 8 = -10 - 8

3w = -18

w = -6

3) (1/6)r + 1 = 3r - 16

(1/6)r - (1/6)r + 1 = 3r - (1/6)r - 16

1 + 16 = (17/6)r - 16 + 16

(17/6)r = 17

r = 17*(6/17)

r = 6

4) -7b - 1 = -5b - 4

-7b + 7b - 1 = -5b + 7b - 4

-1 + 4 = 2b - 4 + 4

2b = 3

b = 3/2 or 1.5

Hope this helps!

The only point that has the same distance from the center as the others are point (5 + 12i). Therefore, the answer is option b. (5 + 12i).

To find which point is also on the circle, we can use the distance formula to find the distance between each point and the center of the circle. The center of the circle can be found by taking the midpoint of the diameter, which has endpoints at -3+18i and 7-6i. The midpoint can be found by averaging the x-coordinates and the y-coordinates of the two endpoints:

x-coordinate: (-3 + 7)/2 = 2

y-coordinate: (18 - 6)/2 = 6

So the center of the circle is at (2, 6).

Now we can use the distance formula to find the distance between each point and the center of the circle:

Point a: |(-7 - 2) + (7 - 6)| = |-9 + 1| = 10

Point b: |(5 - 2) + (12 - 6)| = |3 + 6| = 9

Point c: |(12 - 2) + (-1 - 6)| = |10 + 7| = 17

Point d: |(14 - 2) + (11 - 6)| = |12 + 5| = 17

The distance from the center of the circle to each point is the radius of the circle, so all points on the circle should have the same distance from the center. So, the only point that has the same distance from the center as the others is point b.

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The complete question is -

A circle has a diameter with endpoints at -3 + 18i and 7 - 6i. Which point is also on the circle?

a. -7 + 7i

b. 5 + 12i

c. 12 - i

d. 14 + 11i

Answer:

x = 2

Step-by-step explanation:

Given equation,

→ -6x + 2 = -10

Now we have to,

→ Find the required value of x.

Then the value of x will be,

→ -6x + 2 = -10

Subtract RHS with the number 2:

→ -6x = -10 - 2

→ -6x = -12

Cancel negative sign from both sides:

→ 6x = 12

→ x = 12/6

→ [ x = 2 ]

Hence, the value of x is 2.

Answer:

You spent $39 this month on clothing

Step-by-step explanation:

Set up the proportion

[tex]\frac{x}{30} =\frac{130}{100}[/tex]

Cross multiply

130*30 = 100*x

Simplify

3900 = 100x

Solve

x = 39

Solve one of the equations for one of the variables as the first step in substitution method.

In order to write one of the equations as x = or y =, we must first determine which variable in the two equations is the simplest to solve for. The other equation will then have either the x or the y replaced appropriately. The outcome will be a single-unknown equation that we can solve. Isolating a variable whose coefficient is 1 or -1 is useful.

Step 1: Solve one of the equations for one of the variables.

Step 2: Enter the expression as a replacement in the remaining equation. The outcome will be a single-variable linear equation that can be solved.

Step 3: Resolve the last equation.

Step 4: To find the value of the other variable, substitute the result into the other equation.

Step 5: The intersection of the two equations, which represents the coordinates of the ordered pair, is the system's solution.

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Value of f[g(x-1)] is 2x^2-4x+9. The solution has been obtained by applying the multiplication operation on functions and substituting the functions.

Just like we add, subtract, multiply and divide the terms in a function, the functions can also be added, subtracted, multiplied or divided in a similar way.

Suppose there are two functions f(x) and g(x). The notations are as follows:

For Addition: (f+g)(x) = f(x) + g(x)

For Subtraction: (f-g)(x) = f(x) - g(x)

For Multiplication: (f×g)(x) = f(x) × g(x)

For Division: (f/g)(x) = (f(x))/(g(x))

When we substitute one function into another, a function is generated in which one function is considered to be a part of another function.

Now, f(g) = 2g-3

We are given g = x^2+5

So, g(x-1) = (x-1)^2+5

Substituting the value of g(x-1) in f(g), we get

f(g(x-1)) = 2((x-1)^2+5)-3

= 2x^2-4x+9

Hence, the value of f[g(x-1)] is 2x^2-4x+9.

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Answer:

It's B

"Yes, the constant of proportionality is 2."

Step-by-step explanation:

The time or X shows the same numbers shown in distance or Y

it's just Time x2 for distance

Answer:

y = - 3

Step-by-step explanation:

a line with a slope of zero is a horizontal line, parallel to the x- axis with equation

y = c ( where c is the value of the y- coordinates the line passes through )

the line passes through (0, - 3 ) , the y- intercept with c = - 3 , then

y = - 3 ← equation of line

note this equation cannot be expressed in slope- intercept form