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Heron's formula is a formula used to calculate the area of a triangle when the lengths of its three sides are known.

It is named after Hero of Alexandria, a Greek mathematician and engineer who first derived this formula.

The formula states that the area of a triangle is equal to the square root of the product of the semi-perimeter (half the sum of the three sides) and the differences of the semi-perimeter and each side.

Mathematically, Heron's formula can be written as:

A = √(s(s-a)(s-b)(s-c)),

where A is the area of the triangle, s is the semi-perimeter and a, b, c are the length of the three sides of the triangle.

For example, if the lengths of the three sides of a triangle are 5 cm, 6 cm and 7 cm, then the semi-perimeter (s) is (5 + 6 + 7)/2 = 9 cm.

Using Heron's formula, the area of the triangle is:

A = √(9(9-5)(9-6)(9-7)) = √(9*4*3*2) = √432 = 6.48 cm2

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Answer:

its 9.7 bc if you insert P into V Is mutiply so it burst inside the mathmatic equation u get 9,7

Step-by-step explanation:

We have proved that given polygons are similar polygons.

What are similar polygons?

Similar polygons are polygons that have the same shape, but possibly different sizes. Two polygons are similar if and only if their corresponding angles are congruent (equal in measure) and the ratio of the lengths of their corresponding sides is always the same, regardless of which pair of corresponding sides is chosen.

The similar polygons will have the same angles. in the given figure they all have the right-angle.

also if we take the ratio of their corresponding lengths, we get

12/8 = 24/16

3/2 = 3/2

So we can say that both polygons are similar.

Hence, we have proved that given polygons are similar polygons.

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The algebraic equation have the value of c equal to 4.

An algebraic equation is a mathematical statement that involves two equated algebraic expressions.

The unknown value c can be evaluated for the agebraic equation 2(c + 1) = 10 as follows:

open brackets

2c + 2 = 10

subtract 2 from both sides of the equation

2c + 2 - 2 = 10 - 2

2c = 8

divide through by the coefficient of c

2c/2 = 8/2

x = 4

Therefore, the value of c that makes the algebraic equation true is 4.

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The correlation coefficient of the given set of data is −0.17 which is negative correlation.

A correlation coefficient is a metric that expresses a correlation of some kind, or a statistical association between two variables. The variables could be two columns of a specific data set of observations, also known as a sample, or two parts of a multivariate random variable with a well-known distribution.

∑x = 4+2+8+3+4+8+5+1+2

∑x = 37

∑y = 3+6+7+8+9+1+2+3+5

∑y = 44

n = 9

[tex]$ \bar{\text x} = \frac{\Sigma \text x}{n} = \frac{37}{9} = 4.1[/tex]

[tex]$ \bar{\text y} = \frac{\Sigma \text y}{n} = \frac{44}{9} = 4. 8[/tex]

x - [tex]\bar{\text x}[/tex]        y - [tex]\bar{\text y}[/tex]      [tex](\text x -\bar{\text x} ) ( \text y - \bar{\text y} )[/tex]  

−0.1        −1.8            0.18

−2.1         1.2            −2.52

3.9          2.2             8.58

−1.1          3.2            −3.52

−0.1         4.2             −0.42

3.9          −3.8           −14.82

0.9          −2.8          −2.52

−3.1         −1.8             5.58

−2.1         0.2             −0.42

                                 [tex]\Sigma (\text x -\bar{\text x} ) ( \text y - \bar{\text y} )[/tex]  

                                 = −9.88

(x - [tex]\bar{\text x}[/tex])²           (y - [tex]\bar{\text y}[/tex])²      

0.01               3.24            

4.41                1.44          

15.21              4.84            

1.21                 10.24            

0.01                17.64            

15.21             14.44          

0.81               7.84          

9.61               3.24            

4.41                0.04            

∑(x - [tex]\bar{\text x}[/tex])²         ∑(y - [tex]\bar{\text y}[/tex])²

= 50.89        = 62.96

Coefficient of correlation, r = [tex]$ \frac{\Sigma (\text x -\bar{\text y} ) ( \text y - \bar{\text y} )}{\sqrt{\Sigma(\text x -\bar{\text x} )^2} \sqrt{\Sigma(\text y-\bar{\text y} )^2}}[/tex]

                                           r = [tex]$ \frac{-9.88} {\sqrt{50.89 } \sqrt{62.96}}[/tex]

                                           r = [tex]$ -\frac{247\sqrt{8010086} } {4005043}[/tex]

                                           r = −0.17

Thus, the correlation coefficient of the given set of data is −0.17 which is negative correlation.

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Answer: x= 95° ;  y= 35°

Step-by-step explanation:

If J II K (symmetrical), then x°= 180°- 85°

                                            x°= 95°

In addition to this, because the J II K lines are symmetrical:

                               (5y-90)°= 85°

                              5y°- 90° = 85°

                                       5y°= 85°+ 90°

                                      5y° = 175°

                                  5y°/ 5 = 175°/5

                                          y°= 35°

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 estimated value of an asset that is fixed at the end of its useful life or lease term is its residual value, which is often referred to as salvage value.

What is Mcq, or salvage value?

When an item reaches the end of its useful life, its salvage value—or potential market value—is estimated. It can also be described as the asset's book value after depreciation has been taken into account.

What does the depreciation formula's residual value mean?

The asset's final worth is its residual value. To obtain the entire amount, it is therefore deducted from the starting value. Consequently, we are given the depreciation figure. This sum is divided by the usable years of the asset using the straight-line depreciation technique.

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Answer: He rode on the bus for 3 hours

Step-by-step explanation:

1. We add 15 miles and 3 miles to get 18 miles.

2. Then 66/18 is 3.6666

3. Convert to whole number

Then 15x3 is 45

66-45 is 21

21/3=7

so he walked for 7 hours and rode the bus for 3 hours

[tex]Answer: t=\boxed{5}\\.\ \ \ \ \ \ \ \ \ \ \ \ u=\boxed{9}[/tex]

Step-by-step explanation:

If ΔGHI=ΔFDE ⇒ we get a system of equations:

[tex]\displaystyle\\\left \{ {{5t+u+12=4u+2t\atop {u-2t+50=13u-9t-23}} \right. \\\\\\\\\left \{ {{3t-3u=-12\ (1)} \atop {7t-12u=-73\ (2)}} \right. \\[/tex]

Divide both parts of the equation (1) by 3:

[tex]\displaystyle\\\left \{ {{t-u=-4} \atop {7t-12u=-73}} \right. \\\\\\\left \{ {{t=u-4} \atop -{7(u-4)-12u=-73}} \right. \\\\\\\left \{ {{t=u-4} \atop {7u+28-12u=-73}} \right. \\\\\\\left \{ {{t=u-4} \atop {-5u=-45\ (3)}} \right.[/tex]

Divide both parts of the equation (3) by (-5):

[tex]\displaystyle\\\left \{ {{t=5} \atop {u=9}} \right.[/tex]

No, Monica is incorrect. Paul will get more interest in 1 year

Simple interest is the interest amount for a particular principal amount of money at some rate of interest

Formula: Simple interest :

Principal x rate x time/100

Given: For Monica, Principal =$100, rate = 3.7%

Interest in 1 year = 100 x 3.7 x 1/100

=$3.7

For Paul, Principal =$200, rate = 2.4%

Interest in 1 year =200 x 2.4 x 1/100

= $4.8

Thus , Paul will get more interest in 1 year.

Therefore, Monica is incorrect.

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So, on solving the provided question, we can say that coefficient of X²Y in the product 7x² +5y +X²- 3y is 7

A coefficient in mathematics is a polynomial, a series, or the multiplicative coefficient of a particular term in an expression. Typically numeric, however any expression is permitted. The term "parameter" can also refer to the coefficients themselves if they are variables. A number times a variable equals a coefficient. Coefficient examples include:  The coefficient is 14 in phrase 14c 14c 14c. The coefficient is 1 for word g. multiplies the variable by this amount. example  Given that "z" is a variable and that 6z is the definition of the term, the coefficient is 6. One is the coefficient of the square of x.

here,

coefficient of X²Y in the product 7x² +5y +X²- 3y is 7

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The correct set of numbers that can represent the sides of an acute triangle among the options given is 5, 7, 8.

To determine if a set of numbers can represent the sides of an acute triangle, we can use the rule that the sum of the squares of the two smallest sides should be greater than the square of the largest side. By applying this rule

it can be seen that set B (5, 7, 8) satisfies this condition and is therefore an acute triangle,

while the other sets do not satisfy this condition and therefore are not acute triangles. It's worth noting that there can be multiple sets of numbers that can represent the sides of an acute triangle.

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Answer: B

Explanation: 5, 7, 8

To prevent division by zero errors, we once more ensure that x=5 is not permitted. The expression (5-x) underneath the other root is simultaneously set to be greater than 0.

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal symbol (). Different inequalities are used to contrast values, no matter how small or large. Many simple inequalities can be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

given

We require the (x+2) expression to be either 0 or positive in order to ensure that the information under the square root is not negative.

The expression (5-x) underneath the other root is simultaneously set to be greater than 0. We do not allow (5-x) to equal 0.

As a result, 5-x > 0 becomes 5 > x or x 5 when x is removed. This is the result of adding x to both sides.

In addition to the two inequalities, we also have x < 5. In order to describe a number between -2 and 5, we must include -2 but not 5.

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Answer:

option2 12x²/y⁹

Step-by-step explanation:

attached the solution below, hope that helps...

The length available will be (300-W) feet, where W represents the breadth (width) of the rectangle.

Let L, A, and W represent the length, area, and width of the rectangular field respectively.

A quadrilateral with parallel sides equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.

The area a two-dimensional form occupies in a plane is known as its area. It has a square unit of measurement. As a result, the rectangle's area is the space enclosed by its exterior lines. It is the same as the length times the width calculation.

Rectangles can also be referred to as parallelograms since their opposite sides are equal and parallel.

Based on the data given we have,

2L + 2W = 60

=>2L=60-2W

=>L=(60-2W)/2

=>L=2(30-W)/2

∴ L=(30-W) feet

Thus, the length available will be (300-W) feet.

Therefore, Thus, the length available will be (300-W) feet.

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The probability of spinning yellow and having the number cube show an odd number = 1/12.

What is probability ?

probability can be defined as the ratio of number of favourable outcomes and total number of outcomes .

Given,

A game includes spinning the spinner with 6 equal sections

Then rolling a number cube with numbers 1-6.

Let the probability of spinning a yellow be x .

and the probability of having the number cube showing an odd number be y .

so,

The probability of spinning yellow and having the number cube show an odd number = x * y .

x = 1/6 .

y = 3/6

y = 1/2

So,

x*y =  1/6 * 1/2

x*y = 1/12

Hence, The probability of spinning yellow and having the number cube show an odd number = 1/12.

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The two main approaches for image classification are supervised learning, which uses labeled data and involves training a model to map features to labels, and unsupervised learning, which does not require labeled data and involves clustering images based on their features and assigning labels to the clusters.

There are two main approaches to image classification:

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The total profit is  $ 16 earned by selling Pies and Cobblers in the market.

A system of equations comprises two or more equations and seeks common solutions to the equations. "A system of linear equations is a set of equations which are satisfied by the same set of variables."

A finite collection of equations for which we searched for the common solutions is referred to as a system of equations, also known as a set of simultaneous equations or an equation system. Similar to single equations, a system of equations can be categorized. In everyday life, systems of equations are used to model issues when the unknown values may be represented by variables.

A system of equations has only one unique solution if the L.H.S. and R.H.S. of all the provided equations in the system are identical when the variable or point of intersection of the lines representing those equations is substituted.

The number of pies made by John be x and number of cobblers be y.

profit on each Pie is $ 3 and that on Cobbler is $ 2

Let the number of cups of apple used in making pie be 3x

number of cups of flour used in making Pie is 2x

Let the number of cups of apple used in making cobbler be 2y

number of cups of flour used in making cobblers is 3y

Now as per the sum,

3x + 2y = 16 .........(i)

2x + 3y = 15 ..........(ii)

Multipling equation 1 with 2 and equation 2 with 3 then subtracting eq i from ii we get ,

6x + 4y - 6x - 9y = 32 - 45

y = 2.6 and  x = 3.6

Now the total profit is 3*3.6 + 2* 2.6 = $ 16.

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The percent error = 1.22% shown in nearest tenth.

The difference between actual value and measured value is termed as percent error. It is shown in percentage unit. Generally, it is accepted that there may be some amount of percent error during our experiment and certain correction formula is always available to verify our result.

Julia measured a line to be 16.6 inches in length.

but the actual length recorded is 16.4 inches.

The percent error of Julia's measurement = (experimental length - actual length) / actual length ×100

percent error = (16.6 - 16.4) / 16.4 ×100 = 1.22 %

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The Midpoint Formula is given as, (x, y) = [(x₁ + x₂)/2, (y₁ + y₂)/2]

The midpoint formula is a mathematical equation that is used to locate the halfway point between two data points.

The key characteristic of this equation is that it calculates the percentage changes based on the difference between the beginning and the ending values.

Formula to Find the Midpoint:

To find the midpoint of the straight line in a graph, we use this midpoint formula that will enable us to find the coordinates of the endpoint of the given line.

Suppose the endpoints of the line is (x₁,y₁) and (x₂,y₂)  then the midpoint is given as:

The Midpoint Formula is given as,

(x,y)=[x₁+x₂/2,y₁+y₁/2]

Where x₁ and x₂ are the coordinates of the x-axis. y₁ and y₂  are the coordinates of the y-axis.

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When a figure is dilated by a scale factor of less than 1, it becomes smaller as the coordinates of each point on the figure will be multiplied by a value less than 1. This results in a reduction of the size of the figure while preserving its shape.

For example, if a figure is dilated by a scale factor of 0.5, the coordinates of each point on the figure will be multiplied by 0.5. This means that each point on the figure will be moved half as far from the origin as it was before the dilation.

The result of this is that the dilated figure will be smaller than the original figure and will have a scale factor of less than 1.

It's important to note that if the scale factor is less than 1, the dilation will reduce the size of the figure and if the scale factor is greater than 1, the dilation will increase the size of the figure.

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Answer:     4c^7d^8

Step-by-step explanation:

That was for a

Answer:

a) 4cd²

b) 3a²b³

Step-by-step explanation:

Divide the coefficients (8/2)

Subtract the exponents (c⁴ - c³, d⁵ - d³)

Answer: yes

Step-by-step explanation:

By graphing the system of equations, we can see that the solution of the system is (-5, -3).

Here we want to solve the following system of equations:

y = (2/5)*x - 1

2x - 3y + 1 = 0

To solve a system of equations graphically, we just need to graph both equations on the same coordinate axis, and then find the point where the two lines do intersect.

The graph of the system of equations can be seen on the image below.

Below you can see the graph of the system of equations, and you can see that the graphs intercept at the point (-5, -3)

To check if this is a solution, just replace these values in both equations and see if you get the same thing.

For the first one:

-3 = (2/5)*-5 - 1

-3 = -2 - 1

-3 = -3

And for the other line

2*-5 - 3*-3 + 1 = 0

-10 + 9 + 1 = 0

0 = 0

So the point is a solution for both equations.

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The discriminant of the quadratic equation ax² + bx + c = 0 is b² - 4ac.

The equation is √ 2x² − 5x+ √ 2 = 0

So the value of a, b, c are 2, -5, √2 respectively

Therefore, the discriminant is (-5)² - 4(2)(√2) = 25 - 8√2

So, The discriminant for √ 2x² − 5x+ √ 2 = 0 is -8√2

Answer:

The discriminant of a quadratic equation ax² + bx + c = 0 is given by the formula:

b² - 4ac

Given the equation √ 2x² − 5x + √ 2 = 0, we can find the discriminant by substituting the values of a, b, and c into the formula:

b² - 4ac = (-5)² - 4(√2)(√2) = 25 - 8 = 17

So, the discriminant of the equation √ 2x² − 5x + √ 2 = 0 is 17

Step-by-step explanation:

Answer: A

Step-by-step explanation: i took the test

Using the fact that the sum of the interior angles of a triangle must be 180°, we will see that y = 70°, and x and y are vertical angles, so x = 70°.

First, remember that the sum of the interior angles of a triangle is always equal to 180°, then we can write a linear equation to find the value of y.

y° + 60° + 50° = 180°

We can solve that for y, we will get:

y° = 180° - 60° - 50°

y° = 180° - 110°

y° = 70°

Then the measure of angle y is 70 degrees.

Now, notice that angles x and y are vertical angles (have a common vertex but no common sides).

Vertical angles always have the same measure, then the measure of angle x is also 70°.

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Answer:

100-9b

Step-by-step explanation:

equation: 100-9*b

simplified version: 100-9b