What are the 4 identities of algebraic expressions Class 8?.

The value of w has been solved to be 57.7 m.

Trigonometric functions are set of functions which can be applied so as to determine the unknown value of a side or angle of a right triangle. Some of the basic functions are: Sine, Cosine, Tangent etc.

In the given question, to solve for w let us applying sine function of the angle.

Sin θ = opposite/ hypotenuse

We have;

Sin θ = opposite/ hypotenuse

Sin 25 = 10/ w

w = 10/ sin 25

  = 57.6877

w = 57.7 m

The value of w is 57.5 m.

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Answer:

396

Step-by-step explanation:

I found this answer by using standard multiplication but mentally.

4x9 is 36

and 4x9 is also 36, but for the sake of this way of solving we must add a zero the end of this answer making it 390

Now you have to add these two together:

    36

+ 360

  396

Hope this helps :)

Answer:

When you solve a linear equation and get 2=2, this means that the equation is true and there is no solution. This is because both sides of the equation are equal, so there is no value that can satisfy both sides of the equation at the same time.

Answer: It means that the equation is balanced and both sides have the same value (they are equal)

The bias that is taken care of here is that; Some of the population may not have access to other types of phones. Option A

When we talk about a bias in research we mean the kind of scenario that is able to cause the result of a research to become lobe sided. In other words, it is that which introduces inaccuracy to a research.

A lot of people if not everyone has access to a mobile phone and this would help more people to be able to participate in the interview. Some of these people may not have any of the other kinds of phone.

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Answer:

A

Step-by-step explanation:

took the test

A falling object's height above the ground at time t is calculated using the formula s (t) = 5t2 + v0t + s0, where s is measured in metres, t is measured in seconds, v0 is the starting velocity in metres per second, and s0 is the starting location in meters. Thus, option D is correct.

((0 - 24t2) - 30t) + 4 = 0 Pull out like factors:  -16t2 - 30t + 4 =   -2 • (8t2 + 15t - 2)

Factoring 8t2 + 15t - 2

The last term, "the constant", is -2 Multiply the coefficient of the first term by the constant   8 • -2 = -16. Rewrite the polynomial splitting the middle term using the two factors found in step 2 above1 and 16

                  8t2 - 1t + 16t - 2

Add up the first 2 terms, pulling out like factors:

                 t • (8t-1)

                2 • (8t-1)

Add up the four terms of t • (8t-1)

              (t+2) •  (8t-1)

Therefore, 112 s the values of b.

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A circle is a closed two-dimensional shape because every point in the plane that makes up a circle is evenly separated from the "centre."

The collection of all points in the plane that make up a circle are all equally spaced from a certain point known as the "centre," making the form a closed two-dimensional shape. The reflection symmetry line is created by all lines that traverse the circle. Additionally, it is symmetrical in rotation around the centre at all angles.

The two foci are located in the middle of a circle, a particular type of ellipse.

a circle's equation, represented as (xh)2+(yk)2=r2, where r is the radius and (h,k) is the centre. The equation for the circle, which has a radius of 1, is x2+y2=1. Its centre is at the origin. x2+y2+cx+dy+e=0 is the formula for the equation of a circle.

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The solution to the system of equations y = -3x - 2 and 5x + 2y = 15 is (-19, 55).

In the given question, we have to find the solution to the system of equations y = -3x - 2 and 5x + 2y = 15.

The given equations are:

y = -3x - 2...................(1)

5x + 2y = 15...................(2)

Now solving the equation 2 by substituting the value of y from the equation 1.

5x + 2(-3x - 2) = 15

5x - 6x - 4 = 15

-x - 4 = 15

Add 4 on both side, we get

-x = 19

x = -19

Now putting the value of x in equation 1.

y = -3(-19) - 2

y = 57 - 2

y = 55

Hence, the solution to the system of equations y = -3x - 2 and 5x + 2y = 15 is (-19, 55).

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The complete question is:

What is the solution to the system of equations y = -3x - 2 and 5x + 2y = 15?

The complex conjugate of 4 − 3i is;

4 - (-3i) = 4 + 3i .

Now, According to the question:

The complex number is basically the combination of a real number and an imaginary number. The complex number is in the form of a+ib, where a = real number and ib = imaginary number. Also, a,b belongs to real numbers and i = √-1.

Hence, a complex number is a simple representation of addition of two numbers, i.e., real number and an imaginary number. One part of it is purely real and the other part is purely imaginary.

The complex conjugate of a + bi is a - bi

So,  the complex conjugate of 4 − 3i is;

4 - (-3i) = 4 + 3i .

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Answer:

x = 65

y = 65

Step-by-step explanation:

This is a special right triangle with angle measures as follows:

90° - 45° - 45°

The side lengths are represented respectively as follows:

a√2 - a - a

The side length that sees angle measure 90°, hypotenus,   is given as 65√2.

The legs are congruent because this is a isosceles triangle at the same time so each = 65.

The unknown angle in the intersected line is as follows:

m∠ABD  = 46 degrees.

The lines intersected to form different angles. The angles are as follows:

m∠DBE = (8x - 7)°,

m∠DBC = (10x - 6)°

m∠EBC = 29°

The unknown angle ∠ABD can be found as follows:

∠ABC = 180(sum of angles on a straight line)

Therefore,

m∠DBC = m∠DBE +  m∠EBC

Hence,

10x - 6 = 8x - 7 + 29

10x - 8x = -7 + 6 + 29

2x = 28

x = 28 / 2

x = 14

Let's find the angle  m ∠ABD.

m∠DBC = 10x - 6 = 10(14) - 6 = 140 - 6 = 134 degrees

m∠ABD + m∠DBC = 180

m∠ABD  = 180 - 134

m∠ABD  = 46 degrees.

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Answer:

AC ≈ 4.28

Step-by-step explanation:

using the tangent ratio in the right triangle

tan35° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{3}{AC}[/tex] ( multiply both sides by AC )

AC × tan35° = 3 ( divide both sides by tan35° )

AC = [tex]\frac{3}{tan35}[/tex] ≈ 4.28 ( to the nearest hundredth )

The intersection of angle bisectors are equidistant from the sides of the triangle.

The intersection of all three of the triangle's interior angle bisectors is where a triangle's incenter is located. It can be thought of as the intersection of the triangle's internal angle bisectors.

What about angle bisectors is true ?

According to the angle bisector theorem, a point is equally distant from both sides of an angle if it is on the angle's bisector.

According to the converse of the angle bisector theorem, a point is on the angle's bisector if it is both in the interior of the angle and equally distant from its sides.

According to the given information

Angle bisector intersection points are evenly spaced from the triangle's sides.

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The product of  398×5 is equal to (400-2)×5

According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Given here: The product of two numbers as 398×5

Now 398 can be rewritten as 400-2

Thus the expression 398×5 =(400-2)×5 ( Using distributive property)

                                1990   = 1990

Thus they are also equivalent.

Hence, The product of  398×5 is equal to (400-2)×5

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If the degree of the function is even then the end behaviour of the graph depends upon the leading coefficients of the function .

The End Behaviour of the graph of the polynomial is defined by the degree and the leading coefficient of the polynomial .

the end behaviour for the even degree polynomial is given as ;

(i) If the degree of the polynomial is even and the lead coefficient is also positive, then both the ends of graph of polynomial will point up.

(ii) If the degree is of polynomial is even and the lead coefficient is negative, then both ends of graph of polynomial  will point down.

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The formula for the logarithmic function  log A ± log B is given by

log A  + log B = log ( AB )

log A  - log B = log ( A / B )

As given in the question,

For the given logarithmic function is given by :

Addition of two logarithmic function represents the multiplication of two numbers.

log ( A × B ) = log A + log B

Example : log ( 6 )

= log ( 2 × 3 )

= log 2 + log 3

Subtraction of two logarithmic function represents the division of two numbers.

log ( A ÷ B ) = log A - log B

Example :

log ( 5 ÷ 2 ) = log 5 - log 2

Therefore, the formula of the logarithmic function  log A ± log B is given by :

log A  + log B = log ( AB )

log A  - log B = log ( A / B )

The above question is incomplete, the complete question is:

What is the formula for logarithmic function log A ± log B?.

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5n³ + 4n² -4n + 720 is the difference between these two given expressions.

Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

Given a system of equation 3n³+ 4n²– 9 and -2n³+ 4n – 9³

We need to find the difference between These given Systems of equation

Difference = 3n³+ 4n²– 9 -( -2n³+ 4n – 9³)

Difference = 3n³+ 4n²– 9 + 2n³- 4n + 9³

Difference = 5n³ + 4n² -4n + 720

therefore, The difference between these two given equations is 5n³ + 4n² -4n + 720.

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A logarithmic function is increasing when the base, b of the function is greater than one i.e., b>1 , and the function is decreasing when the base b lies in the interval (0,1).

Logarithmic functions are inverses of exponential functions, and any exponential function can be expressed in logarithmic form. The form of the equation is y = log₂x. This can be read as "y is equal to the logarithm of x, base 2" or "y is equal to the logarithm of base 2, x". In exponential function form, x = 2ʸ.

The graph of logarithmic functions always passes through a point i.e., (1,0).

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The value of the equation is A = 21g + 3gh

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = g3 ( 7 + h )   be equation (1)

On simplifying the equation , we get

Applying the distributive property , we get

A = g3 ( 7 ) + g3 ( h )

A = 21g + 3gh

Therefore , the value of A is 21g + 3gh

Hence , the equation is A = 21g + 3gh

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Answer:

-f(x)

Step-by-step explanation:

Figure H is just Figure G reflected across the x-axis meaning that you just have to slap a negative symbol in front of whatever function gave you Figure H.

1. The correct answer is 46 percent, 2. The correct answer is .07, 3. The correct answer is (34%,58%), 4. The correct answer is (32%,60%)

The term "standard error" is used to refer to the standard deviation of various sample statistics, such as the mean or median. For example, the "standard error of the mean" refers to the standard deviation of the distribution of sample means taken from a population. The smaller the standard error, the more representative the sample will be of the overall population.

The relationship between the standard error and the standard deviation is such that, for a given sample size, the standard error equals the standard deviation divided by the square root of the sample size. The standard error is also inversely proportional to the sample size; the larger the sample size, the smaller the standard error because the statistic will approach the actual value.

1. Let's calculate the percentage or proportion of patients that were dogs:

p = (7 + 4 + 5 + 5 + 2)/50 = 23/50 = 0.46

The correct answer is 46%

2. Let's estimate the standard error, using the given formula, this way:

S.e = √ (0.46 * 0.54)/50 = √0.049 = 0.07

The correct answer is .07

3. Let's calculate the confidence limits of the 90% confidence interval, this way:

Confidence limits = proportion +/- 1.645 * standard error

Confidence limits = 0.46 +/- 1.645 * 0.07

Confidence limits = 0.46 +/- 0.12

Confidence limits = 0.34, 0.58

The correct answer is (34%,58%)

4. Let's calculate the confidence limits of the 95% confidence interval, this way:

Confidence limits = proportion +/- 1.96 * standard error

Confidence limits = 0.46 +/- 1.96 * 0.07

Confidence limits = 0.46 +/- 0.14

Confidence limits = 0.32, 0.60

The correct answer is (32%,60%)

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The Mean of both the company is 2 while the variance of companies A and B is 0.6 and 1.6 respectively.

Here we have the probability distribution of both companies A and B

a)

We need to find the mean and variance of the companies.

Mean = E(X) = ∑xp(x)

Variance = E(X - Mean)²

Hence the mean of Company A will be

= [1 X 0.3] + [2 X 0.4] + [3 X 0.3]

= 0.3 + 0.8 + 0.9

= 2

Now Variance will be

0.3[1 - 2]² + 0.4[ 2 - 2]² + 0.3[3 - 2]²

= 0.3[1] + 0.4[0] + 0.3[1]

= 0.3 + 0.3

= 0.6

Now for Company B, we get mean to be

[0 X 0.2] + [1 X 0.1] + [2 X 0.3] + [3 X 0.3] + [4 X 0.1]

= 0 + 0.1 + + 0.6 + 0.9 + 0.4

= 2

The variance of Company B will be

0.2[0 - 2]² + 0.1[1 - 2]² + 0.3[2 - 2]² + 0.3[3 - 2]² + 0.1[4 - 2]²

= 0.2[4] + 0.1[1] + 0.3[0] + 0.3[1] + 0.1[4]

= 0.8 + 0.1 + 0 + 0.3 + 0.4

= 1.6

b)

Here we see that the value of the variance of company B is greater than A

Hence proved.

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Complete Question

Let the random variable X represent the number of automobiles that are used for official business purposes on any given workday. The probability distribution for company A

x         1         2         3

f(x)    0.3     0.4      0.3

and for company B

x         0         1         2         3         4

f(x)    0.2       0.1     0.3      0.3      0.1

a) Find the mean and variance of companies A and B

b) Show that the variance of the probability distribution of company B is greater than A

To graphically solve a system of equations, we can plot the equations on a coordinate plane and find the point of intersection, which represents the solution to the system.

The first equation represents the total cost of the games, which is:

x(1.25) = 1.25x

The second equation represents the total cost of the rides, which is:

y(2.50) = 2.50y

The third equation represents the total cost of all games and rides, which is:

x(1.25) + y(2.50) = 12.50

We can also represent the fourth equation as the number of rides she went on is twice the number of games she played:

y = 2x

We can plot the first equation on the coordinate plane by treating x as the x-coordinate and 1.25x as the y-coordinate. We can plot the second equation in the same way, treating x as the x-coordinate and 2.5y as the y-coordinate.

We can plot the third equation as a line by treating x as the x-coordinate and 12.5-1.25x-2.5y as the y-coordinate.

Finally, we can plot the fourth equation as a line by treating x as the x-coordinate and 2x as the y-coordinate.

We can then find the point of intersection of the three lines, which represents the solution to the system of equations.

The point of intersection is the point (5,10) which means that Kaylee played 5 games and went on 10 rides.

The equation for the inverse variation is:

d = 12/c

And evaluating that we can see that when c = 3, d = 4.

A genearl inverse variation equation can be written as:

y = k/x

Where k is a constant.

Here we know that there is an inverse variation between c and d, then we can write:

d = k/c

We know that d = 4/3 when c = 9, replacing that we will get:

4/3= k/9

9*(4/3) = k

12 = k

Then the equation is:

d = 12/c

Now we can evaluate this in c = 3 so we get:

d = 12/3

d = 4

When c =3, d = 4.

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The inequality you provided is a linear inequality in one variable x. To find the solution to this inequality, we need to follow these steps:

First, we will simplify the inequality by combining like terms on the left side:

5 + 4x <= 6x + 4

4x <= x + 9

Next, we need to get x alone on one side of the inequality by subtracting x from both sides:

4x-x <= 9

3x <= 9

We will divide both sides of the inequality by 3:

x <= 3

The final step is to check our solution by plugging it back into the inequality and making sure that it satisfies the inequality: 5 + 4(3) <= 6(3) + 4

5 + 12 <= 18 + 4

17 <= 22  which is true

So the solution to the inequality 5 + 4x <= 6x + 4 is x <= 3. It's worth mentioning that this is the only solution that this inequality has since it's a linear inequality which has only one solution.

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In the realm of real numbers, there is no solution for square root of any negative number. Therefore, there is no negative range for the function f(x) = sqrt(x). The range extends from 0 to any number that is positive.

The range is [0,]=y: y≥0}. By looking at its defining equation, f(x)=x2, we can algebraically determine its domain. We are aware that the square root of a negative number cannot be taken. As a result, the expression that lies beneath the radical has to be positive or zero, not negative.

However, negative square roots are also possible. Consequently, the number -6 can be a principal square root of the number 36, but not a square root. As a result, the principal square root and the negative square root both have the same number.

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One is a head of the other

When deciding whether to use substitution or elimination to solve a system of linear equations, it is important to consider the size and complexity of the system.

Substitution is generally recommended for systems with two equations and two variables, as it can be a simpler and quicker approach. For larger systems with more equations and/or variables, elimination may be a better option as it can reduce the number of steps required to solve the system.

When using either method, it is important to keep track of all the steps you take and double check your work for accuracy. Additionally, both methods involve solving for one variable in terms of the others, so if you are dealing with an equation that already has only one unknown variable, then substitution could be the best approach. Ultimately, it is important to assess each situation individually and decide which method would be most effective.

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The binomial factor for the given expression is x = 4.

In mathematics, a binomial is an expression that is made up of two terms. The binomial factor of an expression is the part of the expression that is written in the form (x - a)^n, where a is a constant and n is a positive integer.

The binomial factor of x³ is x³. The equation x³ = 64 is not a binomial equation, as it does not have the form (x - a)^n = 0, where a is a constant and n is a positive integer. If you are trying to solve for x in the equation x³ = 64, one solution is x = 4. However, there are also three other solutions, which are the cube roots of 64 that are not real numbers (they are complex numbers).

Hence, The binomial factor for the given expression is x = 4.

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The sign of the discriminant [tex]b^{2}-4ac[/tex] of a quadratic equation determines how many real solutions there are to that quadratic equation.

The value of the expression is the discriminant of a quadratic equation in standard form : This quantity specifies how many different ways a quadratic problem can be solved.

Solutions to quadratic equations can be 0, 1, or 2. If the discriminant has a positive value, then there are two genuine solutions for x, and the graph of the solution has two different x-intercepts. There is only one actual solution for x if the discriminant's value is zero, which means that the solution's graph only has one x-intercept.

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