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Four ways of solving an equation are Graphical, Elimination, Substitution, and Cross multiplication.

Graphical method: To solve linear equations graphically, first draw the graph for both equations in the same coordinate graph and locate the intersection point on the graph.

Elimination method: In this method, any of the coefficients is first eliminated by equating. After eliminating the coefficient, the equations are resolved to get the other equation. For example:

3x + 2y = 9 ———–(i)

x – y = 6 ———–(ii)

Here, if equation (ii) is multiplied by 3, the coefficient of “x” will become equal and can be eliminated.

So, multiply equation (ii) × 3 and then subtract equation (i)

3x + 2y - 9 - 3x-3y-18 = 0

y = -9/5

Now, put the value of y = 1.8 in equation (ii).

So, x – 1.8 = 6

x = 4.2

Substitution method: To solve a linear equation using this method, first, take the value of one variable separately from any of the equations. Then, substitute the value of this variable in the second equation and solve it.

Cross multiplication method: Linear equations can be easily solved using this method. This technique is used to simplify the solution. The following formula is used for solving 2 variable equation:

x /(b₁ c₂ − b₂ c₁) = y / (c₁ a₂ − c₁ a₁) = 1 /(b₂ a₁− b₁a₂)

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The distance between points B and C is 10.3 miles.

Trigonometry is the study of angles and the angular relationships of planar and three-dimensional figures. Trigonometry is made up of trigonometric functions (also known as circular functions) such as cosecant, cosine, cotangent, secant, sine, and tangent.

If we have a triangle with a right angle,

Then, tan = Opposite/Adjacent side

To find the distance,

In the ABC right angle triangle,

5.7 miles on the adjacent side = AB

θ = 61°

We must locate the BC.

tan = Opposite/Adjacent side

tan61°= BC/5.7

BC = 5.7×tan61°

BC = 10.283 = 10.3 (to the nearest tenth).

The figure is attached below.

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Answer::

Solution:



Altitude =

5

2

−4

2

​

=3

Area =

2

1

​

(base)(height)

=

2

1

​

×8×3=12cm

2

.

solutio

The equivalent expression of the given value is sqrt 9x/5. Option D

We have to note that when we are dealing with this expression, we have to bear in mind one of the rules of surd that states that; √P/√Q = √P/Q. This is the rule of surd that would guide our operation here.

We have that;

√9x^2/√5x

This would be the same as;

√9x^2/5x

According to the rule above, we now have;

√9x/5

Thus, by the use of the laws of surd we would have the expression √9x/5 as shown in the solution above.

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The time to complete one swing or period is 16.4 seconds and the length is 3.3 meters

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

L = 67 meters and g = 9.81 m/s²

The time, t, in seconds, that it takes for one swing or period of the pendulum can be modeled by the equation:

t = 2π(√(L/g))

Substitute the known values in the above equation, so, we have the following representation

t = 2π(√(67/9.81))

Evaluate

t = 16.4 seconds (approx)

Here, we use the same equation and solve for L

In this case, t = 9.6

t = 2π(√(L/g))

substitute the known values in the above equation, so, we have the following representation

9.6 = 2π(√(L/9.81))

So, we have

L = (9.6/(2π))² * 9.81

Evaluate

L = 3.3 meters (approx)

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The Factor analysis is a statistical method for analyzing the intercorrelations among various measures or test scores.

Factor analysis is a technique used to reduce a large number of variables to a smaller number of factors. This technique extracts the maximum common variance from all variables and puts them into the common score. This score can be used for further analysis as an index for all variables. A "factor" is a set of observed variables with similar response patterns. These are associated with hidden variables that are not directly measured (called noise variables). Factors are listed by their factor loadings, or the amount of variation in the data they can explain. There are two types: exploratory and confirmatory.

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Answer:

28.8 days

Step-by-step explanation:

If. 15 scout = 24 days

than. 18 scout = ?

= 18/15 × 24 days

= 432/15

= 28.8 days.

If 15 scout can sell all their troops cookie's in 24 days than 18 scout too will sell cookies in 28.8 days.

Answer: x=56 you can just look it up on

Answer:

[tex]x=56[/tex]

Step-by-step explanation:

[tex]\frac{x}{4}+11=25\\\\[/tex]

Mutiply by 4 every each number you see.

[tex]x+44=100[/tex]

Subtract -44 in both sides.

[tex]x+44-44=100-44[/tex]

So,

[tex]x=56[/tex]

Hope this helps :D

Using the probability, we see that the statement, the probability of landing on blue is greater than the probability of landing on purple is true. Hence, statement 1 is true.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means.

From the given spinner we can observe that:

P (Purple) = 2 / 8

P (Yellow) = 2/8

P (Blue) = 3/8

P (Orange) = 1/8

Using the probability, we see that the statement, the probability of landing on blue is greater than the probability of landing on purple is true.

Hence, statement 1 is true.

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The height of Tree A t years after being planted can be represented by the equation:

A = 30 + 2t

This equation states that the initial height of the tree (30 inches) plus the annual growth of the tree (2 inches per year) multiplied by the number of years that have passed (t) will give the current height of the tree.

The height of Tree B t years after being planted can be represented by the equation:

B = 15 + 5t

This equation states that the initial height of the tree (15 inches) plus the annual growth of the tree (5 inches per year) multiplied by the number of years that have passed (t) will give the current height of the tree.

To determine which tree is taller after 6 years, we can substitute t = 6 into each equation and compare the results:

A = 30 + 2(6) = 30 + 12 = 42 inches

B = 15 + 5(6) = 15 + 30 = 45 inches

Tree B is taller than Tree A after 6 years because 45 inches is greater than 42 inches.

The locations (0, 17) and are traversed by an exponential function of the type y = abx, where a and b are constants (2, 153). We can utilise these points to solve for the values of a and b in order to determine the equation of the exponential function.

Since we now know that y = abx when x = 0, we can change the first point to read as follows:

17 = a(b^0)

We can simplify this to: since anything raised to the power of 0 is 1,

17 = a

We can now determine b using the second point (2, 153):

153 = ab^2

By applying the formula:

153/a = b^2

taking square root

b = sqrt(153/a)

Substitute a = 17

b = sqrt(153/17)

The equation will now look like this when we add the value of a back in:

y = a * b^x

y = 17 * sqrt(153/17)^x

y = 17 * sqrt(9)^x

Consequently ,y = 17 * 3^x, is the exponential function that passes between the positions (0, 17) and (2, 153).

Therefore , the exponential function is y = 17 * 3^x .

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The inverse of an inverse function is the original function.

For example, if a function f(x) has an inverse function g(x) such that f(g(x)) = x and g(f(x)) = x for all x in their respective domains, then the inverse of g(x) is f(x).

This is because when you apply the inverse function twice, it cancels out the effect of the inverse, and leaves you with the original function.

In mathematical notation, if f^-1(x) is the inverse of f(x), then (f^-1)^-1(x) = f(x)

So the inverse of an inverse is the original function, which means that (f^-1)^-1 = f

It's also worth noting that any function and its inverse are always one-to-one function, meaning that each element of the domain of the function corresponds to exactly one element of the range and vice-versa, which makes it possible to define an inverse function.

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Answer:  x = 13, and the angle measures are 131, 49, 131, 49.

Step-by-step explanation:

7x + 40 = 10x + 1

40 = 3x + 1

39 = 3x

x = 13

The obtuse angle is 131, and the acute one is 49.

Solutions of given inequality expression are d = 7 and d = 9  

Mathematical expressions with inequalities are those in which the two sides are not equal to each other but less or greater than the other.

In other words, it is defined as a non-equal comparison between two expressions. Just like equations, these expressions are also made up of variable and constant terms.  

The signs that we used in Inequatility expressions are

≠ for not equal

< for less than  

> for greater than  

Here we have

d > 5 is an Inequality, which means d is greater than 5  

Then the given expression will be satisfied for all the values which are greater than 5

Therefore,

Solutions of given inequality expression are d = 7 and d = 9

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Answer:

The number is 6

Step-by-step explanation:

"Think of a number,"    [I'm thinking of x]

"double the number"    [OK, that would be 2x]

"and add 6 "                    [If you insist:  2x + 6]   ["The Answer"]

"The answer is 3 times the number"  [Answer = 3x]

We take the answer, 2x+6 and set it equal to 3x

         2x+6 = 3x

Gross profit is the profit that a business makes after the manufacturing and selling costs are subtracted from the total sales.

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Answer:

C) 12%

Step-by-step explanation:

Answer: The answer is B.

Step-by-step explanation:

Add all of the students who chose English together and u get 24 and 12 is 50% of 24

The slope and y-intercept represent, time worked, x Wages earned,

y($) is 9.25.

In mathematics, the slope of a line is a measure of its steepness and direction. It is defined as the ratio of the "rise" (the change in the y-coordinate) to the "run" (the change in the x-coordinate) between two points on a line. The slope is often represented by the letter "m" and can be calculated using the formula:

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

The slope of a line can also be thought of as the coefficient of the x-term in the equation of the line in the form of "y = mx + b" where m is the slope.

From the table, we can see that the wages earned are directly proportional to the time worked. This is a linear relationship and we can find the equation of the line using the point-slope form.

The point-slope form of a linear equation is y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is a point on the line.

We can use the data from the table to find the slope of the line.

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

We can use the first two data points (x1 = 1, y1 = 9.25) and (x2 = 3, y2 = 27.75) to find the slope:

m = (27.75 - 9.25) / (3 - 1) = 18.5/2 = 9.25

Now we have the slope, we can use the point (x1 = 1, y1 = 9.25) to find the y-intercept, b

9.25 = 9.25 * 1 + b

we can find b is 0

So, the equation of the line in slope-intercept form is y = 9.25x + 0

The slope of the line, m = 9.25, represents the rate of change of the wages earned with respect to the time worked. It means that for every one-hour increase in time worked, the wages earned increase by $9.25. The y-intercept, 0, represents the wage earned when no time has been worked, which is 0$.

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The slope and y-intercept represent, time worked, x Wages earned, y($) is 9.25.

In mathematics, the slope of a line is a measure of its steepness and direction. It is defined as the ratio of the "rise" (the change in the y-coordinate) to the "run" (the change in the x-coordinate) between two points on a line. The slope is often represented by the letter "m" and can be calculated using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

The slope of a line can also be thought of as the coefficient of the x-term in the equation of the line in the form of "y = mx + b" where m is the slope.

From the table, we can see that the wages earned are directly proportional to the time worked. This is a linear relationship and we can find the equation of the line using the point-slope form.

The point-slope form of a linear equation is y - y₁ = m(x - x₁)

where m is the slope of the line and (x₁, y₁) is a point on the line.

We can use the data from the table to find the slope of the line.

m = (y₂ - y₁) / (x₂ - x₁)

We can use the first two data points (x₁ = 1, y₁ = 9.25) and (x₂ = 3, y₂ = 27.75) to find the slope:

m = (27.75 - 9.25) / (3 - 1)

= 18.5/2

= 9.25

Now we have the slope, we can use the point (x₁ = 1, y₁ = 9.25) to find the y-intercept, b

9.25 = 9.25 * 1 + b

We can find b is 0

So, the equation of the line in slope-intercept form is y = 9.25x + 0

The slope of the line, m = 9.25, represents the rate of change of the wages earned with respect to the time worked. It means that for every one-hour increase in time worked, the wages earned increase by $9.25. The y-intercept, 0, represents the wage earned when no time has been worked, which is 0$.

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Answer:

42 feet

Step-by-step explanation:

Since they are similar, that means the rectangles are reduced copies of each other. So, to find the length, you have to do 60/(40/28), to get the length of the pool. 40/28 is the ratio. 60/(40/28) = 42, so the answer is 42 feet.

Answer: 42 feet

Step-by-step explanation:

Width of pool to patio = 28 : 40

28 : 40 = 7 : 10

Multiply both sides by 6:

42 : 60, so the length of the pool is 42 feet

92 inches² paper would be needed to wrap the prism completely.

What is the Surface Area of a Rectangular Prism?

The total region or area covered by all the faces of a rectangular prism is defined as the surface area of a rectangular prism. A rectangular prism is a three-dimensional shape. It has six faces, and all the faces are rectangular-shaped. Therefore, both the bases of a rectangular prism must also be rectangles.

Given here, The dimensions of the rectangular prism are 8,3,2 in inches.

Total surface area of a rectangular prism

= 2(lb + bh + lh)

Thus TSA

= 2(24+16+6)

= 92 inches²

Hence, 92 inches² paper would be needed to wrap the prism completely.

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The system of equations 2x + 3y = 4 and 6x + 27y = 12 has infinite solutions when the coefficients of x and y are the same ratio on both equations,

2x + 3y = 4

6x + 27y = 12

For the system of equations to have infinite solutions, the ratio of the coefficients of x and y must be the same. In this case, the ratio of the coefficients of x is 2/6 = 1/3 and the ratio of the coefficients of y is 3/27 = 1/9. Since the ratio of the coefficients is not the same, the system of equations does not have infinite solutions.

Hence, the value of k for which the system of equations 2x + 3y = 4 and 6x + 27y = 12 has infinite solutions is not exist.

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The modal  number of the pairs of shoes owned by the children is 3 pairs of shoes.

In mathematics, the modal number or mode, is the number that appears on the data set the most times out of all the numbers that appear on a set of numbers or data.

In the case of this line graph on the number of pairs of shoes that children own, the modal number would be 3 pairs of shoes as this is the highest number according to the fact that 5 students own 3 pairs of shows.

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The question is:

What is the modal number of pairs of shoes owned by the children?

A commutative property in math is

Commutativity says that the numbers we are dealing with can be shifted or swapped without affecting the answer. This property applies to addition and multiplication, but not to subtraction and division.

a + b = b + a; where a and b are

integers. Example: 3 + 4 = 4 + 3 = 7.

a × b = b × a; where a and b are

non-zero integers. Example :

2×3 = 3×2 = 6

So this rule simply states that you can change the order of numbers in a question by adding or multiplying them without affecting the answer.

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To be a function, each x-value (or input) can only be used once.  Each x-value (or input) can only be paired with a single y-value (or output).

If any x-value (or input) is paired with more than one y-value (or output), it's not a function.

Top Left:

Not a function

"rock" and "leaf" are paired with two outputs.

Top Right:

Not a function

The one input goes to three outputs.

Bottom Left:

Function

Each x-value/input is used only once.

Bottom Right:

Not a function

The x-value of 4 is used twice and paired with two different y-values.

Yes, 64 a cube number.

64 is the cube of 4.

As, 4 x 4 x 4 = 64

The cubes are made up of values that are obtained by multiplying integers by themselves three or four times. The cube's original number can be found by raising any natural number to the power of three.

Cubes are the numbers that are produced when an integer is multiplied by itself three times. We can find cubes for any number, whether it be an integer or a fraction. In order for the cube of a whole number (x) to produce a perfect cube, the cube root of x3 must equal x. The procedure of locating cubes is thus the opposite of locating the cube root.

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Answer:

f = 21

Step-by-step explanation:

since the rectangles are scaled copies then the ratios of corresponding sides are in proportion, scaled copy to original, so

[tex]\frac{f}{28}[/tex] = [tex]\frac{9}{12}[/tex] ( cross- multiply )

12f = 28 × 9 = 252 ( divide both sides by 12 )

f = 21

Factorization by remarkable identities use the following identities, a²  + 2ab + b² , a²  - 2ab + b² , a²  - b² , and x²  + x (a + b) + ab.

An algebraic expression is factorized when it is written as the product of its factors. These variables, factors, or algebraic expressions might be present.

Use of Identities in Factorization utilizing identities is substantially simpler when employing some of the identities that exist.

Several expressions that need to be factored have the following forms or may be transformed into them: a²  + 2ab + b²,  a²  - 2ab + b² , a²  - b² , and x² + x (a + b) + ab. Using Identities, I, II, III, and IV, it is simple to factorize these expressions.

Using each identity individually, we will study factorization in this part.

(a + b)²  = a²  + 2ab + b²

(a - b)²  = a²  - 2ab + b²

a²  – b²  = (a + b) (a – b)

(x + a) (x + b) = x²  + x (a + b) x + ab

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Complete question:

How to do factorisation by remarkable identities?

By setting one side of a quadratic equation to zero, factoring the resulting polynomial, and then using the Zero Product Property, you can obtain the solutions, or roots, of these equations.

According to the Principle of Zero Products, if ab = 0, then either an or b, or both a and b, are 0, or both are 0. The roots of a function (f (x) can be any function) are the answers to y = f (x) when y = 0. These are the locations where an equation's graph crosses the x-axis.

To use factoring to solve a quadratic equation:

1. Convert the equation to standard form with a zero on one side.

2. Factor the non-zero side.

3. Reset each component to zero.

4. Solve each of the ensuing equations.

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The zeros of a polynomial are the values of x that make the polynomial equal to 0.

To find the zeros, you need to set the equation equal to 0 and solve for x. The multiplicity of a zero is the number of times that the factor (x – zero) is a factor of the polynomial. To find the multiplicity of a zero, you need to find the highest power that x appears in the equation. For example, if the equation is (x-2)2•(x+1)3, then the zero is 2, and the multiplicity is 2.

The zeros of a polynomial are the values of x that make the equation equal to zero. The multiplicity of a zero is the number of times the factor (x - zero) occurs in the equation. To find the zeros and multiplicity of a polynomial, the polynomial needs to be factored into linear factors. The zeros are the x-intercepts of the equation (where the graph crosses the x-axis). The multiplicity is the power of the factor (x - zero). For example, if the equation is (x-2)^2(x-5), the zeros are x=2 and x=5 and the multiplicity of the zeros is 2 for x=2 and 1 for x=5.

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The side length of the square is 18.5 m

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

a = Radical s

where s is the area of the square.

Rewrite the above equation

So, we have the following representation

a √s

Given that the area of a square is 343m

We have

a =√343

Evaluate the root

a =18.5

Hence, the side length is 18.5 meters

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