Factorisation by remarkable identities

No, A right angle is equal to 90 degrees.

In geometry and trigonometry, a right attitude is an angle of precisely ninety stages radians similar to 1 / a 4 turn. If a ray is placed in order that its endpoint is on a line and the adjacent angles are equal, then they may be right angles. The time period is a calque of Latin angulus rectus; here rectus manner "upright", regarding the vertical perpendicular to a horizontal baseline.

Closely related and crucial geometrical concepts are perpendicular strains, which means lines that form right angles at their factor of intersection, and orthogonality, which is the assets of forming right angles, usually implemented to vectors. The presence of a proper angle in a triangle is the defining factor for right triangles, making the proper perspective basic to trigonometry.

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The length of the shadow of Hayden is approximately 32 inches.

Charlie and Hayden are standing outside.  Charlie is 64 inches tall and casts a shadow of 30 inches.

Hayden is 68 inches tall. The length of the shadow of Hayden can be calculated as follows:

Using proportion,

64 / 30 = 68 / x

where

x = length of the shadow of Hayden

Therefore,

64 / 30 = 68 / x

cross multiply

64x = 68 × 30

64x = 2040

divide both sides by 64

x = 2040 / 64

x = 31.875

Hence,

Length of the shadow of Hayden = 32 inches

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Answer:

Rs16.968

Step-by-step explanation:

solution

given

i=3415

r=5%

time=4yrs 3 months

=4.25 yrs

we know,

p=Ix100/tr

= 3415x100/4.25x5

=Rs16.98

©Thank You

Answered By Solution 49

Answer: d

Step-by-step explanation:

-2/5 is the absolute value of - |- 2/5|

An expression is combination of variables, numbers and operators.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.

Given that negative absolute value of negative two fifths.

- |- 2/5|

Solving the modulus we get;

|- 2/5| = 2/5

Then negative,

- 2/5

Hence - 2/5 is the absolute value

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Answer:

√21 is irrational

Step-by-step explanation:

√21 = 4.58257569495584 which is a non-terminating decimal.

Therefore √21 is irrational.

Answer: No, it cannot be a rational number.

Step-by-step explanation:

A rational number is defined to be a whole number (ex. 1, 2, 3) or can be decimals that continuously repeat the digits after the point. In the case of a square root, they can be rational--but this only applies to perfect squares: √100, √64, √16, etc, which would give an outcome of a whole number. Therefore, √21 is not a rational number, as the decimal value is 4.57257, and is not continuous (ex. 3.666666).

The value of x from the given  linear equation is -1 and y = 1

A linear polynomial over a field, from which the coefficients are taken, can be equalized to zero to produce a linear equation.

A line in the Euclidean plane is formed by a linear equation's solutions, and every line may be thought of as the collection of all solutions to a linear equation with two variables. This is where the term "linear" for this class of equations came from

It is given that y = 3x+4 (i) and y = x+2 (ii)

Put equation i) = ii)

Then, we get 3x+4 = x+2

2x = -2

x = -1.

Put the value of x in equation ii)

y = -1+2

y = 1

Hence, the value of x from the given  linear equation is -1 and y = 1

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So the value of x is 4.8

15x + 48= 120

Now we send the 48 on the right side.

15x= 120-48.

Here we subtract 48 from 120 we get

15x= 72

In the next step we divide the both sides with 15

15x/15= 72/15

x=4.8

So the value of x is 4.8  

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The volume of a rectangular prism is given by the product of its length, width, and height, which is V = l * w * h, where l is the length, w is the width, and h is the height.

We are given that the volume of the prism is 3w^3 + 14w^2 + 8w. We can use this information to find the height of the prism by dividing the volume by the product of the length and width.

We know that the length of the prism is 2 more than three times the width (l = 3w + 2). Therefore, the product of the length and width is l*w = (3w + 2) * w = 3w^2 + 2w

Now we can divide the volume by the product of the length and width to find the height of the prism:

V / (l * w) = (3w^3 + 14w^2 + 8w) / (3w^2 + 2w) = 3w + 14 + 8/3w^2 + 2w

So, the height of the prism is 3w + 14 + 8/3w^2 + 2w

Which is a simplified expression for the height of the prism, in terms of the width.

Answer:

20 times

Step-by-step explanation:

40 / 2 = 20?? sorry if im wrong

The hypotenuse is the longest side of a triangle which is opposite to the right angle.

A right triangle's hypotenuse is always the side that faces the right angle. This side is longest in a right triangle. The other two sides are those that are opposed and close by. The labels on these sides relate to an angle.

The word "hypotenuse," which refers to the longest side, is derived from two Greek roots that mean "to stretch." One side is across from another at a particular angle. The non-hypotenuse side that lies next to a particular angle is known as the neighboring side.

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Answer:

84

Step-by-step explanation:

V = IWH

V = (6)(7)(2)

[84]

Answer:

0.456 kg

Step-by-step explanation:

Answer:

I thought it was 61 too but I guess it's 121

Step-by-step explanation:

-9 + 10^2 - [-55/11] x (-6)

( - [-55/11] x (-6) ) do this first so [55/11] x (6)

then its -9 + 10^2 + [55/11] x (6)

             -9 + 100 + [5] x (6)

                      91 + 30

                          121

Answer:738

Step-by-step explanation:

The value of the expression as given in the task content is; 28.

It follows from the task content that the value of the expression is to be determined given the parameters for m and n.

Since the given expression is; | m² - 7 | + n²

Therefore, when m = -2 and n = 5, we have that;

| (-2)² - 7 | + 5²

= | 4 - 7 | + 25

= | -3 | + 25

= 3 + 25

= 28.

Ultimately, the value of the expression according to the given parameters is; 28.

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Answer:

In a right rectangular prism, a cross section can be cut on a slant to produce a variety of additional shapes. Depending on the angle of the cut, the cross section can be a triangle, quadrilateral, pentagon, or hexagon. The maximum number of "sides" of a cross section (plane section) equals the number of faces (surfaces) of the solid

Answer:

a rectangle

Step-by-step explanation:

When a geometric plane slices a prism so that the cut is parallel to the plane of the base, the cross section will have the shape of the base. So, in the case of a right rectangular prism, the cross section is a rectangle.

The expression (3z⁴)² is equivalent to 9z⁸

An equation is an expression showing the relationship between numbers and variables.

The law of exponents states that raising a number with an exponent is equal to multiplying the exponent times the power. It is given as:

(xᵃ)ᵇ = xᵃᵇ

Given that:

(3z⁴)²

Applying the law of exponents:

= (3)²(z⁴)²

= 9z⁸

(3z⁴)² is equal to 9z⁸

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Answer: x - 15

Step-by-step explanation:

The answer is x - 15

Answer:

x-15

Step-by-step explanation:

the triangles can be proved similar by AA congruence.

What is congruent of the triangle?

The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.

Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."

As both the triangles are right angle so the left side triangle the angles are 90, 54 and 38.

Similarly for the right-sided triangle again the angles are 90, 54 and 38.

Hence the triangles can be proved similar by AA congruence.

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Answer:

AA

Step-by-step explanation:

yes

Its called quantitative variables.

Numerical measures of individuals are including:

These are examples of quantitative variables because their values can be added, subtracted, and mathematically manipulated to provide meaningful results.

The primary numerical measure for qualitative data is called the proportion, and it is expressed as a percentage of the total data values in each category. The most frequent numerical measurements for quantitative data are the mean, median, mode, range, variance, and standard deviation. Other numerical measures include the percentiles and range.

The quantitative variables offer numerical measurements of the people being studied. On the values of a quantitative variable, arithmetic operations such as addition and subtraction can be done, and the resulting meaningful results can be interpreted in a variety of ways.

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The Parallel lines never intersect, but they must be in the same plane and the perpendicular lines intersect at right angle and must be coplanar .

The Parallel lines are defined as the two lines which are in the same plane that are at equal distance from each other and never intersect or meet .

The Characteristics are :

(i) Parallel liens are always parallel and are at equidistant from each other. (ii) Parallel lines are non-intersecting lines.

(iii) We can say that Parallel lines meet at infinity.

The Perpendicular lines are formed when the two lines meet each other at a right angle or 90 degrees.

The Characteristics are :

(i) The Perpendicular lines always intersect at the right angle.

(ii) If the two lines are perpendicular to a same line, then they both are said to be parallel to each other and never intersect.

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Yes. There is the square root of 1. The square root of 1 is 1. The square root of 1 is always taken with positive sign. Square root of 1 is a rational number.

The square root of any number is an inverse mathematical operation of a square. square root is the the value which gives the number when it is multiplied by itself. The symbol √ is used to indicate the square root. A number is said to be a rational number that can be made by dividing an integer by an integer. It can be written as a fraction. There are so many ways to find square roots. whose square and the square root are equal is 1. It is neither prime nor composite. Square root of 1 is never be a negative number. It always taken as positive. From the natural numbers only perfect squares have square roots and negative numbers aren’t members of the set.

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The original price of the TV is $4691.5

percentage, a relative value indicating hundredth parts of any quantity.

Given that You walk into a store and see a sign that says "Tv: 47% off, only pay $1,500 today!"

We have to find the original price of the TV.

Convert 47% to decimal value.

47/100=0.47

Now multiply 0.47 with x which gives 1500

0.47x=1500

Divide both sides by 0.47

x=1500/0.47

x=$3191.48

Now add $1500 and $3191.5 to find the original price.

1500+3191.5

$4691.5

Hence, the original price of the TV is $4691.5

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The value of log 2 to the base 10 is  0.3010.

                 [tex]log_1_02[/tex] = 0.3010.

Now, According to the question:

The value of log 2, to the base 10, is 0.301. The log function or logarithm function is used in most mathematical problems that hold the exponential functions. Log functions are used to eliminate the exponential functions when the equation includes exponential values.

The logarithmic function is defined by:

                    if [tex]log_ab[/tex]= x, then [tex]a^x[/tex] = b.

Where,

x is the logarithm of a number ‘b.’

‘a’ is the base of the log function.

Now,

Let us discuss how to find the value of log 2 using a common log function and natural log function.

Value of  [tex]log_1_02[/tex]

The log function of 2 to the base 10 is denoted by “ [tex]log_1_02[/tex]”.

According to the definition of the logarithmic function,

Base, a = 10 and [tex]10^x[/tex]= b

With the use of logarithm table, the value of log 2 to the base 10 is given by 0.3010.

                 [tex]log_1_02[/tex] = 0.3010

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This indicates that Rio has advanced 3 steps from his starting position.

Rio has now advanced five steps from his starting position.

8 backward steps.

Rio has moved 5 - 8 = - 3 steps from his starting place, according to this calculation.

Rio has now advanced (-3 + 9) = 6 steps from his starting place.

3 backward steps.

This indicates that Rio has advanced 6 – 3 = 3 steps from his starting position.

Note: Include the stages as you proceed.

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N(b) =75 because p(b) =n(b) /n(s)

0.75=n(b)/100

n(b)=0.75*100=75

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The equation which represents the same line as the points in the table is y = -3/4 x + 2. (Option C)

The equation of the points given in the table can be determined by using the slope-intercept form which is given by:

y = mx + b

where m is the slope of the line and b is the y-intercept.

The slope of the line can be determined by:

m = rise/run = Δy/ Δx = (y2 – y1)/(x2 – x1)

Hence, taking two points from the table say (-4, 5) and (0, 2)

m = (2 – 5)/(0 – (-4)) = -3/4

y intercept is the value of y when x = 0

From the table, y-intercept b = 2

Hence, the equation of the line is: y = -3/4 x + 2

Note: The question is incomplete. The complete question is attached.

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Answer:

(a) 7.68 dollars

(b) 1927.07 pesos

Step-by-step explanation:

Setting up a conversion factor will be helpful in helping us solve this problem. A conversion factor shows the relationship between two different units, and and is used to convert from one unit to the other.

Our conversion factor is 1 U.S. Dollar = 19.61 Mexican pesos. To convert units, we can turn the conversion factor into a ratio (U.S. dollar ÷ 19.61 Mexican pesos or vice versa) and then multiply the given amount by the ratio. The unit that we want to end up with should always be in the numerator, and the unit we want to convert from should always cancel out in the denominator. This will be demonstrated when we solve the problems below:

(a) We want to convert from pesos to dollars, so we will multiply by the conversion factor (1 dollar / 19.61 pesos).

(b) Now we want to convert from dollars to pesos, so we will multiply by the conversion factor (19.61 pesos / 1 dollar).