What is a solution set in math?.

Step-by-step explanation:

58 = 2(l+b)

58 = 2(x+x)+5

58 = 2x + 5

2x = 58-5

2x = 53

x = 53/2

x = 26.5

So, length = 26.5 + 5 = 31.5

Hence, the length and breadth are 31.5 and 26.5 respectively.

The two triangles in this problem are similar, and the reason for their similarity is given as follows: AA.

Similar triangles are triangle that share these following two features:

The two right triangles in this problem are similar, as they have two common angle measures, given as follows:

As the angles have two common angle measures, the reason is given as follows:

AA.

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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

Answer:270

Step-by-step explanation:

We have to find (f/g)(5). Therefore, (f/g)(5) is 270.

Answer:738

Step-by-step explanation:

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 interior angle measurement of a regular polygon with 42 sides is 150 degrees.

The interior angle measure of a regular polygon is determined by the formula (n-2)*180/n, where n is the number of sides of the polygon. In the case of a regular polygon with 42 sides, this formula can be expressed as (42-2)*180/42, which simplifies to 150 degrees. Therefore, the interior angle measure of a regular polygon with 42 sides is 150 degrees. This means that each interior angle of the polygon is 150 degrees. The exterior angle measure of a regular polygon with 42 sides would be 10 degrees, which can be calculated by subtracting the interior angle measure from 180 degrees. Knowing the angle measure of both the interior and exterior angles of a regular polygon with 42 sides is useful for a variety of applications, such as modeling or designing.

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The quotient of the expression -6x²y + 12x² + 15zy - 15 divided by -3 is 2x²y - 4x² - 5zy + 5

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

quotient of  -62"y' + 12x2? 15zy - 15 divided by -3

Express properly

So, we have

-6x²y + 12x² + 15zy - 15 divided by -3

To solve this question, we simply divide each term of the expression by -3

So, we have the following representation

(-6x²y + 12x² + 15zy - 15)/-3

Evaluate the quotient

2x²y - 4x² - 5zy + 5

Hence, the solution is 2x²y - 4x² - 5zy + 5

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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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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:

√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 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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The highest common factor of 48 and 504​ is 24.

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

The highest common factor or HCF of a group of numbers is the greatest number which divides the given numbers without remainder.

48 = 2 * 24

504 = 2 * 21 * 24

The HCF of 48 and 504 is 24

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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

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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Answer:

84

Step-by-step explanation:

V = IWH

V = (6)(7)(2)

[84]

Answer:

0.456 kg

Step-by-step explanation:

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

The jam recipe that has more strawberry flavor is Recipe A.

In order to determine which recipe has more strawberry flavor, determine how many cups of strawberry is needed for one cup of sugar. In order to do this, divide the cups of strawberry by the cups of sugar.

Cups of strawberry needed for one cup of sugar = cups of strawberry / cups of sugar

Cups of strawberry needed for one cup of sugar in recipe A = 3 ÷ 1/2

3 x 2 = 6  

Cups of strawberry needed for one cup of sugar in recipe B = 5 ÷ 1 = 5

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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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Yes, it is possible to draw a triangle.

This will be done by the property: the sum of two sides of a triangle should be more than the third side.

(5cm + 9cm) =10 cm

14 cm = 10 cm

LHS>RHS

A triangle is possible.

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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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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Since division by zero is not defined, 1/0 is not infinity, and 0/0 is not indeterminate.

We must keep in mind that, except in the case of limitations, the value of 1 divided by 0 is infinite. The phrase "infinity" denotes the size of the number. When it comes to limits, we merely presume that limit x's value tends toward something rather than being equal to anything. We thus treat it as infinite.

Since it is not a real number, infinity is only used to symbolise extraordinarily big real numbers. The result of 1 divided by infinity is 0. The quotient of nonzero real numbers that divide infinity is infinity, and the rule of thumb is that any real number divided by infinity is zero.

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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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The Area of the rectangle is (40x²+ 49x + 15)cm²

The area of a rectangle in geometry is the region covered by the rectangle in a two-dimensional plane.  The area of the rectangle is the region occupied by a rectangle within its four sides or boundaries.

A rectangle is a sort of quadrilateral, a two-dimensional object with four sides and four vertices. The rectangle's four angles are all right angles or equal to 90 degrees. The rectangle's opposite sides are equal and parallel to one other.

Given that,

Length of rectangle=(8x+5)cm

Breadth of rectangle=(5x+3)cm

Area of rectangle=Length×Breadth

Area of rectangle=(8x+5)(5x+3) = (40x²+ 49x + 15)cm²

Therefore, the Area of the rectangle is (40x²+ 49x + 15)cm²

Correct question: A rectangle is (8x+5)cm long and (5x+3)cm broad.

Find its area or perimeter.

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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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Answer:

SQ = 24

PT = 12

<QPR = 23°

Step-by-step explanation:

SQ= 12+12=24

PT=12

<PRS is alternate to <QPR

<QPR=23°

a. The integral to determine the area enclosed by the inner loop is:

A = ∫0^2π2+4sin(θ)dθ

This integral can be solved using the substitution u = 4sin(θ). This will give us the following integral:

A = ∫0^2π2 + udu

Next, we apply the power rule to the integral and solve for A.

A = 2θ + (u^2)/2 | 0^2π

A = 2θ + (4sin(θ)^2)/2 | 0^2π

A = 2π + 4[1 - cos(2θ)]/2 | 0^2π

A = 2π + 2 - cos(2π)

A = 4π - 1

b. To find the area between the loops, we can use the following integral:

A = ∫2^4π2+4sin(θ)dθ

Using the same substitution, we have:

A = ∫2^4π2 + udu

A = 2θ + (u^2)/2 | 2^4π

A = 2θ + (4sin(θ)^2)/2 | 2^4π

A = 2π + 4[1 - cos(2θ)]/2 | 2^4π

A = 2π + 2 - cos(4π)

A = 4π + 1

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