Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 21 to 49

52 tiles are there in the 25th figure in this pattern.

A pattern is described as a series of recurring symbols, figures, or numbers. Any form of event or object can be related to a pattern.

A pattern has a rule that specifies which items fall within the pattern's umbrella and which do not.

A pattern in mathematics is a recurring arrangement of numbers, forms, colors, and other elements.

Any kind of event or object can be connected to the Pattern.

A pattern is referred to as a rule or a way in which a group of numbers is related to one another.

Sometimes a pattern is also referred to as a sequence.

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The required value of the constant of proportion is 2.

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of constant of variation

When a quantity varies directly with others, then we have a relation, y = kx, where k is the constant of the proportion     —-- 1

Given the relation is y = 2x            —-- 2

On comparing both the equation 1 and 2, we have,

k = 2

Hence, the required value of constant of variation is 2.

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Answer:  No, the sides do not form a right triangle.

============================================================

Explanation:

Let c = 20 be the largest or longest side. If we had a right triangle, then this side is the hypotenuse.

a = 14 and b = 15 are the other sides in either order.

Plug the values into the pythagorean theorem equation. Evaluate each side separately until getting a single numeric value.

[tex]a^2 + b^2 = c^2\\\\14^2 + 15^2 = 20^2\\\\196 + 225 = 400\\\\421 = 400\\\\[/tex]

The last equation is false, so the first equation is false for those a,b,c values mentioned. This shows us we do not have a right triangle.

For more information, check out the pythagorean theorem converse.

no

Does a triangle with sides 14, 15 and 20 can form a right triangle?

To check if a triangle is a right one, we can follow these steps:

Step 1: Take the longest side as the candidate for the hypotenuse (c). Here, the longest side is that of lenght 20. So, c = 20. The other sides are leg A (a) and leg B (b). In this case we can assume that a = 14 and b = 15 .

Step 2: Now plug in these values in the formula below to check its validity:

c2 = a2 + b2

202 = 142 + 152

400 ≠ 421

As both sides of the above equation are not equal, we can surely say that the triangle [14 15 20] is NOT a right triangle.

The expression for diagonal of a rectangle is d= √ (a2 + b2).

Consider a rectangle PQRS in which let PR and QS be the diagonals.

Then, there are two triangles obtained and they are ΔRPS and ΔRPQ

The angle that is common between the two triangles is ∠p

The common side is PQ

Hence, PS=QR

Therefore, ΔRPS≅ΔRPQ

Also, QS=PR the diagonals of a rectangle are equal in length.

By using the Pythagorean theorem, the length of the diagonal of rectangle is                   d = √ (l2 + w2)

From the given data the length of the rectangle(l) PQ =a

The width of the rectangle(w) QR = b

Hence the expression for diagonal of rectangle is d= √ (a2 + b2).

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Answer:

The formula for a rectangle's diagonal is d=(a2 + b2).

Step-by-step explanation:

Let PR and QS be the diagonals of the rectangle PQRS.

Following that, two triangles—RPS and RPQ—are obtained.

The common angle between the two triangles is p.

PQ is the common side.

So, PS=QR.

Consequently, RPSRPQ

A rectangle's diagonals are also equal in length since QS=PR.

The Pythagorean theorem shows that d = (l2 + w2) is the length of the diagonal of a rectangle.

The length of the rectangle (l) PQ =a from the provided data

Rectangular width (w) = QR = b

Therefore, d=(a2 + b2) is the expression for the diagonal of a rectangle.

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When certain mapping in the plane has the following property: Each pair of points A and B is mapped to another pair or points A' B' such that quadrilateral AA'BB' is parallelogram, the transformation is reflection.

Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.

When a figure is translated, it is moved in any direction.

Flipping a figure over a line is called reflection.

Rotation is the process of turning a figure a specific amount around a point.

When we dilate a figure, we increase or decrease its size.

In this case, since the figure is flipped, over a line is called reflection.

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By substitution, the solution of the system of equations, 4p + 2q = 8 and q = 2p + 1, is (p , q) = (3/4 , 5/2).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in p and q,

4p + 2q = 8     (equation 1)

q = 2p + 1     (equation 2)

Since the second equation is already expressed in q in terms of p, substitute the second equation to the first equation.

4p + 2q = 8     (equation 1)

4p + 2(2p + 1) = 8

4p + 4p + 2 = 8

Combining all terms containing the variable p on one side and the constants on the other side of the equality, and solving for p.

4p + 4p + 2 = 8

4p + 4p = 8 - 2

8p = 6

p = 6/8

p = 3/4

Substitute the value of p in the second equation and solve for q.

q = 2p + 1

q = 2(3/4) + 1

q = 6/4 + 1

q = 5/2

Hence, the solution of the given system of equations is (p , q) = (3/4 , 5/2).

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The solution of the given equation 7y + 4 = 3 - 2y is 29/2.

According to the given qestion.

We have a linear equation in one variable 7y + 4 = 3 - 2y.

So, the solution of the given linear equation in one variable  7y + 4 = 3 - 2y is given by

7y + 4 = 3 - 2y

⇒ 7y + 2y + 4 = 3    ( adding 2y both the sides)

⇒ 9y  = 3 - 4

⇒ 9y = -1

⇒ y = -1/9

Now, we will check whether y = -1/9 is the solution of the given equation 7y + 4 = 3 - 2y  or not.

Thereofore,

LHS

= 7(-1/9) + 4

= -7/9 + 4

= -7 + 36/9

= 29/9

Similarly

RHS

= 3 - 2(-1/9)

= 3 + 2/9

= (27 + 2)/9

= 29/2

Here, LHS = RHS

Hence, the solution of the given equation 7y + 4 = 3 - 2y is 29/2.

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The given sequence 10,20,30,40, ........... forms an arithmetic sequence. The common difference is found to be 10.

The difference between the two mathematical orders is a fixed value in Arithmetic Progression (AP). Another name for it is Arithmetic Sequence.

We'd come around a few specific words in AP that were labeled as:

Some formulas related to AP are-

Now, for the stated sequence is: 10,20,30,40, ...........

Let us suppose the first term is'a₁' = 10.

Let us suppose 'a₂' = 20 is the second term.

Let us suppose the third term is 'a₃' = 30.

Let us suppose the fourth term be 'a₄' = 40.

d = a₂ - a₁      

Substitute the values;

d = 20 - 10 = 10       ........(equation 1)

Now consider the other set;

d = a₃ - a₂    

d = 30 - 20 = 10      .......(equation 2)

Comparing equation 1 and 2, the common difference is same.

Thus, the given sequence forms an AP.

The common difference is found to be 10.

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Answer:

9+8-6+6=29

Step-by-step explanation:

MATHAMATICS please check this i don't know x or×

The number of different 3-digit number if each of those digits is only allowed to be used once is 60

The digits are given as:

2, 4, 5, 7, 9

There are 5 digits represented in the above list

If each of those digits is only allowed to be used once, then we have the following possibilities

The number of 3-digit number codes is

Number =  5 * 4 * 3

Evaluate the product

Number = 60

Hence, the number of different 3-digit number if each of those digits is only allowed to be used once is 60

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The  Δ A B C with base AB that is a unit long has been drawn below.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

Δ A B C is a isosceles triangle.

Now isosceles triangle is a triangle whose two sides are equal.

In the Δ A B C, AC = BC

Hence "The  Δ A B C with base AB that is a unit long has been drawn below".

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Answer:

[tex]f(x)=\frac{1}{2}x+-6[/tex] or y=1/2x+-6

Step-by-step explanation:

You can use any two points on a line to find slope. For example, I used:

(x1, y1) 2, -5

(x2, y2) 4, -4

To find slope, the following formula is needed:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Input our values:

[tex]m=\frac{(-4)-(-5)}{4-2}[/tex] which means m=1/2

b is equal to y-intercept which is -6

The equation is:

[tex]y=\frac{1}{2}x+-6[/tex]

to get the equation of any straight line, we simply need two points off of it, let's use the points from the picture below.

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{(-8)}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{(-4)}}} \implies \cfrac{-4 +8}{4 +4} \implies \cfrac{ 4 }{ 8 }\implies \cfrac{1}{2}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-8)}=\stackrel{m}{\cfrac{1}{2}}(x-\stackrel{x_1}{(-4)}) \implies y +8= \cfrac{1}{2} (x +4) \\\\\\ y+8=\cfrac{1}{2}x+2\implies {\LARGE \begin{array}{llll} y=\cfrac{1}{2}x-6 \end{array}}[/tex]

Hence, proved the reflective property of segment congruence.

We need to write a two-column proof for the property reflective property of segment congruence.

In geometry, the reflexive property of congruence states that an angle, line segment, or shape is always congruent to itself.

Two angles are congruent if and only if they have equal measures. Two segments are congruent if and only if they have equal measures. Two triangles are congruent if and only if all corresponding angles and sides are congruent.

Consider, XY≅AB

Prove that, AB≅XY

Proof: XY≅AB (given)

XY=AB (Definition of the congruent segment)

AB=XY (Symmetric property of equality)

AB≅XY (Definition of the congruent segment)

Hence, proved the reflective property of segment congruence.

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The range of given set of data is 15.

We have a set of numbers.

We have to determine its range.

The range is the difference between the smallest and highest number in a list.

According to the question, we have the following set of elements -

40, 41, 52, 54, 50, 39, 43, 54.

Arrange it in ascending order -

39  40  41  43  50  52  54  54

Now -

Range = Highest number - Lowest number

Range = 54 - 39

Range = 15

Hence, the range of given set of data is 15.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Question reads..}[/tex]

[tex]\large\boxed{\text{What is the range of 40, 41, 52, 54, 50, 39, 43, 54 \bf ?}}[/tex]

[tex]\huge\textbf{To find your range, you have to..}}[/tex]

[tex]\large\boxed{\text{You have to find the difference between the largest number in the}}\\\\\large\boxed{\text{data plot from the smallest number in data plot.}}[/tex]

[tex]\huge\textbf{The range formula is..}[/tex]

[tex]\large\boxed{\rm{largest\ number - smallest\ number = range}}[/tex]

[tex]\huge\textbf{The data plot..}[/tex]

[tex]\large\boxed{\rm{40, \ 41, \ 52, \ 54, \ 50, \ 39, \ 43, \ 54}}[/tex]

[tex]\huge\textbf{Now let us answer the question..}[/tex]

[tex]\large\boxed{\rm{40, \ 41, \ 52, \ 54, \ 50, \ 39, \ 43, \ 54}}\\\\\large\boxed{\rm{The\ largest\ number\ in \ the \ plot\rightarrow 54}}\\\\\large\boxed{\rm{The \ smallest \ number\ in\ the\ data plot\rightarrow 39}}[/tex]

[tex]\huge\textbf{Your equation should be:}[/tex]

[tex]\large\boxed{\rm{54 - 39}}}\\\\\large\boxed{\rm{Simplify \ it}}\\\\\large\boxed{\rightarrow 15}}[/tex]

[tex]\huge\textbf{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{15}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

y - 9.1x - 3.6 = 0 is an equation of the line y=9.1 x+3.6 in standard form

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

Standard form of an equation is given as ax + by + c = 0

Here is given

⇒ y = 9.1 x+3.6

⇒ y - 9.1x - 3.6 = 0

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The measures of m [tex]\angle[/tex] A = 30º, m [tex]\angle[/tex] D = 30º, measure of arc AC = 60º and measure of arc BD = 60º.

The arcs exists congruent because they have equal measures.

Congruent arcs are arcs on circles that have the same degree measure and have congruent radii. A minor arc is one with a degree measure between 0º and 180º. A semicircle is an arc with a degree measure of 180º. A major arc is one with a degree measure between 180º and 360º.

If two arcs have the same length and are segments of congruent circles, they are congruent arcs. Because any circle is congruent to itself, two arcs of equal length that are part of the same circle are congruent arcs.

The measures of m [tex]\angle[/tex] A = 30º, m [tex]\angle[/tex] D = 30º, measure of arc AC = 60º and measure of arc BD = 60º.

The arcs exists congruent because they have equal measures.

The complete question is:

In this problem, you will investigate the relationship between the arcs of a circle that are cut by two parallel chords.

Use a protractor to find m \angle A and m \angle D. Then determine the measure of arc AC and BD. What is true about these arcs? Explain

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Answer:

Step-by-step explanation:

a. 18² and 19² and 6³

b. 26² and 27² and 9³

c. 29² and 30²

d. 35² and 36² and 11³

The value of the linear equation 12x+10=54-10x, X=22.

An algebraic equation of the form y=mx+b is referred to as a linear equation involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a linear equation of two variables, where y and x are the variables.

Given that,

Moira chooses 10x on the left side of the equation,

And on the right side she chooses 10x

Given equation is 12x+10=54-10x

12x+10-10=54-10x-10 (subtract -10 on both sides)

12x=44-10x

12x-10x=44 (sending 10x on left side of the equation)

2x=44

X=22

Therefore the value of linear equation 12x+10=54-10x is X=22.

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Put in 2 of the second spoon (1 teaspoon) and 1 of the third spoon (1/2 teaspoon).

The required first term is 100 and the common ratio is 1.1 and the 11th term is 285.

Geometric progression is a sequence of series whose ratio with adjacent values remains the same.

Here,
Orignal price iss 100
Appreciates 10% each year,
So price on next year = 100 + 100 * 10 / 100
So the price next year = 110
Similarly price on the next year becomes in a series = 100, 110, 121,
Now, the first term of geometric progression = 100
Common difference = 110 / 100 = 1.1
11 the term = 100 * 1.1 ¹¹
11the term = 285

Thus, the required first term is 100 and the common ratio is 1.1 and the 11th term is 285.

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We can make an unlimited number of obtuse triangles when given two sides but no angle measurement, such as a = 10 and b = 8.

For illustration:

If we have side lengths of 10 and 8 and an angle value of 90 to 360 degrees, how many different obtuse triangles can we create?

Make a triangle with sides of 10 and 8 metres, an angle of 120 degrees, and a third side that may be adjusted to your preferred length using a protractor. You have built a triangle.

By changing the length and angle of the third side, we can produce a completely different triangle that is similar to this one.

It's imperative to keep in mind that you choose the side lengths and angle. It's implied that you could make a different decision. By employing the same angles, an unlimited number of different triangles can be formed.

Thus, using a single angle and a single side length, we may create an unlimited number of triangles.

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Step-by-step explanation:

b(h) = 212 - 1.72×h/1000

what is h, when b = 190 ?

190 = 212 - 1.72×h/1000

-22 = -1.72×h/1000

22000 = 1.72×h

h = 22000/1.72 = 12,790.69767... ≈ 12,791 ft

The height of the Kudzu vine after 15 days is 8 m.

The initial measurement of length of Kudzu vine =

0.5 metres

Length of the Kudzu vine after seven days = 4 m

[tex]Let \: the \: (x _{1},y _{1}) =(0 ,0.5)[/tex]

[tex]Let \: the \: (x _{2},y _{2}) =( 7,4)[/tex]

The rate of the growth of the Kudzu vine per day is,

The slope formula is,

[tex]m = \frac{(y _{2} - y _{1}) }{ (x _{2} - x _{1}) }[/tex]

[tex]m = \frac{4 - 0.5}{7 - 0} [/tex]

[tex] = \frac{3.5}{7} [/tex]

= 0.5

Rate of growth of Kudzu vine per day is 0.5 per day.

Let the height of the Kudzu vine after fifteen days be y2.

The height of the Kudzu vine after fifteen days is,

[tex]m = \frac{(y _{2} - y _{1}) }{ (x _{2} - x _{1}) }[/tex]

[tex]0.5= \frac{y _{2} - 0.5 }{15 - 0} [/tex]

Now, multiplying 15 on both the sides. [tex]7.5 = y _{2} - 0.5[/tex]

[tex]y _{2} = 8[/tex]

Therefore, the height of the Kudzu vine after fifteen days is 8 m.

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Answer:

13

Step-by-step explanation:

divide the 24 by two so you can find one side of the two right triangles. you get 12. now that you have 12 and the 5 from the other side use a^2+b^2=c^2 to solve for the missing side where a=5 b=12 and c=? so 12 squares is 144 and 5 squared is 25 so add then up and you get 169=c^2. lastly square the 169 and you end up with 13 :)

Answer:

No

Step-by-step explanation:

-2(4-x) = 2x+8

Distribute the -2 on the left hand side

-2 *4 -2*-x = 2x+8

-8 +2x = 2x+8

They are not equal so it is not an identity

Answer: not an idenfity

Step-by-step explanation:

[tex]-2(4-x)=2x+8\\(-2)(4)+(-2)(-x)=2x+8\\-8+2x=2x+8\\2x-8\neq 2x+8[/tex]

Answer: Maybe D, I'm not sure

Step-by-step explanation:

It is true that the expressions √3 + 5 and √2x/3y  cannot be simplified while the expression (x + y)3/2 can be simplified

Expressions are mathematical statements that are represented by variables, coefficients and operators

Expression 1

The expression is given as

√3 + 5

The above expression is a combination of a radical expression and an integer

The radical expression √3 cannot be simplified

This means that the expression √3 + 5 cannot be simplified

Hence, the expression √3 + 5  cannot be simplified

Expression 2

The expression is given as

√2x/3y

The above expression is a combination of radical expressions

However, the radical expressions do not have a common factor

This means that the expression √2x/3y cannot be simplified

Hence, the expression √2x/3y  cannot be simplified

Expression 3

The expression is given as

(x + y)3/2

Open the bracket

(x + y)3/2 = 3/2x + 3/2y

This means that the expression (x + y)3/2 can be simplified

Hence, the expression (x + y)3/2 can be simplified

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Answer: f(2)=-10     f(-3)=15

Step-by-step explanation:

Let the number conceived be x.

Hence,

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

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

f(x)=-5x

Thus,

f(2)=(-5)(2)

f(2)=-10

f(-3)=(-5)*(-3)

f(-3)=15

The three types of congruence transformations are rotation, reflection, and translation is TRUE.

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

Reflection is a mirror image of a graph about any axis.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

If we rotate a triangle by any angle in any direction either clockwise or anti the dimension will remain the same so it will be congruent.

If we reflect a triangle about any axis then also it will remain the same so it will be congruent.

If we transform by any amount either horizontal or vertical then it will remain the same so it will be congruent.

Hence "The three types of congruence transformations are rotation, reflection, and translation is TRUE".

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The perimeter of parallelogram BCDE is 38 .

The plotting of the points B(2,-8), C(2, 1), D(-3, 5), and E(-3,-4) is given below.

Using distance formula , put [tex]x_1=2, \ y_1 =-8[/tex] and [tex]x_2=2, \ y_2 =1[/tex] in equation (1) , we get BC

      [tex]BC=\sqrt{(2-2)^2+(1-(-8))^2} \\BC=\sqrt{0+(1+8)^2} \\BC=\sqrt{(9)^2} \\BC= 9[/tex]

Using distance formula , put [tex]x_1=2, \ y_1 =1[/tex] and [tex]x_2=-3, \ y_2 =5[/tex] in equation (1) ,we get CD

       [tex]CD=\sqrt{(-3-2)^2+(5-1)^2} \\CD=\sqrt{(-5)^2+(4)^2} \\CD=\sqrt{25+16} \\CD=\sqrt{100} \\CD=10[/tex]

Using distance formula , put [tex]x_1=-3, \ y_1 =5[/tex] and [tex]x_2=-3, \ y_2 =-4[/tex] in equation (1) ,we get DE

       [tex]DE=\sqrt{(-3-(-3))^2+(-4-5)^2} \\DE=\sqrt{(-3+3)^2+(-9)^2} \\DE=\sqrt{0+81} \\DE=\sqrt{81} \\DE=9[/tex]

Using distance formula , put [tex]x_1=2, \ y_1 =-8[/tex] and [tex]x_2=-3, \ y_2 =-4[/tex] in equation (1) ,we get BE

     [tex]BE=\sqrt{(-3-2)^2+(-4-(-8))^2} \\BE=\sqrt{(-5)^2+(-4+8)^2} \\BE=\sqrt{25+(4)^2} \\BE=\sqrt{25+16} \\BE=\sqrt{100} \\BE=10[/tex]

Perimeter [tex]=10+10+9+9=38[/tex]

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