Simplify each complex fraction.
3 /x-4 / 1 - 2/x - 4

y varies directly with x and 1/9 is the constant of variation

y = kx                    (where k is a constant)

y = x/9

y = (1/9)x

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.

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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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Answer:

z = 53

Step-by-step explanation:

Comment

The three angles of any triangle add up  to 180o. There are no exceptions to this rule.

Formula

2z + z - 15 + 36 = 180                Combine like terms on the left.

Solution

3z + 21 = 180                              Subtract  21 from both sides

3z + 21 - 21 = 180 - 21                Combine

3z = 159                                      Divide both sides by 3

z = 53

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:

[tex]y = \dfrac{5}{2}x - 7[/tex]

Step-by-step explanation:

Step-by-step explanation:

Take any two points (x1, y1) and (x2, y2) from the table

Slope intercept equation is y = mx + b where m is slope and b = y-intercept

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

In this case

Let's choose the last two points

These are (6,  8) and (8, 13)

Slope = (13 - 8)/(8-6) = 5/2

So the equation is y = (5/2)x + b

To compute b, plug in x, y values for any point and solve for b

Choose the first point (0, -7)

Plug in:

-7 = (5/2)(0) + b

-7 = 0 + b or b = -7

So the equation of the line is
[tex]y = \dfrac{5}{2}x - 7[/tex]

We can verify by computing the y value for another point and seeing it agrees with table values

Choose point (4, 3)

y = 5/2 x 4 - 7

= 10 - 7 = 3

which agrees with the table value for y which is 3 when x = 4

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 sum of all the angles of the polygon is 8640 and each angle is measured at 172.8

The sum of all the angles of a polygon having n sides is given by the formula (n-2)* 180

To find out the sum of all the interior angles of a polygon we need to put the value of n with the number of sides of polygon which is 50

Sum of all interior angles of the given polygon = (50-2)*180

            = 48*180

            =8640

To find out the degree of each angle of the given regular polygon is the division of the sum of interior angles of the polygon with number of sides of the polygon = 8640/50  which is 172.8

The correct question is - Calculate the sum of the interior angles of a polygon with 50 sides: (i)in degrees (ii) degree of each angle of the polygon

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2500\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\dotfill &1\\ t=years\dotfill &15 \end{cases} \\\\\\ A=2500\left(1+\frac{0.055}{1}\right)^{1\cdot 15} \implies A=2500(1.055)^{15}\implies A \approx 5581.19[/tex]

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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The equation of the line in standard form passing through the point (-4 , 2) with slope equal to 3 is 3x - y = -14.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Using the point slope form, plug in the values of the slope and the point to set up the equation.

(y - y1) = m(x - x1)

where m = 3 and (x1 , y1) = (-4 , 2)

(y - 2) = 3(x - -4)

y - 2 = 3(x + 4)

y - 2 = 3x + 12

To write the equation in standard form, arrange the variable(s) in one side and the constant(s) in the other.

y - 2 = 3x + 12

3x - y = -2 -12

3x - y = -14

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A percentage in mathematics is a number or ratio that can be expressed as a fraction of 100.

The percent of the given number 19 % of 82 is 15.58.

A percentage in mathematics is a number or ratio that can be expressed as a fraction of 100. The term percent comes from the Latin "per centum" which means per hundred. The symbol percentage is used to represent percentage.

Let the equation be 19 % of 82

Percentage = (value/total value) × 100 %.

Since, finding the fraction of a number is same as multiplying the fraction with the number, we have

19 % of 82 = 19/100 of 82

19/100 × 82 = 15.58

Therefore, the percent of the given number19 % of 82 is 15.58.

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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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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]

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 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:

Givens

Let the angle = x

Let it's supplement = 180 - x

Equation

x + 9 = 2*(180 - x)                  Remove the brackets

Solution

x + 9 = 360 - 2x                     Add 2x to both sides

x + 2x + 9 = 360 - 2x + 2x     Combine

3x + 9 = 360                          Subtract 9 from both sides

3x + 9-9 = 360-9                   Combine

3x = 351                                 Divide both sides by 3

3x/3=351/3

x = 117

Answer

Given angle = 117

Supplement = 180 - 117 = 63

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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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]

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:

Step-by-step explanation:

This number would be between 3,300 and 3,400.  Which number would 3387 be closer to?  3350 would be right in the middle and 3387would be larger than 3350 so 3387 is closer to 3400.

The initial cost of the purchases is  $40.81.

The initial cost of the purchases is the sum of the total cost of each items bought. The total cost of each item bought is the product of the size of the items bought and their price.

The mathematical operations that would be used to determine the initial cost are addition and multiplication. Addition is the process of determining the product of two or more numbers. Multiplication is the process of determining the product of two or more numbers.

Total cost of cheese = 1/4 x 2.49 = $0.62

Total cost of Slice ham = 2.5 x 3.29 = $8.23

Total cost of 4 loaves of bread = 4 x 2.89 = $11.56

Total cost of 5 bags of potato chips = (2 x 3) + $1.95 = $7.95

Total cost of Salsa = 3 x 4.15 = $12.45

The initial cost of the purchase : $12.45+ $7.95 + $11.56 + $8.23 + $0.62 = $40.81

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Answer:

7.2 units

Step-by-step explanation:

Hello, and welcome to Brainly!

You are sometimes offered to find the distances between two points on a graph. But how are we to do this you ask?

The distance formula measures the distance in units from point A to point B. The formula is d=[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] where Point A is depicted as [tex](x_1, y_1)[/tex] and Point B is depicted as [tex](x_2, y_2)[/tex].

To start this problem, let's label a random point as A, and the other as B.

A: (-9, 3) where [tex]x_1=-9, y_1=3[/tex]
B: (-7, -4) where [tex]x_2=-7, y_2=-4[/tex]

Let's use the distance formula to solve this distance. Fill in the known variables.

d=[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

d=[tex]\sqrt{(-7--9)^2+(-4-3)^2}[/tex]

[tex]d=\sqrt{(2)^2+(-7)^2}[/tex]                 Note that (-7--9) cancels out the two negatives and turns into (-7+9), which is 2.
[tex]d=\sqrt{4+49} \\d=\sqrt{53} \\d=7.2[/tex]

The distance between these two points is 7.2 units.

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

Answer: 122 I'm think I'm not sure tho

Step-by-step explanation:

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 area inside of the home is [tex]452.16 ft^2[/tex]

It is given that circular dwelling has a diameter of 24 feet then , radius will be [tex]r=\frac{24}{2} =12 \ feet[/tex]

Putting r = 12 feet in equation (1) , we get

       [tex]A=3.14\times( 12) ^2\\A=3.14\times144\\A= 452.16 ft^2[/tex]

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Answer:

C

Step-by-step explanation:

hope this works for you :)

The value of x in the equation -2/5 * x = 10 is x = -25

The expression is given as

-2/5 * x = 10

Express the fraction as decimal

So, we have

-0.4 * x = 10

Evaluate the product

So, we have

-0.4x = 10

Divide both sides of the equation by -0.4

So, we have

-0.4/-0.4x = 10/-0.4

Evaluate the quotient

So, we have

x = 10/-0.4

Evaluate the quotient

So, we have

x = -25

Hence, the value of x in the equation -2/5 * x = 10 is x = -25

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