the characteristics and properties of a linear equation

The expressions for the total length of each segment are x + 1, d + 4, and y + 3.

The total length of the segments will be the sum of the part so the segments.

Let's say a line segment AB is divided into two parts x and y then the expression for the length of the segment will be x + y.

Now,

For the first segment,

The two parts are x and 1.

The expression of the total length of the segment is:

x + 1

For the second segment,

The two parts are d and 4.

Then the expression for the total length of the segment is:

d + 4

For the third segment,

The two parts are y and 3.

Then the expression for the total length of the segment is:

y + 3

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The complete question is mentioned below:

Write the expression that represents the total length of each segment shown.

Answer:

option a is the right answer

Answer:

Step-by-step explanation:

Ok so vertical means straight up and down if you have forgotten so

First lets look at 2x=y no that is not correct because it is not going striagt up and down

The answer is C  so I dont have to go through them all it is C

The missing value of inverse variation  is 2.5

The inverse variation property states that , whenever the product of values of two quantities is a constant value then there is opposite variation between these two corresponding values. Or we can also say that if the productive nature of two corresponding values is constant, then one quantity is inversely varies with second quantity.

Let say if x and y are two values and k is a constant value, then

According to inverse variation

k = xy or y = k/x

In the given question,

Take the order pair (2,5)

As it is an inverse variation, we can substitute it

y=k/x  

5=k/2

K=10

Now find the inverse variation equation

y=k/x

Also, k=10

Solve this equation for the second pair (4,y)

As, y=k/x

   y = 10/4 = 5/2 = 2.5

Therefore, missing value is 2.5

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If Twelve cubes are stacked its surface area is: 36a² and how  would the surface area change if the top two cubes are removed is 6a².

a. Surface area

If the length of one side is a the area of one surface is a²

Hence,

Area=a²

a²(6+6+6+6+6+6)

=36a²

b. Change in surface area change if the top two cubes are removed:

a²(6×2+5×2+4×2)

a²(12 + 10 + 8)

=30a²

Hence,

36a²-30a²

=6a²

Therefore  If Twelve cubes are stacked its surface area is: 36a² and how  would the surface area change if the top two cubes are removed is 6a².

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Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

Anytime something does a 180 rotation it just flips the sign

Example: (-4, -6) 180 rotation (4, 6)

So for yours, it would be (-1, -2) 180 rotation (1, 2)

If you are still confused don't hesitate to ask :)

Answer:

3h - 6

Step-by-step explanation:

→ Minus 2 from both sides

h - 2 = d / 3

→ Multiply both sides by 3

3h - 6 = d

Step-by-step explanation:

h=d/3+2

h=d/5

d=5h

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The numbers that will work are all numbers less than 12

The statement is given as:

One half of a number is more than six less than the same number

Let the number be represented with x

So, the mathematical expression is

1/2x > x - 6

Subtract x from both sides

-1/2x > -6

Multiply both sides by -2

x < 12

Hence, the numbers that will work are all numbers less than 12

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Answer: The Answer is 5+1=5 or B

Step-by-step explanation:

This is because 5+1 does not = 5

the mid point of the points C and D is M = ( 4 , - 1 / 2 ).

We are given the coordinates of the point:

C ( 1 , - 6 )

D ( 7 , 5 )

We need to find the mid point M for it.

Here, we have:

x₁ = 1

x₂ = 7

y₁ = - 6

y₂ = 5

We know that the formula for mid point is given by:

M = ( x₁ + x₂ / 2, y₁ + y₂ / 2 )

Substituting the values, we get that:

M = ( 1 + 7 / 2 , - 6 + 5 / 2 )

M = ( 8 / 2 , - 1 / 2 )

M = ( 4 , - 1 / 2 )

Therefore, we get that, the mid point of the points C and D is M = ( 4 , - 1 / 2 ).

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Answer:

3x-6/2[tex]\sqrt{x-1[/tex]

Step-by-step explanation:

1. first we have to get the denominator the same, so we multiply by [tex]\sqrt{x-1[/tex] to the first fraction top and bottom which leaves as with

3(x-1)/2[tex]\sqrt{x-1[/tex]   -  3/2[tex]\sqrt{x-1[/tex]

- we can expand the numerator of the first fraction which becomes

3x-3/ 2[tex]\sqrt{x-1[/tex]  -  3/2[tex]\sqrt{x-1[/tex]

2. we can now subtract te fraction as we have the same denominator this gives us

3x-6/2[tex]\sqrt{x-1[/tex]

3. your final answer would be  

3x-6/2[tex]\sqrt{x-1[/tex]

{If the question asked to simplify your answer you would rationalize your answer by multiplying top and bottom by [tex]\sqrt{x-1[/tex] to give you the answer of

(3x-6)[tex]\sqrt{x-1[/tex]/2x-2}

The inverse of the function f(x)=√x+6 will be x²-12x+36.

A function that can reverse into another function is known as an inverse function or anti-function.

The given function is,

f(x)=√x+6

As we know inverse of the function is shown as,

y = f(x)

y=√x+6

For inverse function, we have to replace the variable's place value,

x=√y+6

√y=x-6

Squaring both sides,

(√y)²=(x-6)²

y=x²+36-12x

Hence,the inverse of the function f(x)=√x+6 will be x²-12x+36.

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The exponential form of the expression= [tex]y^{8/3}[/tex]

To expresses it in an exponential form we have expression:

[tex]\sqrt[3]{y^{8} }[/tex]

As we have to express as

[tex]a^{m}[/tex]/ [tex]a^{n}[/tex] = [tex]a^{m}[/tex][tex]a^{-n}[/tex]

          = [tex]a^{m-n}[/tex]

From the question we have

[tex]\sqrt[3]{y^{8} }[/tex]

[tex](y^{8}) ^{1/3}[/tex]

[tex]y^{8/3}[/tex]

Therefore the exponential form of the expression is [tex]y^{8/3}[/tex]

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The difference in her clothes and her books will be 57kg.

The difference in shipping cost if she has to pay $80 per kg of books and $200 per kg of clothing will be $19800.

From the information, Maya has 70 kilograms of books and 127 kg kilograms of clothing to send through the postal service, the difference in her clothes and her books will be:

= Weight of clothes - Weight of books

= 127 kg - 70 kg

= 57 kg

The difference in shipping cost if she has to pay $80 per kg of books and $200 per kg of clothing will be:

= 127(200) - 70(80)

= 25400 - 5600

= $19800

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$57.96   is  the value of each function after five years.

How does exponential growth utilise e?

Let the principle sum be P

Let the number of years be n

Thus the total sum for n years is

P( 1 + 3/100)ⁿ      →      P( 103/100)ⁿ

= $50 ( 103/100)⁵

= $57.96

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Myron has least amount of money which is  $1,698

According to the question

Given that ,

amount of saving of Myron is $1,698

amount of saving of Robert is  $1,898

Toby has $100 less than Robert

amount of saving of Toby is   $100 less than Robert

 Robert has  $1,898

amount of saving of Toby = $1,898 - 100

                                            = $ 1,798

Myron has least amount of money which is  $1,698

Savings account is a basic account type that lets you deposit money safely with a bank. It ensures safety and access to your money whenever you need. You can withdraw your funds, either digitally or in person, at any point in time.

Having a savings account is a liquid investment, so you have the ease of using your funds any time for transactions. A savings account also earns decent returns;

A savings account is like a virtual locker that safeguards your money and pays a certain amount of interest. As opposed to a fixed deposit (FD), you can use the money in your savings account whenever you need. A savings account also has other uses.

With your savings bank account, you make transactions, receive payments, pay your credit bills, and make investments. You can also pay for utilities such as electricity bills, ration, mobile phone recharges, and shopping. A savings account safeguards your money from theft and misplacement and reduces the stress that comes with carrying too much cash.

how to calculate saving

If the daily amount is Rs 3 lakhs and the interest rate on the savings account is 4% per year, the computation will be Interest on a monthly basis = Daily Balance * (Number of days) *Interest / (Days in the year)3 lakhs * 30 * (4/100) / 365 = Rs 986 per month in interest Daily

balance: 3 lakh

Number of days: 30

Interest: 4%

Days in the year: 365

According to Bank, "Savings bank interest will be calculated on the daily balances maintained in your account. Savings Bank interest will be paid at quarterly intervals."

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Answer: because it's is involved in everyday life, without math we would never have a fraction of the technology we have today

Step-by-step explanation:

Answer: we have to use our brain- =w=

Step-by-step explanation:

so basically right we should only need to know how to count money and maybe multiply bc thats what u do in life why do we need to do algebra for real life ocasions- smh

Answer:

It is the third one down.

Step-by-step explanation:

The two smaller angles would be the same measurement because the angle bisector cuts the big angle down the middle.    So, if the big angle was 90°, the two smaller angels would be 45°.  

Answer:

3

Step-by-step explanation:

its 3 because An angle bisector is a ray that divides an angle into two congruent angles  if you multiply the measurement of GLH by two you will get the measurement of GLI. Which is the same as adding the measurement of GLH and HLI since they have the same measurement

Congruent: The same

Function models for inverse variation is y = 50.1/x and find y when x=-5 will be -10.

A function model or functional representation is an organized depiction of the functions (activities, actions, processes, and operations) inside the modeled system or subject area.

Inverse variation formula is y = k. 1/x

⇒ for x = 25 and y = 2,

The value of k will be -

k = y . x

k = 25 . 2

k = 50

⇒ y = 50 . 1/x is our function

⇒ for x = -5,

⇒ y = 50 / -5

⇒y = -10

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The unknow angle of the triangle is as follows:

m∠C = 46.2°

A triangle is a three-sided polygon that consists of three edges and three vertices.

In simpler term, a triangle is a kind of polygon that 3 sides and 3 angles.

Therefore, the sum of angles in a triangle is equals to 180 degrees.

Hence, the sum of angles in ΔABC is 180 degrees.

Therefore,

m∠A + m∠B + m∠C = 180°

m∠A = 32.1°

m∠B = 101.7°

m∠C = x

32.1 + 101.7 + x = 180

x + 133.8  = 180

x = 180 - 133.8

x = 46.2 degrees.

Therefore, the unknow angle of the triangle is as follows:

m∠C = 46.2°

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Answer: 46.2

Step-by-step explanation:

Answer:

[tex]3^{-6} = \left(\frac{1}{3}\right)^{-6}[/tex]

Answer:

Step-by-step explanation:

Exponent Law a^-r = 1/a^r

(1/3^6)

Answer:

Base = 12cm

Height = 24cm

Step-by-step explanation:

Hello glittersplanet,

The formula for the area of a triangle is A = 1/2 b * h where A equals the area, b equals the base, and h equals the height. You are given the area in this problem.

Let the following conditions apply:

Base = x

Height 2x <-------Problem states the height is twice its base, correct?

Therefore:

A = 1/2 b*h

144 = 1/2 (x)(2x)

Simplify by removing the fraction by multiplying through by 1/2 and you are left with x^2 correct? Therefore:

144 = x^2

x = √144

x = 12

Therefore, base = x = 12 while height = 2x = 2(12) = 24

x = √144

Footing-x=12

Height-x2=24

They are about same distance from sea level.

Sean is exploring a coral reel below level= 91 feet

Liz is hiking above sea level= 91 feet

 When, we compare both distance from sea level, both have the sane distance. Although, the distance between both Sean and Liz is 91+91= 182 feet.

When compare the level of both , both are at 91 feet one is below the sea level and another is above the sea level. Hence, both are at the same distance from the sea level.

Hence, the correct answer is both at 91 feet from seal level.

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The solutions of a and b are 0 and 0 respectively using matrix.

We have given two equations 3a + 5b = 0 and a+b = 0

This can be written as AX=B

Where  [tex]A=\left[\begin{array}{ccc}3&5\\1&1\\\end{array}\right][/tex]      and  [tex]X=\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]    ,  [tex]B=\left[\begin{array}{ccc}0\\0\\\end{array}\right][/tex]

A is the coefficient matrix, X the variable matrix and B the constant matrix.

     [tex]|A|=3(1)-5(1)\\|A|=3-5=-2[/tex]

  Since [tex]|A|\neq 0[/tex]

Hence, the system of equations is consistent and has a unique solution given

A inverse is given by [tex]A^{-1}=\frac{adjA}{|A|}[/tex]     ....(2) and adj(A) is given by [tex]adjA=C^T[/tex]

       [tex]M_{11}=1\\M_{12}=1\\M_{21}=5\\M_{22}=3[/tex]              

Then Co -factors will be        

            [tex]C_{11}=1\\C_{12}=-1\\C_{21}=-5\\C_{22}=3[/tex]

Matrix C is represented by

      [tex]C=\left[\begin{array}{ccc}1&-1\\-5&3\\\end{array}\right] \\\\C^T=\left[\begin{array}{ccc}1&-5\\-1&3\\\end{array}\right][/tex]

Putting |A| = -2 and transpose of C in equation (2) , we get

 [tex]A^{-1}=\frac{1}{-2} \left[\begin{array}{ccc}1&-5\\-1&3\\\end{array}\right][/tex]

Putting the value of A inverse in equation (1) , we get

      [tex]X=\frac{1}{-2} \left[\begin{array}{ccc}1&-5\\-1&3\\\end{array}\right]\left[\begin{array}{ccc}0\\0\\\end{array}\right]\\\\\left[\begin{array}{ccc}a\\b\\\end{array}\right]=\left[\begin{array}{ccc}0\\0\\\end{array}\right][/tex]

On comparing , we get a =0 , b= 0

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