Factor the sums of two squares. SEE EXAMPLE 5
34. 4x² + 49
35. x² + 1
36.36 + 100a²
38.16² +25
37. 18y² +8
39. x² + y²

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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The graph that correctly models the situation is option B which has it that  A graph shows the hiking in the number of hours on the x-axis and distance in miles on the y-axis. The function starts from (0, 0), (3, 6), (4, 6), and (8, 16)

Given data

After 3 hours of hiking and at 6 miles from their starting point

one-hour break to eat lunch and take pictures

4 more hours, they reach their campsite 16 miles away from their starting point

x representing number of hours and y representing the distance travelled in miles

The started from origin

( 0, 0 )

3 hours of hiking and at 6 miles from their starting point

( 0 + 3, 0 + 6 ) = ( 3, 6 )

one-hour break to eat lunch and take pictures, no distance covered

( 3 + 1. 6 + 0 ) = ( 4, 6 )

4 more hours, they reach their campsite 16 miles away from their starting point. ( 16 hours is the total distance covered )

( 4 + 4, 16 + 0 ) = ( 8, 16 }

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The expression that represents the perimeter of the rectangle is: 8/3w + 10 units

Perimeter of rectangle = 2(length + width).

Let the width be represented as variable w

Width = w

Length of the rectangle = 1/3w + 5 units

Thus, substitute the values into the formula

Perimeter of the rectangle = 2(1/3w + 5 + w)

Simplify

Perimeter of the rectangle = 2(4/3w + 5)

Perimeter of the rectangle = 8/3w + 10 units

Therefore, the expression that represents the perimeter of the rectangle is: 8/3w + 10 units

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yes, if the value of the coin is 1 dollar, then it will exceed the million dollars within 28 days.

It will depend on the original value of the coin, value that we don't know, so I will assume that the value of the coin is $1.

If this coin doubles each day, then the day zero its value is $1.

After one day its value is 2*$1 = $2

After another day its value is 2*$2 = $4

And so on, this is modeled by the exponential equation:

y = $1*(2)^x

Where y is the total value and x is the number of days.

After 28 days (this means we use x = 28) the value will be:

y = $1*(2)^28 = $268,435,456

That is a lot more than one million dollars.

So yes, if the value of the coin is 1 dollar, then it will exceed the million dollars within 28 days.

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Answer: Distributive Property

Step-by-step explanation:

if you multiply x by y it is xy and if you multiply x by z its xz so that makes it equal to xy+xz

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}

Answer:

is the solve for x the question

Step-by-step explanation:

Answer:

The slope is 4/3

Step-by-step explanation:

An x-intercept is the value of

x when y = 0

, so an x-intercept of 3

can be written as a coordinate on the graph as

(3,0).

Likewise, an

y

-intercept is the value of

y

when

x

=

0

, so an

y

-intercept of

−

4

can be written as a coordinate on the graph as

(

0

,

−

4

)

Now we have two points,

(

3

,

0

)

and

(

0

,

−

4

)

.

To find the slope given two points, we use the formula

rise

run

, or

y

2

−

y

1

x

2

−

x

1

.

Plug in the given points into the formula:

−

4

−

0

0

−

3

=

−

4

−

3

=

4

3

Therefore, the slope is

4

3

.

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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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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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)

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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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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so so much to do with the way you are you going to be able to get the vaccine and I will be there in a few minutes to get the vaccine and I will 57

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 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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Express 3 and 9 as a product of their prime factors then in index form. 9=3x3=3^2. 3=3^1.  Apply the power rule (a^m)^n = a^mn to simplify. Indices depict: a^m x a^n = a^m+n

9= 3^2

3= 3^1

(3^1)^1/3 x (3^2)^1/3 = 3^1/3 x (3^2)^1/3 = 3^1/3 x (3^1x3^1)^1/3

3^1/3x3^1/3x3^1/3=  3^(1/3+1/3+1/3) = 3^1

=3

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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

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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Since the digit "5" is a recurring (repeating) in the given decimal, its fraction is equal to 23/90.

A fraction can be defined as a numerical quantity which isn't expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

In Mathematics, a fraction comprises two (2) main parts and these include the following:

Since the digit "5" is a recurring (repeating) in the given decimal, its fraction can be written as follows:

0.25555556 = (25 - 2)/90

0.25555556 = 23/90

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The length of segment [tex] \overline{MN} [/tex] found using properties of an equilateral triangle and segment addition postulate is 10

Segment addition postulate states that a line AC contains a point B if we have AB + BC = AC

The sides of ∆PQR are equal to 5, therefore, ∆PQR is an equilateral triangle

According to the mid segment theorem, we have;

RQ || MN

RQ = 0.5 × MN

RP || ON

RP = 0.5 × ON

PQ || MO

PQ = 0.5 × MO

Therefore, from alternate interior angles theorem, we have;

‹PRQ = ‹RPM

‹PQR = ‹QPN

‹QRP = ‹RQO

However, ‹PRQ = ‹PQR = ‹QPR = 60°, which gives;

∆MRP and ∆QPN are equilateral triangles of side length 5

From which we have;

MR = RP = MP = 5

PN = QN = PQ = 5

MN = MP + PN; Segment addition postulate

Therefore;

MN = 5 + 5 = 10

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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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Answer:13

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

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.