Write a two-column proof. (Lesson 4-4)
Given: Δ L M N is isos. with LM ≅ NM , and MO bisects ∠L M N .
Prove: Δ M L O ≅ ΔM N O

The property that justifies the following statement, if 7(x-3)=35 then 35=7(x-3) is the symmetric property.

Symmetric property is one of the properties of equality which states that if there is an equality sign (=) between two values or numbers, then the two values will always remain equal even if you change the sides of the values. Therefore if ab = cd, then cd = ab

Hence, according to this property, the left side of the equation can be transferred to the right side and the right side of the equation can be transferred to the left side as the order of the equation can be ignored.

The symmetric property also justifies that if the values on the two sides are not equal, then they will remain unequal even if the sides are changed. That is if ab ≠ cd, then cd ≠ ab.

So, according to the symmetric property, the statement, if 7(x-3)=35 then 35=7(x-3) is valid.

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The value of variable x for the given expression 2=x . 4/√3 is (√3 /2).

As given in the question,

Given expression :

2=x . 4/√3

To get the value of variable x

Multiply both the side of the expression by √3

2 × √3 =  ( x × 4 × √3 ) / √3

Divide both the side of the expression by 4

( 2 × √3 ) /4 = (x × 4 ) / 4

⇒ x = √3 / 2

Therefore, the value of variable x for the given expression 2=x . 4/√3 is

(√3 /2).

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  The value of the geometric mean of the numbers 20 and 25 is.

Gm ( 20, 25) = 10√5

To solve this problem we define geometric mean.

   The geometric mean is defined as a type of measure that is calculated as the root of a product between a set of numbers, it can be expressed as follows:

Gm (a,b,c) = √(a×b×c)

  Then in our case that we have the values 40 and 15, these are equivalent to the variables a and b

  We substitute and solve for the square root

Gm (20, 25) = √20×25

Gm (20, 25) = √500

Gm (20, 25) = √5×100

Gm ( 20, 25) = 10√5

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The 7th term of the Arithmetic Progression (AP) is found using the common difference formula.

In Arithmetic Progression, the difference between the two arithmetical orders is just a constant value (AP). Arithmetic Sequence is another name for it.

We'd come across the few key phrases in AP that were denoted as:

As shown below, the AP can also be described in terms of common differences.

Now, according the given condition in the question.

Let the 5th term is defined by 'a₅'.

Let the 6th term is defined by 'a₆'.

Let the 7th term is defined by 'a₇'.

The common difference of the can be calculated as;

d = a₆ - a₅

Now, for the second case, it could be written as;

d = a₇ - a₆

So,

a₇ = d + a₆.

Therefor, the 7th term of an AP can be computed by adding the common difference to the 6th term of an AP.

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The sequence  1/4, 1, 4, 16,  . . . . is a geometric sequence and its 10th term is 65,536

To determine whether the sequence is an arithmetic or geometric one, we need to check the relation between two consecutive terms.

If it is an arithmetic sequence, then:

 a(n) = a(n-1) + d

where d is the common difference.

If it is a geometric sequence, then:

 a(n) = a(n-1) . r

where r is the common ratio.

The given sequence is:

   1/4, 1, 4, 16,  . . . .

In this sequence:

a(1) = 1/4

a(2) = 1

a(3) = 4

a(4) = 16

Notice that

a(2) : a(1) = 1 : 1/4 = 4

a(3) : a(2) = 4 : 1 = 4

and so on

Since the ratio of consecutive terms are constant, then the given sequence is a geometric sequence. Furthermore, its ratio, r = 4.

To find the 10th term, use the formula:

a(n) = a(1) . rⁿ⁻¹

Substitute n = 10, r = 4, and a(1) = 1/4

a(10) = 1/4 . 4⁹

a(10) = 4⁸  = 65,536

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Answer:

0.714

Step-by-step explanation:

Argument

The total number of cards = 5 yellow. 3 blue and 7 red = 15 cards in all.

The probability of choosing a yellow card first is 5/15 = 1/3.

We are now down to 14 cards

There are 3 blue cards.

P(yellow then blue) = 1/3 * 3/14

P(yellow then blue) = 1/14 = 0.0714

x less than or equal to 6 is the following is not a way to represent the solution of the inequality.

What is inequality in math?

2(x − 1) ≤ 10

2x - 2 ≤ 10

2x ≤ 10 + 2

2x ≤ 12

x ≤ 6

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Arithmetic Progression is a recursive mathematical sequence in which the next term is generated by adding the previous term with a fixed number that is called the Common difference represented by 'd'. This is calculated by the difference between any two terms in the given sequence.

The formula to calculate the 12th term of an Arithmetic Progression is :

                                    =>  [tex]a_{12} = a_{(12-1)} + d[/tex]    

Here, a = first term, n = nth term, and d = common difference

In the given question, First term a = 7, n = 12, and calculating d,

                                 => [tex]d = a_{2} - a_{1}[/tex]  => d = 6

But for a12 we need to find out a11, a10, a9, a8, a7, a6 using the same formula we get :

[tex]a_{6} = 37, a_{7} = 43, a_{8} = 49, a_{9} = 55, a_{10} = 61, a_{11} = 67[/tex]

Now for a12 we have a11 = 67, by using formula :

                                  [tex]a_{12} = a_{11} +d[/tex]

                                  [tex]a_{12} = 73[/tex]

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Approximately 291 people can attend the party.

Given,

The rent of the meeting room at the convention center = 400

Additional fee for each person who attends the party = 5.50

The amount raised by the senior class for the party = 2000

Now we have to find the number of people can attend the party.

That is,

Amount raised by seniors – rent of meeting room = 2000 – 400 = 1600

Now,

The number of people can attend the party = (Amount raised by seniors – rent of meeting room) / additional fee for each person

= 1600 / 5.50

= 290.91

That is, approximately 291 people can attend the party.

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Answer:

Step-by-step explanation:

yes the answer is correct 100 + 30 = 130

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Answer:

it is correct

Step-by-step explanation:

100

+ 30

___

=130

___

Answer:

a₁ = 8 and r = 16

Step-by-step explanation:

the sequence has a common ratio r between consecutive terms and is therefore geometric , that is

r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{2^{7} }{2^3}[/tex] = [tex]2^{(7-3)}[/tex] = [tex]2^{4}[/tex] = 16

r = [tex]\frac{a_{3} }{a_{2} }[/tex] = [tex]\frac{2^{11} }{2^7}[/tex] = [tex]2^{(11-7)}[/tex] = [tex]2^{4}[/tex] = 16

r = [tex]\frac{a_{4} }{a_{3} }[/tex] = [tex]\frac{2^{15} }{2^{11} }[/tex] = [tex]2^{(15-11)}[/tex] = [tex]2^{4}[/tex] = 16

the first term a₁ = 2³ = 8

4600 is the loan's future value, a, or the total amount due at time t.

What Is Simple Interest?

P=$4000

r=5%

t=3 years

Now we have to find th loans future value A.

So

Simple interest me I=prt=(4000)(.05)(3)=600

Total due is Principal + Interest =4000+600= 4600

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The solution for f in expression 21 = 7e - 4f is (7e - 21) / 4

Given,

The expression: 21 = 7e - 4f

We have to solve this expression for f:

Then,

21 = 7e - 4f

Add 4f to both sides

21 + 4f = 7e - 4f + 4f

Then we will get,

21 + 4f = 7e

Add -21 to both sides

21 + 4f - 21 = 7e - 21

Then we will get,

4f = 7e - 21

Take 4 from left hand side to right hand side.

That is,

f = (7e - 21) / 4

Therefore, the solution for f in expression 21 = 7e - 4f is (7e - 21) / 4

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He will owe a simple interest of $229.50

Simple interest is defined as the extra amount of money that is paid by the lender to the borrower for the amount of money that is taken on loan when returning the amount.

The simple interest on the principal is calculated by using the formula

I = P · R · T ,

Here I is the interest , P is the principal , R is the rate and T is the time.

Given in the question the amount of money loaned = $3600 , this is the principal (P) ,

Rate (R) = 4.25% = 0.0425

Time (T) is given  18 months which is equivalent to 1.5 years

Now the interest will be calculated by :

I = 3600 × 0.0425 × 1.5

I = 229.50

Therefore the interest earned is $ 229.50 .

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Question:✨Jin borrows $3,600 and plans to pay the loan off in 18 months. How much simple interest will he owe if it takes 18 months to repay the loan? Round to the nearest cent.

Answer: Ok took me a while to get the answer but

He will owe a simple interest of $229.50

Simple interest is defined as the extra amount of money that is paid by the lender to the borrower for the amount of money that is taken on loan when returning the amount.

The simple interest on the principal is calculated by using the formula

I = P · R · T ,

Here I is the interest , P is the principal , R is the rate and T is the time.

Given in the question the amount of money loaned = $3600 , this is the principal (P) ,

Rate (R) = 4.25% = 0.0425

Time (T) is given  18 months which is equivalent to 1.5 years

Now the interest will be calculated by :

I = 3600 × 0.0425 × 1.5

I = 229.50

Have an awesome night/day<3

The rate of change of the volume is  9123 . 185   inches³/min.

What is volume of the sphere?

Volume of sphere is

   V = 4/3 π r³

differentiating with respect to time

[tex]\frac{dv}{dt} = \frac{4}{3} \pi . 3r^{2} . \frac{dr}{dt}[/tex]

[tex]\frac{dv}{dt} = 4\pi r^{2} . \frac{dr}{dt}[/tex]

now [tex]\frac{dr}{dt} = 6 inches/min ,[/tex]     when r = 11

[tex]\frac{dv}{dt} = 4\pi (11)^{2} . 6[/tex]

    = 2904 π      cubic inches per minute

    ≅ 9123 . 185   inches³/min

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We get the following order:

1, 4, 7, 10, ....

Given that each term has a common difference, this is an arithmetic

sequence. In this instance, the next item in the series is obtained by multiplying the preceding term by 3.

The formula for arithmetic series is as follows:

an = a + (n - 1)d

Our first term is now a1 = 1.

Common variation d=3

Therefore, by entering these numbers into the given formula,

an = 1 + (n-1)3

an = 3n - 2

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Answer:

Step-by-step explanation:

Length of an arc of a circle = rC  where r = radius and r is the angle in radians

So, the answer is 4000(0.54+0.55)

= 3960 miles.

The value of the reverse permutation is F-¹(3) = 5.

An inverse permutation is one in which each number as well as the number of the place it occupies are swapped.

For, the given values in the question;

So, if you remove the last point, (5,3), the inverse is a function because it contains only the points.

F= {(2, 6), (3, 1), (4, 5), and (5,3)}.

Thus, it can be written as;

F: 2 → 3 → 4 → 5

F: 6 → 1 → 5 → 3.

Thus, F-¹(3); 3 →  5.

F-¹(3) = 5.

Therefore, the value of the reverse permutation is F-¹(3) = 5.

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The value of c so that cx-d=2x+4 has No Solution is c=2.

In the given question ,

we have

cx-d=2x+4       ....(i)

Given that d = 2 ,

We substitute the value of d=2 in equation (i)

On substituting we get

cx-2=2x+4

Simplifying further we get

cx=2x+4+2

cx=2x+6

cx-2x=6

x(c-2)=6

x=6/(c-2)

For x to have NO SOLUTION the denominator should be 0.

because when denominator becomes 0 the value becomes not defined , hence will have no solution.

Substituting the denominator = 0

we get c-2=0

c=2.

Therefore , the value of c so that cx-d=2x+4 has No Solution is c=2.

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you would divide both sides by 2. in this case that would be 2x/2 and 5/2.

Answer:

Tell what each power means but don't determine its value

Functions can be reflected on the x-axis, the y-axis, or both axes. For example, function reflection y= f(x) can be written as y= -f(x) or y= f(-x) even y= -f(-x). There are four types of function or graph transformations: reflection, rotation, translation, and dilation. In mathematics, especially geometry, mirror or mirroring means flipping, so basically, the mirroring of a function is the mirror image of a given function or graph. Hence the reflection function is commonly known as the reflection function.

The function's reflection should be similar in size and shape to the original function.

f(x)=2x-6; y -axis

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The expression which is equivalent to 7 3/4 subtracted by 1/2 will be ( 31 / 4 ) - ( 2 / 4 ).

We are given a statement:

7 3/4 subtracted by 1/2

We need to write an expression to represent the same.

We know that:

7 3/4 can also be written as an improper fraction as:

31 / 4

And 1 / 2 can be written as an equivalent fraction to 2 / 4.

Subtracting the values, we will get the expression as:

( 31 / 4 ) - ( 2 / 4 )

Therefore, the expression which is equivalent to 7 3/4 subtracted by 1/2 will be ( 31 / 4 ) - ( 2 / 4 ).

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The percent decrease is 10.16%

Percent decrease can be calculated by dividing the decrease by the original value and multiplying by 100

The first step is to calculate the decrease

= 4.33 - 3.89

= 0.44

The percent decrease can be calculated as follows

= 0.44/4.33 × 100

= 0.1016 × 100

= 10.16

Hence the percent decrease is 10.16 %

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Answer:

(B)  10.16%

Step-by-step explanation:

Correct on my quiz.

Answer:

No; 1,200 will cause her to exceed 1,500.

Step-by-step explanation:

Luna has,

→ consumed 900 cal

→ burned 500 cal

She wants to keep her daily calorie,

→ 1,500 cal/day

Calories she have left to consume,

→ 1500 - (900 - 500)

→ 1500 - 400

→ 1100 cal

Hence, she has to consume 1100 cal more to reach 1,500 cal/day.

The value of the 4 is in the hundredth value.

The probability that the break will occur within 20 meters of a pole is 12.5%.

Probability:

The term probability refers the possible occurrence of the required event.

Given,

A 320 meter long tightrope is suspended between two poles.

Here we assume that the line has an equal chance of breaking anywhere along its length.

Now, we need to determine the probability that the break will occur within 20 meters of a pole.

From the given question,

The line has an equal chance of breaking anywhere along its length.

The first and last 20meters form,

=> [ (20 + 20) / 320 ] x 100

=> [ 40 / 320 ] x 100

=> [ 1 / 8 ] x 100

=> 12.5 %.

Therefore, the probability that a break will occur within 20 meters of a pole is about 12.5%.

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For n= 4 the term = 1/18

A geometric sequence is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Here the sequence is in a geometric sequence, as there is a common ratio between the two-term of the sequence.

Common ratio= 2/12 = [tex]\frac{1}{3}[/tex]/2=1/6

To find the nth term of the geometric sequence we have a formula

[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]

where a = first term of the sequence

           r= common ratio

           n = number of term

To find the term where n= 4, we have,

[tex]a_{4}[/tex]= 12[tex]\frac{1}{6}^{4-1}[/tex]

   = 12[tex]\frac{1}{6}^{3} }[/tex]

   = 12/216

   =1/18

Therefore for n= 4 we have the term 1/18.

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Answer:

5 dollars a month

Step-by-step explanation:

There are 12 months in a year, so we divide the yearly amount by 12

60/12 = 5

5 dollars a month