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3 years ago

Identify the pair of angles as corresponding alternate interior, both or neither

Mathematics

2 answers:

aalyn [17]3 years ago

8 0

Answer:

alternate interior angles

Step-by-step explanation:

Identify the pair of angles m<4 and m<7 as corresponding alternate interior, both or neither

we know that

<u>Alternate interior angles</u> are two congruent interior angles which lie on different parallel lines and on opposite sides of a transversal.

$m$ ------> by alternate interior angles

Stella [2.4K]3 years ago

6 0

the right answer is 7 and 4 because the angles are between the two lines that are not the transversal and are on diagonal opposite sides of the transversal.

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MATH WORD PROBLEM

Sloan [31]

cost of one regular admission ticket = $ 10

cost of one senior citizen ticket = $ 5

<h3><u>Solution:</u></h3>

Let "r" be the cost of one regular admission ticket

Let "s" be the cost of one senior citizen ticket

Given that,

<em><u>On day 1 you sold 30 Regular Admission tickets and 20 Senior Citizen tickets for a total of $400</u></em>

So we can frame a equation as:

30 Regular Admission tickets x cost of one regular admission ticket + 20 Senior Citizen tickets x cost of one senior citizen ticket = $ 400

$30 \times r + 20 \times s = 400$

30r + 20s = 400 ----- eqn 1

<em><u>Day two you sell 40 Regular Admission tickets and only 10 Senior Citizen tickets for a total of $450</u></em>

So we can frame a equation as:

40 Regular Admission tickets x cost of one regular admission ticket + 10 Senior Citizen tickets x cost of one senior citizen ticket = $ 450

$40 \times r + 10 \times s = 450$

40r + 10s = 450 ---- eqn 2

<em><u>Let us solve eqn 1 and eqn 2 to find values of "r" and "s"</u></em>

Multiply eqn 2 by 2

80r + 20s = 900 --- eqn 3

Subtract eqn 1 from eqn 3

80r + 20s = 900

30r + 20s = 400

(-) ---------------------

50r = 500

Substitute r = 10 in eqn 1

30r + 20s = 400

30(10) + 20s = 400

300 + 20s = 400

20s = 100

cost of one regular admission ticket = $ 10

cost of one senior citizen ticket = $ 5

4 0

4 years ago

-2,-7,-12 ,.... is an arithmetic sequence Find the sum of its first 20 terms ?

nlexa [21]

Given sequence:

-2,-7,-12 ,..

Unknown;

Find the sum of the first 20 terms = ?

Solution:

The sequence is -2,-7,-12 ,..

To find he sum of n-terms of a sequence, we use the expression below;

Sₙ = $\frac{n}{2} (2a + (n-1)d)$

where n is the number of terms = 20

a is the first term = -2

d is the common difference= -7 - (-)2 = -5

Now input the parameters and solve;

Sₙ = $\frac{20}{2} (2(-2) + (20 - 1) x -5)$

Sₙ = 10(-4 + -5(19)) = 10(-99) = -990

The sum of the first 20 terms of the sequence is -990

4 0

4 years ago

The expression 210,000\left(1.02\right)^x210,000(1.02)

Bad White [126]

Answer:

The house is increasing in value by 2% each year.

Correct the increase is 1.02 per year the value of b>0 and the percentage of increase each year is:

$\frac{1.02-1}{1} *100 = 2\%$

Step-by-step explanation:

For this case if we have this expression

$210000(1.02)^x$

We have the same functional forma like the exponential model given by:

$y = a b^x$

Where a = 210000 represent the constant or initial value and b = 1.02 represent the base.

So let's analyze the possible options:

The house has a starting value of 1.02.

False the starting value for this case is 210000 since if x=0 then we see that the value is 210000

The house is decreasing in value by 2% each year.

False the increase is 1.02 each year so then in % we have

$\frac{1.02-1}{1} *100 = 2\%$

We have an increase of 2% each year

The house is increasing in value by 2% each year.

Correct the increase is 1.02 per year the value of b>0 and the percentage of increase each year is:

$\frac{1.02-1}{1} *100 = 2\%$

The value of the house is changing by 0.02% each year.

False the increase is 2% per year

4 0

3 years ago

If f(x) = 2x - 5 , Find f(3). <br> Substitute 3 for x then type your final answer.

gavmur [86]

Answer:

here x is given 3 so put it on given eqa 2×3-5=1

4 0

3 years ago

Determine whether the series is convergent or divergent. 1 2 3 4 1 8 3 16 1 32 3 64 convergent divergent Correct:

Vanyuwa [196]

Answer:

This series diverges.

Step-by-step explanation:

In order for the series to converge, i.e. $\lim_{n \to \infty} a_n =A$ it must hold that for any small $\epsilon$ >0, there must exist $n_0\in \mathbb{N}$ so that starting from that term of the series all of the following terms satisfy that $|a_n-A|n_0$ .

It is obvious that this cannot hold in our case because we have three sub-series of this observed series. One of them is a constant series with $a_n=1$ , the other is constant with $a_n=3$ , and the third one has terms that are approaching infinity.

Really, we can write this series like this:

$a_n=\begin{cases} 1 \ , \ n=4k+1, k\in \mathbb{N}_0\\ 2^{k}\ , \ n=2k, k\in \mathbb{N}_0\\3\ , \ n=4k+3, k\in \mathbb{N}_0\end{cases}$

If we denote the first series as $b_n=1$ , we will have that $\lim_{k \to \infty} b_k=1$ .

The second series is denoted as $c_k=2^k$ and we have that $\lim_{k \to \infty} c_k=+\infty$ .

The third sub-series $d_k=3$ is a constant series and it holds that $\lim_{k \to \infty} d_k=3$ .

Since those limits of sub-series are different, we can never find such $n_0\\$ so that every next term of the entire series is close to one number.

To make an example, if we observe the first sub-series if follows that A must be equal to 1. But if we chose $\epsilon =1$ , all those terms associated with the third sub-series will be out of this interval $(A-1, A+1)=(0, 2)$ .

Therefore, the observed series diverges.

5 0

4 years ago