MATHEMATICS COLLEGE

A.3(f) The line graphed on the grid represents the first of two equations in a system of linear equations.20
-16
12
-8
-20 -16 -12
-
-4
48
12
16 2024
-8
-12
16
If the graph of the second equation in the system passes through (-12, 20) and (4,12), which statement is true?

Answers

Answer 1
Answer: I don’t any idea for this

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2) Zoe was practicing for a marathon. She practiced for six days, runningfour miles each day. How many miles did Zoe run altogether?

Given: Z2 and Z4 are vertical angles.
Prove: Z2 = Z4

Answers

Step-by-step explanation:

we know about vertical angels that are equal

so <2=<4

(in fact they are congruent angles)

we found those only from the definition of vertical angles.

Final answer:

In geometry, vertical angles (like Z2 and Z4) formed by two intersecting lines are always equal. Therefore, if Z2 and Z4 are defined as vertical angles, they are equal in measurement. This is a fundamental concept of geometry.

Explanation:

In the field of Geometry, vertical angles are always congruent, which means they have the same measure in degrees. When you have two intersecting lines, they create vertical angles that are across from one another. Therefore, if Z2 and Z4 are defined as vertical angles, they must be equal in measurement.

Here is an explicit step-by-step explanation:

  1. In the given, we have two intersecting lines that form Z2 and Z4.
  2. By the properties of vertical angles, we know that angles positioned opposite each other (like Z2 and Z4) are equal.
  3. Therefore, we can conclude that Z2 = Z4.

Learn more about Vertical Angles

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Write an algebraic expression to represent the phrase below.a number n decreased by 5
please help

Answers

Answer

5-n

Step-by-step explanation:

An arena receives $1,700 per event for 12 concerts. If the costs for this sponsorship total $14,000, what is the profit margin for the concert sponsorship?

Answers

Answer:

total profit margin for all 12 concert is $6,400.

profit margin for all one concert is  $533.33

Step-by-step explanation:

Amount of money received for one event = $1700

Total no of concert = 12

Total money received for 12 event = Amount of money received for one event * Total no of concert

Total money received for 12 event  = $1700 *12 = $20,400

Total cost of sponsorship = $14,000

Profit margin is the difference money invested and money earned.

here total investment is $14,000

Total money earned is  $20,400

Therefore profit margin = money earned - total investment

= $20,400 -  $14,000 = $6,400

Therefore total profit margin for all 12 concert is $6,400.

However to calculate profit margin for one concert we can simply divide the total profit margin for all 12 concert by no of concert (i.e 12)

profit margin for one concert = total profit margin for all 12 concert/total no of concert  = $6,400/12 = $533.33

profit margin for all one concert is  $533.33

25-foot long board is to be cut into two parts. The longer part is one foot more than twice the shorter part. How long is each part?

Answers

To solve this problem you must apply the following proccedure:

 1. You have that 25-foot long board is to be cut into two parts. Then, the first equation is:

 a+b=25

 2. The longer part is one foot more than twice the shorter part:

 a=1+2b

 3. The system of equation is:

 a+b=25
 a=1+2b

 4. When you solve it, you obtain:

 a=25-b

 25-b=1+2b
 25-1=2b+b
 24/3=b
 b=8 ft

 a=1+2(8)
 a=17 ft

B(n)=2^n A binary code word of length n is a string of 0's and 1's with n digits. For example, 1001 is a binary code word of length 4. The number of binary code words, B(n), of length n, is shown above. If the length is increased from n to n+1, how many more binary code words will there be? The answer is 2^n, but I don't get how they got that answer. I would think 2^n+1 minus 2^n would be 2. Please help me! Thank you!

Answers

Answer:

More number of words that can be made: \bold{2^n}

Please refer to below proof.

Step-by-step explanation:

Given that:

The number of binary code words that can be made:

B(n) =2^n

where n is the length of binary numbers.

Binary numbers means 2 possibilities either 0 or 1.

Here, suppose if we have 5 as the length of binary number.

And there are 2 possibilities for each digit.

So, total number of possibilities will be 2* 2* 2* 2* 2 = 2^5

If the length of binary number is 2.

The total words possible are 2^2.

These numbers are:

{00, 01, 10, 11}

If the length of binary number is 3. (increasing the 'n' by 1)

The total words possible are 2^3.

These words are:

{000, 001, 010, 100, 011, 101, 110, 111}

So, number of More binary words = 8 - 4 = 4 or 2^2 or 2^n.

So, the answer is 2^n.

Let us try to prove in generic terms:

B(n) = 2^n

Increasing the n by 1:

B(n+1) = 2^(n+1)

Number of more words made by increasing n by 1:

B(n+1) -B(n)= 2^(n+1) -2^n\n\Rightarrow 2* 2^(n) -2^n\n\Rightarrow 2^n(2-1)\n\Rightarrow \bold{2^n}

Hence, proved that:

More number of words that can be made: \bold{2^n}

Final answer:

When the length of a binary code word increases from n to n+1, the number of additional binary code words is equal to the number of binary code words of length n, which is 2^n.

Explanation:

When the length is increased from n to n+1, the number of binary code words of length n+1 is equal to the number of binary code words of length n multiplied by 2. This is because for each binary code word of length n, we can append a 0 or a 1 to create two new binary code words of length n+1. Therefore, the number of additional binary code words is equal to the number of binary code words of length n, which is2^n.

Learn more about Binary code words here:

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When a sample size is greater than 10, the standard deviation of the sample is an accurate predictor of the population standard deviation. A. True B. False

Answers

Answer:

false because 40 is still very very small

Step-by-step explanation:
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