MATHEMATICS HIGH SCHOOL

2. How many solutions does this system have? 2x + y = 3, 6x = 9 – 3yA) 1
B) None
C) Infinite
D) 2

Answers

Answer 1
Answer:

Answer:

The system of equation has infinite solution.

C is correct.

Step-by-step explanation:

We are given system of equation

2x + y = 3

6x = 9 – 3y

First we re-write the second equation in standard form

So, we add 3y both sides

6x+3y=9 ---------------- (2)

2x+y = 3-----------------  (1)

Multiply equation 1 by 3

3(2x)+3y = 3(3)

6x+3y=9

Subtract new equation from 2nd equation

6x-6x + 3y-3y = 9-9

0=0

LHS=RHS

This is true statement. If statement is true then infinite number of many solution.

Hence, The system of equation has infinite solution.

Answer 2
Answer: 2x + y = 3
6x = 9 - 3y
        ↓
2x + y = 3
6x + 3y = 9

3(2x + y = 3)
3(2x) + 3(y) = 3(3)
6x + 3y = 9

There is an infinite number of solutions in the system (the answer is C).

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As part of a community service project at your high school, you are organizing a fund-raiser at the neighborhood movie theater. Money raised will benefit a summer camp for children with special needs. The admission charge is $10.00 per person, $5.50 of which is used to pay the movie theater’s rental fee. The remainder is donated to the summer camp fund.There are two variables involved in this problem. Which variable can best be designated as the dependent variable? As the independent variable?
a.
Independent variable - number of persons attending (or number of tickets sold);
Dependent variable - the amount donated
b.
Independent variable - the amount donated;
Dependent variable - number of persons attending (or number of tickets sold)
c.
Independent variable - number of persons attending (or number of tickets sold);
Dependent variable - the amount of the admission per person
d.
Independent variable - number of persons attending (or number of tickets sold);
Dependent variable - the amount paid towards the movie theater’s rental fee.

Answers

Independent variable is number of persons attending (or number of tickets sold) and Dependentvariable  is the amount donated

What is Statistics?

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The number of persons attending (or number of tickets sold) is the independent variable because it is the variable that we can control or manipulate.

The amount donated, on the other hand, depends on the number of persons attending and is thus the dependent variable.

The more people that attend the fund-raiser, the higher the amount donated to the summer camp fund.

Independent variable - number of persons attending (or number of tickets sold);

Dependent variable - the amount donated

Hence, Independent variable is number of persons attending (or number of tickets sold) and Dependent variable  is the amount donated

To learn more on Statistics click:

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The answer is
A.
Independent variable - number of persons attending (or number of tickets sold);
Dependent variable - the amount donated

Because, the number of persons attending is independent. No one knows how many people are attending. But the amount donated is depended upon the number of people attending.

An airplane is traveling at a speed of 200 km/h. Identify the correct conversion factor setup required to compute the speed of the airplane in m/s.

Answers

Answer:

Speed = 55.56 m/s

Step-by-step explanation:

Given:

An airplane is travelling at the speed of 200 km/h.

We need to convert this in meter/second.

1 km = 1000 meters

1 hour = 3600 seconds

Speed = Distance/Time

Speed = (200*1000)/(1*3600)

= 200000/3600 meter/second

Speed = 55.56 m/s

Hope this will helpful.

Thank you.

Identify whether these series are divergent or convergent geometric series and find the sum, if possible.

Answers

A geometric series:
\sum^(\infty)_(i=1)=a_1 * r^(i-1)
It's convergent if |r|<1.
It's divergent if |r|≥1.
The sum can be found if it's a convergent series; it's equal to (a_1)/(1-r).

3.
\sum^(\infty)_(i=1) 12 ((3)/(5))^(i-1) \n \na_1=12 \nr=(3)/(5) \n \n|r|<1 \hbox{ so it's convergent} \n \n\sum^(\infty)_(i=1) 12 ((3)/(5))^(i-1)=(12)/(1-(3)/(5))=(12)/((5)/(5)-(3)/(5))=(12)/((2)/(5))=12 * (5)/(2)=6 * 5=30

The answer is: This is a convergent geometric series. The sum is 30.

4.
\sum^(\infty)_(i=1) 15(4)^(i-1) \n \n a_1=15 \n r=4 \n \n |r| \geq 1 \hbox{ so it's divergent}

The answer is: This is a divergent geometric series. The sum cannot be found.

Order the numbers from least to greatest.-0.5, 3, -3, 1.2
The order of the numbers from least to greatest is (blank)

Answers

The order of the numbers from least to greatest is -3, -0.5, 1.2, 3.

How do we order the numbers from least to greatest?

For us to order the numbers from least to greatest, we first have to arrange the numbers in ascending order based on their values as follows -3, -0.5, 1.2, and 3.

Step 1: Compare -3 with the other numbers because -3 is the smallest, it comes first.

Step 2: We compare -0.5 with the remaining numbers.

Step 3: We evaluate 1.2 in comparison to the remaining numbers.

Step 4: 3, being the largest among the provided values is positioned at the end of the sequence.

Hence, the order of the numbers from least to greatest is -3, -0.5, 1.2, 3.

Learn more about how toorder the numbers at brainly.com/question/155227

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Answer:

The order of the numbers from least to greatest is -3, -0.5, 1.2, 3.

Help with math word problem, 10 pointsA Web music store offers two versions of a popular song. The size of the standard version is 2.4 megabytes (MB). The size of the high-quality version is 4.2 MB. Yesterday, the high-quality version was downloaded four times as often as the standard version. The total size downloaded for the two versions was 4992 MB. How many downloads of the standard version were there?

Answers

I hope this helps you

What is the solution of the system of equations below?2x + 3y = 7
x + y = 3
(1) (1,2)
(2) (2,1)
(3) (4,-1)
(4) (4,1)

Answers

\begin{cases}2x + 3y = 7 \n x + y = 3 \ \ / *(-2) \end{cases}\n \n\begin{cases}2x + 3y = 7 \n -2x - 2y = -6\end{cases}\n+ \ ------- \ny=1\n \n2x + 3\cdot1 = 7

2x+3=7 \ \ |-3\n \n 2x+3-3=7-3\n \n2x=4 \ \ /:2 \n \nx=2 \n \n \begin{cases} x=2 \n y=1 \end{cases}
2x + 3y = 7
x + y = 3

x = 3 - y

substituting for x,

2(3 - y)  + 3y = 7

= 6 - 2y + 3y = 7
6 + y = 7

thus, y = 1

x = 3 - y

= 3 - 1
= 2.

Thus, x = 2 , y = 1

Thus, (2) is correct.
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