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atroni [7]
3 years ago
15

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If

the system has one solution, name it.
y = -x + 5
y = x - 3

a) one solution; (1, 4)
b) infinitely many
c) no solution
d) one solution; (4, 1)

Mathematics
1 answer:
natima [27]3 years ago
6 0

Answer:

  d)  one solution; (4, 1)

Step-by-step explanation:

It often works well to follow problem directions. A graph is attached, showing the one solution to be (4, 1).

_____

You know there will be one solution because the lines have different slopes. Each is in the form ...

  y = mx + b

where m is the slope and b is the y-intercept.

The first line has slope -1 and y-intercept +5; the second line has slope 1 and y-intercept -3. The slope is the number of units of "rise" for each unit of "run", so it can be convenient to graph these by starting at the y-intercept and plotting points with those rise and run from the point you know.

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Select the correct answer. Consider these three numbers written in scientific notation: 6. 5 × 103, 5. 5 × 105, and 1. 1 × 103.
Karo-lina-s [1.5K]

Scientific notation uses expression which gives easy access of order. The greatest number is 5.5 \times 10^5 .It is greater by smallest number by 500  times.

<h3>How to convert a number to scientific notation?</h3>

It is usually of the form a.bc.. \times 10^kexponent of 10 starts)

(we have 1 ≤ |a| < 10 ) (where |a| is magnitude of a without sign)

This notation is used to get some idea of how large or small a number is in terms of power of 10.

<h3>What are some basic properties of exponentiation?</h3>

If we have a^bbase and 'b' is called power or exponent and we call it "a is raised to the power b" (this statement might change from text to text slightly).

Exponentiation(the process of raising some number to some power) have some basic rules as:

a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\ a^b \times a^c = a^{b+c}

The given numbers are:

  • First number = 6.5 \times 10^3 = 6500
  • Second number = 5.5 \times 10^5 = 550000
  • Third number = 1.1 \times 10^3 = 1100

The smallest number is 1,100 and greatest is 550,000

Getting the division to get to know how many times the greatest number is larger than the smallest number, we get:

\dfrac{5.5 \times  10^5}{1.1 \times 10^3} = \dfrac{5.5 \times 10^{5-3}}{1.1} = \dfrac{5.5}{1.1} \times 10^2 = 5 \times 10^2 = 500

Thus, it is found that greatest number is 5.5 \times 10^5 . It is greater by smallest number by 500  times.

Learn more about scientific notation here:
brainly.com/question/3112062

6 0
2 years ago
How to divide 288 by 30?
igor_vitrenko [27]
I took 288 and divided by 30 it gave me 9.6

And when i took 30 and divide it by 288 it gave me 0.104


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Answer:

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