Definitions and examples of rational, irrational, and nonzero numbers

Answers

Answer 1
Answer: rational are number that dont repeat and you can make it into a fraction

irrational are numbers that go on forever and never stop

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Solve each system using elimination PLEASE HELP!!!1.8X+5Y=6
3X-2Y=10
2.-3x+8y=10
5y+6y=80
3. 4x+12y=-24
3x-6y=-18
4.5x-6y=48
2x+5y=-3
please help show all work

Answers

1.
8x+5y=6 \ \ \ |* 2 \n3x-2y=10 \ \ \ |* 5 \n \n16x+10y=12 \n\underline{15x-10y=50} \n16x+15x=12+50 \n31x=62 \ \ \ |/ 31 \nx=2 \n \n3x-2y=10 \n3 * 2-2y=10 \n6-2y=10 \ \ \ |-6 \n-2y=4 \ \ \ |/ (-2) \ny=-2 \n \n(x,y)=(2,-2)

2.
-3x+8y=10 \ \ \ |* 5 \n5x+6y=80 \ \ \ |* 3 \n \n-15x+40y=50 \n\underline{15x+18y=240 \ \ } \n40y+18y=50+240 \n58y=290 \ \ \ |/ 58 \ny=5 \n \n5x+6y=80 \n5x+6 * 5=80 \n5x+30=80 \ \ \ |-30 \n5x=50 \ \ \ |/ 5 \nx=10 \n \n(x,y)=(10,5)

3.
4x+12y=-24 \n3x-6y=-18 \ \ \ |* 2 \n \n4x+12y=-24 \n\underline{6x-12y=-36} \n4x+6x=-24-36 \n10x=-60 \ \ \ |/ 10 \nx=-6 \n \n3x-6y=-18 \n3 * (-6)-6y=-18 \n-18-6y=-18 \ \ \ |+18 \n-6y=0 \ \ \ |/ (-6) \ny=0 \n \n(x,y)=(-6,0)

4.
5x-6y=48 \ \ \ |* 2 \n2x+5y=-3 \ \ \ |* (-5) \n \n10x-12y=96 \n\underline{-10x-25y=15} \n-12y-25y=96+15 \n-37y=111 \ \ \ |/ (-37) \ny=-3 \n \n2x+5y=-3 \n2x+5 * (-3)=-3 \n2x-15=-3 \ \ \ |+15 \n2x=12 \ \ \ |/ 2 \nx=6 \n \n(x,y)=(6,-3)

True or false 2 quarts is > 10 pints

Answers

1quart=2pints
convert 2 points to quarts
2 quarts=2 times 2 pints=4 pints

now we have
4pints>10pints
false since 4>10

FALSE

Which fraction shows 32/48 in simplest form

Answers

32÷16=2
48÷16=3

so 2/3
32 / 8 = 4
48 / 8 = 6
4/6 can be reduced by two
2/3 is the final answer.


How many solutions does the equation have? a+5=1/5(5a+25)

Answers

a + 5 = (1)/(5) (5a + 25)

First, simplify (1)/(5) (5a + 25) to (5a+25)/(5) / Your problem should look like: a + 5 =  (5a+25)/(5)
Second, multiply both sides by 5. / Your problem should look like: 5a + 25 = 5(a + 5)
Third, expand to get rid of parenthesis. / Your problem should look like: 5a + 25 = 5a + 25
Fourth, both sides are equal, resulting it having infinite solutions.

Answer: infinite solutions

Joan walked 23 1/4 miles in a week. Her sister walked 69 3/4 miles during the same week. How many times farther did Joan’s sister walk than Joan?

Answers

joans sister walked 3 times farther.

23 1/4 * 3 = 69 3/4

joans sister walked 3 times farther.

What is the solution to the equation? 2q + 18 = –5q – 3

Answers

2q+ 18= -5q -3
⇒ 2q+ 5q= -3 -18
⇒ 7q= -21
⇒ q= -21/7
⇒ q= -3

Final answer: q= -3~