Answer:
a) x = 60. b) b = 110. c) x = 20. d) x = 30.
Explanation:
For question a, 2x and 120° are opposite (vertical) angles so they must be the same measure according to the vertical angle theorem by definition, given they are angles formed by the transversal cutting two parallel lines. 2x = 120, so x = 60.
For question b, 130° and b + 20 are corresponding angles of the transversal cutting parallel lines, so they must be the same measure according to corresponding angle theorem(same side, one angle inner, and the other exterior of that) by definition. Given that they are both pairs of the same angle, they must be corresponding angles. 130° = b + 20, b = 110.
For question c, 120° and 2x + 20 are same side interior angles so they must be supplementary(add up to 180°) by definition. This is on the *same side* of the transversal inside the two parallel lines cut by it. 120° + 2x + 20° = 180°, x = 20°.
For question d, They are also on the same side but on the left so the same property of corresponding angles applies, so 3x + 10, and 100° must be the same measure. Therefore 3x + 10 = 100°, and x = 30.
Answer:
Infinite solutions.
Step-by-step explanation:
A ratio, which is essentially a fraction, can be written in an infinite number of ways and still have the same value..
As an example:
2/1 = 2
6/3 = 2
As long as both the top and bottom of a fraction are multiplied by the same value, the fraction will keep the same value.
So, any ratio that's a multiple of 1/5 is equivalent.
Answer:
1,728,000
Step-by-step explanation:
there are 86400 seconds in a day so you have to multiply 86400 times 20
One second I need to think and I’ll answer it promise!
Start by solving for x in the first problem:
3x=3+9y
x=1+3y
Then plug that into the second equation:
6(1+3y)-3y=-24
6+18y-3y=-24
15y=-30
y=-2
Then plug that back into first equation:
3x-9(-2)=3
3x+18=3
3x=-15
x=-5
Then I would check your answer by plugging those into both equations:
3(-5)-9(-2)=3
-15+18=3
3=3 CHECK
6(-5)-3(-2)=-24
-30+6=-24
-24=-24 CHECK
So the answer is x=-5 y=-2