Answer:
1. this is the definition of a midpoint - bc the definition of a midpoint is: “If a point is a midpoint of a segment, then it divides that segment into two congruent parts” or “If a point divides a segment into two congruent parts, then it's the midpoint of that segment.”
2. this is the division property of equality -"The division property of equality states that when we divide both sides of an equation by the same non-zero number, the two sides remain equal". so, in this situation we want to isolate x which means dividing both sides by 20. This will keep both sides equal just more simplified ( before, it was 20 and 100, after dividing both sides by 20 it is 1 and 5 which is the same ratio therefore they are still equal)
3. this one's the subtraction property of equality- this property means you can subtract the same number from both sides of an equation and get an equivalent equation. in this situation, they subtracted 15 from both sides to get AB = 30 and it ends being still being equal to AB + 15= 45.
4. this is the symmetric property of equality - "This property states that if a = b, then b = a. That is, we can interchange the sides of an equation, and the equation is still a true statement." "it states that values are still equal no matter which side of the equal sign they're on." That's why its possible for XY=ST and ST=XY
5. this is definition of congruence - which basically states that if a value of one thing is equal to the value of another thing those two things can be called congruent.
6. this is substitution property- this is the property that allows you to substitute one value for another in an equation. the property states that if
x = y, then x can be substituted in for y in any equation, and y can be substituted for x in any equation, just like what they show here with 5AB substituting for CD in the equation.
i hope this helped! im not that good at explaining so if u have more questions lmk!
Answer:
x = 22.5
Step-by-step explanation:
1/12 ÷30 is equal to 1/360 or in decimal form is a repetitive decimal which is .2777777777777777777777....
The first time I solved this problem, I did it in a way that I had to
mess with changing fractions to common denominators and all that.
Suddenly, however, the clean and easy way to do it dawned on me.
Here it is:
-- There are 56 marble in the bag.
-- The probability of pulling a red marble is 5/8, so
5/8 of the 56 marbles must be red.
5/8 of 56 = 35 red marbles.
-- The probability of pulling a green marble is 1/7,
so 1/7 of the 56 marbles must be green.
1/7 of 56 = 8 green marbles.
-- The red and green marbles make up (35 + 8) = 43
of the 56 marbles in the bag.
-- The rest of them are yellow.
There are (56 - 43) = 13 yellow marbles in the bag.
-- The probability of pulling a yellow marble is 13/56 . (about 23.2%)
No messy fractions at all !
That's the way I like it !
