Answer:
Eric's statement is false.
Step-by-step explanation:
When a positive and a negative number is added, pay attention to what number has a greater absolute value. If the positive number is greater, then the answer will be positive. In the negative number is greater, then the answer will be negative. For example, 23 + (-4) is going to end up as a positive sum, since 23 has a greater absolute value than -4. On the other hand, (-23) + 4 is going to end up as a negative number since -23 has a greater absolute value than 4.
Answer:
4:16 or 1:4
Step-by-step explanation:
1/5 of 20 = 4
there are 4 red marbles
there are 16 blue marbles
4:16 or 1:4
Answer:
Slope m=2, y-intercept b=5 --> y=2x+5
Slope m=3, y-intercept b=5 --> y=3x+5
Slope m=5, y-intercept b=4 --> y=5x+4
Step-by-step explanation:
The slope number goes with x, and the y-intercept gets either added or subtracted from the end of the equation depending on weather it's positive or negative. (subtracted if it's negative and added if it's positive)
Answer:
Step-by-step explanation:
Transformation from figure 1 to figure 2,
Translation of figure 1 by 6 units to the left.
Transformation of figure 1 to figure 3,
Reflection of figure 1 across y-axis.
Transformation from figure 1 to figure 4,
Translation of figure 1 by 6 units to the left and 4 units down.
Transformation from figure 1 to figure 5,
Translation of figure 1 by 3 units left and 6 units down.
Transformation from figure 1 to figure 6,
Reflection of figure 1 across x-axis.
Answer:
We have to prove,
(A \ B) ∪ ( B \ A ) = (A U B) \ (B ∩ A).
Suppose,
x ∈ (A \ B) ∪ ( B \ A ), where x is an arbitrary,
⇒ x ∈ A \ B or x ∈ B \ A
⇒ x ∈ A and x ∉ B or x ∈ B and x ∉ A
⇒ x ∈ A or x ∈ B and x ∉ B and x ∉ A
⇒ x ∈ A ∪ B and x ∉ B ∩ A
⇒ x ∈ ( A ∪ B ) \ ( B ∩ A )
Conversely,
Suppose,
y ∈ ( A ∪ B ) \ ( B ∩ A ), where, y is an arbitrary.
⇒ y ∈ A ∪ B and x ∉ B ∩ A
⇒ y ∈ A or y ∈ B and y ∉ B or y ∉ A
⇒ y ∈ A and y ∉ B or y ∈ B and y ∉ A
⇒ y ∈ A \ B or y ∈ B \ A
⇒ y ∈ ( A \ B ) ∪ ( B \ A )
Hence, proved......