The line y = x + 3 has slope 1, so we look for points on the curve where the tangent line, whose slope is dy/dx, is equal to 1.
y² = x
Take the derivative of both sides with respect to x, assuming y = y(x) :
2y dy/dx = 1
dy/dx = 1/(2y)
Solve for y when dy/dx = 1 :
1 = 1/(2y)
2y = 1
y = 1/2
When y = 1/2, we have x = y² = (1/2)² = 1/4. However, for the given line, when y = 1/2, we have x = y - 3 = 1/2 - 3 = -5/2.
This means the line y = x + 3 is not a tangent to the curve y² = x. In fact, the line never even touches y² = x :
x = y² ⇒ y = y² + 3 ⇒ y² - y + 3 = 0
has no real solution for y.
Answer: 21/100
Step-by-step explanation:
Number of green marbles = 21
Number of blue marbles = 35
Number of red marbles = 18
Number of yellow marbles = 26
Total number of marbles = 100
The probability of choosing a free marble will be:
= Number of green marbles / Tot number of marbles
= 21 / 100
Answer:
1
Step-by-step explanation:
1. Convert the mixed number to an improper fraction to match the rest of the problem (this just makes it easier for now, the answer will still be a mixed number)
-1
becomes 
2. Re-write the new equation. When there is a "+" in front of a set of parentheses the expression doesn't change aside from removing the plus signs.
The new equation becomes
3. Calculate. Just work out the new expression.
The answer is 
4. Convert to a simplified mixed decimal.
27 goes into 20 once with seven left over, making the answer 1
Answer:
for 8/24 the answer will be 1/3.
and for 8/32 the answer will be 1/4.
and for 6/30 the answer will be 1/5.
and for 12/24 the answer will be 1/2.
and for 9/21 the answer will be 3/7.
and for 5/20 the answer will be 1/4
Step-by-step explanation:
