Answer: A
Step-by-step explanation:
This is because 25%= 25/100, and that reduces to 1/4. Also, whenever it says something OF something, it means to multiply. In this case, 1/4 OF 1000= 1/4x1000= 250.
*Even though it seems that multiplying will just make the number bigger, when you multiply with a fraction, it actually gets smaller* For example 1/3 of 3= 1/3x3= 1
Answer: 50 calories
Step-by-step explanation:
One serving of a certain brand of microwave popcorn provides 150 calories, 90 of which are from fat. The fraction that comes from fat:
= 90/150 = 3/5
One serving of a certain brand of low-sodium pretzels provides 120 calories, 12 of which are from fat. The fraction that comes from fat here:
= 12/120 = 1/10
The fat that are provided by a 100 calorie serving of the microwave popcorn would be:
= 3/5 × 100
= 60
The fat that are provided by a 100-calorie serving of the pretzels would be:
= 1/10 × 100 = 10
The difference from fat that are provided by a 100 calorie serving of the microwave popcorn than are provided by a 100-calorie serving of the pretzels would be:
= 60 - 10
= 50 calories
Answer:
Slope: 1/5
Step-by-step explanation:
-1,2
4,3
-1 - 2 = -1
-1 - 4 = -5
-1/-5 = 1/5
If <em>x</em>² + <em>y</em>² = 1, then <em>y</em> = ±√(1 - <em>x</em>²).
Let <em>f(x)</em> = |<em>x</em>| + |±√(1 - <em>x</em>²)| = |<em>x</em>| + √(1 - <em>x</em>²).
If <em>x</em> < 0, we have |<em>x</em>| = -<em>x</em> ; otherwise, if <em>x</em> ≥ 0, then |<em>x</em>| = <em>x</em>.
• Case 1: suppose <em>x</em> < 0. Then
<em>f(x)</em> = -<em>x</em> + √(1 - <em>x</em>²)
<em>f'(x)</em> = -1 - <em>x</em>/√(1 - <em>x</em>²) = 0 → <em>x</em> = -1/√2 → <em>y</em> = ±1/√2
• Case 2: suppose <em>x</em> ≥ 0. Then
<em>f(x)</em> = <em>x</em> + √(1 - <em>x</em>²)
<em>f'(x)</em> = 1 - <em>x</em>/√(1 - <em>x</em>²) = 0 → <em>x</em> = 1/√2 → <em>y</em> = ±1/√2
In either case, |<em>x</em>| = |<em>y</em>| = 1/√2, so the maximum value of their sum is 2/√2 = √2.
Answer:
2√2.
Step-by-step explanation:
We use the Pythagoras Theorem:
x^2 = 2^2 + 2^2
x^2 = 8
x = √8
= 2√2.
