Answer: 
Step-by-step explanation:
The first thing you must remember is the mulplication of signs. You know that:
You can observe that the number inside the parentheses is positive (+) and the sign that is outside the parentheses is negative (-), therefore, when you multiply these signs you get a negative sign (-). Then you get:
Now, you need to add these numbers. And the result obtained is:
Answer:
x>5/2
Step-by-step explanation:
4x>10
x>10/4
x>5/2
Volume of first oil = A, volume of second oil = B, volume of mixture = M
A = ?, B = 4l, M = A + B
40%A + 25%B = 30%M
40%A + 25%4l = 30%(A+4l)
<span>40%A + 25%4l = 30%A + 30%4l
40A + 100l = 30A + 120l
40A - 30 A = 120l - 100l
10A = 20l
A = 2l
</span>
Answer: 2 litres of 40% oil dressing.
Also note: That's an approximation, because the volumes are not strictly additive. For example: mixing 50ml pure ethanol with 50ml water will give you about 95ml of mixture. To get an accurate answer, you'd have to measure the volume of the final mixture and then divide your total oil content by that<span>.</span>
Answer:
1: 7 2: 3
Step-by-step explanation:
Answer:
13 ft/s
Step-by-step explanation:
t seconds after the boy passes under the balloon the distance between them is ...
d = √((15t)² +(45+5t)²) = √(250t² +450t +2025)
The rate of change of d with respect to t is ...
dd/dt = (500t +450)/(2√(250t² +450t +2025)) = (50t +45)/√(10t² +18t +81)
At t=3, this derivative evaluates to ...
dd/dt = (50·3 +45)/√(90+54+81) = 195/15 = 13
The distance between the boy and the balloon is increasing at the rate of 13 ft per second.
_____
The boy is moving horizontally at 15 ft/s, so his position relative to the spot under the balloon is 15t feet after t seconds.
The balloon starts at 45 feet above the boy and is moving upward at 5 ft/s, so its vertical distance from the spot under the balloon is 45+5t feet after t seconds.
The straight-line distance between the boy and the balloon is found as the hypotenuse of a right triangle with legs 15t and (45+5t). Using the Pythagorean theorem, that distance is ...
d = √((15t)² + (45+5t)²)
