Answer:
Step-by-step explanation:
9(3−2x)=2(10−8x)
Step 1: Simplify both sides of the equation.
9(3−2x)=2(10−8x)
(9)(3)+(9)(−2x)=(2)(10)+(2)(−8x)(Distribute)
27+−18x=20+−16x
−18x+27=−16x+20
Step 2: Add 16x to both sides.
−18x+27+16x=−16x+20+16x
−2x+27=20
Step 3: Subtract 27 from both sides.
−2x+27−27=20−27
−2x=−7
Step 4: Divide both sides by -2.
−2x
−2 = −7
/−2
x=
7/
2
Answer:
x=
7/
2
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)
The correct answer is 0.1
Given:
Interest = 4,275
interest rate = 2.5%
term = 18 years
Principal = ?
Interest = Principal * interest rate * term
4,275 = P * 2.5% * 18
4,275/ (2.5% * 18) = P
4,275 / 0.45 = P
9,500 = P
Your mom deposited 9,500 when you were born.
