Answer:
Plane Speed (x) = 378 mph
Step-by-step explanation:
Equation
d = r * t
Givens
With the wind
- d = 1680 miles
- t = 4 hours
- r = x + y
Against the wind
- d = 1680
- t = 5 hours
- r = x - y
Equation
The distances are the same, so you can solve for x in terms of y and then deal with the actual distance.
(x + y)*4 = (x - y)*5 Remove the brackets on both sides
Solution
- 4x + 4y = 5x - 5y Subtract 4x from both sides
- 4y = -4x + 5x - 5y Combine
- 4y = x - 5y Add 5y to both sides
- 5y + 4y = x
- x = 9y
Solution part 2
Now take one of the distance formulas and solve for x first then y.
- (x - y)*5 = 1680 Substitute 9y for x
- (9y - y)*5 = 1680 Subtract on the left
- 8y * 5 = 1680 Multiply on the left
- 40y = 1680 Divide by 40
- y = 1680/40
- y = 42 That's the speed of the wind.
- (x - y)*5 = 1680 Substitute the wind speed for y
- (x - 42)*5 = 1680 Divide both sides by 5
- (x - 42) = 1680 / 5 Do the division on the right
- (x - 42) = 336 Add 42 to both sides.
- x = 336 + 42
- x = 378 mph Plane's speed
Answer:
33k - 15
Step-by-step explanation:
Given expression,
By the distributive property,
By combining like terms,
∵ Further simplification is not possible,
Hence, the required simplified form of the given expression is,
Answer:
190.5 centimeters.
Step-by-step explanation:
First you need to convert 6ft 3 inches into just inches. There are 12 inches in a foot. 12 x 6 is 72. 72 inches + 3 = 75 inches. 75 inches x 2.54 = 190.5 centimeters.
Answer:
Option D
Step-by-step explanation:
Formula to use: V=
b=base of triangle a=altitude of triangle h=height of prism
Doing 
is essentially finding the area of the triangle and after multiplying by h will give you the volume of the triangular prism.
Solve: V = 
or option D
Ps. Altitude is perpendicular or 90 degrees to the side I used for the base, so it wouldn't be option C.
Answer:
y = 
x² - x + 
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (1, 3 ), thus
y = a(x - 1)² + 3
To find a substitute (- 1, 5) into the equation
5 = a(- 1 - 1)² + 3 ( subtract 3 from both sides )
2 = 4a ( divide both sides by 4 )
a = , thus
y = (x - 1)² + 3 ← expand factor using FOIL
y = (x² - 2x + 1) + 3 ← distribute parenthesis
= x² - x + + 3
= x² - x +
