Answer:
Step-by-step explanation:
Begin the solution by squaring both sides of the given equation. We get:
(3x - 4)^2 = 2x^2 - 2x + 2, or:
9x^2 - 24x + 16 = 2x ^2 - 2x + 2
Combining like terms results in:
7x^2 - 22x + 14 = 0
and the coefficients are a = 7, b = -22, c = 14, so that the discriminant of the quadratic formula, b^2 - 4ac becomes (-22)^2 - 4(7)(14) = 92
According to the quadratic formula, the solutions are
-b ± √discriminant -(-22) ± √92 22 ± √92
x = ------------------------------- = ----------------------- = ------------------------
2a 14 14
Original price:
6(3.5)
21
New Price:
1.15(21)
24.15
24.15-21
$3.15 more
Example: 2x + 6 < -8
There's 2 steps to solve this one.
2x + 6 < -8
Subtract 6 from both sides
2x < -14
Divide both sides by 2
x< -7
Answer:
D
Step-by-step explanation:
Firstly, the question is phrased very very badly as the four answers provided are coordinate points rather than how far apart the cities are in units.
To calculate the distance between two points, we have to use Pythagoras' Theorem as it's just pretty much a right-angle triangle. Please look at the (terribly drawn) image provided.
Keep in mind that these points are only roughly placed on the map.
But firstly, to use Pythagoras' Theorem (a^2 + b^2 = c^2), we must find the length of the two sides.
To find the length of the horizontal line (which from now on I'll refer to as 'a'), we must subtract the smaller x value from the larger one.
47 - 35 = 12
To find the length of the vertical line (which from now on I'll refer to as 'b'), we must subtract the smaller y value from the larger one.
122 - 78 = 44
I assume that the answer you should pick is D. (12, 44)
However, that doesn't exactly answer the question... it's worded a little weirdly.
To solve the rest of the equation, do the following:
Now that we know that the length of a = 12 and the length of b = 44, we can use Pythagoras' Theorem.
a^2 + b^2 = c^2
12^2 + 44^2 = c^2
144 + 1936 = c^2
2080 = c^2
c = 
c = 45.61
The answer is 45.61 units.
Answer:
C
Step-by-step explanation: