Answer:
32/9
Step-by-step explanation:
Translating the word problem into a symbolic equation yields:
3n - 3 = 5/6
Solve this for the number (n):
Multiplying both sides of this equation by 6 clears out the fraction term:
18n - 18 = 5
Adding 18 to both sides isolates 18n: 18n = 23
Then the number is n = 23/18, and:
one more than twice this number n is 2(23/18) + 1, or:
46/18 + 18/18, or 64/18, or (reducing this result)
32/9
Answer:
24 km/h and 17 km/h
Step-by-step explanation:
We know that when two cyclists are traveling together, they will meet in the same time as if one cyclist with the combined speed of the two cyclists travelled the whole length. We don't know the speeds of the cyclists, so let's assign the one with the slower speed "x", and the one with the faster speed "x+7" the combined speeds is "2x+7"
Since the speed = distance / time, we can plug in the values
2x+7=205/5
2x+7=41
2x=34
x=17
We substitute x into the equation for the speed of the cyclists
Cyclist 1's speed: x, so their speed is 17 km/h
Cyclist 2's speed: x+7, so their speed is 17 + 7, or 24 km/h
Answer:
0
Step-by-step explanation:
Because 2^3 is 8 and if you multiply it by 0 it will just be 0
Answer:
Two times at (-1,0) and (2.5,0)
Step-by-step explanation:
When the graph intersects or touches x-axis, y is equal to 0
so y = -2x^2 + 3x + 5
=> 0 = -2x^2 + 3x + 5
The formula to solve a quadratic equation of the form ax^2 + bx + c = 0 is equal to x = [-b +/-√(b^2 - 4ac)]/2a
so a = -2
b = 3
c = 5
substitute in the formula
x = [-3 +/- √(3^2 - 4x-2x5)]/2(-2)
x = [-3 +/- √(9 + 40)]/(-4)
x = [-3 +/- 7]/(-4)
x1 = (-3 + 7)/(-4) = 4/-4 = -1
x2 = (-3 - 7)/(-4) = -10/-4 = 5/2 = 2.5
so the graph has two x-intercepts (-1,0) and (2.5,0), therefore it intersects x-axis two times
