Answer:
Step-by-step explanation:
- speed = distance / time
- time = distance / speed
a)
i)
<u>Time taken at the first part:</u>
ii)
<u>Time taken at the second part:</u>
- (190 - 105) / (x + 12) =
- 85/(x + 12)
b)
<u>If time is 3 hours and 15 minutes = 3 1/4 hours = 13/4 hours, the equation is:</u>
- 105/x + 85/(x + 12) = 13/4
- 4(x + 12)*105 + 4(85x) = 13x(x + 12)
- 13x² - 604x - 5040 = 0
c)
<u>Solve the equation:</u>
- 13x² - 604x - 5040 = 0
- x = [604 ± √((-604)² + 4*13*5040) ]/26 =
- [604 ± √626896]/26 =
- [604 ± 791.77]/26
- x = (604 + 791.77)/26 = 53.68 km/h (taking positive root only)
d)
- 105/x = 105/53.68 h = 1.956 h = 1 h 0.956*60 min = 1 h 57 min (rounded)
- 85/(53.68 + 12) = 85/65.68 = 1.294 h = 1 h 0.294*60 min = 1 h 18 min (rounded)
Answer:
Option A is correct
True, ΔABC and ΔDEF must be congruent.
Explanation:
LA theorem or Postulates states that given two right triangles, where one acute angle and a leg of one of the triangles are congruent to an angle and a leg of the other triangle, then the two triangles are congruent.
In ΔABC and ΔDEF
AB = DE [Leg] [Given in the figure]
[Given]
[Acute angle] [Given in the figure]
Then, by the LA theorem or Postulates;
therefore, ΔABC 
ΔDEF .
Answer:
y = 6x +1
Step-by-step explanation:
To write the slope-intercept form equation for a line, you need to know the slope and the y-intercept. These can be found from their respective formulas.
__
<h3>slope</h3>
The slope of a line between points (x1, y1) and (x2, y2) is given by the formula ...
m = (y2 -y1)/(x2 -x1)
For points (-1, -5) and (0, 1), the slope is ...
m = (1 -(-5))/(0 -(-1)) = 6/1
m = 6
<h3>y-intercept</h3>
The y-intercept is the value of y where the line crosses the y-axis. That axis is where x = 0. There is a formula that can be used to find the y-intercept from the slope and a point on the line:
b = y -mx . . . . . y-intercept of line with slope m through point (x, y)
However, one of the given points is already the y-intercept: (0, 1). It tells you b=1.
<h3>equation</h3>
The slope-intercept equation is ...
y = mx +b
y = 6x +1
Percent means per one-hundred. change the mixed number to an improper fraction. rule:
a b/c=(ac+b)/c
20/3 and as a percent p/100 this is:
20/300 so
24(20/300)
480/300
$1.60
