Answer: Elizabeth and Manuel have a distance of 4 meters between them.
Step-by-step explanation: Please refer to the picture attached.
From the information given, Elizabeth is directly behind Hannah and directly left of Manuel. That means we have three points which are HEM, that is, we now have triangle HEM. The longest side (hypotenuse) which is the distance between Hannah and Manuel is given as 5 meters while the other side the distance between Hannah and Elizabeth is given as 3 meters.
We shall apply the pythagoras theorem in solving for the unknown side, EM.
The Pythagoras theorem states thus;
AC² = AB² + BC²
Where AC is the hypotenuse, and AB and BC are the other two sides.
Substituting for the known values, we now have;
5² = 3² + EM²
25 = 9 + EM²
Subtract 9 from both sides of the equation
16 = EM²
Add the square root sign to both sides of the equation
√16 = √EM²
4 = EM
Therefore the distance between Elizabeth and Manuel is 4 meters
Step-by-step explanation:
Answer:
m = - 8 ± 6
Step-by-step explanation:
Given
m² + 16m - 8 = 0 ( add 8 to both sides )
m² + 16m = 8
To complete the square
add ( half the coefficient of the m- term )² to both sides
m² + 2(8)m + 64 = 8 + 64
(m + 8)² = 72 ( take the square root of both sides )
m + 8 = ± = ± = ± 6
Subtract 8 from both sides
m = - 8 ± 6
On question 9, x = 0.46284330
Hi there!
The general formula of A line in slope-intercept form is the following:
In this formula m represents the slope of the line. Therefore, we can conclude that m = 2/5.
We also know that the line passes through the point (-3, -1) and we can therefore substitute this coordinate into the formula of the line.
x = -3 and y = -1
Multiply first.
And finally add 1 1/5 to both sides of the equation.
We can now switch sides.
Now we've found our value of n, which we can substitute into the formula of our line. Hence, in slope-intercept form, we find the following: