We will use substitution to solve this system of linear equations, as the first equation has x and y with no coefficients, which makes it easier to find one in terms of the other. We can then substitute that value in the other equation and find the values of x and y.
x = y + 5 ---> equation 1
3x + 2y = 5 ---> equation 2
From equation 1, we get the value of x as y + 5. Using the substitution method, we can find the value of y by substituting (y+5) for x in the 2nd equation.
3(y+5) + 2y = 5
3y + 15 + 2y = 5
5y = 5 - 15
5y = -10
y = -2
Subsituting this value of y in (y+5), we can find x.
x = y + 5
x = -2 + 5
x = 3
Therefore, x = 3 and y = -2.
I will also solve this using elimination method.
Let us multiply equation 1 by 2, so that we get 2y in both equations.
2x = 2y + 10
3x + 2y = 5
Let us add both the equations.
2x + 3x + 2y = 5 + 2y + 10
5x = 15 + 2y - 2y
5x = 15
x = 3
Substituting this value of x in equation 1, we get
x = y + 5
3 = y + 5
y = 3 - 5
y = -2
Therefore, x = 3 and y = -2.
Answer:
96
Step-by-step explanation:
The maximum height reached by the pebble modeled by the quadratic function,
, can be found by finding the vertex.
Let's first find the t-coordinate of the vertex . The max height will correspond to this value of t which means we have to find the h(t)-coordinate.
When comparing 
to 
, we see that:
We need to evaluate the following to find the t-coordinate of the vertex:
So now to find the correspond h(t)-coordinate, we will need to replace t in 
with 1:
Answer:
h = 417.81 meters
The altitude of the plane is 417.81 meters
Step-by-step explanation:
given;
The initial height of the girl h0 = 400 m
Horizontal distance from the airport d = 40 m
Angle of elevation of the plane ∅= 24°
The altitude of the plane when the picture was taken is equal to initial height of the girl plus the elevation height.
h = he + h0
And he (elevation height) can be derived as;
he = dtan∅
he = 40tan24°
Substituting into the equation;
h = 40tan24° + 400
h = 417.81 meters
The altitude of the plane is 417.81 meters
Answer:
Step-by-step explanation:
71 grams would definitely be an outlier on the high side, whereas "most" species would weigh much less. Thus, the graph of this distribution of weights would be skewed towards the lower side, that is, to the left.
