Answer:
Step-by-step explanation:
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Answer:
x = -4
y = -12
Step-by-step explanation:
Since y is 3x,
3x = 2x - 4
On solving we get x as -4
Substitute x and we get y as -12
Answer:
The inverse is y = x + 5
Step-by-step explanation:
The general equation of a straight line is;
y = mx + c
In this case , the y-intercept is -5
So the partial equation is;
y = mx - 5
To get m, we use the x-intercept
The x-intercept coordinate is (5,0)
Insert this in the equation , we have;
0 = 5m-5
5m = 5
m = 5/5
m= 1
The equation of the line is thus;
y = x-5
So we want to find the inverse of this;
Replace x with d
y = d-5
Make d the subject of the formula
d = y + 5
replace d with x
x = y + 5
now replace x with y
So we have
y = x + 5
We are given
Andre rode his bike at a constant speed he rode 1 mile in 5 minutes
Firstly, we will find constant speed
In 5 minutes , distance travelled =1 miles
so, we get speed
Let's assume T is time in minutes
D is the distance in miles
we know that
so, we can plug value
and we get
so, we get
...............Answer
Answer:
g(-4) = -1
g(-1) = -1
g(1) = 3
Explanation:
If you are given a function that is defined by a system of equations associated with certain intervals of x, just find which interval makes x true, and then substitute x into the equation of that interval.
For example, given g(-4), this is an expression which is asking for the value of the equation when x = -4. So -4 is not ≥ 2, so ¼x - 1 will not be used. -4 is also not ≤ -1 and ≤ 2, so -(x - 1)² + 3 will not be used either. So in turn, we will just use -1 which is always -1 so g(-4) will just be -1, right because there is no x variable in -1 so it will always be the same.
Using the same idea as before g(-1) is g(x) when x = -1 so -1 will not be a solution because -1 is not less than -1 (< -1). -1 is not ≥ 2 either so we will be using the second equation because -1 is part of the interval -1≤x≤2 (it is a solution to this inequality), therefore -(x - 1)² + 3 will be used.
As x = -1, -(x - 1)² + 3 = -(-1 - 1)² + 3 = -(-2)² + 3 = -4 + 3 = -1.
It is a coincidence that g(-1) = -1.
Now for g(1), where g(x) has an input of 1 or the value of the function where x = 1, we will not use the first equation because x = 1 → x < -1 → 1 < -1 [this is false because 1 is never less than -1], so we will not use -1.
We will use -(x - 1)² + 3 again because 1 is not ≥ 2, 1≥2 [this is also false]. And -1 ≤ 1 < 2 [This is a true statement]. Therefore g(1) = -(1 - 1)² + 3 = -(0)² + 3 = 3
