M = - 1/5
y = m x + b
7 = - 1/5 · ( - 3 ) + b
7 = 3/5 + b
b = 7 - 3/5
b = 35/5 - 3/5
b = 32/5
The equation is:
y = - 1/5 x + 32/5 or : y = - 0.2x + 6.4
Answer:
<h2>The solution is -9 < x < 17.</h2>
Step-by-step explanation:
|x-4|<13.
The above equation means, whatever the actual value of x is, the value of (x - 4) must be greater than - 13 and less than 13.
Hence, -13 < x - 4 < 13 or, -9 < x < 17. The value of x will be in between -9 and 17. The value of x can not be -9 or 17.
Answer:
Step-by-step explanation:
To do these the main think to consider is the boundaries of the functions. In other words, check when the boundary is true and use that function. And so,
If we look at 1a.) f(-3) this means that x=-3. Now check the boundary condition of both equations first. For 6x-1 use it only if x<0 well is -3<0? Yes, so we will use this function. But let's check why we won't use 7x+3 this is because the boundary is x≥0 and since x=-3, -3≥0 is false so we dont use that function. Therefore:
f(x)=6x-1
f(-3)= 6(-3) - 1 = -18 - 1 = -19
1b.) Same idea so we will use 7x+3 because 0≥0 is true and so:
f(x)= 7x + 3
f(0) = 7(0) + 3 = 0 + 3 = 3
1c.) We will use the second equation since 4≥0 is true and so:
f(x) = 7x + 3
f(4) = 7(4) + 3 = 28 + 3 = 31
You will use the same logic to solve 2 and 3. Good luck! Hope this helps!
To dea with absolute values you need to apply the definition of absloute value OR get rid of it by squaring both sides of the equality.
Let's try it by using the definition of the absolute value:
So, having that in mind, we must split the initial equation into two.
Then, we end up with two equations:
Both yield the solutions:
So your answer would be the second option
