Answer:
When we have a function like:
This function will have a discontinuity only if it diverges, and a divergence can happen when the denominator is equal to zero and the numerator is different than zero.
In this case, we have the equation:
Here the denominator is:
h(x) = x + 2
This is equal to zero when:
x + 2 = 0
x = -2
Now we need to see what happens with the numerator when x = -2
g(-2) = (-2)^2 + 2*(-2) = 0
Is equal to zero.
Then we need to see the limit when x -> -2, and use the L'Hopital theorem.
Because we have zero over zero at that point, we need to look at the quotients of the derivatives of both numerator and denominator.
Then the function does not diverge, then the function has no discontinuity.
We also could look at the graph of f(x) to see it:
Our function is a linear function, and this is because the numerator is x times the denominator, then the function is:
f(x) = x.
First, divide 340 miles by 20 gallons of gas, to see how many miles you have per gallon. 340 divided by 20 = 17 mpg. Next you multiply 17 mpg by 25 gallons of gas to see how many miles you can go.
17 times 25 = 425 miles. Your answer is 425 miles.
Answer <u>(assuming it can be in slope-intercept format)</u>:
Step-by-step explanation:
When knowing the y-intercept of a line and its slope, we can write an equation representing it in slope-intercept form, or 
.
1) First, find the slope of the equation. Use the slope formula, 
, to find the slope. Substitute the x and y values of the given points into the formula and simplify:
Thus, the slope is 
.
2) Usually, we would have to use one of the given points and the slope to put the equation in point-slope form. However, notice that the point (0,7) has an x-value of 0. All points on the y-axis have an x-value of 0, thus (0,7) must be the y-intercept of the line. Now that we know the slope of the line and its y-intercept, we can already write the equation in slope-intercept format, represented by the equation . Substitute 
and 
for real values.
Since represents the slope, substitute in its place in the equation. Since represents the y-intercept, substitute 7 in its place. This gives the following equation and answer:
Answer:
x = -10
Step-by-step explanation:
-2x - 10y = 20 (plug y=0)
-2x = 20
x = 20/-2
x = -10
