Answer:
See explanation and hopefully it answers your question.
Basically because the expression has a hole at x=3.
Step-by-step explanation:
Let h(x)=( x^2-k ) / ( hx-15 )
This function, h, has a hole in the curve at hx-15=0 if it also makes the numerator 0 for the same x value.
Solving for x in that equation:
Adding 15 on both sides:
hx=15
Dividing both sides by h:
x=15/h
For it be a hole, you also must have the numerator is zero at x=15/h.
x^2-k=0 at x=15/h gives:
(15/h)^2-k=0
225/h^2-k=0
k=225/h^2
So if we wanted to evaluate the following limit:
Lim x->15/h ( x^2-k ) / ( hx-15 )
Or
Lim x->15/h ( x^2-(225/h^2) ) / ( hx-15 ) you couldn't use direct substitution because of the hole at x=15/h.
We were ask to evaluate
Lim x->3 ( x^2-k ) / ( hx-15 )
Comparing the two limits h=5 and k=225/h^2=225/25=9.
Answer:
Stefan originally spent $110.
Stefan made a profit of $44.
Step-by-step explanation:
Given that:
Stefan sold the bike and helmet for $137 and $17
Total amount = 137+17 = $154
This is 140% of the price Stefan originally paid.
Let,
x be the original price paid by Stefan
140% of x = $154
Therefore,
Stefan originally paid $110 for the bicycle and helmet.
Profit made by Stefan = 154-110 = $44
Hence,
Stefan originally spent $110.
Stefan made a profit of $44.
a dozen is 12 jumbo muffins, so 3 dozen is 36 muffins.
We know how much sugar is needed for 8 muffins, and 36 divided by 8 is equal to 4. So we need four times the previous amount.
1.5 tsp x 4 = 6 teaspoons.
Answer: -3/4
Step-by-step explanation: just use two random points. I used (90, 30) and (50,60)
Subtract the y’s and that would be the numerator and same for the x’s in the same order that you did for the y’s and that would be the denominator. Simplify and you’re done.