Janie is analyzing a quadratic function f(x) and a linear function g(x). Will they intersect?
2 answers:
Answer:
Option (D) is correct.
No, They will not intersect.
Step-by-step explanation:
Given Points for g(x), (1,2) , (2,4) and (3,6)
Since g is a linear function then it must be in form of g(x) = mx +c where, c is constant and m is slope.
We first calculate the slope using,
Here, consider
Substitute above, we get slope as,
Thus, equation becomes g(x) = 2x + c ...(1)
For c plug the values in (1),
(1,2) ⇒ 2= 2 + c ⇒ c = 0
Thus, Equation of G(x) is 2x.
When we plot it it do not intersect f(x).
Thus, Option (D) is correct.
No, They will not intersect.
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Given that the jeweler has alloys that are 25% gold, 50% gold, and 82% gold.
As he wants to make 14 grams of an alloy by adding two different alloys that is precisely 75% gold, so one alloy must have a percentage of gold more than 75%.
One alloy is 82% gold and, the second can be chosen between 25% gold, 50% gold, so there are two cases.
Case 1: 82% gold + 50% gold
Let x grams of 82% gold and y grams of 50% gold added to make x+y=14 grams of 75% gold, so
75% of 14 = 82% of x + 50% of y
[as x+y=14]
grams
and grams.
Hence, 10.9375 grams of 82% gold and 3.0625 grams of 50% gold added to make 14 grams of 75% gold.
Case 2: 82% gold + 25% gold
Let x grams of 82% gold and y grams of 25% gold added to make x+y=14 grams of 75% gold, so
75% of 14 = 82% of x + 25% of y
grams
and grams.
Hence, 12.28 grams of 82% gold and 1.72 grams of 50% gold added to make 14 grams of 75% gold.