Y = f(x) = -3x
y = -3x
y = (constant) x
y is proportional to x.<span>
Hence we can say Y is proportional to x , having (-3) as proportionality Constant. hope this helps</span>
Answer:
a. the investment earns 4%
b. yes
Step-by-step explanation:
The "rule of 72" says that an investment earning compound interest at x% will double in value after 72/x years. That is, ...
f(x) = 72/x
__
<h3>a.</h3>
We interpret f(4) to mean Becky's friend is interested in the doubling time for an investment that earns 4% interest.
__
<h3>b.</h3>
Using the above formula, ...
f(4) = 72/4 = 18
The friend's math is correct.
If <em>x</em> + 1 is a factor of <em>p(x)</em> = <em>x</em>³ + <em>k</em> <em>x</em>² + <em>x</em> + 6, then by the remainder theorem, we have
<em>p</em> (-1) = (-1)³ + <em>k</em> (-1)² + (-1) + 6 = 0 → <em>k</em> = -4
So we have
<em>p(x)</em> = <em>x</em>³ - 4<em>x</em>² + <em>x</em> + 6
Dividing <em>p(x)</em> by <em>x</em> + 1 (using whatever method you prefer) gives
<em>p(x)</em> / (<em>x</em> + 1) = <em>x</em>² - 5<em>x</em> + 6
Synthetic division, for instance, might go like this:
-1 | 1 -4 1 6
... | -1 5 -6
----------------------------
... | 1 -5 6 0
Next, we have
<em>x</em>² - 5<em>x</em> + 6 = (<em>x</em> - 3) (<em>x</em> - 2)
so that, in addition to <em>x</em> = -1, the other two zeros of <em>p(x)</em> are <em>x</em> = 3 and <em>x</em> = 2
Answer:
18
Step-by-step explanation:
subtract 32 and 14
<span>The answer is that the fraction of 1/2 pint is 1 cup. To solve this you must know the equivalence between pints and cups, and use the notion of proportions. Two cups equal one pint. Then you can state this proportion: 1 pint / 2 cups = x pint / 1 cup. When you solve for x you get: x = 1/2. Which means that 1 cup is 1/2 of 1 pint. </span>
