Answer:
Step-by-step explanation:
We can use the Polynomial Remainder Theorem. It states that if we divide a polynomial P(x) by a <em>binomial</em> in the form (x - a), then our remainder will be P(a).
We are dividing:
So, a polynomial by a binomial factor.
Our factor is (x + k) or (x - (-k)). Using the form (x - a), our a = -k.
We want our remainder to be 3. So, P(a)=P(-k)=3.
Therefore:
Simplify:
Solve for <em>k</em>. Subtract 3 from both sides:
Factor:
Zero Product Property:
Solve:
So, either of the two expressions:
Will yield 3 as the remainder.
Using the given function, it is found that the snowball traveled 4 feet when the height is 20 feet.
<h3>What is the function for the ball's height?</h3>
The height when x feet are traveled is given by:
h(x) = -0.5x² + 6x + 4.
When the height is of 20 meters, we have that h(x) = 20, hence:
20 = -0.5x² + 6x + 4.
0.5x² - 6x + 16 = 0
x² - 12x + 32 = 0
(x - 8)(x - 4) = 0
For the first time: x - 4 = 0 -> x = 4.
The snowball traveled 4 feet when the height is 20 feet.
More can be learned about functions at brainly.com/question/25537936
Answer:
y = 5x+7
Step-by-step explanation:
Parallel lines have the same slope so y = 5x+9 is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope is 5
The new line will have a slope of 5
y = 5x+b
We know a point on the line (-2,-3)
Substitute this point into the equation
-3 = 5(-2)+b
-3 = -10+b
-3+10 = b
7 = b
y = 5x+7
Answer:
Step-by-step explanation:
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