From the table, y varies directly as x. Therefore, the constant of variation is k = 2 and y = 2x.
<h3>How to find a direct variation?</h3>
For direct variation,
y ∝ x
Therefore,
y = kx
where
- k = constant of proportionality
Hence,
(-2, -4)
-4 = -2k
k = -4 / -2
k = 2
(-4, -8)
y = -4(2) = -8
Therefore,
k = 2 and y = 2x
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Answer:
x^4 -53x^2 +108x +160
Step-by-step explanation:
If <em>a</em> is a zero, then (<em>x-a</em>) is a factor. For the given zeros, the factors are ...
p(x) = (x +8)(x +1)(x -4)(x -5)
Multiplying these out gives the polynomial in standard form.
= (x^2 +9x +8)(x^2 -9x +20)
We note that these factors have a sum and difference with the same pair of values, x^2 and 9x. We can use the special form for the product of these to simplify our working out.
= (x^2 +9x)(x^2 -9x) +20(x^2 +9x) +8(x^2 -9x) +8(20)
= x^4 -81x^2 +20x^2 +180x +8x^2 -72x +160
p(x) = x^4 -53x^2 +108x +160
_____
The graph shows this polynomial has the required zeros.
Answer:
14 feet and 5 inches
Step-by-step explanation:
11 feet + 2 feet= 13 feet
9 inches + 8 inches = 17 inches
17 inches = 1 foot and 5 inches
13 + 1 = 14 feet
5 inches + 0 inches = 5 inches