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4 years ago

Determine whether y varies directly with x. Find the constant of variation. Write the function rule x 5 7 9 y 6 11 16

Mathematics

1 answer:

daser333 [38]4 years ago

4 0

Answer:

a) y does NOT vary directly with x

b) y = 2.5x -6.5

Step-by-step explanation:

If variation were direct the ratios of y to x would be constant. They are not:

6/5 ≠ 11/7

y does not vary directly with x.

y changes by 5 from 6 to 11 when x changes by 2 from 5 to 7. Then the slope of the linear function rule is (change in y)/(change in x) = 5/2. Using a point-slope form of the equation of a line, we can write the rule as ...

y = m(x -h) +k . . . . . . . . for a line of slope m through point (h, k)

y = (5/2)(x -5) +6

y = 2.5x -6.5 . . . . . simplify

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3 years ago

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Snezhnost [94]

Answer:

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Step-by-step explanation:

If A=[1 0 -1 7] find K such that A^2-8A-ki-KI=0

Given the 2×2 matrices

A = $\left[\begin{array}{ccc}1&0\\-1&7\\\end{array}\right]$

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A² = $\left[\begin{array}{ccc}1&0\\-1&7\\\end{array}\right]$ $\left[\begin{array}{ccc}1&0\\-1&7\\\end{array}\right]$

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8A = 8 $\left[\begin{array}{ccc}1&0\\-1&7\\\end{array}\right]$

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Since $I = \left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right] \\$

$KI = \left[\begin{array}{ccc}K&0\\0&K\\\end{array}\right]$

Substitute the resulting matrices into the expression above:

A^2-8A-KI = $\left[\begin{array}{ccc}1&0\\-8&49\\\end{array}\right]$ - $\left[\begin{array}{ccc}8&0\\-8&56\\\end{array}\right]$ - $\left[\begin{array}{ccc}K&0\\0&K\\\end{array}\right]$ = $\left[\begin{array}{ccc}0&0\\0&0\\\end{array}\right]$

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-7 = k

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