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WARRIOR [948]
3 years ago
13

If f(2)=9 and f(-1)=14, write a linear function that fits this scenario. Be sure to use proper notation. HELP!!

Mathematics
1 answer:
olya-2409 [2.1K]3 years ago
4 0

Answer:

The required linear function is: f(x) = $ \frac{-5}{3}x + \frac{37}{3} $

Step-by-step explanation:

We are given that f(x) is a linear function and it takes the value 9 when x = 2 and 14 when x = -1.

Now the general form of any linear function is: f(x) = ax + b.

Substituting these values in the general form we get:

f(2) = 9  = 2a + b

f(-1) = 14 = -a + b

Solving these two equations we get:

b = 37/3

Substituting this in the second equation to find 'a'.

a = -5/3

Therefore, the function f(x) = $ \frac{-5}{3} $x + $ \frac{37}{3} $.

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What is the positive root of the equation x 2 + 5x = 150? a0
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<span>Simplifying x2 + 5x = 150 Reorder the terms: 5x + x2 = 150 Solving 5x + x2 = 150 Solving for variable 'x'. Reorder the terms: -150 + 5x + x2 = 150 + -150 Combine like terms: 150 + -150 = 0 -150 + 5x + x2 = 0 Factor a trinomial. (-15 + -1x)(10 + -1x) = 0 Subproblem 1Set the factor '(-15 + -1x)' equal to zero and attempt to solve: Simplifying -15 + -1x = 0 Solving -15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -1x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1x = 0 + 15 -1x = 0 + 15 Combine like terms: 0 + 15 = 15 -1x = 15 Divide each side by '-1'. x = -15 Simplifying x = -15 Subproblem 2Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solutionx = {-15, 10}</span>
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