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motikmotik
3 years ago
13

Determine the solutuon for x^2-3x-28>0

Mathematics
1 answer:
natita [175]3 years ago
6 0

Answer:

 x < -4 or x > 7.

Step-by-step explanation:

We first determine the critical points by solving x^2 - 3x - 28 = 0:

x^2 - 3x - 28 = 0

(x - 7)(x + 4) = 0

x = 7, - 4

so the critical points are  -4 and  7.

Create a Table   (pos = positive and neg = negative):

Value  of           x< - 4        -4  < x < 7         x > 7    

---------------------|----------- |--------------------- |---------------------

x + 4                  NEG           POS                 POS

x - 7                    NEG           NEG                POS

(x + 4)(x - 7)         POS           NEG                POS

So the function is positive (>0) for x < -4 or x > 7.

You can also do this by drawing the graph of the function.

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Step-by-step explanation:

John deposits $5 per week and has $10, so his equation is 5x + 10.

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5x + 10 = 3x + 20

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4 0
2 years ago
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I need the answer fast
Mars2501 [29]

Answer:

The quadratic equations and their solutions are;

9 ± √33 /4 = 2x² - 9x + 6.

4 ± √6 /2 = 2x² - 8x + 5.

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Explanation:

Any quadratic equation of the form, ax² + bx + c = 0 can be solved using the formula x = -b ± √b² - 4ac / 2a. Here a, b, and c are the coefficients of the x², x, and the numeric term respectively.

We have to solve all of the five equations to be able to match the equations with their solutions.

2x² - 8x + 5, here a = 2, b = -8, c = 5.                                                  x = -b ± √b² - 4ac / 2a = -(-8) ± √(-8)² - 4(2)(5) / 2(2) = 8 ± √64 - 40/4.     24 can also be written as 4 × 6 and √4 = 2. So                                                                                     x = 8 ± 2√6 / 2×2= 4±√6/2.

2x² - 10x + 3, here a = 2, b = -10, c = 3.                                                   x =-b ± √b² - 4ac / 2a =-(-10) ± √(-10)² - 4(2)(3) / 2(4) = 10 ± √100 + 24/4. 124 can also be written as 4 × 31 and √4 = 2. So                                                                              x = 10 ± 2√31 / 2×2 = 5 ± √31 /2.

2x² - 8x - 3, here a = 2, b = -8, c = -3.                                                    x = -b ± √b² - 4ac / 2a = -(-8) ± √(-8)² - 4(2)(-3) / 2(2) = 8 ± √64 + 24/4.     88 can also be written as 4 × 22 and √4 = 2. So                                                                             x = 8 ± 2√22 / 2×2 = 4± √22/2.

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2x² - 9x + 6, here a = 2, b = -9, c = 6.                                                    x = -b ± √b² - 4ac / 2a = -(-9) ± √(-9)² - 4(2)(6) / 2(2) = 9 ± √81 - 48/4.                                                                             x = 9 ± √33 / 4 .

Step-by-step explanation:

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Step-by-step explanation:

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