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3 years ago

The function f(x)=−2(0.25)x+1 is shown. Select from the drop-down menus to correctly describe the end behavior of f(x).

Mathematics

1 answer:

Viktor [21]3 years ago

6 0

Answer:

cos 59° = x/16

x = 16 cos 59°

x = 8.24

BC is given 23 mi

Maybe AB is needed

AB = √34² + 23² = 41 (rounded)

BC² = AB² - AC²

BC = √(37² - 12²) = 35

Let the angle is x

cos x = 19/20

x = arccos (19/20)

x = 18.2° (rounded)

See attached

Added point D and segments AD and DC to help with calculation

BC² = BD² + DC² = (AB + AD)² + DC²

Find the length of added red segments

AD = AC cos 65° = 14 cos 65° = 5.9

DC = AC sin 65° = 14 sin 65° = 12.7

Now we can find the value of BC

BC² = (19 + 5.9)² + 12.7²

BC = √781.3

BC = 28.0 yd

All calculations are rounded

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lara [203]

The answer is X = 16

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7. Use the quadratic formula to find the solution(s). x² + 2x - 8 = 0

morpeh [17]

Hey there!

Use the quadratic formula to find the solution(s). x² + 2x - 8 = 0

Answer :

x = -4 or x = 2 ✅

Explanation :

Quadratic formula : ax² + bx + c = 0 where a ≠ 0

The number of real-number solutions (roots) is determined by the discriminant (b² - 4ac) :

If b² - 4ac > 0 , There are 2 real-number solutions

If b² - 4ac = 0 , There is 1 real-number solution.

If b² - 4ac < 0 , There is no real-number solution.

The roots of the equation are determined by the following calculation:

$x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}$

Here, we have :

a = 1
b = 2
c = -8

1) Calculate the discriminant :

b² - 4ac ⇔ 2² - 4(1)(-8) ⇔ 4 - (-32) ⇔ 36

b² - 4ac = 36 > 0 ; The equation admits two real-number solutions

2) Calculate the roots of the equation:

▪️ (1)

$x_1 = \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ x_1 = \frac{ - 2 - \sqrt{36} }{2(1) } \\ \\ x_1 = \frac{ - 2 - 6}{2} \\ \\ x_1 = \frac{ - 8}{2} \\ \\ \blue{\boxed{\red{x_1 = -4}}}$

▪️ (2)

$x_2 = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ x_2 = \frac{ - 2 + \sqrt{36} }{2(1)} \\ \\ x_2 = \frac{ - 2 + 6}{2} \\ \\ x_2 = \frac{4}{2} \\ \\ \red{\boxed{\blue{x_2 = 2}}}$

>> Therefore, your answers are x = -4 or x = 2.

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X ² - x - 4 = 0
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