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hjlf
3 years ago
14

Find the missing side of the triangle. leave your answer in simplest radical form

Mathematics
1 answer:
KIM [24]3 years ago
8 0

missing side is x} = 10.15 mi .

<u>Step-by-step explanation:</u>

Here we have the following info from the figure: A right angled triangle with following dimensions

Perpendicular = x

base = \sqrt{122}

Hypotenuse = 15

By Pythagoras Theorem :

Hypotenuse^2 = Perpendicular^2 + base^2

⇒ Hypotenuse^2 = Perpendicular^2 + base^2

⇒ 15^2 = x^2 + (\sqrt{122})^2

⇒ 225 = x^2 + 122

⇒ x^2 = 225-122

⇒ x^2 = 103

⇒ (x^2)^\frac{1}{2} = (103)^\frac{1}{2}

⇒ x} = (103)^\frac{1}{2}

⇒ x} = 10.15

Therefore, missing side is x} = 10.15 mi .

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Consider the function h(x) =x2 – 12x + 58.
alekssr [168]

Answer:

The correct option is;

x ≥ 6; h⁻¹(x) = 6 +√(x - 22)

Step-by-step explanation:

Given the function, h(x) = x² - 12·x + 58

We can write, for simplification;

y = x² - 12·x + 58

Therefore;

When we put x as y to find the inverse in terms of x, we get;

x = y² - 12·y + 58

Which gives;

x - x = y² - 12·y + 58 - x

0 = y² - 12·y + (58 - x)

Solving the above equation with the quadratic formula, we get;

0 = y² - 12·y + (58 - x)

x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}

a = 1, b = -12, c = 58 - x

Therefore;

x = \dfrac{-(-12)\pm \sqrt{(-12)^{2}-4\times (1)\times (58 - x)}}{2\times (1)}= \dfrac{12\pm \sqrt{144-232 + 4 \times x)}}{2}

x =  \dfrac{12\pm \sqrt{4 \times x - 88}}{2} =  \dfrac{12\pm \sqrt{4 \times (x - 22)}}{2}  = \dfrac{12\pm 2 \times \sqrt{ (x - 22)}}{2}

x = \dfrac{12\pm 2 \times \sqrt{ (x - 22)}}{2} = {6 \pm  \sqrt{ (x - 22)}}

We note that for the function, h(x) = x² - 12·x + 58, has no real roots and the real minimum value of y is at x = 6, where y = 22 by differentiation as follows;

At minimum, h'(x) = 0 = 2·x - 12

x = 12/2 = 6

Therefore;

h(6) = 6² - 12×6 + 58 = 22

Which gives the coordinate of the minimum point as (6, 22) whereby the minimum value of y = 22 which gives √(x - 22) is always increasing

Therefore, for x ≥ 6, y or h⁻¹(x) = 6 +√(x - 22)  and not 6 -√(x - 22) because 6 -√(x - 22) is less than 6

The correct option is  x ≥ 6; h⁻¹(x) = 6 +√(x - 22).

7 0
2 years ago
Gimme the radius circumference and area<br> plsss i beg
Gala2k [10]

Answer:

radius = 5.75 units

circumference = 36.11 units

Area = 103.81625 square units

Step-by-step explanation:

Radius = 11.5 / 2 = 5.75

Circumference = 11.5 x 3.14 = 36.11

Area = 5.75 x 5.75 x 3.14 =

33.0625 x 3.14 =

103.81625 units square

This is all if pi = 3.14

Hope that helps!

4 0
2 years ago
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1st) 275+70-50      Lastly: Subtract  -350 - 295 = - 55
       
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345 - 50 = 295
7 0
3 years ago
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i found the answer by doing 29 minus 36 and the answer is how many females are on the gardening club
6 0
3 years ago
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