Answer:
The diagonal is about 14 m
Step-by-step explanation:
A = s^2
98 = s^2
so
s = √98
diagonal c^2 = 98 + 98
c^2 = 196
c = √196
c ≈ 14
Answer:
The diagonal is about 14 m
Answer:
, ![\frac{5-\sqrt{17}}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B5-%5Csqrt%7B17%7D%7D%7B4%7D)
Step-by-step explanation:
One is asked to find the root of the following equation:
![2x^2+1=5x](https://tex.z-dn.net/?f=2x%5E2%2B1%3D5x)
Manipulate the equation such that it conforms to the standard form of a quadratic equation. The standard quadratic equation in the general format is as follows:
![ax^2+bx+c=0](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc%3D0)
Change the given equation using inverse operations,
![2x^2+1=5x](https://tex.z-dn.net/?f=2x%5E2%2B1%3D5x)
![2x^2-5x+1=0](https://tex.z-dn.net/?f=2x%5E2-5x%2B1%3D0)
The quadratic formula is a method that can be used to find the roots of a quadratic equation. Graphically speaking, the roots of a quadratic equation are where the graph of the quadratic equation intersects the x-axis. The quadratic formula uses the coefficients of the terms in the quadratic equation to find the values at which the graph of the equation intersects the x-axis. The quadratic formula, in the general format, is as follows:
![\frac{-b(+-)\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%28%2B-%29%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
Please note that the terms used in the general equation of the quadratic formula correspond to the coefficients of the terms in the general format of the quadratic equation. Substitute the coefficients of the terms in the given problem into the quadratic formula,
![\frac{-b(+-)\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%28%2B-%29%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
![\frac{-(-5)(+-)\sqrt{(-5)^2-4(2)(1)}}{2(2)}](https://tex.z-dn.net/?f=%5Cfrac%7B-%28-5%29%28%2B-%29%5Csqrt%7B%28-5%29%5E2-4%282%29%281%29%7D%7D%7B2%282%29%7D)
Simplify,
![\frac{-(-5)(+-)\sqrt{(-5)^2-4(2)(1)}}{2(2)}](https://tex.z-dn.net/?f=%5Cfrac%7B-%28-5%29%28%2B-%29%5Csqrt%7B%28-5%29%5E2-4%282%29%281%29%7D%7D%7B2%282%29%7D)
![\frac{5(+-)\sqrt{25-8}}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B5%28%2B-%29%5Csqrt%7B25-8%7D%7D%7B4%7D)
![\frac{5(+-)\sqrt{17}}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B5%28%2B-%29%5Csqrt%7B17%7D%7D%7B4%7D)
Rewrite,
![\frac{5(+-)\sqrt{17}}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B5%28%2B-%29%5Csqrt%7B17%7D%7D%7B4%7D)
, ![\frac{5-\sqrt{17}}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B5-%5Csqrt%7B17%7D%7D%7B4%7D)
The speed of a yacht traveling a distance of 1.357 km in 165 minutes is 0.5 km/h
<h3>What is Speed?</h3>
The speed of an object is the distance covered by the object in respect to time.
Mathematically:
![\mathbf{Speed = \dfrac{distance}{time}}](https://tex.z-dn.net/?f=%5Cmathbf%7BSpeed%20%3D%20%5Cdfrac%7Bdistance%7D%7Btime%7D%7D)
![\mathbf{Speed = \dfrac{1.375 \ km}{165 minutes }}](https://tex.z-dn.net/?f=%5Cmathbf%7BSpeed%20%3D%20%5Cdfrac%7B1.375%20%5C%20km%7D%7B165%20minutes%20%7D%7D)
- We know that 60 minutes = 1 hour
- 165 minutes = 2.75 hours
![\mathbf{Speed = \dfrac{1.375 \ km}{2.75 \ hours}}](https://tex.z-dn.net/?f=%5Cmathbf%7BSpeed%20%3D%20%5Cdfrac%7B1.375%20%5C%20km%7D%7B2.75%20%5C%20hours%7D%7D)
Speed = 0.5 km/hour
Learn more about calculating speed here:
brainly.com/question/4931057
Please note that you have to use the reason vert. opp. angles to find x, hope it helps:)