To figure out if the ordered pairs are a solution to the equations, you would need to plug in the points. Your points are ordered as (x,y)
You would plug in the number that's in the x spot in x, and the number in the y spot in y.
Let's start of with the first problem:
First thing you would do is plug in (-1) to x, and 6 to y.
Your equations would look like this:
6(-1) + 3(6) = 18
2(-1) + 6 = 7
What you would now do is solve the equations. When you solve them, you would get these answers
12 = 18
4 = 7
For #1, it would be no solution because the numbers do not equal each other. (Fun fact) If one of them ends up as a solution, but the other is no solution, the answer would be no solutions because BOTH of them have to be a solution to the equations given in order to be a solution.
If you do the same strategy, (plugging in the numbers to x and y), you would get the rest of the answers for the problems.
I hope this helps, if you need any more assistance, I would be glad to help!
Answer:
$2,500
Step-by-step explanation:
$350 per day for 25 days
350*25=2450
Add the 50 for insurance and that makes it 2500
If its wrong im sorry
![\bf \begin{cases} f(x)=2-x^{12}\\ g(x)=x^2-9\\ g(x)\div f(x)=\frac{g(x)}{f(x)} \end{cases}\implies \cfrac{x^2-9}{2-x^{12}}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%0Af%28x%29%3D2-x%5E%7B12%7D%5C%5C%0Ag%28x%29%3Dx%5E2-9%5C%5C%0Ag%28x%29%5Cdiv%20f%28x%29%3D%5Cfrac%7Bg%28x%29%7D%7Bf%28x%29%7D%0A%5Cend%7Bcases%7D%5Cimplies%20%5Ccfrac%7Bx%5E2-9%7D%7B2-x%5E%7B12%7D%7D)
now, for a rational expression, the domain, or "values that x can safely take", applies to the denominator NOT becoming 0, because if the denominator is 0, then the rational turns to
undefined.
now, what value of "x" makes this denominator turn to 0, let's check by setting it to 0 then.
![\bf 2-x^{12}=0\implies 2=x^{12}\implies \pm\sqrt[12]{2}=x\\\\ -------------------------------\\\\ \cfrac{x^2-9}{2-x^{12}}\qquad \boxed{x=\pm \sqrt[12]{2}}\qquad \cfrac{x^2-9}{2-(\pm\sqrt[12]{2})^{12}}\implies \cfrac{x^2-9}{2-\boxed{2}}\implies \stackrel{und efined}{\cfrac{x^2-9}{0}}](https://tex.z-dn.net/?f=%5Cbf%202-x%5E%7B12%7D%3D0%5Cimplies%202%3Dx%5E%7B12%7D%5Cimplies%20%5Cpm%5Csqrt%5B12%5D%7B2%7D%3Dx%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0A%5Ccfrac%7Bx%5E2-9%7D%7B2-x%5E%7B12%7D%7D%5Cqquad%20%5Cboxed%7Bx%3D%5Cpm%20%5Csqrt%5B12%5D%7B2%7D%7D%5Cqquad%20%5Ccfrac%7Bx%5E2-9%7D%7B2-%28%5Cpm%5Csqrt%5B12%5D%7B2%7D%29%5E%7B12%7D%7D%5Cimplies%20%5Ccfrac%7Bx%5E2-9%7D%7B2-%5Cboxed%7B2%7D%7D%5Cimplies%20%5Cstackrel%7Bund%20efined%7D%7B%5Ccfrac%7Bx%5E2-9%7D%7B0%7D%7D)
so, the domain is all real numbers EXCEPT that one.
(2,716 feet) x (1mile / 5,280 feet) = <em>0.5144 mile</em> (rounded)
Lyra's speed of travel is 6.71 feet per seconds and Lyra's direction of travel is 27 degrees north of east
<h3>How to determine the speed of travel?</h3>
The diagram that represents the scenario is added as an attachment.
Let x represents Lyra's speed of travel.
The value of x is calculated using the following Pythagoras theorem.
![x = \sqrt{3^2 + 6^2}](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%7B3%5E2%20%2B%206%5E2%7D)
Evaluate the exponents
![x = \sqrt{9 + 36}](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%7B9%20%2B%2036%7D)
Evaluate the sum
![x = \sqrt{45}](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%7B45%7D)
Evaluate the exponent
x = 6.71
Hence, Lyra's speed of travel is 6.71 feet per seconds
<h3>How to determine the direction of travel?</h3>
The direction (∅) is calculated using the following tangent ratio.
![\tan(\theta) = \frac 36](https://tex.z-dn.net/?f=%5Ctan%28%5Ctheta%29%20%3D%20%5Cfrac%2036)
Evaluate the quotient
![\tan(\theta) = 0.5](https://tex.z-dn.net/?f=%5Ctan%28%5Ctheta%29%20%3D%200.5)
Take the arc tan of both sides
![\theta = \tan^{_1}(0.5)](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20%5Ctan%5E%7B_1%7D%280.5%29)
Evaluate
![\theta = 27](https://tex.z-dn.net/?f=%5Ctheta%20%3D%2027)
Hence, Lyra's direction of travel is 27 degrees north of east
Read more about speed and distance at:
brainly.com/question/4931057
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