A. square root property
![3x^2-192=0\\x^2-66=0\\x^2=66\\x= -\sqrt{66} or \sqrt{66}](https://tex.z-dn.net/?f=3x%5E2-192%3D0%5C%5Cx%5E2-66%3D0%5C%5Cx%5E2%3D66%5C%5Cx%3D%20-%5Csqrt%7B66%7D%20or%20%5Csqrt%7B66%7D)
it has one value with x which is x^2 and it cn be easily solved without having to factorise, quadratic formula cant be used as it need ax^2+bx+c=0 format
B. factorising
![x^2-x-6=0\\x^2+2x-3x-6=0\\(x+2)(x-3)=0\\x+2=0 and x-3=0\\x= -2 \\x= 3](https://tex.z-dn.net/?f=x%5E2-x-6%3D0%5C%5Cx%5E2%2B2x-3x-6%3D0%5C%5C%28x%2B2%29%28x-3%29%3D0%5C%5Cx%2B2%3D0%20%20and%20%20x-3%3D0%5C%5Cx%3D%20-2%20%5C%5Cx%3D%203)
i just felt like this was easier to factorise than the other 2 options left
C. Completing the square
![x^2-6x-7=0\\(x-3)^2=0\\x= -1\\x= 7](https://tex.z-dn.net/?f=x%5E2-6x-7%3D0%5C%5C%28x-3%29%5E2%3D0%5C%5Cx%3D%20-1%5C%5Cx%3D%207)
same reason personal preference
D- Quadratic
![x^2-17x-7=0\\x=\frac{-(-17)+\sqrt{(-17)^2-4(1)(-7)} }{2(1)} \\x=\frac{-(-17)-\sqrt{(-17)^2-4(1)(-7)} }{2(1)}\\x=17.4\\x=-0.402](https://tex.z-dn.net/?f=x%5E2-17x-7%3D0%5C%5Cx%3D%5Cfrac%7B-%28-17%29%2B%5Csqrt%7B%28-17%29%5E2-4%281%29%28-7%29%7D%20%7D%7B2%281%29%7D%20%5C%5Cx%3D%5Cfrac%7B-%28-17%29-%5Csqrt%7B%28-17%29%5E2-4%281%29%28-7%29%7D%20%7D%7B2%281%29%7D%5C%5Cx%3D17.4%5C%5Cx%3D-0.402)
the 17 kinda threw me off and i didnt wanna get on factorising or doing completing the square so quadratic formal
Answer:
Harper is 17 and Cadence is 44.
Step-by-step explanation:
First, we can set up an equation to displays the sum of both ages.
Let x = Harper's age and y = Cadence's age
x+y=61
8 years ago, this means the sum will decrease by a total of 16 as we have to subtract 8 from both variables
The equation to represent 8 years ago is: x+y=45
Now we can write another equation to represent Cadence being 4 times older than Harper (8 years ago)
y=4x
We can substitute this back into the equation we had for the ages 8 years ago.
x+(4x) = 45
5x=45
x=9
Now, Harper's age 8 years ago is 9 years old. We add 8 to this number to determine that Harper is currently 17 years old.
We can insert this into the original equation to determine Cadence's age.
17+y=61
y=44
Thus, Cadence is currently 44 years old
Answer:
51
Step-by-step explanation:
(64/28) X 21 = x-3
48 = x - 3
+3 +3
51
X+6. An expression does not have an equal sign.
D. $43.264 is the correct answer