Answer:
A= 3 2/4 or 3 1/2 simplified
B= 9 13/15
Step-by-step explanation:
I don't know how to do an explanation of this, its kinda complicated.
5 3/4 - 2 1/4 should be easy to subtract because it has the same denominator. 5-3 equals 2 and 3/4-1/4 equals 2/4. So it should be 2 2/4, then I simplify it and get 2 1/2.
7 2/3 + 2 1/5 is a little more complicated. I first have to find it's common denominator which is 15. Next you rewrite the question to 7 10/15+ 2 3/15.
It should equal 9 13/15 when you add it.
Hope this helps!
Angles 24 degrees and 26 degrees are acute angles.
Answer:
7 hope this helps(✿◠‿◠)
Step-by-step explanation:
Answer: ![(-5.5,4.062)\ \text{and}\ (-5.5,-8.062)](https://tex.z-dn.net/?f=%28-5.5%2C4.062%29%5C%20%5Ctext%7Band%7D%5C%20%28-5.5%2C-8.062%29)
Step-by-step explanation:
Given
The two vertices of a equilateral triangle are ![(-9,-2)\ \text{and}\ (-2,-2)](https://tex.z-dn.net/?f=%28-9%2C-2%29%5C%20%5Ctext%7Band%7D%5C%20%28-2%2C-2%29)
Suppose the third vertex is ![(x,y)](https://tex.z-dn.net/?f=%28x%2Cy%29)
Side length in equilateral triangle are equal.
![\Rightarrow \sqrt{\left( -2+9\right)^2+\left( -2+2\right)^2}=\sqrt{\left( x+9\right)^2+\left( y+2\right)^2}\\\text{squaring both sides}\\\\\Rightarrow 7^2=\left( x+9\right)^2+\left( y+2\right)^2\quad \ldots(i)\\\\](https://tex.z-dn.net/?f=%5CRightarrow%20%5Csqrt%7B%5Cleft%28%20-2%2B9%5Cright%29%5E2%2B%5Cleft%28%20-2%2B2%5Cright%29%5E2%7D%3D%5Csqrt%7B%5Cleft%28%20x%2B9%5Cright%29%5E2%2B%5Cleft%28%20y%2B2%5Cright%29%5E2%7D%5C%5C%5Ctext%7Bsquaring%20both%20sides%7D%5C%5C%5C%5C%5CRightarrow%207%5E2%3D%5Cleft%28%20x%2B9%5Cright%29%5E2%2B%5Cleft%28%20y%2B2%5Cright%29%5E2%5Cquad%20%5Cldots%28i%29%5C%5C%5C%5C)
Similarly,
![\Rightarrow \sqrt{\left( -2+9\right)^2+\left( -2+2\right)^2}=\sqrt{\left( x+2\right)^2+\left( y+2\right)^2}\\\\\Rightarrow 7^2=\left( x+2\right)^2+\left( y+2\right)^2\quad \ldots(ii)](https://tex.z-dn.net/?f=%5CRightarrow%20%5Csqrt%7B%5Cleft%28%20-2%2B9%5Cright%29%5E2%2B%5Cleft%28%20-2%2B2%5Cright%29%5E2%7D%3D%5Csqrt%7B%5Cleft%28%20x%2B2%5Cright%29%5E2%2B%5Cleft%28%20y%2B2%5Cright%29%5E2%7D%5C%5C%5C%5C%5CRightarrow%207%5E2%3D%5Cleft%28%20x%2B2%5Cright%29%5E2%2B%5Cleft%28%20y%2B2%5Cright%29%5E2%5Cquad%20%5Cldots%28ii%29)
Subtract (i) and (ii)
![\Rightarrow \left( x+9\right)^2-\left(x+2\right)^2=7^2-7^2\\\\\Rightarrow (x+9+x+2)(x+9-x-2)=0\\\Rightarrow (2x+11)7=0\\\\\Rightarrow x=-\dfrac{11}{2}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cleft%28%20x%2B9%5Cright%29%5E2-%5Cleft%28x%2B2%5Cright%29%5E2%3D7%5E2-7%5E2%5C%5C%5C%5C%5CRightarrow%20%28x%2B9%2Bx%2B2%29%28x%2B9-x-2%29%3D0%5C%5C%5CRightarrow%20%282x%2B11%297%3D0%5C%5C%5C%5C%5CRightarrow%20x%3D-%5Cdfrac%7B11%7D%7B2%7D)
Insert the value of
in equation (ii)
So, two possible vertex are ![(-5.5,4.062)\ \text{and}\ (-5.5,-8.062)](https://tex.z-dn.net/?f=%28-5.5%2C4.062%29%5C%20%5Ctext%7Band%7D%5C%20%28-5.5%2C-8.062%29)