Given:
The product of a particular number is 65.
Second value is given by the sum of 8 and the original number.
To find:
The unknown number.
Solution:
Let x be the unknown number.
Then, second number = x+8
The product of a particular number is 65.
![x\times (x+8)=65](https://tex.z-dn.net/?f=x%5Ctimes%20%28x%2B8%29%3D65)
![x^2+8x=65](https://tex.z-dn.net/?f=x%5E2%2B8x%3D65)
![x^2+8x-65=0](https://tex.z-dn.net/?f=x%5E2%2B8x-65%3D0)
Splitting the middle term, we get
![x^2+13x-5x-65=0](https://tex.z-dn.net/?f=x%5E2%2B13x-5x-65%3D0)
![x(x+13)-5(x+13)=0](https://tex.z-dn.net/?f=x%28x%2B13%29-5%28x%2B13%29%3D0)
![(x-5)(x+13)=0](https://tex.z-dn.net/?f=%28x-5%29%28x%2B13%29%3D0)
Using zero product property, we get
and ![x+13=0](https://tex.z-dn.net/?f=x%2B13%3D0)
and ![x=-13](https://tex.z-dn.net/?f=x%3D-13)
So, the unknown number is either 5 or -13.
Therefore, the correct option is B.
Answer:
a = -6/5
Step-by-step explanation:
For the graphs to be parallel the graphs should have same slope(m)
So we rewrite both our equations in the slope-intercept form then compare the slope to find the value of a like this,
This equation is the slope-intercept form we convert both our equations in this form firstly taking equation 1
![5y=-2x+10\\\\y=\frac{-2x+10}{5} \\\\y=\frac{-2}{5}x+\frac{10}{5} \\\\y=\frac{-2}{5}x+2](https://tex.z-dn.net/?f=5y%3D-2x%2B10%5C%5C%5C%5Cy%3D%5Cfrac%7B-2x%2B10%7D%7B5%7D%20%5C%5C%5C%5Cy%3D%5Cfrac%7B-2%7D%7B5%7Dx%2B%5Cfrac%7B10%7D%7B5%7D%20%5C%5C%5C%5Cy%3D%5Cfrac%7B-2%7D%7B5%7Dx%2B2)
so if we compare it with y = mx + b the coefficient of x is m and hence
m= -2/5 now solving for equation 2
![3y=ax-15\\\\y=\frac{ax-15}{3} \\\\y=\frac{ax}{3}-\frac{15}{3} \\\\y=\frac{a}{3}x-5\\\\](https://tex.z-dn.net/?f=3y%3Dax-15%5C%5C%5C%5Cy%3D%5Cfrac%7Bax-15%7D%7B3%7D%20%5C%5C%5C%5Cy%3D%5Cfrac%7Bax%7D%7B3%7D-%5Cfrac%7B15%7D%7B3%7D%20%20%5C%5C%5C%5Cy%3D%5Cfrac%7Ba%7D%7B3%7Dx-5%5C%5C%5C%5C)
so here if we compare it with y = mx + b the coeffienct of x is a/3 so since parallel lines have same slope by the formula:
![m_1=m_2](https://tex.z-dn.net/?f=m_1%3Dm_2)
we equation both the slope to each other to find the value of a like this,
![m_1=m_2\\\\\frac{-2}{5}=\frac{a}{3}\\\\-2(3)=a(5)\\\\-6=5a\\-6/5=a](https://tex.z-dn.net/?f=m_1%3Dm_2%5C%5C%5C%5C%5Cfrac%7B-2%7D%7B5%7D%3D%5Cfrac%7Ba%7D%7B3%7D%5C%5C%5C%5C-2%283%29%3Da%285%29%5C%5C%5C%5C-6%3D5a%5C%5C-6%2F5%3Da)
so the value of a equals
a= -6/5
Answer:
Triangle 1(ABC) and Triangle 3(XYZ) are similar since all their angles are equal
In Traingle XYZ m of angle Y is 85 degree..
Hope it helps u...