X=6y
sum of their reciprocals
(1/x)+(1/y)=7
x=6y
1/6y+1/y=7
1/6y+6/6y=7
7/6y=7
times both sides by 6y
7=42y
divide both sides by 42
1/6=y
x=6y
x=6(1/6)
x=6/6
x=1
the numbers are 1 and 1/6
Answer:
12x + 2
Step-by-step explanation:
Let the number be represented by x.
Then five times the number = 5*x
Seven times the number = 7*x
Sum of 5 times the number minus -2 = ![\[5*x - (-2)\]](https://tex.z-dn.net/?f=%5C%5B5%2Ax%20-%20%28-2%29%5C%5D)
= ![\[5x +2\]](https://tex.z-dn.net/?f=%5C%5B5x%20%2B2%5C%5D)
Adding seven times the number to this expression yields, ![\[5x+2+7x\]](https://tex.z-dn.net/?f=%5C%5B5x%2B2%2B7x%5C%5D)
![\[= (5+7)x+2\]](https://tex.z-dn.net/?f=%5C%5B%3D%20%285%2B7%29x%2B2%5C%5D)
![\[= 12x+2\]](https://tex.z-dn.net/?f=%5C%5B%3D%2012x%2B2%5C%5D)
So the simplified expression corresponds to 12x + 2.
Answer:
Angle A is 101
Angle B is 79
Angle C is 83
Angle D is 97
Step-by-step explanation:
Vertical angles are congruent, which applies to C.
Lines are parallel so 79 and angle B are the same
Angle a is 101 because its a supplementary angle
Angle D is 97 because its also a supplementary angle so you subtract 83 from 180.
Lets say our number is 237x8
2+3+7+8+x should be divisible by 6.
20+x should be divisible by 6.
x=4
The opposite angles of an inscribe quadrilateral are supplementary.
angle P + angle R = 180
6x + 7 + 12x + 11 = 180
18x + 18 = 180
18x = 162
x = 9
Now we will substitute in the value of x to find angle P and R.
angle P = 6(9)+7 = 61
angle R = 12(9)+11 = 119
Now we will find the value of y.
angle Q + angle S = 180
10y + 7 + 3(3y + 7) = 180
10y + 7 + 9y + 21 = 180
19y + 28 = 180
19y = 152
y = 8
Now substitute in the value of y to find angle Q and S.
angle Q = 10(8)+7 = 87
angle S = 3(3*8+7) = 93
Hope this helps :)
