Answer:
13/16
Step-by-step explanation:
To add these two fractions multiply the first fraction by 2 to get equivalent denominators so 6/16+7/16 then add the numerators to get 13/16.
Here we are given the expression : z+ (z+6)
In this we will use the concept of like terms.
Like terms are terms whose variables (and their exponents such as the 2 in x²) are the same. In other words, terms that are "like" each other.
so here we have z and z which have same exponent which is 1.
So we can say that z and z are like terms.
So adding z and z we get 2z
so our expression becomes 2z+3
Now we may use distributive property here which is :
ab + ac = a(b+c)
where "a" is gcf of the two terms.
so in our expression 2z+6 , gcf is 2
taking 2 common out we have 2(z+3).
So answer is option c) 2(z+3).
Let's put this in terms of a system of equations. Let's call the numbers x and y, with x being the larger integer and y the smaller one. Since they are consecutive odd integers, we know that:
x = y + 2
The constraint is:
xy= 3(x+y) + 71 Simplify
xy = 3x + 3y + 71 Plug in (y+2) for x:
(y + 2) y = 3(y + 2) + 3y + 71 Simplify
y² + 2y = 3y + 6 + 3y + 71 Subtract 6y from both sides, add 71+6
y² -4y = 77
y² - 4y - 77 = 0
Factor:
(y - 11) (y+7) = 0
y = 11 or y=-7
When y = 11, x = 13, since x = y+2
Plug in to make sure:
xy = 3(x+y) + 71
11*13 = 3 (11 + 13) + 71
143 = 3 (24) + 71
143 = 72 + 71
143 = 143
Our values work!
Answer: 11, 13
i think the answer is the first one
