What is the value of x
1 answer:
You might be interested in
Answer:
The true statements are;
(i) m - n = n - m
(ii) +m (-n) = m - n
(iii) 0 = m - n
Step-by-step explanation:
We are given that m and n are both integers and we have to select all the statements that are true if m and n are also equal to each other.
(i) The given situation is: m - n = n - m
LHS = m - n
= m - m {because m and n are equal}
= 0
RHS = n - m
= n - n {because m and n are equal}
= 0
Hence, the given statement is true because LHS = RHS = 0.
(ii) The given situation is: +m (- n) = m - n
LHS = +m (- n)
= m - n
= m - m {because m and n are equal}
= 0
RHS = m - n
= n - n {because m and n are equal}
= 0
Hence, the given statement is true because LHS = RHS = 0.
(iii) The given situation is: 0 = m - n
LHS = 0
RHS = m - n
= m - m {because m and n are equal}
= 0
Hence, the given statement is true because LHS = RHS = 0.
(iv) The given situation is: m + n = 0
RHS = 0
LHS = m + n
= m + m {because m and n are equal}
= 2m
Hence, the given statement is not true because LHS RHS.
The second system of equations,
is correct.
We know that Bethany's age is x. Since Laura is 13 years older, her age is x+13. The product of their ages is equal to twice Amanda's age, and Amanda's age is y. This gives us:
x(x+13) = 2y
Using the distributive property, we have
x²+13x=2y
Dividing everything by 2 (to isolate y), we have:
x²/2 + (13/2)x = y
If we take 20 years off of Bethany's age, it is now represented as x-20. Taking 20 years off of Laura's age would be (x+13-20) or x-7. The product of their ages now is equal to David's age; David is 11 years older than Amanda, so his age is y+11. This gives us:
(x-20)(x-7)=y+11
Multiplying the binomials we have:"
x*x - 7*x - 20*x - 20(-7) = y+11
x²-7x-20x--140=y+11
x²-27x+140=y+11
To isolate y, subtract 11 from both sides:
x²-27x+140-11 = y+11-11
x²-27x+129 = y
is correct.
We know that Bethany's age is x. Since Laura is 13 years older, her age is x+13. The product of their ages is equal to twice Amanda's age, and Amanda's age is y. This gives us:
x(x+13) = 2y
Using the distributive property, we have
x²+13x=2y
Dividing everything by 2 (to isolate y), we have:
x²/2 + (13/2)x = y
If we take 20 years off of Bethany's age, it is now represented as x-20. Taking 20 years off of Laura's age would be (x+13-20) or x-7. The product of their ages now is equal to David's age; David is 11 years older than Amanda, so his age is y+11. This gives us:
(x-20)(x-7)=y+11
Multiplying the binomials we have:"
x*x - 7*x - 20*x - 20(-7) = y+11
x²-7x-20x--140=y+11
x²-27x+140=y+11
To isolate y, subtract 11 from both sides:
x²-27x+140-11 = y+11-11
x²-27x+129 = y