Answer:
The pairs are (13,15) and (-15,-13).
Step-by-step explanation:
If n is an odd integer, the very next odd integer will be n+2.
n+1 is even (so we aren't using this number)
The sum of the squares of (n) and (n+2) is 394.
This means
(n)^2+(n+2)^2=394
n^2+(n+2)(n+2)=394
n^2+n^2+4n+4=394 since (a+b)(a+b)=a^2+2ab+b^2
Combine like terms:
2n^2+4n+4=394
Subtract 394 on both sides:
2n^2+4n-390=0
Divide both sides by 2:
n^2+2n-195=0
Now we need to find two numbers that multiply to be -195 and add up to be 2.
15 and -13 since 15(-13)=-195 and 15+(-13)=2
So the factored form is
(n+15)(n-13)=0
This means we have n+15=0 and n-13=0 to solve.
n+15=0
Subtract 15 on both sides:
n=-15
n-13=0
Add 13 on both sides:
n=13
So if n=13 , then n+2=15.
If n=-15, then n+2=-13.
Let's check both results
(n,n+2)=(13,15)
13^2+15^2=169+225=394. So (13,15) looks good!
(n,n+2)=(-15,-13)
(-15)^2+(-13)^2=225+169=394. So (-15,-13) looks good!
Answer:
x=-1 or 5 or 2
Step-by-step explanation:
x³-6x²+3x+10=0
(x+1)(x-5)(x-2)=0
x+1=0 ⇒ x=-1
x-5=0 ⇒x=5
x-2=0 ⇒ x=2
To solve this, we need to follow <em>PEMDAS </em>(Order of Operations)
P: Parenthesis
E: Exponents
M: Multiplication
D: Division
A: Addition
S: Subtraction
Following this order of math will get you your answer for any math problem.
First we'll do -4*1/3, which gets us -4/3. Then we'll add 5 to get
<em>:)</em>
(r - s)³ + r²
= (-3 - (-4))³ + (-3)²
= (-3 + 4)³ + 9
= 1³ + 9
= 1 + 9
= 10
Answer:
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x).
Step-by-step explanation:
For any value of x g(x) is always greater than h(x) and for any value of x, h(x) will always be greater than g(x) are not true.
The given function is:
g(x) = x^2 and h(x) = –x^2
x=0
g(0)=(0)^2 = 0
h(0)= -(0)^2 = 0
Now check the condition for x = -1
put x =-1 in the given functions.
g(x)=x^2
g(-1) = (-1)^2 = 1
h(x)= -x^2
h(-1) = -(-1)^2 = -1
g(x)>h(x)
Now take a positive value of x= 3
Put the value in the given functions:
g(3) = (3)^2 = 9
h(3) = -(3)^2 = -9
g(x)>h(x)
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x)....
