Answer:
<u>28.5 and 32.5</u>
Step-by-step explanation:
<em>create an equation to solve:</em>
x + (x+4) =61
2x + 4 = 61 combine like terms
2x = 57 subtract 4 from both sides
x = 28.5 divide 2 from both sides
28.5 is the smaller number
the larger number is 4 more so:
28.5 + 4 = 32.5
32.5 is the larger number
check your work:
28.5 + 32.5 = 61
The answer is a.
I hope this helped
Answer: a) √50
b) n = 1 + 7i
Step-by-step explanation:
first, the modulus of a complex number z = a + bi is
IzI = √(a^2 + b^2)
The fact that n is complex does not mean that n doesn't has a real part, so we must write our numbers as:
m = 2 + 6i
n = a + bi
Im + nI = 3√10
Im + n I = √(a^2 + b^2 + 2^2 + 6^2)= 3√10
= √(a^2 + b^2 + 40) = 3√10
a^2 + b^2 + 40 = 3^2*10 = 9*10 = 90
a^2 + b^2 = 90 - 40 = 50
√(a^2 + b^2 ) = InI = √50
The modulus of n must be equal to the square root of 50.
now we can find any values a and b such a^2 + b^2 = 50.
for example, a = 1 and b = 7
1^2 + 7^2 = 1 + 49 = 50
Then a possible value for n is:
n = 1 + 7i
