Answer
-17
<u>Explanation</u>
y−5x−3 for x = 2 and y = -4
We solve this question by substituting the values of y and x.
y−5x−3 = -4 - 5(2) - 3
= -4 - 10 -3
= -14 - 3
= -17
Sum/difference:
Let
This means that
Now, assume that 
is rational. The sum/difference of two rational numbers is still rational (so 5-x is rational), and the division by 3 doesn't change this. So, you have that the square root of 8 equals a rational number, which is false. The mistake must have been supposing that was rational, which proves that the sum/difference of the two given terms was irrational
Multiplication/division:
The logic is actually the same: if we multiply the two terms we get
if again we assume x to be rational, we have
But if x is rational, so is -x/15, and again we come to a contradiction: we have the square root of 8 on one side, which is irrational, and -x/15 on the other, which is rational. So, again, x must have been irrational. You can prove the same claim for the division in a totally similar fashion.
We assume the two numbers are x and (x+1)
so x^2+(x+1)^2=421
x^2+(x^2+2x+1)=421
2x^2+2x-420=0
According to the formula of quadratic
x=14 or-15
cuz we know the two numbers are integers
so x=14
therefore the other number is 15
To make sure that's correct
14^2+15^2=421
Hope that helps you!!
Answer: 46 years
Step-by-step explanation:
Let the father's age be x and the son's age be y, then 3 years ago:
Father = x - 3
son = y - 3
Then , from the first statement :
x - 3 = 3 ( y - 3 )
x - 3 = 3y - 9
x = 3y - 9 + 3
x = 3y - 6 .......................................... equation 1
In five years time
father = x + 5
son = y + 5
Then , from the second statement
x + 5 = 2 ( y + 5 )
x + 5 = 2y + 10
x = 2y + 10 - 5
x = 2y + 5 ........................ equation 2
Equating equation 1 and 2 , we have
3y -6 = 2y + 5
add 6 to both sides
3y = 2y + 5 + 6
subtract 2y from both sides
3y - 2y = 11
y = 11
substitute y = 11 into equation 1 to find the value of x
x = 3y - 6
x = 3(11) - 6
x = 33 - 6
x = 27
This means that the father is presently 27 years and the son is presently 11 years.
In four years time
father = 27 + 4 = 31
son = 11 + 4 = 15
sum of their ages in four years time will be
31 + 15 = 46 years
Answer:
Step-by-step explanation: number 1 is x <-15 because first simplify both sides of equation -1/5 x > 3 then multiple both sides by 5/(-1) (5/-1) x (-1x5) > (5/-1) x (3) which x < -15
