They give us 2 pieces to the puzzle. Both are positive numbers...x and y.
1.) 1 number is 1 less than twice another number. (x = 2y -1)...and
2.) the sum of their squares is 106. (x^2 + y^2 = 106).
substitute the value for x into the second equation.
(2y-1)^2 + y^2 = 106
(2y-1) (2y-1) + y^2 = 106 (use distributive property)
4y^2 - 2y - 2y + 1 + y^2 = 106 (subtract 106 from both sides)
4y^2 - 2y - 2y + 1 + y^2 - 106 = 106 - 106 (combine like terms)
5y^2 - 4y - 105 = 0 (factor)
(y-5) (5y-21) = 0 (set to 0)
y - 5 = 0
y = 5
substitute the 5 into the equation for y (x = 2(5) - 1)
x = 9 if we square 9, we get 81.
subtracted from 106 we have 25...the square root of 25 is 5.
our answers are 5 and 9.
Three consecutive even integers can be represented by x, (x+2), and (x+4).
(x + (x + 2) + (x + 4)) - 10 = -22 Get rid of the parentheses
x + x + 2 + x + 4 - 10 = -22 Combine like terms (x + x + x) and (2 + 4 - 10)
3x - 4 = -22 Add 4 to both sides
3x = -18 Divide
x = -6
Check you work.
x = -6
x + 2 = -4
x + 4 = -2
(-6 - 4 - 2) - 10 = 22
-12 - 10 = -22
So, your three integers are -6, -4, and -2 .
Answer:
Step-by-step explanation:
perp. -5
y + 7 = -5(x - 4)
y + 7 = -5x + 20
y = -5x + 13
Answer:
We conclude that the equivalent expression is:
Step-by-step explanation:
Given the expression
Remove parentheses: (a) = a
Multiply the numbers: 3 × 2 = 6
Multiply the numbers: 4 × 5 = 20
Multiply the numbers: 4 × 2 = 8
Thus, we conclude that the equivalent expression is:
Answer: 9 /17 as fraction 9.143 Simplify
Step-by-step explanation:
