Answer:
1) I know that the sum will be negative because a negative number added to another negative number will still be a negative number.
2) First, I simplified -35 + (-61) to -35 - 61, which just equals -96.
-54 + 17 equals 54-17 = 37.
-96 < 37, so -35 + (-61) is less.
Step-by-step explanation:
The explanation is in the answer section, since your homework asked for me to explain.
Let the integers be x-1, x, x+1.
(x+1)² = (x-1)² + x² -140
x² + 2x + 1 = x² - 2x + 1 + x² - 140
2x = -2x + x² - 140
x² -4x -140 = 0
x² -14x +10x -140 = 0
x(x - 14) + 10(x - 14) = 0
(x - 14)(x + 10) = 0
x = 14 or -10
Going back to the criteria mentioned in the question and checking,
--- When x = -10
(-9)² = (-11)² + (-10)² - 140
81 = 121 + 100 - 140
81 = 81
--- When x = 14
(15)² = (13)² + (14)² - 140
225 = 169 + 196 - 140
225 = 225
Since both values satisfy the condition, both values are correct.
Hence, the 3 consecutive integers can be: -11, -10, -9 OR 13, 14, 15.
Answer:
Step-by-step explanation:
Arithmetic sequence:
Here a is the first term and d is the common difference.
⇒ ------------(I)
⇒ a + 19d = 100 ---------(II)
Subtract equation (I) from (II)
(I1) a + 19d = 100
(II) a + 13d = 46
<u>- - -</u>
6d = 54
d = 54 ÷ 6
Substitute d = 9 in equation(I) and find 'a',
a + 13*9= 46
a + 117 = 46
a = 46 - 117
a = -71
= -71 + 18
= -53
= -71 + 54
= -17
= -71 + 9*n - 1 *9
= -71 + 9n - 9
= -71 - 9 + 9n
= - 80 + 9n
<h3>For 10 pounds, both companies cost the same</h3>
<em><u>Solution:</u></em>
Let "x" be the pounds
<em><u>Company A charges $2.50 per pound plus a $20 service charge</u></em>
Cost : 2.50x + 20 ------ eqn 1
<em><u>Company B charges $4.50 per pound without any service charge</u></em>
Cost : 4.50x ------- eqn 2
<em><u>At what weight does it cost the same for both companies?</u></em>
For both companies to cost the same, eqn 1 must be equal to eqn 2
2.50x + 20 = 4.50x
4.50x - 2.50x = 20
2x = 20
Divide both sides by 2
x = 10
Thus for 10 pounds, both companies cost the same
Hello :
(4x^3)(2x)^-4=(4x^3)<span> (2^-4)(x^-4)
=(4/16)(x^-1) = 1/4x</span>