Answer:
-197.2
Step-by-step explanation:
Since it is arithmetic series, first find the difference d between the two know series.
3.8 - 6 = - 2.2
d = -2.2
a = 6
Tn = -29.2
Looking for the n term, use the linear method.
Tn = a+( n - 1)d
Substitute all the parameters
-29.2 = 6+( n - 1 ) -2.2
-29.2 = 6 - 2.2n + 2.2
- 29.2 = 8.2 - 2.2n
-29.2 - 8.2 = - 2.2n
-37.4 = -2.2n
n = 37.4/ 2.2
n = 17 terms.
To Find the exact sum of the arithmetic series, use the sum formula below
Sm = n/2( 2a + (n - 1)d)
Sm = 17/2( 2 × 6 + ( 17 - 1 ) -2.2
Sm = 17/2(12 - 35.2)
Sm = 8.5( - 23.2)
Sm = - 197.2
Therefore, the exact sum of the arithmetic series is -197.2
Answer:
(4.2 units)
Step-by-step explanation:
By inspection of the illustration we can see that leg DE has length 3 and that leg DF also has length 3. By the Pythagorean Theorem, 3^2 + 3^2 = 2(3^2); thus, the length of the hypotenuse EF is 3√2, or approximately 4.24 units. The third answer choice (4.2 units) is the correct one.
Answer:
1, 4 or 7
Step-by-step explanation:
The divisibility rule/shortcut for 3 is that the sum of its digits is divisible by 3. So, you currently have 29 (7+1+7+6+2+6+0), and you have to make that number divisible by 3.
adding 1 gets you 30, which we know is divisible by 3.
then, instead of trying every digit, we can note that
30 , 33 , 36 , 39 ....
are divisible by 3.
But the most we can add to the sum of 29 is 9 (because that is the highest digit possible)--so numbers above 38 are irrelevant
so, we want to find out if we can make 29 into 30, 33, or 36
adding 1 to 29 = 30
adding 4 to 29 = 33
adding 7 to 29 = 36
So, by making the first digit 1 , 4 , or 7, you make the number divisible by 3 (making the sentence true)
Answer:
Step-by-step explanation:
1) x² + 6x + 11 = 0
a = coefficient of x² = 1
b = coefficient of x = 6
c = Constant = 11
Roots = (-b ± √b² - 4ac)/2a
Roots = 
2) 2x² - 16x = 50
Divide the whole equation by 2
x² - 8x = 25
Divide the coefficient of x (i. e 8 ) by 2 = 8/2 = 4, Now add 4 to both sides of the equation
x² - 8x + 4 = 25 + 4
x² - 2*4*x + 2² = 29
(x - 2)² = 29
Take square root both side
Answer:
Step-by-step explanation:
