Let the integers be x-1, x, x+1.
Given,
x -1 + x + x + 1 = 21 + 2(x - 1)
3x = 21 + 2x - 2
x = 19
Hence, the three integers are 18, 19 and 20.
There are 36 combinations, 5 combinations equal 8
(2,6) (3,5) (4,4) (5,3) (6,2) all equal 8
The chance of rolling 8 is 5/36 (combinations that equal 8/total combinations)
5/36=.13888...
Answer:
An equation modeling the situation is : 4 m + 6 n = 180
Step-by-step explanation:
Here, the total number of guests in the banquet hall = 180
Let us assume number of tables ordered with capacity of
4 people each = m
And number of tables ordered with capacity of 6 people each = n
So, total number of people in m tables = m x ( Capacity of 1 table)
= m x (4) = 4 m
And, total number of people in n tables = n x ( Capacity of 1 table)
= n x (6) = 6 n
So, the total capacity of ( m + n) tables = 4 m + 6 n
Also, the total required capacity = 180
⇒ 4 m + 6 n = 180
Hence, an equation modeling the situation is : 4 m + 6 n = 180
Answer:
86.6 feet (3 s.f.)
Step-by-step explanation:
Please see attached picture.
tan60°= height of tower/ 50
Height of tower
= 50tan60°
= 50√3
= 86.6 ft (3 s.f.)
tanѲ= opp/ adj
Answer:
4(k - 3)(3k + 5)
Step-by-step explanation:
Given
12k² - 16k - 60 ← factor out 4 from each term
= 4(3k² - 4k - 15) ← factor the quadratic
Consider the factors of the product of the coefficient of the k² term and the constant term which sum to give the coefficient of the k term
product = 3 × - 15 = - 45 , sum = - 4
Factors are - 9 and + 5
Use these factors to split the middle term
3k² - 9k + 5k - 15 → ( factor the first/second and third/fourth terms
= 3k(k - 3) + 5(k - 3) ← factor out (k - 3)
= (k - 3)(3k + 5)
Hence
12k² - 16k - 60 = 4(k - 3)(3k + 5) ← in factored form
