A scientist wishes to determine whether there
1 answer:
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Answer:
base = 5 m
Step-by-step explanation:
The area (A) of a triangle is calculated using the formula
A = bh ( b is the base and h the height )
here h = 3b + 1 ( 1 m greater than 3 times the base ), hence
A = b(3b + 1) = 40
Multiply both sides by 2
b(3b + 1) = 80 ← distribute and rearrange
3b² + b - 80 = 0 ← in standard form
Consider the factors of the product of the coefficient of the b² term and the constant term which sum to give the coefficient of the b- term
product = 3 × - 80 = - 240 and sum = 1
The factors are - 15 and + 16
Use these factors to split the b- term
3b² - 15b + 16b - 80 = 0 ( factor the first/second and third/fourth terms )
3b(b - 5) + 16(b - 5) = 0 ← factor out (b - 5)
(b - 5)(3b + 16) = 0
Equate each factor to zero and solve for b
b - 5 = 0 ⇒ b = 5
3b + 16 = 0 ⇒ b = -
However, b > 0 ⇒ b = 5
The base of the triangle is 5 m
Question:
Consider the sequence of numbers:
Which statement is a description of the sequence?
(A) The sequence is recursive, where each term is 1/4 greater than its preceding term.
(B) The sequence is recursive and can be represented by the function
f(n + 1) = f(n) + 3/8 .
(C) The sequence is arithmetic, where each pair of terms has a constant difference of 3/4 .
(D) The sequence is arithmetic and can be represented by the function
f(n + 1) = f(n)3/8.
Answer:
Option B:
The sequence is recursive and can be represented by the function
Explanation:
A sequence of numbers are
Let us first change mixed fraction into improper fraction.
To find the pattern of the sequence.
To find the common difference between the sequence of numbers.
Therefore, the common difference of the sequence is 3.
That means each term is obtained by adding to the previous term.
Hence, the sequence is recursive and can be represented by the function