Answer:
b ≈ 101.52
Step-by-step explanation:
Given two sides and the angle between, the Law of Cosines is useful.
b^2 = a^2 +c^2 -2ac·cos(B)
b^2 = 105^2 +9^2 -2·105·9·cos(65°) ≈ 10307.251
b ≈ √10307.251
b ≈ 101.52
The product of two positive consecutive integers is 24 more than 6 times the first number.
1 answer:
Answer:
The product of two integers is 72.
Step-by-step explanation:
Let,
x and x+1 be the two consecutive positive integers.
According to given statement;
The product of two positive consecutive integers is 24 more than 6 times the first number.
x(x+1) = 6x+24
Either,
x-8 = 0
x=8
Or,
x+3 = 0
x=-3
As the integer is positive, therefore, the two integers are 8 and 9.
Product of two integers = 8*9 = 72
Hence,
The product of two integers is 72.
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Answer and Explanation:
Given : The quadratic function
To find : Determine the following ?
Solution :
The x -intercept are where f(x)=0,
So,
Applying middle term split,
The x-intercepts are (4,0) and (-3,0).
The smallest x-intercept is x=-3
The largest x-intercept is x=4
The y -intercept are where x=0,
So,
The y-intercept is y=12.
The quadratic function is in the form,
On comparing, a=-1 , b=1 and c=1 2
The vertex of the graph is denote by (h,k) and the formula to find the vertex is
For h, The x-coordinate of the vertex is given by,
For k, The y-coordinate of the vertex is given by,
The vertex of the function is
The x-coordinate of the vertex i.e. is the axis of symmetry,
So, (solved above)
The axis of symmetry is .