Answer:
b = 60
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
b² + 63² = 87²
b² + 3969 = 7569 ( subtract 3969 from both sides )
b² = 3600 ( take the square root of both sides )
b = = 60
Answer:
p = 5/7
Step-by-step explanation:
The given function is:
for -4 ≦ x < 1
for 1 ≦ x ≦ 5
Part a)
A continuous function has no breaks, jumps or holes in it. So, in order for g(x) to be continuous, the point where g(x) stops during the first interval -4 ≦ x < 1 must be equal to the point where g(x) starts in the second interval 1 ≦ x ≦ 5
The point where, g(x) stops during the first interval is at x = 1, which will be:
The point where g(x) starts during the second interval is:
For the function to be continuous, these two points must be equal. Setting them equal, we get:
3 = 7p - 2
3 + 2 = 7p
p =
Thus the value of p for which g(x) will be continuous is .
Part b)
We have to find p by setting the two pieces equal to each other. So, we get the equation as:
Substituting the point identified in part (a) i.e. x=1, we get:
This value agrees with the answer found in previous part.
Answer: r=14
Step-by-step explanation:
because they are vertical angles
7r+6=8r-8
solving for r you get
r=14
Answer:
9 < x < 17 is the possible length of the third side of a triangle.
Step-by-step explanation:
The Triangle Inequality theorem defines that if we are given two sides of a triangle, the sum of any two given sides of a triangle must be greater than the measure of the 3rd side.
Given the two sides of the triangle
Let 'x' be the length of 3rd size.
According to the Triangle Inequality theorem,
The difference of two sides < x < The sum of two sides
13 - 4 < x < 13+4
9 < x < 17
Therefore, 9 < x < 17 is the possible length of the third side of a triangle.
Answer:
24 blue cars
Step-by-step explanation:
Set up a proportion to solve this...
40/5 = x/3 (forty red cars is to five red cars as 'x' number of blue cars is to 3 blue cars)
Now solve by cross multiplying...
120 = 5x
24 = x