Answer:
40
Step-by-step explanation:
Going from left to right
We need to find the angle from the first triangle
The sum of the angles of a triangle is 180
80+25+x = 180
Combine like terms
105+ x = 180
Subtract 105 from each side
105-105+x = 180-105
x = 75
Then we have 3 angles that make a straight line and a straight line is 180
x + 50 + y = 180
75+ 50 + y = 180
Combine like terms
125 + y = 180
Subtract 125 from each side
125-125+y = 180-125
y = 55
We now have the triangle on the right
The angles add to 180
55+85+ ? = 180
Combine like terms
140+ ? = 180
Subtract 140 from each side
140+? - 140 = 180-140
? = 40
The population size after 6 years and after 8 years are 147 and 169 population respectively
<h3>Exponential functions</h3>
The standard exponential function is expressed as y = ab^x
where
a is the base
x is the exponent
Given the function that represents the population size P (t) of the species as shown;
For the population size after 6 years
For the population after 8 years
Hence the population size after 6 years and after 8 years are 147 and 169 population respectively
Learn more on exponential function here: brainly.com/question/2456547
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(The answer is 12.082.) Juan used 12.082 meters of rope.
A translation of 2 units up will increase the y coordinate by 2 units and a translation by 5 units to the left will decrease the x coordinate by 5. Hence after these translations point (2,2) becomes
<span>(2 - 5 , 2 + 2) = (-3,4) </span>
When point (-3,4) is reflected in the x axis, its y coordinate changes sign and point (-3 ,4) becomes
<span>(-3,-4)</span>
If the surface area of the cylinder is 12π square meters. Then the radius of the sphere will be 1.7 meters.
<h3>What is a cylinder?</h3>
A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.
A cylinder has a height of 4 meters and a radius of 1.5 meters.
Then the approximate radius of a sphere that has the same surface area as the cylinder.
We know that the Surface area of the cylinder will be is given as
Surface area = 2πrh
Surface area = 2 x π x 1.5 x 4
Surface area = 12π square meters
Then we have
Surface area of sphere = surface area of cylinder
4πr² = 12π
r² = 3
r = 1.7 meters
More about the cylinder link is given below.
brainly.com/question/3692256
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