Two angles in a triangle add up to 115° what is the size of the third angle
2 answers:
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Given:
Consider the completer question is "If ∆BTS≅∆GHD, BS=25, TS=14, BT=31, GD=4x-11, m∠S=56, m∠B=21 and m∠H=(7y+5), find the values of x and y.
To find:
The values of x and y.
Solution:
We have,
(Given)
(CPCTC)
Divide both sides by 4.
In ∆BTS,
(Angle sum property)
Now,
(CPCTC)
Divide both sides by 7.
Therefore, the value of x is 9 and value of y is 14.
The amount of the radioactive material in the vault after 140 years is 210 pounds
<h3>How to determine the amount</h3>We have that the function is given as a model;
f(x) = 300(0.5)x/100
Where
- x = number of years of the vault = 140 years
- f(x) is the amount in pounds
Let's substitute the value of 'x' in the model
f(x) = 300(0.5)x/100
f(140) = 210 pounds
This mean that the function of 149 years would give an amount of 210 pounds rounded up to the nearest whole number.
Thus, the amount of the radioactive material in the vault after 140 years is 210 pounds
Learn more amount radioactive decay here:
#SPJ1
Answer:
b) There is translation 3 units to the right and 1 unit up
c) The domain is {x I x > 3}
The equation of the asymptote is x = 3
Step-by-step explanation:
* Lets revise the rule of the translation
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
* Now lets solve the problem
b) ∵ f(x) =
∵ The parent function is
∴ x is changed to (x - 3), that means there is a translation 3 units
to the right
∵ We add the parent function by 1, that means there is a translation
1 unit up
* There is translation 3 units to the right and 1 unit up
c) To find the domain of the function, find the values of x which
make the function undefined
∵ is undefined
∴ x - 3 can not be 0
∵ x - 3 = 0 ⇒ add 3 to both sides
∴ x = 3
∴ The domain of the function is all real number greater than 3
* The domain is {x I x > 3}
∵ x can not be 3
∴ There is a vertical asymptote, its equation is x = 3
* The equation of the asymptote is x = 3
# Look to the attached graph for more understand for the domain
and the equation of the asymptote
