The answer to the above question can be explained as under -
We know that, the sum of angles of triangle is 180°.
So, vertex angle plus base angles are equal are equal to 180°.
Let the vertex angle be represented by "v" and base angles be represented by "b".
Thus, v + b + b = 180°
So, v + 2b = 180°
Next, the question says, the vertex angle is 20° less than the sum of base angles.
Thus, 2b - 20° = v
<u>Thus, we can conclude that the correct option is A) v + 2b = 180°, 2b - 20° = v</u>
28 bags if you include the cat food (which you would)
Answer:
B
Step-by-step explanation:
First calculate BD using sine ratio in Δ BCD and the exact value
sin60° =
, thus
sin60° =
=
=
=
( cross- multiply )
2BD = 12
( divide both sides by 2 )
BD = 6
-----------------------------------------------------------
Calculate AD using the tangent ratio in Δ ABD and the exact value
tan30° =
, thus
tan30° =
=
=
=
( cross- multiply )
AD = 6
( divide both sides by
)
AD = 6 → B
Check out the attached image for the drawing of how this would look. The drawing isn't 100% needed but it helps I think.
Based on the figure shown in the attachment, we have a right triangle with the adjacent leg of 80 (this leg is closest to the bottom 12 degree angle) and an opposite leg of h
In short,
adjacent = 80
opposite = h
We'll use the tangent rule
tan(angle) = opposite/adjacent
tan(12) = h/80
80*tan(12) = h
h = 80*tan(12)
h = 17.0045249336018 <<-- see note below
So the lighthouse is roughly
17.0045249336018 meters tall
Answer: 17.0045249336018Note: Make sure you are in degree mode. The value is approximate. Round this answer however you need to
Our parent function is f(x)=x^2. A vertical stretch by a factor of k means that every point (x,f(x)), has been transformed into (x,kf(x)). Alex is clearly incorrect as our parent function has been transformed to (x,9f(x)), not (x,3f(x)). A horizontal stretch(or compression) by a factor of k means our function has been transformed to (x/k,f(x)). Here, Marta is saying our function should look like (3x,f(x)). This can also be achieved by plugging 3x into the parent function, which would give us f(3x)=(3x)^2, so it seems that Marta is the correct one.