Answer:
<D = 100
<E =30
<F =50
Step-by-step explanation
Given that triangles triangle ABC and triangle DEF are similar, this means that their angles are congruent i.e
<A = <D
<B = <E
<C = <F
Given
<A = 100 then <D = 100
<B = 30°, then <E = 30°
To get <F, we will use the expression
<D+<E+<F = 180 (sum of angles in a triangle is 180°)
100+30+<F = 180
130+<F = 180
<F = 180-130
<F = 50°
Hence the measure of <F is 50°
In both cases you may well benefit from graphing the functions.
Do you recognize f(x) = (x + 1)^2 - 1 as a quadratic function, whose graph is that of a parabola that opens up? By comparing this to y = a(x-h)^2 + k, we see that a=1, h= -1 and k = -1. The vertex is at (h,k), which here is the point (-1, -1). This is the minimum value of the function. Thus, the range of this function is [-1, infinity).
Now for the function f(x) = 7x - 11: This is a linear function whose graph is (surprise!) a straight line. When x increases, y increases, without limits to either. Similarly, when x decreases, y decreases.
Thus the range includes all real numbers: (-infinity, infinity).
Answer: 36 degrees
Step-by-step explanation:
subtract 5 from 30=25
add 11 to 25
25+11=36
