The answer is G bc the range is the y values and the graph shows the y values greater than one
CT=90°
BTA=90°
x=29
CT=37
TA=20
CA=57
Step-by-step explanation:
they say BT is an altitude ( or height) . Altitudes are perpendicular meaning that:
BTC =90°
BTA=90°
Therefore:
(3x+3)°=90°
3x=90-3
3x=87°
x=29
CT:
x+8
=29+8
=37
TA:
x-9
=29-9
=20
CA:
=CT+TA
=37+20
=57
Either the question is wrong or it is must be "for all positive integers number" . Because for real number there are examples where it is not true . For example x = 1/2 it gives 0 which is a even number . For all positive integers the statement is true by following proof :
<span>f(x) = 2x-1 </span>
<span>f(x)%2 = (2x-1)%2 = (2x-1+2)%2 = (2x+1)%2 = ((2*(x%2))%2 + 1)%2 </span>
<span>now x%2 is either 1 or 0 </span>
<span>for x%2 = 1 </span>
f(x)%2 = ((2*(1))%2 +1)%2 = (2%2+1)%2 = 1
for x%2 = 0
f(x)%2 = ((2*(0))%2 + 1)%2 = (0+1)%2 = 1
So in all cases f(x)%2 = 1 so f(x) must be odd for all positive integers
Here is another proof by mathematical induction :
<span>let x = 1 be base condition then </span>
<span>f(1) = 1 so it is true for that </span>
<span>Lets assume f(x) is odd </span>
then f(x+1) = 2(x+1)-1
f(x+1) = 2x+2-1
f(x+1) = 2x+1
<span>f(x+1) = 2x-1 + 2 </span>
<span>f(x+1) = f(x) + 2 </span>
<span>f(x) = odd </span>
<span>so f(x) + 2 must be odd.</span>
The answer is all multiples of 90 degrees.
Answer: 90 deg, 180 deg, 270 deg