Answer:
m∠DCQ=56°
Step-by-step explanation:
step 1
Find the measure of arc ABC
we know that
The inscribed angle is half that of the arc it comprises
so
m∠D=(1/2)[arc ABC]
we have
m∠D=78°
substitute and solve for arc ABC
78°=(1/2)[arc ABC]
156°=[arc ABC]
Rewrite
arc ABC=156°
step 2
Find the measure of arc DC
we know that
arc ABC+arc AD+arc DC=360° -----< by complete circle
substitute the given values
156°+92°+arc DC=360°
arc DC=360°-248°
arc DC=112°
step 3
Find the measure of angle DCQ
we know that
The inscribed angle is half that of the arc it comprises
so
m∠DCQ=(1/2)[arc DC]
we have
arc DC=112°
substitute
m∠DCQ=(1/2)[112°]=56°
Answer:
1. 4
2. No solution in real numbers, in complex it is 11i and -11i
3. 4
4. 17
5. 8
Step-by-step explanation:
1. f = sqrt(16) = 4
2. No real solution
3. h^2 = 16, h = 4
4. k-4 = 13, k = 17
5. 2m-1=15, m = 8
Answer:
YES
Step-by-step explanation:
just replace x=3, y=2
5.3 - 3.2 = 15 - 6 = 9
so it is a solution
9514 1404 393
Explanation:
(In order avoid issues with the Brainly censor, we're going to rename point F as point G in this answer. Wherever you see G, you can use F in your own response to this question.)
<u><em>General Approach</em></u>
The perpendicular lines tell you these are right triangles. There are a few ways to show right triangles are congruent, one of which is the "HL theorem." It requires you show the hypotenuse and one leg are congruent in the two triangles.
Here, the hypotenuses, DE and AG, are shown as congruent. All that remains is to show one leg is congruent. We have no information about legs BE and CG, but we do have information that will let us show legs AC and DB are congruent.
_____
<em><u>Proof</u></em>
1. DE ≅ AG, DC ≅ AB, GC⊥AC, EB⊥DB . . . . given
2. m∠EBD = 90°, m∠GCA = 90° . . . . definition of perpendicular lines
3. CD + CB = DB . . . . segment sum theorem
4. AB + CB = DB . . . . substitution property of equality (CD→AB)
5. AB +CB = AC . . . . segment sum theorem
6. DB = AC . . . . transitive property of equality
7. ΔACG ≅ ΔDBE . . . . HL theorem
Set the 2 equations equal to each other since they both equal Y. then solve for X by moving all constants to one side and the X's to the other. you should get x=-3