Answer:
∠BAD=20°20'
∠ADB=34°90'
Step-by-step explanation:
AB is tangent to the circle k(O), then AB⊥BO. If the measure of arc BD is 110°20', then central angle ∠BOD=110°20'.
Consider isosceles triangle BOD (BO=OD=radius of the circle). Angles adjacent to the base BD are equal, so ∠DBO=∠BDO. The sum of all triangle's angles is 180°, thus
∠BOD+∠BDO+∠DBO=180°
∠BDO+∠DBO=180°-110°20'=69°80'
∠BDO=∠DBO=34°90'
So ∠ADB=34°90'
Angles BOD and BOA are supplementary (add up to 180°), so
∠BOA=180°-110°20'=69°80'
In right triangle ABO,
∠ABO+∠BOA+∠OAB=180°
90°+69°80'+∠OAB=180°
∠OAB=180°-90°-69°80'
∠OAB=20°20'
So, ∠BAD=20°20'
8(7) = 56
7(6) = 42
6(5) = 30
5(4) = 20
4(3) = 12
3(2) = 6
∴ 3 = 6
Answer:
Rule: If working with an inequality and you either mult. or div. by a negative number, you must reverse the direction of the inequality symbol.
Step-by-step explanation:
Your job here is to simplify 9t-4>32, in which the variable (t) is already positive. Here you do NOT switch signs or reverse the direction of the inequality symbol. Adding 4 to both sides, we get 9t > 36, or t > 4.
If, however, you had -9t-4>32 to work with, the situation would be different because t in this inequality is negative. Adding 4 to both sides results in:
-9t > 36. To solve for t, we must divide both sides by -9 AND reverse the direction of the inequality symbol:
t < -4.
Rule: If working with an inequality and you either mult. or div. by a negative number, you must reverse the direction of the inequality symbol.
32.
V = L*w*h
Where:
V= Volume
L= Length = x+5
w= width = x-2
h= height = 6
Replacing with the values given:
V= (x+5) * (x-2) * 6
V =[ (x*x) + (x*-2) + (5*X) +5*-2) ] * 6
V= [ x^2 - 2x + 5x - 10 ] * 6
V= [ x^2 + 3x - 10] *6
V= (x^2*6) + (3x*6)+ ( - 10 * 6)
V= 6x^2 + 18x - 60
