Answer:
Port r is 100° from Port p and 26km from Port p
Step-by-step explanation:
Lets note the dimension.
From p to q = 15 km = a
From q to r = 20 km= b
Angle at q = 50° + 45°
Angle at q = 95°
Ley the unknown distance be x
Distance from p to r is the unknown.
The formula to be applied is
X²= a²+ b² - 2abcosx
X²= 15² + 20² - 2(15)(20)cos95
X²= 225+400-(-52.29)
X²= 677.29
X= 26.02
X is approximately 26 km
To know it's direction from p
20/sin p = 26/sin 95
Sin p= 20/26 * sin 95
Sin p = 0.7663
P= 50°
So port r is (50+50)° from Port p
And 26 km far from p
<em>1) 5 c + 4 = - 26
5 c = -26 -4
5 c = -30
c = -30 / 5
c = -6 so correct option is B..
2) 3 x - x +2 = 12
2 x +2 = 12
2x = 12-2
2x = 10
x = 10/2
x= 5 so correct option is D
3 ) 3 ( x + 1 )+ 6 = 33
3x + 3 + 6 = 33
3x + 9 = 33
3x = 33-9
3x = 24
x = 24/3
x = 8 so correct option is B
4) y/-6=9
y=9 x -6
y= - 54 there is no such option i guess question is missing
5)(x + 4) /2 = 7
x +4 = 7 x 2
x + 4 = 14
x = 14-4
x = 10 so correct option is D
6)1/3 ( 2x - 8) = 4
2x/ 3 - 8 /3 = 4
2x - 8 / 3 = 4
2x - 8 = 4 x 3
2x - 8 = 12
2x = 12 + 8
2x = 20
x = 20/2
x = 10 so correct option is C
</em>
Answer:
3(x + 4) = 3(x) + 3(4)
3(x + 4) = 3x + 12
3x + 12 = 3x + 12
Subtract 12 from both sides
3x + 12 - 12 = 3x + 12 - 12
3x = 3x
3x - 3x = 3x - 3x
= 0
Answer:
15°.
Step-by-step explanation:
1. Angles ADC and CDB are supplementary, thus
m∠ADC+m∠CDB=180°.
Since m∠ADC=115°, you have that m∠CDB=180°-115°=65°.
2. Triangle BCD is isosceles triangle, because it has two congruent sides CB and CD. The base of this triangle is segment BD. Angles that are adjacent to the base of isosceles triangle are congruent, then
m∠CDB=m∠CBD=65°.
The sum of the measures of interior angles of triangle is 180°, therefore,
m∠CDB+m∠CBD+m∠BCD=180° and
m∠BCD=180°-65°-65°=50°.
3. Triangle ABC is isosceles, with base BC. Then
m∠ABC=m∠ACB.
From the previous you have that m∠ABC=65° (angle ABC is exactly angle CBD). So
m∠ACB=65°.
4. Angles BCD and DCA together form angle ACB. This gives you
m∠ACB=m∠ACD+m∠BCD,
m∠ACD=65°-50°=15°.
Have a good Day!
