Answer:
6. x = 28 degrees
7. z = 1.6 cm
Step-by-step explanation:
6.
Notice that you can use the property that tells us that the addition of all internal angles of a triangle must give 180 degrees, then you write the following equation:
50 + 69 + (2 x +5) = 180
combine like terms:
119 + 2 x + 5 = 180
124 + 2 x = 180
subtract 124 from both sides:
2 x = 56
divide by 2 both sides:
x = 56 / 2
x = 28 degrees
Problem 7.
If the two triangles are congruent, then the side MN must equal side RS.
Since MN measure 1,8 cm, then RS must also measure 1.8 cm
and we can write the equation:
1.8 = 3 z - 3
adding 3 to both sides:
1.8 + 3 = 3 z
4.8 = 3 z
dividing both sides by 3:
z = 4.8 / 3
z = 1.6 cm
Answer:
d = 6
Step-by-step explanation:
The nth term of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₄ = 23 and a₁₁ = 65 , then
a₁ + 3d = 23 → (1)
a₁ + 10d = 65 → (2)
Subtract (1) from (2) term by term to eliminate a₁
10d - 3d = 65 - 23
7d = 42 ( divide both sides by 7 )
d = 6
Answer:
Step-by-step explanation:b
Answer:
-13/84
Step-by-step explanation:
Calculation to Find the exact value of the trigonometric expression
First step is to find tan(u)
Based on the information given we were told that sin(u) = -3/5 which means if will have -3/5 in the 4th quadrant would have triangle 3-4-5
Hence:
tan(u)=-3/4
Second step is to calculate tan(v)
In a situation where cos(v) is 15/17 which means that we would have triangle 8-15-17
Hence:
tan(v) = 8/15
Now Find the exact value of the trigonometric expression using this formula
tan(u+v) = (tan(u) + tan(v))/(1-tan(u)tan(v)
Where,
tan(u)=-3/4
tan(v)=8/15
Let plug in the formula
tan(u+v)=(-3/4)+(8/15)÷[1-(-3/4)(8/15]
tan(u+v)=(-45+32)÷(60-24)
tan(u+v)=-13/84
Therefore exact value of the trigonometric expression will be -13/84
