The degree of the third angle within the triangle will be 58
The angle of a line is 180 so we can find x by doing
180-58 = 122°
Plug it into the midpoint formula.
x1+x2/2; y1+y2/2
R (-5,4) S (3,2)
-5+3/2; 4+2/2
-2/2; 6/2
(-1,3) or "C"
I hope this helps!
~cupcake
Answer:
a=-2
We move all terms to the left:
2(2a+3)-6-(5a+2)=0
We multiply parentheses
4a-(5a+2)+6-6=0
We get rid of parentheses
4a-5a-2+6-6=0
We add all the numbers together, and all the variables
-1a-2=0
We move all terms containing a to the left, all other terms to the right
-a=2
a=2/-1
a=-2
Step-by-step explanation:
We move all terms to the left:
2(2a+3)-6-(5a+2)=0
We multiply parentheses
4a-(5a+2)+6-6=0
We get rid of parentheses
4a-5a-2+6-6=0
We add all the numbers together, and all the variables
-1a-2=0
We move all terms containing a to the left, all other terms to the right
-a=2
a=2/-1
a=-2
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Applying the trigonometry ratio and rationalization, the missing lengths are:
1. x = 12/√3; y = 2√3
2. x = 5√2; y = 5√2
3. b = 24
4. 4√3
5. 5√3
<h3>What are the Trigonometry Ratio?</h3>
The trigonometry ratios are represented as follow:
- SOH is sin ∅ = opp/hyp
- CAH is cos ∅ = adj/hyp
- TOA is tan ∅ = opp/adj.
1. To find x, apply SOH:
opp = 6
hyp = x
adj = y
∅ = 60°
Equation:
sin 60 = 6/x
x = 6/sin 60
x = 6/√3/2 (sin 60 = √3/2)
x = 6 × 2/√3
x = 12/√3
Rationalize
x = 12/√3 × √3 /√3
x = 12√3/3
x = 4√3
To find y, apply TOA:
tan 60 = 6/y
y = 6/tan 60
y = 6/√3 (tan 60 = √3)
Rationalize
y = 6/√3 × √3 /√3
y = 6√3 / 3
y = 2√3
2. To find x, apply SOH:
opp = x
hyp = 10
adj = y
∅ = 45°
Equation:
sin 45 = x/10
x = (10)(sin 45)
x = 10 × 1/√2 (sin 45 = 1/√2)
x = 10/√2
Rationalize
x = 10/√2 × √2 /√2
x = 10√2/2
x = 5√2
To find y, apply CAH:
cos 45 = y/10
y = (10)(cos 45)
y = 10 × 1/√2 (cos 45 = 1/√2)
y = 10/√2
Rationalize
y = 10/√2 × √2 /√2
y = 10√2/2
y = 5√2
3. To find b, apply Pythagorean theorem:
b = √(25² - 7²)
b = 24
4. 12/√3
Rationalize
12/√3 × √3 /√3
12√3/3
4√3
5. 15/√3 × √3 /√3
15√3 /3
5√3
Learn more about trigonometry ratios on:
brainly.com/question/10417664
Answer:
29.5 mm
Step-by-step explanation:
We are told that the average monthly rainfall for 6 months was 28.5 mm.
Thus, total for the 6 months = 28.5 × 6 = 171 mm
Now, we are told that it rained 1 mm extra each month.
So extra for the six months = 1 × 6 = 6mm
New total for 6 months = 171 + 6 = 177 mm
So, new average for 6 months = 177/6 = 29.5 mm
