Answer:
x=21
y=45
z=101
Step-by-step explanation:
Angles crossing each other are congruent
86=4x+2
84=4x
x=21
Quadrilateral has 360 degrees
86 + 86 + 2y+4 + z-7 = 360
172 + 2y+4 + z-7 = 360
2y+4=94
2y=90
y=45
z-7=94
z=101
mark brainliest please!
Answer:
51/12 - 23/4
find the LCM of 12 and 4
51-69/12= -18/12= -9/6 = -3/2 = -1.5
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:
7/16
Step-by-step explanation:
assume she had 8/8 units of sea shells, she then left 1/8 at home
so: 8/8-1/8=7/8
so she has 7/8 units of shells still at home
and she gives half to her friend
so: 7/8*1/2=7/16
She gave 7/16 of the original amount of shells she had to her friend
Answer:
-4
Step-by-step explanation:
The slope is given by
m = (y2-y1)/( x2-x1)
= ( 13-5)/(-2 -0)
= 8/-2
= -4
