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Vlad [161]
3 years ago
12

Given the triangle below, answer the following:

Mathematics
2 answers:
OLEGan [10]3 years ago
7 0

Answer:

Step-by-step explanation:

question no . 5

ratio of angle L

take angle as reference angle

using cos rule

cos L = base / hypotenuse

= 4/5

ratio of angle N

take angle N as reference angle

using sin rule

sin N = opposite / hypotenuse

= 4/5

for measure of angle L

cos L = 4/5

cos L = 0.8

L = cos^{-1}(0.8)

L = 36.9

for meanure of angle N

sin N = 4/5

sin N = 0.8

N = sin^{-1}(0.8)

N = 53.1

Alona [7]3 years ago
7 0
<h2>Answer:</h2>

<h2>Step-by-step Explanation:</h2>

<h3>(a) angle L ratio: cosL = 4/5 </h3><h3> angle N ratio: sinN = 4/5</h3><h3>(b) m angle L = cos ^-1(4/5) = 37° </h3><h3> m angle N = sin ^-1(4/5) = 53° </h3><h3>(c) m angle L + m angle N = 90° </h3>

<h2>HOPE IT HELPS!!!!</h2>
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PLEASE GUYS HELP ITS DUE TONIGHT​
KATRIN_1 [288]

Answer:

20. AB = 42

21. BC = 28

22. AC = 70

23. BC = 20.4

24. FH = 48

25. DE = 10, EF = 10, DF = 20

Step-by-step explanation:

✍️Given:

AB = 2x + 7

BC = 28

AC = 4x,

20. Assuming B is between A and C, thus:

AB + BC = AC (Segment Addition Postulate)

2x + 7 + 28 = 4x (substitution)

Collect like terms

2x + 35 = 4x

35 = 4x - 2x

35 = 2x

Divide both side by 2

17.5 = x

AB = 2x + 7

Plug in the value of x

AB = 2(17.5) + 7 = 42

21. BC = 28 (given)

22. AC = 4x

Plug in the value of x

AC = 4(17.5) = 70

✍️Given:

AC = 35 and AB = 14.6.

Assuming B is between A and C, thus:

23. AB + BC = AC (Segment Addition Postulate)

14.6 + BC = 35 (Substitution)

Subtract 14.6 from each side

BC = 35 - 14.6

BC = 20.4

24. FH = 7x + 6

FG = 4x

GH = 24

FG + GH = FH (Segment Addition Postulate)

4x + 24 = 7x + 6 (substitution)

Collect like terms

4x - 7x = -24 + 6

-3x = - 18

Divide both sides by -3

x = 6

FH = 7x + 6

Plug in the value of x

FH = 7(6) + 6 = 48

25. DE = 5x, EF = 3x + 4

Given that E bisects DF, therefore,

DE = EF

5x = 3x + 4 (substitution)

Subtract 3x from each side

5x - 3x = 4

2x = 4

Divide both sides by 2

x = 2

DE = 5x

Plug in the value of x

DE = 5(2) = 10

EF = 3x + 4

Plug in the value of x

EF = 3(2) + 4 = 10

DF = DE + EF

DE = 10 + 10 (substitution)

DE = 20

4 0
3 years ago
Hey can you please help me!
melisa1 [442]

Answer:


Step-by-step explanation:

1) Tangent makes 90 degrees with the radius. Hence

a) Angle ABD = 90-angle BDC = 90-61.3 = 28.7

b) Triangle BCD is isosceles since tangents have equal length.

Hence angle BCD = 180-(61.3+61.3) = 57.4

c) Angle BDC = 57.4 (since triangle BCD is isosceles)

d) Angle BAC and Angle BCD are supplementary. Hence angle BAC = 122,6

-------------------------------------------

2) Arc length of minor arc BC = \frac{79.3}{360} (24) = 5.287

b) ARc length of minor arc = circumference -minor arc

= 18.713

---------------------------------------------

3) circumference = pi d = 3.14(9) = 28.26


6 0
4 years ago
What comes after a million, billion and trillion?
Vinil7 [7]
Million, Billion, Trillion, and Quadrillion
7 0
4 years ago
The gas tank of your car is 40% full. There are 8 gallons of gas in the tank. What is the capacity of the gas tank?
andreyandreev [35.5K]
Percentage by which the gas tank of the car is full = 40%
Amount of gas in the gas tank = 8 gallons
Let us assume the capacity of the gas tank = x gallons
Then
40% * x = 8
(40/100) * x = 8
4x/10 = 8
4x = 8 * 10
4x = 80
x = 80/4
   = 20 gallons
So the total capacity of the gas tank of the car is 20 gallons. I hope the procedure is clear to you.
7 0
4 years ago
Read 2 more answers
Two houses on the same side of the street have house numbers that are consecutive
DochEvi [55]

Answer:

28 and 30

Step-by-step explanation:

'x' = 1st consecutive #

'x+2' = 2nd consecutive #

x + x+2 = 58

2x + 2 = 58

2x = 56

x = 28

x+2 = 30

3 0
3 years ago
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