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2 years ago

8

If L is parallel to M, find the values of x, y, and all 3 angles.

1 answer:

lesya [120]2 years ago

4 0

Answer:

8x - 14 = 5x + 34 (alternate exterior angles)

8x - 5x = 34 + 14

3x = 48

x = 48/3

x = 16

5y + 16 + 8x - 14 = 180 (linear pair)

5y + 16 + 8(16) - 14 = 180

5y + 16 + 128 - 14 = 180

5y + 130 = 180

5y = 180 - 130

5y = 50

y = 50/5

y = 10

∠ (8x - 14) = 114 [(8 × 16 -14)=114]

∠ (5x + 34) = 114 [(5 × 16 +34)=114]

∠ (5y + 16) = 66 [(5 × 10 +16)=66]

hope this helps you!

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A) Write the sequence of natural numbers which are multiplied by 3 ?

Volgvan

Answer:

a) 3, 6, 9, 12, 15,..., $3\cdot n$ , b) 4, 7, 10, 13, 16,..., $3\cdot n +1$ , c) Both sequences are arithmetic.

Step-by-step explanation:

a) The sequence of natural numbers which are multiplied by 3 are represented by the function $f(n) = 3\cdot n$ , $n\in \mathbb{N}$ . Let see the first five elements of the sequence: 3, 6, 9, 12, 15,...

b) The sequence of natural numbers which are multiplied by 3 and added to 1 is represented by the function $f(n) = 3\cdot n + 1$ , $n\in \mathbb{N}$ . Let see the first five elements of the sequence: 4, 7, 10, 13, 16,...

c) Both sequences since differences between consecutive elements is constant. Let prove this statement:

(i) $f(n) = 3\cdot n$

$\Delta f = f(n+1) -f(n)$

$\Delta f = 3\cdot (n+1) -3\cdot n$

$\Delta f = 3$

(ii) $f(n) = 3\cdot n +1$

$\Delta f = f(n+1)-f(n)$

$\Delta f = [3\cdot (n+1)+1]-(3\cdot n+1)$

$\Delta f = 3$

Both sequences are arithmetic.

8 0

2 years ago

Find S15 for the geometric series 72 + 12 + 2 + 1/3 +…

Gemiola [76]

S1 = 72
S2 = 12 = 72*(1/6)
S3 = 2 = 72*(1/6)^2
.
.
.
S15 = 72*(1/6)^14 = 9.18*10^(-10)

5 0

3 years ago

Please help by solving this

faust18 [17]

Answer:

Step-by-step explanation:

The value of n should be equal to -27.

7 0

2 years ago

Adam has 3 meters of fabric. He plans to cut the fabric into pieces that are ¼ meter long. How many pieces of fabric will Adam h

pickupchik [31]

Answer:

12 pieces of fabric

Step-by-step explanation:

3 / 0.25 = 12

4 0

3 years ago

Keeping in mind the rules for significant figures, determine how many milliliters there are in 0.073 gallons. 1 gallon = 4 quart

andreev551 [17]

we are given

there are in 0.073 gallons

we can see that there are two non-zero places after decimals

so, there are two siginificant figures

step-1: Change gallons to quarts

we know that

1 gallon = 4 quarts

so, we can write as

$0.073gallons=0.073*1gallon$

$0.073gallons=0.073*4quarts$

$0.073gallons=0.292quarts$

step-2: Change into liter

$0.073gallons=0.292quarts$

we know that

1 liter = 1.057 quarts

or

$1 quart=\frac{1}{1.057} litre$

$0.073gallons=0.292*1quarts$

$0.073gallons=0.292*\frac{1}{1.057} litre$

$0.073gallons=0.27625 litre$

step-3: Change into millilitre

we know that

$1L=1000mL$

$0.073gallons=0.27625*1 litre$

$0.073gallons=0.27625*1000 mL$

Since, it is asking for only two significant figures

so, we can also write as

$0.073gallons=0.28*1000 mL$

$0.073gallons=280 mL$ ...................Answer

3 0

3 years ago