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fgiga [73]
3 years ago
7

Trigonometry

Mathematics
1 answer:
artcher [175]3 years ago
7 0

The area of the triangle XYZ is 29.1 square units

Explanation:

Given that the measurements of the sides of the triangle XYZ are XY = 13, XZ=8 and m\angle X=34^{\circ}

We need to determine the area of the triangle XYZ

<u>Area of the triangle:</u>

The area of the triangle can be determined using the formula,

Area=\frac{1}{2} yz \ sin X

Substituting the values, we get,

Area=\frac{1}{2}(13)(8) \ sin 34

Simplifying, we get,

Area=\frac{1}{2}(104) (0.56)

Multiplying the terms, we get,

Area=\frac{58.24}{2}

Dividing the terms, we have,

Area=29.12

Rounding off to the nearest tenth, we get,

\text {Area}=29.1

Thus, the area of the triangle XYZ is 29.1 square units.

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For each of these lists of integers, provide a simple formula orrule that generates the terms of an integer sequence that begins
Anuta_ua [19.1K]

Answer:

b) next three terms of the sequence are 47, 51, 55

c) The next three terms are 1100, 1101, 1110

d) The next three items in the sequence are therefore, 8,8,8

f) The next three terms are 654729075, 13749310575, 316234143225

g) Therefore the next three items in the sequence are 0,0,0

Step-by-step explanation:

b)7, 11, 15, 19, 23, 27, 31, 35, 39, 43, ...

the common difference, d = T_{2} - T_{1} = 11 - 7 = 4

a_{n} = a_{n-1} + 4

43 + 4 = 47

47 + 4 = 51

51 + 4 = 55

next three terms of the sequence are 47, 51, 55

c)  1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011,...

Each of these terms are binary numbers of 1,2,3,4........

The 1st next term is the 12th term = 1100₂

The second next term  is the 13th term = 1101₂

The third next term is the 14th term = 1110₂

The next three terms are 1100, 1101, 1110

d)  1, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, ...

1 is repeated 1 time , 2 is repeated 3 times, 3 is repeated 5 times, 5 is repeated 7 times, the next number will sure be repeated 9 times( the repetition follows an odd number pattern)

To know the next number that will be repeated 9 times:

1+2 = 3

2+3 = 5

3 + 5 = 8

The pattern is that the previous summation adds to the preceding number

The next three items in the sequence are therefore, 8,8,8

f)  1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425,...

The above sequence follows the pattern a_{n} = a_{n-1} (2n -1)\\

The next three terms are the 10th, 11th and 12th terms

a₁₀ = 34459425((2*10)-1)

a₁₀ = 654729075

a₁₁ = 654729075((2*11)-1)

a₁₁ = 13749310575

a₁₂ = 13749310575((2*12)-1)

a₁₂ = 316234143225

The next three terms are 654729075, 13749310575, 316234143225

g) 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1,...

The sequence changes between 1 and 0. 6 zeros are expected next

Therefore the next three items in the sequence are 0,0,0

8 0
2 years ago
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The ratio of pennies: nickels is proportional to the ratio of nickels: dimes, and to the ratio of dimes: quarters. If you have o
vekshin1

Answer:

11 cents

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6(3X +5 ) = 7(2x +2)
boyakko [2]

Answer:

X=-4 last answer i got i hope it is helpful have a nice day

Step-by-step explanation:

Let's solve your equation step-by-step.

6(3x+5)=7(2x+2)

Step 1: Simplify both sides of the equation.

6(3x+5)=7(2x+2)

(6)(3x)+(6)(5)=(7)(2x)+(7)(2)(Distribute)

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Step 2: Subtract 14x from both sides.

18x+30−14x=14x+14−14x

4x+30=14

Step 3: Subtract 30 from both sides.

4x+30−30=14−30

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Step 4: Divide both sides by 4.

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4

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x=−4

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Answer:

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