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tensa zangetsu [6.8K]
3 years ago
9

I need help with this​

Mathematics
1 answer:
Svetllana [295]3 years ago
7 0

Answer:

m∠z = 106°

Step-by-step explanation:

From the figure attached,

By exterior angle theorem,

m∠z = a + 68°

By linear pair theorem,

m∠a + 142° = 180°

m∠a = 180° - 142°

        = 38°

Therefore, m∠z = 38° + 68°

                          = 106°

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An arithmetic sequence "a" starts with 84, 77 define "a" recursively
sweet [91]

Answer:

First, let's define an arithmetic sequence:

In an arithmetic sequence, the difference between any two consecutive terms is always the same.

Then we can write it in a general way as:

aₙ = a₁ + (n - 1)*d

where:

aₙ is the n-th term of the sequence.

d is the constant difference between two consecutive terms.

a₁ is the initial term of our sequence.

Now in this case we know that the first terms of our sequence are:

84, 77, ...

Then we know the initial term of our sequence:

a₁ = 84.

And the value of d can be calculated as:

d = a₂ - a₁ = 77 - 84 = -7

Then the general way of writing this sequence is:

aₙ = 84 + (n - 1)*(-7)

And the recursion relation is:

aₙ = aₙ₋₁ - 7

So for the n-th term, we must subtract 7 of the previous term.

4 0
3 years ago
If total employee benefits are calculated as a percentage of their gross pay, which of the following employees receives the larg
vlabodo [156]

Consider all employees.

A.

  • gross pay $32,600 - 100%,
  • total job benefits $33,600 - x%.

Then

\dfrac{32,600}{33,600}=\dfrac{100}{x},\\ \\32,600\cdot x=33,600\cdot 100,\\ \\x=\dfrac{33,600\cdot 100}{32,600}=\dfrac{33,600}{326} \approx 103.07.

Employee A receives 3.07% of gross pay in employee benefits.

B.

  • gross pay $32,900 - 100%,
  • total job benefits $34,000 - x%.

Then

\dfrac{32,900}{34,000}=\dfrac{100}{x},\\ \\32,900\cdot x=34,000\cdot 100,\\ \\x=\dfrac{34,000\cdot 100}{32,900}=\dfrac{34,000}{329} \approx 103.34.

Employee B receives 3.34% of gross pay in employee benefits.

C.

  • gross pay $33,400 - 100%,
  • total job benefits $33,900 - x%.

Then

\dfrac{33,400}{33,900}=\dfrac{100}{x},\\ \\33,400\cdot x=33,900\cdot 100,\\ \\x=\dfrac{33,900\cdot 100}{33,400}=\dfrac{33,900}{334} \approx 101.50.

Employee C receives 1.50% of gross pay in employee benefits.

D.

  • gross pay $33,700 - 100%,
  • total job benefits $34,700 - x%.

Then

\dfrac{33,700}{34,700}=\dfrac{100}{x},\\ \\33,700\cdot x=34,700\cdot 100,\\ \\x=\dfrac{34,700\cdot 100}{33,700}=\dfrac{34,700}{337} \approx 102.97.

Employee D receives 2.97% of gross pay in employee benefits.

Answer: correct choice is B.

7 0
3 years ago
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Identify the expression equivalent to 2x + 8 by substituting x = 7 and x = 5.
Nat2105 [25]

Answer:

the answer is C ;P

Step-by-step explanation:

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3 years ago
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Simplify the following expression: 35 + (–13) + (+8) – (–6).
Zina [86]
A. 36 is the correct answer
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A car has 15 gallons of gas in its tank. The car travels 35 miles per gallon of gas. It uses 135 of a gallon of gas to go 1 mile
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2.86 gallons

Step-by-step explanation:

If 1/35 gallon of gas = 1 mile

To travel 100 miles,

1/35 * 100

= 0.0286 * 100

= 2.86 gallons

Therefore, the car needs 2.86 gallons of gas to travel 100 miles

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3 years ago
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