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4 years ago

Five angles of a hexagon measure 119, 129, 104, 139, and 95. What is the measure of the sixth angle?

Mathematics

1 answer:

SIZIF [17.4K]4 years ago

8 0

Answer:

134°

Step-by-step explanation:

The sum of interior angles of a regular polygon is: (n - 2)180

Hexagon has six sides, n is 6

Sum of it's angles is (6 - 2)180 = 720

sum of our hexagon:

119 + 129 + 104 + 139 + 95 + x = 720°

x is 134°

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Helga [31]

Answer:

1.2

Step-by-step explanation:

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3 years ago

As part of your retirement plan, you want to set up an annuity in which a regular payment of $35,000 is made at the end of each

Finger [1]

Answer:

Option d)$401,447.24

Step-by-step explanation:

We are given that as part of your retirement plan, you want to set up an annuity in which a regular payment of $35,000 is made at the end of each year at rate of 6% compounded annually for 20 years

So first of all we need to find the future value of annuity using the formula as shown below :

$FV= p\frac{[(1+\frac{r}{n})^{(n)(t)}-1)]}{\frac{r}{n}}$

Here, FV = future value of annuity

p = $35000 (annual deposit)

r is rate = 6% = 0.06

n = number of compounding = 1 ( as we are compounding annually )

t = number of years = 20

So plugging in all the values in the formula , we get

$FV= 35000\frac{[(1+\frac{0.06}{1})^{(1)(20)}-1)]}{\frac{0.06}{1}}$

Simplifying further , we get

$FV= 35000\frac{[(1+0.06)^{20}-1)]}{0.06}$

Plugging in the given values in the calculator , we get

FV = $ 1287495.69

So far we have got the Total amount for annuity , from here we need to use the concept of compound interest and find the principal amount to be deposited to get the required total amount of $ 1287495.69

The formula for compound interest when compounded annually is given by:

$A=P(1+r)^t$

Here A = 1287495.69 (Total amount required)

P = ( principal amount to be deposited to meet the required total amount )

r = 6% = 0.06

t = 20

So plugging in all the known values in the formula , we get

$1287495.69= P(1+0.06)^{20}$

simplifying further, we get

$\frac{1287495.69}{(1.06)^{20}}= P$

so required amount to be deposited is given by :

P = $401,447.24

Hope it was helpful !:)

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3 years ago

Which solid figure has a base that is a polygon and triangular faces that meet

sladkih [1.3K]

The answer is c. prism

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3 years ago

Read 2 more answers

1/32(x-4){2} +1/16(x-7){2} -12.5

frez [133]

Answer:

The chosen topic is not meant for use with this type of problem. Try the examples below.

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Step-by-step explanation:

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3 years ago

How to solve number 44

solniwko [45]

OK.

Let's say a member and a non member each visit the garden ' V ' times.

The non-member's cost for each visit is $6 .
The non member's cost for ' V ' visits is 6 V .
His total cost for the year is 6 V .

The member's cost for each visit is $3.
The member's cost for ' V ' visits is 3V .
His total cost for the year is 3V + the $24 to join.

We want to know what ' V ' is (how many times each one can visit)
if their total costs are the same.

So let's just write an equation that SAYS their costs are the same,
and see what ' V ' turns out to be.

   Non-member's cost for the year = Member's cost for the year

6 V = 3 V + 24

Subtract 3V from each side: 3 V =    24

Divide each side by 3 : V =    8 .

-- If they both visit the garden 1, 2, 3, 4, 5, 6, or 7 times in the year,
the member will spend MORE than the non member.

-- If they both visit the garden 8 times in the year,
they'll both spend the same amount. ($48)

-- If they both visit the garden MORE than 8 times in the year,
the member will spend LESS than the non-member.
______________________________________________

That was the algebra way to do it.

Now here is the cheap, sleazy, logical, easy way to do it:

The non-member spends (6 - 3) = $3 MORE than the member for each visit ?

After how many visits does the $3 more each time add up to the $24 that
it cost the member to join for the year ?

   $24 / $3 = 8 visits .

5 0

4 years ago