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4 years ago

Help explAin & answer

Mathematics

1 answer:

ad-work [718]4 years ago

3 0

Hello,

Sorry, i don't know the theorem in English

"Théorème des angles extérieurs :
la mesure en degré d’un angle extérieur est égale à la moitié de la différence des arcs interceptés par ses côtés."
Here

2x+15=1/2(10x+20-80)
==>4x+30=10x-60
==>6x=30+60
==>6x=90
==>x=15 °

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WILL MARK AS BRAINLIEST

kompoz [17]

Step-by-step explanation:

The pendulum swings over an angle of 2×(2°30') or 5° so we need to convert this to radian measure first:

$5° × \left(\dfrac{\pi}{180°}\right) = 0.0873\:\text{rad}$

so the arc length is given by

$s = r\theta = (50\:\text{cm})(0.0873\:\text{rad}) = 4.36\:\text{cm}$

7 0

3 years ago

Eric’s average income for the first 4 months of the year is $1,450.25, what must be his

drek231 [11]

Answer:

Average income of Eric for the remaining 8 months = $\$1946$

Step-by-step explanation:

Given: Average income of Eric for the first 4 months of the year is equal to $1,450.25

To find: average income for the remaining 8 months so that his average income for the year is $1,780.75

Solution:

Average income = Total income for the year/Total number of months

Average income of Eric for the first 4 months = $1,450.25

So,

Total income of Eric for the first 4 months = 1,450.25 × 4 = 5801

Let x denotes total income of Eric for the remaining 8 months

Total income for the year = 5801 + x

Therefore,

Average income for the year = $\frac{5801+x}{12}$

Also, average income for the year is $1,780.75

$1780.75=\frac{5801+x}{12}\\1780.75\times 12=5801+x\\21369=5801+x\\21369-5801=x\\15568=x$

Total income of Eric for the remaining 8 months = $15568

Average income of Eric for the remaining 8 months = $\frac{15568}{8}=\$1946$

7 0

3 years ago

Ajax is 5 and 1 fourth feet tall. His sister is 3 eighths foot shorter than Ajax How tall is Ajax Sister?

user100 [1]

Answer:

$4\frac{3}{4}$ feet tall

Step-by-step explanation:

Ajax is "5 and 1 fourth feet tall", which can be written as the mixed number $5\frac{1}{4}$ .

His sister is "3 eighths foot shorter", so she's 3/8 feet shorter than 5 1/4.

So, this is just a subtraction problem:

$5\frac{1}{4} -\frac{3}{8}$

To solve this, we want to convert 5 1/4 into an improper fraction, which is: $\frac{21}{4}$ . Now, we want to find a common denominator. In this case, that common denominator is 8, so $\frac{21}{4} =\frac{42}{8}$ .

Finally, we subtract 3/8 from 42/8: $\frac{42}{8} -\frac{3}{8} =\frac{39}{8}$ . So, Ajax's sister is 39/8 feet. Converting this into a mixed number, we have: 39/8 = 4 $\frac{6}{8} =4\frac{3}{4}$ .