All categories

2 years ago

Given that m angle G- 81", what is m angle I? A)81" B)89 C)91 D)99

Mathematics

2 answers:

andrey2020 [161]2 years ago

7 0

The answer to the question is D)99

seraphim [82]2 years ago

3 0

Answer:

$\text{D) }99^{\circ}$

Step-by-step explanation:

Define a cyclic quadrilateral by a quadrilateral that is circumscribed by a circle. In this case, since the quadrilateral shown is circumscribed by a circle, it is a cyclic quadrilateral.

A property of all cyclic quadrilaterals is that their opposite angles are supplementary, meaning they add up to 180 degrees. Since $\angle G$ and $\angle I$ are opposite angles in the quadrilateral, they must be supplementary. Therefore, we have the equation:

$\angle G+\angle I=180,\\81^{\circ}+\angle I=180,\\\angle I=180-81=\boxed{99^{\circ}}$

You might be interested in

Michael earns $8 an hour to baby sit the Jackson family. How many hours does he have to 1 point

notsponge [240]

Answer:

7 hours

Step-by-step explanation:

56/8=7

7 0

3 years ago

alexandr1967 [171]

Answer:

Step-by-step explanation:

4 0

3 years ago

A model village is built to scale. It has a scale of 1 : 23. A road has a real-life length of 1.61 km. What is the length of the

Bess [88]

Answer:

We need to find how much more or less the ratio becomes

1.61 / 23 = 0.07

we multiply 0.07 with 1 to make the ratio even and get your answer

1 x 0.07 = 0.07 on the map

Hope this helps

Step-by-step explanation:

6 0

3 years ago

A tour bus starts from Memphis and heads to Miami at 50 mph. Three hours later a truck pursues the bus at a speed of 65 mph. How

Nina [5.8K]

Three hours after the bus starts out, it's 150 miles ahead of the truck. Then the truck starts out, and it gains (65-50)=15 miles on the bus every hour. If neither of them ever stops for anything, the truck will catch up to the bus in ( 150/15 ) = 10 hours. . . . (The hint is useless.)

7 0

3 years ago

I need help with this problem from the calculus portion on my ACT prep guide

LenaWriter [7]

Given a series, the ratio test implies finding the following limit:

$\lim _{n\to\infty}\lvert\frac{a_{n+1}}{a_n}\rvert=r$

If r<1 then the series converges, if r>1 the series diverges and if r=1 the test is inconclusive and we can't assure if the series converges or diverges. So let's see the terms in this limit:

$\begin{gathered} a_n=\frac{2^n}{n5^{n+1}} \\ a_{n+1}=\frac{2^{n+1}}{(n+1)5^{n+2}} \end{gathered}$

Then the limit is:

$\lim _{n\to\infty}\lvert\frac{a_{n+1}}{a_n}\rvert=\lim _{n\to\infty}\lvert\frac{n5^{n+1}}{2^n}\cdot\frac{2^{n+1}}{\mleft(n+1\mright)5^{n+2}}\rvert=\lim _{n\to\infty}\lvert\frac{2^{n+1}}{2^n}\cdot\frac{n}{n+1}\cdot\frac{5^{n+1}}{5^{n+2}}\rvert$

We can simplify the expressions inside the absolute value:

$\begin{gathered} \lim _{n\to\infty}\lvert\frac{2^{n+1}}{2^n}\cdot\frac{n}{n+1}\cdot\frac{5^{n+1}}{5^{n+2}}\rvert=\lim _{n\to\infty}\lvert\frac{2^n\cdot2}{2^n}\cdot\frac{n}{n+1}\cdot\frac{5^n\cdot5}{5^n\cdot5\cdot5}\rvert \\ \lim _{n\to\infty}\lvert\frac{2^n\cdot2}{2^n}\cdot\frac{n}{n+1}\cdot\frac{5^n\cdot5}{5^n\cdot5\cdot5}\rvert=\lim _{n\to\infty}\lvert2\cdot\frac{n}{n+1}\cdot\frac{1}{5}\rvert \\ \lim _{n\to\infty}\lvert2\cdot\frac{n}{n+1}\cdot\frac{1}{5}\rvert=\lim _{n\to\infty}\lvert\frac{2}{5}\cdot\frac{n}{n+1}\rvert \end{gathered}$

Since none of the terms inside the absolute value can be negative we can write this with out it:

$\lim _{n\to\infty}\lvert\frac{2}{5}\cdot\frac{n}{n+1}\rvert=\lim _{n\to\infty}\frac{2}{5}\cdot\frac{n}{n+1}$

Now let's re-writte n/(n+1):

$\frac{n}{n+1}=\frac{n}{n\cdot(1+\frac{1}{n})}=\frac{1}{1+\frac{1}{n}}$

Then the limit we have to find is:

$\lim _{n\to\infty}\frac{2}{5}\cdot\frac{n}{n+1}=\lim _{n\to\infty}\frac{2}{5}\cdot\frac{1}{1+\frac{1}{n}}$

Note that the limit of 1/n when n tends to infinite is 0 so we get:

$\lim _{n\to\infty}\frac{2}{5}\cdot\frac{1}{1+\frac{1}{n}}=\frac{2}{5}\cdot\frac{1}{1+0}=\frac{2}{5}=0.4$

So from the test ratio r=0.4 and the series converges. Then the answer is the second option.

8 0

1 year ago