All categories

3 years ago

Point O is the center of the circle. What is the value of X? Answer options: 24, 15, 27, 20

Mathematics

1 answer:

Tanya [424]3 years ago

4 0

Answer: FIRST OPTION

Step-by-step explanation:

To solve this problem you must apply the Intersecting Secant-Tangent Theorem. By definition, when a secant line and a tangent lline and a secant segment are drawn to a circle from an exterior point:

$(Tangent\ line)^2=(Secant\ line)(External\ Secant\ line)$

The total measure of the secant shown is:

$18+Diameter$

If the radius is 7, then the diameter is:

$D=7*2=14$

Therefore:

$Secant\ line=18+14=32$

You also know that:

$External\ Secant\ line=18\\Tangent\ line=x$

Keeping the above on mind, you can substitute values and solve for x:

$x^{2}=32*18$

$x=\sqrt{576}\\x=24$

You might be interested in

A total of 243 adults and children are at a movie theater. There are 109 more adults than children in the theater. If eh represe

Marina86 [1]

The system should look like this:

eh + b = 243
eh - b = 109

6 0

4 years ago

1.) What is the mode of the data ? Show work ( A.3, B.5, C.8, D.10 )

ArbitrLikvidat [17]

Hey there.

1.) The mode is the number that's most frequent in a given list.
In our list, we have 2, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 9, 10.
Our most frequent number is 6; therefore, our mode is 6.

2.) The median is the number in the middle of a list organized from least to greatest.
2, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 9, 10;
4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 9;
4, 5, 5, 5, 6, 6, 6, 6, 7;
5, 5, 5, 6, 6, 6, 6;
5, 5, 6, 6, 6;
5, 6, 6;
6.
6 is our median.

I hope this helps, despite your answer choices not providing the correct answer.

6 0

3 years ago

Find the distance traveled by a particle with position (x, y as t varies in the given time interval. x = 3?sin2 t, y = 3?cos2 t,

ANTONII [103]

Assuming the particle's position is given by

$\begin{cases}x(t)=3-\sin2t\\y(t)=3-\cos2t\\0\le t\le4\end{cases}$

then the distance traveled over the interval is

$\displaystyle\int_{t=0}^{t=4}\sqrt{\left(\dfrac{\mathrm dx(t)}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy(t)}{\mathrm dt}\right)^2}\,\mathrm dt$
$=\displaystyle\int_0^4\sqrt{(-2\cos2t)^2+(2\sin2t)^2}\,\mathrm dt$
$=\displaystyle\int_0^4\sqrt{4\cos^22t+4\sin^22t}\,\mathrm dt$
$=\displaystyle2\int_0^4\mathrm dt$
$=2(4-0)=8$

5 0

3 years ago

Help please! Brainless and 15 points for correct answer!

inysia [295]

Answer:

Step-by-step explanation:search it in google

7 0

3 years ago

0.77 the digit in the tens place is how many times is the value of the digit in the hundreds place

krek1111 [17]

*Tenths and *hundredths
The digit in the tenths place is 10 times the digit in the hundredths place. hope this helps.

4 0

4 years ago