Can someone help with this pleasee?

Given: AC and AE are common external tangents of G and D. BC= 123 GB=20 and AG=101. What is the measure of AC?

Solnce55 [7]

Answer:

The length of AC is 222 units.

Step-by-step explanation:

Given AC and AE are common external tangents of G and D.

BC= 123 , GB=20 and AG=101.

We have to find the measure of AC.

As, a straight line joined from the center i.e radius is perpendicular to tangent drawn. Therefore,

In ΔABG, by Pythagoras theorem

$AG^2=AB^2+BG^2$

⇒ $101^2=AB^2+20^2$

⇒ $AB^2=10201-400=9801$

⇒ AB=99 units.

Hence, AC=AB+BC=99+123=222 units.

The length of AC is 222 units.

8 0

2 years ago

If line KM bisects angle JKL, angle JKL = 92 degrees, and angle MKL = (5x+1) degrees, find the value of

kherson [118]

The value of the variable x is found to be x = 9.

<h3>What is termed as angle bisector?</h3>

In geometry, an angle bisector is a line that divides an angle into two equal angles.
A bisector is something that divides a shape or thing into two equal portions.
An angle bisector is a ray that divides an angle into two equal components of the same measurement.

A bisected angle divides the two sides in equals.

JKM = LKM

As, both are equal.

Then, each of these angles are 1/2 the angle JKL.

1/2 JKL = MKL

1/2 ×( 92) = 5x + 1

Further simplifying;

46 = 5x+1

Subtract 1 from each side

46-1 = 5x

45 = 5x

Divide each side by 5

45/5 = 5x/5

x = 9

Thus, the value of the unknown variable is found to be x = 9 units.

To know more about the angle bisector, here

brainly.com/question/14399747

#SPJ9

6 0

6 months ago

Combine like terms . What is a simpler form of the expression? 2(x/2 -5)-3/2(x+7/4). Please Explain.

Aleks04 [339]

Are you able to expand everything first? from there you would be able to combine line terms. basically if you have 3x+2x it would combine to 5x because they have x in them.

5 0

3 years ago

Read 2 more answers

If a club charges dues of $200 a year, it will have 50 members. For each $5 it raises its dues, it loses a member. USE AN EQUATI

Vikentia [17]

Answer:

The value is $y = \$ 225$

Step-by-step explanation:

From the question we are told that

The amount charge per year is $k = \$ 200$

The number of members it will have at this amount is $n = 50$

The amount amount increase that will lead to the loss of a single member is $z = \$ 5$

Generally the total amount the club would obtain from its members is mathematically represented as

$I = Amount \ due\ paid * Number \ of members$

Now let x denote the number of member lost

Hence

$I = (k + zx) (n-x )$

=> $I = (200 + 5x) (50-x )$

=> $I = 10000+50x-5x^2$

Thus the number of members that be removed to give the maximum income from dues is obtained by differentiating the above equation and equating it to zero

$\frac{dI}{dx} = 50-10x$