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1.The Chord Intersection Theorem:

If 2 chords of a circle are AB and CD and they intersect at E, then

AE * EB = CE * ED.

Problem.

Two Chords AB and CD intersect  at E.  If AE =  2cm , EB = 4 and CE = 2.5 cm, find the length of ED.

By the above theorem : 2 * 4 = 2.5 * ED

ED = (2 * 4) / 2.5

= 3.2 cm.

2.1. A given chord on a circle is perpendicular to a radius through its center, and it is at a distance less that the radius of the circle.

2. A circle of center O has a radius of 13 units. If a chord AB of 10 units is drawn at a distance, d, to the center of the circle, determine the value of d.

3. From question 2, the radius = 13 units, length of chord = 10 units and distance of chord to center of the circle is d.

A radius that meet the chord at center C, and divides it into two equal parts.

So that;

AC = CB = 5 units

Applying Pythagoras theorem to ΔOCB,

OC = d, CB = 5 units and OB = 13 units

=  +  

169 = 25 +  

169 - 25 =  

144 =  

⇒ d =  

      = 12 units

Therefore, the chord is at a distance of 12 units to the center of the circle

Step-by-step explanation:

Use the Pythagorean Theorem ( [tex]a^{2}+b^{2} =c^{2}[/tex] )

The longest side is c = the hypotenuse, and a and b = the other sides of the triangle.

a = 4                              First: [tex]4^{2}+x^{2}=8.5^{2}[/tex]

b = x                         Second: [tex]16+x^{2}=72.25[/tex]  

c = 8.5                          Third: [tex]x^{2}=56.25[/tex]

                                  Fourth: [tex]x=\sqrt{56.25}[/tex]

                                      Fifth: x = 7.5

Answer: 10.1

Step-by-step explanation:

Answer:

Pentagon and rhombus

Step-by-step explanation:

Answer:

.33333 or rounded .33

Step-by-step explanation:

There are 4 months that end in an r

This means that 1 third of the months end in r or .33

Answer:

-3x-2(5x-7)=-12

-3x-10x+14=-12

-13x+14=-12

-13x=-16

x=2

Answer:

1 3/7 or 10/7

Step-by-step explanation:

2 is also known as 14/7. 14/7 - 4/7 is equal to 10/7 or 1 3/7.

Answer:

The greatest number of cycling outfits that Mr. Trager can buy would be 2.

Step-by-step explanation:

To answer the question, you need to determine the amount Mr. Traeger has left to spend, then find the maximum number of outfits that will cost less than that remaining amount.

Spent so far:

... 273.98 + 3×7.23 +42.36 = 338.03

Remaining available funds:

... 500.00 -338.03 = 161.97

The cycling outfits are about $80 (slightly less), and this amount is about $160 (slightly more), which is 2 × $80.

Mr. Traeger can buy two (2) cycling outfits with the remaining money.

_____

The remaining money is 161.97/78.12 = 2.0733 times the cost of a cycling outfit. We're sure he has no interest in purchasing a fraction of an outfit, so he can afford to buy 2 outfits.

Answer:

Step-by-step explanation:

[tex] \csc(a) = \frac{1}{ \sin(a) } \\ \sin(a) = \frac{15}{25} \\ \\ \csc(a) = \frac{1}{ \frac{15}{25} } \\ \\ \csc(a) = \frac{25}{15} [/tex]

So no one of the above

Answer:

Sure what are the questions?

Step-by-step explanation:

Trusted helper Ace Carlos

Answer:

you didnt put any questions.

Step-by-step explanation:

Answer:

By using SAS which stands for Side, Angle, Side.

Step-by-step explanation:

This means that if we have two angles and side measures that are equal to the corresponding angles and side measures of the other triangle then they are congruent.

The Answer would be C) 88

Answer:

58.5

Step-by-step explanation:

3x11=33

3x3=9

3x11/2=16.5

16.5+9=25.5

25.5+33=58.5

Answer:

1/2

Step-by-step explanation:

y = mx + b is slope intercept form.

b = y intercept. where the line first passes through on the y axis

that number is 3.

y = mx + 3.

to find M (slope) you have to do RISE / RUN.

Run is going left or right from a point

Rise is going up or down from a point.

To make sure you find the slope, when you Rise and Run, it has to hit another point on the graph.

From the y - intercept 3, RISE (go up) 1 and RUN (go left) 2.

So, the slope is 1/2.

Answer:

StartFraction 1 Over 16 EndFraction of a pound

Step-by-step explanation:

Total pounds of sunflower seeds Jordan bought = 9/16 of a pound

Number of snack bags for his lunch = 9

What is the weight of sunflower seeds in each snack bag?

Weight of sunflower seeds in each snack bag = Total pounds of sunflower seeds Jordan bought / Number of snack bags for his lunch

= 9/16 ÷ 9

= 9/16 × 1/9

= (9*1) / (16*9)

= 9 / 144

= 1/16

Weight of sunflower seeds in each snack bag = 1/16 of a pound

Answer:

1/16 of a pound aka A is the correct answer.

Step-by-step explanation:

Answer:

rational

Step-by-step explanation:

its so because they fit equaly

Answer:

the quotient of a number y and negative three point six is less than six point five.

Answer:

4

Step-by-step explanation:

To Obtian the possible dimensions of the array :

List out the factirs of 54 and use a pair of each in multiplication to obtain 54 ; Theb number of multiplication pairs obtained is the number of possible dimensions of the array :

Factors of 54 : 1, 2, 3, 6, 9, 18, 27, 54

Muliplication pairs :

(6 * 9) = 54

(18 * 3) = 54

(27 * 2) = 54

(54 * 1) = 54

Hence, there are 4 possible dimensions of the array

Answer:

640 cm ^2

Step-by-step explanation:

40x4x4 = 640

let's say b = 20 and h = 4

1/2(20)(4) = 40

scale by 4

b= 80 h = 16

1/2(80)(16) = 640

Answer:

29

Step-by-step explanation:

18+3|6-25|-11

21+19-11

29

Answer:

(-2,0)

Step-by-step explanation:

The solution is where the two graphs intersect.

Answer:

1

Step-by-step explanation:

the first one because if you take the expression that you want, and expanding it out, you will get the first one.

Answer:

A

Step-by-step explanation:

(a^2)^3 (b^5)^3

The powers multiply when written like this. They don't add.

a^6 b^15

A

The answers are 4 and 8.

Because:

x^2 - 12x + 32 =

(x - 4)(x - 8)

x - 4 = 0

   +4    +4

x = 4

x - 8 = 0

  +8    +8

x = 8

Answer: 97

Step-by-step explanation:

10+3+3+33+33+15