All categories

3 years ago

Property of Circles: Segment Relationships in Circles

Mathematics

2 answers:

zhuklara [117]3 years ago

5 0

Answer: x=5

Step-by-step explanation:

-Dominant- [34]3 years ago

3 0

Answer:

x = 5

Step-by-step explanation:

Two secants from an external point to a circle, then the product of one secant's external part and the entire secant is equal to the product of the external part and the entire secant of the other, that is

(x - 2)(x - 2 + x + 4) = 4(4 + 5)

(x - 2)(2x + 2) = 4(9) = 36 ← distribute and simplify the left side

2x² + 2x - 4x - 4 = 36

2x² - 2x - 4 = 36 ( subtract 36 from both sides )

2x² - 2x - 40 = 0 ( divide through by 2 )

x² - x - 20 = 0 ← in standard form

(x - 5)(x + 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x + 4 = 0 ⇒ x = - 4

But x > 0 ⇒ x = 5

You might be interested in

The area of a trapezoid is 243cm2. The height is 18cm and the length of one of the parallel sides is 10cm. Find the length of th

Irina18 [472]

Answer:

$Side_2 = 17\ cm$

Step-by-step explanation:

Given

Shape: Trapezoid

$Area = 243cm^2$

$Height = 18cm$

$Side_1 = 10cm$

Required

Determine the length of the second parallel side

The area of a trapezoid is:

$Area = \frac{1}{2}(Side_1 + Side_2) * Height$

Substitute values for Area, Height and Side1

$243 = \frac{1}{2}(10 + Side_2) * 18$

Multiply both sides by 2

$2 * 243 = 2 * \frac{1}{2}(10 + Side_2) * 18$

$486 = (10 + Side_2) * 18$

Divide both sides by 18

$27 = 10 + Side_2$

$Side_2 = 27 - 10$

$Side_2 = 17\ cm$

Hence;

<em>The length of the second parallel side is 17cm</em>

8 0

3 years ago

There are 80 major sources of pollen in state A. These pollen sources are categorized as grasses, weeds, and trees. If the numb

Oxana [17]

Answer:

Grasses: 12

Weeds: 29

Trees: 39

Step-by-step explanation:

Let G, W and T represent number of grasses, weeds, and trees that are major pollen sources.

We have been given that there are 80 major sources of pollen in state A. We can represent this information in an equation as:

$G+W+T=80...(1)$

We are told that the number of weeds is 7 less than thrice the number of grasses. We can represent this information in an equation as:

$W=3G-7...(2)$

We are also told that the number of trees is 3 more than thrice the number of grasses. We can represent this information in an equation as:

$T=3G+3...(3)$

Upon substituting equation (2) and equation (3) in equation (1), we will get:

$G+3G-7+3G+3=80$

$7G-4=80$

$7G-4+4=80+4$

$7G=84$

$\frac{7G}{7}=\frac{84}{7}$

$G=12$

Therefore, there are 12 grasses that are major pollen sources.

Number of weeds that are major pollen sources:

$W=3G-7\Rightarrow 3(12)-7=36-7=29$

Therefore, there are 29 weeds that are major pollen sources.

Number of trees that are major pollen sources:

$T=3G+3\Rightarrow 3(12)+3=36+3=39$

Therefore, there are 39 trees that are major pollen sources.

6 0

3 years ago

Lee is going to make chili for a football party. It will take 1 hour and 10 minutes to prepare all the ingredients and assemble

AlexFokin [52]

Answer:

11:05

Step-by-step explanation:

5 0

3 years ago

two friends travel 150 km and 200 km in time 6 hours and 5 hour respectively. what is the ratio of their average speed?

Minchanka [31]

Answer:

Step-by-step explanation:

5 0

4 years ago

An example of a false and a true equation

lara31 [8.8K]

True equation

2+3 =5

False equation

2+2 = 6

7 0

3 years ago

Read 2 more answers

Property of Circles: Segment Relationships in Circles​

Property of Circles: Segment Relationships in Circles