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3 years ago

Find the length of the unknown segment (x) in each figure. Use theorem of secant segment and

Mathematics

1 answer:

Over [174]3 years ago

5 0

Answer:

1. x = 6 2. x = 9 3. x = 3

Step-by-step explanation:

Use <u>Intersecting Secants Theorem</u>:

If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

1. AC and AD are secants that intersect at point A

So, AB x AC = AE x AD

$x$ x 15 = 6 x (6 + 9)

15 $x$ = 90

$x$ = 6

2. KM and KN are secants that intersect at point K

So, KL x KM = KO x KN

10 x (10 + 8) = $x$ x 20

180 = 20 $x$

$x$ = 9

3. IG and IF are secants that intersect at point I

So, IH x IG = IJ x IF

$x$ x 39 = 9 x (9 + 4)

39 $x$ = 117

$x$ = 3

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Which region labeled in the graph below would represent the solution (the final shaded area) to the system of linear inequalitie

Elena L [17]

Answer:

Region D.

Step-by-step explanation:

Here we have two inequalities:

y ≤ 1/2x − 3

y < −2/3x + 1

First, we can see that the first inequality has a positive slope and the symbol (≤) so the values of the line itself are solutions, this line is the solid line in the graph.

And we have that:

y ≤ 1/2x − 3

y must be smaller or equal than the solid line, so here we look at the regions below the solid line, which are region D and region C.

Now let's look at the other one:

y < −2/3x + 1

y = (-2/3)*x + 1

is the dashed line in the graph.

And we have:

y < −2/3x + 1

So y is smaller than the values of the line, so we need to look at the region that is below de dashed line.

The regions below the dashed line are region A and region D.

The solution for the system:

y ≤ 1/2x − 3

y < −2/3x + 1

Is the region that is a solution for both inequalities, we can see that the only region that is a solution for both of them is region D.

Then the correct option is region D.

5 0

3 years ago

Solve 9x – 3 > 2x + 11. Show each step of your work please.

Y_Kistochka [10]

Let's do this step by step:
Our objective is to find out x.

First, we have to take the '-3' to the right side, and put it next to the 11. When we do this its operation reverses, so it becomes 11 + 3, which is 14.
So we have 9x > 2x + 14.
Then we do the same to the numbers with X, but this time we take the number from the right side to the left. So 2x to the left (reversed) becomes 9x-2x which is 7x.
So 7x > 14
Now let's simplify, 14/7 = 2
so x = 2

6 0

3 years ago

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Wat the Pythagorean theorem

alexandr402 [8]

The Pythagorean theorem:

The theorem that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

<h2>The Pythagorean Theorem</h2><h3>Discoverer: Pythagoras</h3>

In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides. These calculations were discovered just as a tool of the ancient civilization of Babylonians who used it to divide up farmland; this was roughly 1,000 years before the birth of the discoverer, Pythagoras, a Greek philosopher.

The formula comes like this:
$a^2+b^2=c^2$

5 0

2 years ago

Answer asap please and thank you

nadya68 [22]

Answer:

you need to multiply the numbers

Step-by-step explanation:

1/5 ×2/5= 2/25

4 0

3 years ago

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write the equation of the line with the given slope and y-intercept ..slope is -2 and a y-intercept of 5

iragen [17]

Slope-intercept form: y = mx + b

(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)

Since you know:

m = -2

b = 5 Substitute/plug it into the equation

y = mx + b

y = -2x + 5

5 0

3 years ago