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Anna11 [10]
3 years ago
11

In triangle ABC segment DE is parallel to the side AC. (The endpoints of segment DE lie on the sides AB and BC respectively).

Mathematics
1 answer:
ivanzaharov [21]3 years ago
5 0

Answer:

6 dm

Step-by-step explanation:

Triangle DBE is similar to triangle ABC, so their side lengths are proportional.

DE/AC = DB/AB

The length of DB can be found from ...

DB +AD = AB

DB = AB -AD = (15 -10) dm = 5 dm

So, we can fill in the proportion:

DE/(18 dm) = (5 dm)/(15 dm)

DE = (18 dm)·(1/3) . . . . . . . . . . simplify, multiply by 18 dm

DE = 6 dm

_____

It can be helpful to draw and label a figure.

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Graph each linear equation that passes through the given pair of points. Use graph paper.
Naya [18.7K]

Answer:

The easier way to solve this is to find the two points in the coordinate axis, and just draw a line that passes through the two points.

But let's be more complete:

Let's find the equations for each line:

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

1) Here the points are (2,2) and (4,5)

then the slope is:

a = (5 - 2)/(4 - 2) = 3/2

y = (3/2)*x + b

And to find the value of b, we just replace the values of one of the points in the equation, in this case i will use (2, 2)

2 = (3/2)*2 + b

2 = 3 + b

2 - 3 = b

-1 = b

y = (3/2)*x - 1

2) Here the points are (0,1/2) and (2,3/2)

then the slope is:

a = (3/2 - 1/2)/(2 - 0) = 1/2

y = (1/2)*x + b

And to find the value of b, we just replace the values of one of the points in the equation, in this case i will use (0, 1/2)

1/2 = (1/2)*0 + b

1/2 = b

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

3) Here the points are (-1,2) and (5,0)

then the slope is:

a = (0 - 2)/(5 + 1) = -1/3

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

And to find the value of b, we just replace the values of one of the points in the equation, in this case i will use (-1, 2)

2 = (-1/3)*-1 + b

2 = 1/3 + b

2 - 1/3 = b

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y = (-1/3)*x + 5/3

4) Here the points are (-5,-3) and (-3,5)

then the slope is:

a = (5 + 3)/(-3 + 5) = -4

y = -4*x + b

And to find the value of b, we just replace the values of one of the points in the equation, in this case i will use (-3, 5)

5 = -4*-3 + b

5 = 12 + b

5 - 12 = b

-7 = b

y = -4*x - 7

Now that we have all the equations, we can find the graphs.

where the colors are:

(4) green

(3) orange

(2) Blue

(1) Gray.

6 0
3 years ago
Solve each inequality then graph the solution
Artist 52 [7]

Answer:

a is x>3

b is _> x/4 +12

c is x>-3

Step-by-step explanation: hope this helps

4 0
3 years ago
Need help please<br>ansewer fast
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14) 6.20

16) 9.1
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3 years ago
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Drag each tile to the correct box.
ivolga24 [154]

Answer:

1 and 27, 12 and 33, 6 and 24, 36 and 81, 12 and 96.

Step-by-step explanation:

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GCF of 1 and 27: 1

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3 0
3 years ago
How many solutions does the equation 9x-3(x+8)=6x-24
Marina86 [1]
Simplifying
9x + -3(x + 8) = 6x + -24

Reorder the terms:
9x + -3(8 + x) = 6x + -24
9x + (8 * -3 + x * -3) = 6x + -24
9x + (-24 + -3x) = 6x + -24

Reorder the terms:
-24 + 9x + -3x = 6x + -24

Combine like terms: 9x + -3x = 6x
-24 + 6x = 6x + -24

Reorder the terms:
-24 + 6x = -24 + 6x

Add '24' to each side of the equation.
-24 + 24 + 6x = -24 + 24 + 6x

Combine like terms: -24 + 24 = 0
0 + 6x = -24 + 24 + 6x
6x = -24 + 24 + 6x

Combine like terms: -24 + 24 = 0
6x = 0 + 6x
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Add '-6x' to each side of the equation.
6x + -6x = 6x + -6x

Combine like terms: 6x + -6x = 0
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Combine like terms: 6x + -6x = 0
0 = 0

Solving
0 = 0
7 0
3 years ago
Read 2 more answers
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