Which represents the solution to the absolute value equation? 5|2x-4|+1=11

Which of these conditions might be true if polygons ABCD and KLMN are similar? The measures of corresponding angles of ABCD and

AlexFokin [52]

Answer: The correct option is

(A) The measures of corresponding angles of ABCD and KLMN are equal, but the lengths of corresponding sides of ABCD are half those of KLMN.

Step-by-step explanation: We are given to select the correct condition that might be true if polygons ABCD and KLMN are similar.

Two polygons are said to be SIMILAR if corresponding angles are congruent and corresponding sides are proportional.

So, options (B), (C), (D) and (E) are not correct because they contradict conditions of similarity.

In option (A), we have

The measures of corresponding angles of ABCD and KLMN are equal. So, they must be congruent.

And the lengths of corresponding sides of ABCD are half those of KLMN.

So, we can write

$AB=\dfrac{1}{2}KL,~~BC=\dfrac{1}{2}LM,~~CD=\dfrac{1}{2}MN,~~AD=\dfrac{1}{2}KN\\\\\\\Rightarrow \dfrac{AB}{KL}=\dfrac{BC}{LM}=\dfrac{CD}{MN}=\dfrac{AD}{KN}=\dfrac{1}{2}.$

Therefore, the corresponding sides are proportional.

Thus, option (A) is true if two polygons are similar.

3 0

2 years ago

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What is three decimals that have a sum of 10.806

White raven [17]

Answer:

10 + 0.8 + 0.006 = 10.806

Step-by-step explanation:

Pick any two decimal numbers. The third one will be the difference between 10.806 and the sum of the two numbers you picked.

For example, choose 938.2 and 3.0055. Their sum is 941.2055. Then the third number that will make the sum be 10.806 is ...

10.806 -941.2055 = -930.3995

So, your three numbers could be ...

{938.2, 3.0055, -930.3995}

7 0

2 years ago

What is the value of n in the equation –negative StartFraction one-half EndFraction left-parenthesis 2 n plus 4 right-parenthesi

charle [14.2K]

Answer:

one

Step-by-step explanation:

:O

10 0

2 years ago

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Please help me on this question

Serggg [28]

-4 = 8m + 18n
-18n = 8m + 4
/-18 /-18 /-18
n = 8m/-18 + 4/-18

I'm not sure so yeah

7 0

2 years ago

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The two lines, P and Q, are graphed below: Line P is drawn by joining ordered pairs negative 8,15 and 6, negative 12. Line Q is

andreyandreev [35.5K]

Solution:

Keep in mind ,

Equation of line joining two points (a,b) and (p,q) is given by :

$\frac{q-b}{p-a}=\frac{y-b}{x-a}$

Equation of line P which is obtained by joining (- 8,15) and (6, - 12) is given by:

$\frac{y-15}{x+8}=\frac{-12-15}{6+8}\\\\ 14(y-15)=-27(x+8)\\\\ 14 y -210= -27 x - 216\\\\ 27 x+14 y+6=0$

Equation of line Q which is obtained by joining (4,16) and (-9, 10) is given by:

$\frac{y-16}{x-4}=\frac{16-10}{4+9}\\\\ 13(y-16)=6(x-4)\\\\ 13 y -208= 6 x - 24\\\\ 6 x-13 y+184=0$

Equation of line P and Q are

27 x+14 y+6=0-------(1)× 2

6 x-13 y+184=0-------(2)× 9

54 x + 2 8 y+12=0---(1)

54 x -117 y +1656=0----(2)

(1) - (2)

145 y= 1644

y=11.33,

27 x+14 y+6=0-------(1)×13

6 x-13 y+184=0-------(1)×14

351 x + 182 y + 78=0-----(1)

84 x - 182 y +2576=0----(2)

(1) + (2)

435 x + 2654=0

x = - 6.11

So, solution set is (-6.11, 11.33)

Option (C) is true. (−2, 4), because this point makes both the equations incorrect.

8 0

2 years ago