3 years ago

Solve the inequality, x - 1 > 6.

Mathematics

1 answer:

Anna11 [10]3 years ago

5 0

Answer:

x > 7

Step-by-step explanation:

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Find the missing lengths: <br> HI=7 and LH=9, find LK.

Katarina [22]

Answer:

LK=12

Step-by-step explanation:

From the given figure, HI=7 and LH=9, and we know that

$(KH)^{2}=(IH)(HL)$

$(KH)^{2}=7{\times}9$

$(KH)^{2}=63$ (1)

Now, from ΔKHL, we have

$(OH)^{2}=(OK)(OL)$

and from ΔOKH,

$(KH)^{2}=(OH)^{2}+(OK)^2$

$(OK)^2=(KH)^2-(OH)^2$

$(OK)^2=63-(OK)(OL)$

$(OK)^2+(OK)(OL)=63$

$OK(OK+OL)=63$

$OK(KL)=63$ (2)

Also, ΔIKL is similar to ΔOHL, therefore

$\frac{OL}{KL}=\frac{9}{16}$

$\frac{KL-OK}{KL}=\frac{9}{16}$

$1-\frac{OK}{KL}=\frac{9}{16}$

$\frac{7}{16}=\frac{OK}{KL}$

Using equation (2), we get

$\frac{7}{16}=\frac{63}{(KL)^2}$

$(KL)^2=\frac{1008}{7}$

$(KL)^2=144$

$KL=12$

Thus, the value of LK is 12.

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3 years ago

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Answer:

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Step-by-step explanation:

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