3 years ago

What is the value of x?

Mathematics

1 answer:

Katena32 [7]3 years ago

6 0

Answer:

Step-by-step explanation:

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A 10-foot ladder leans against a wall so that it is 6 feet high at the top. The ladder is moved so that the base of the ladder t

konstantin123 [22]

Answer:

The top of the ladder is now at 10 ft.

Step-by-step explanation:

At the start, we have a height H=6, a length L=10 and a base B, that has to be calculated by the Pythagorean theorem:

$B^2=L^2-H^2=10^2-6^2=100-36=64\\\\B=\sqrt{64}=8$

The base is moved twice the distance the height moves up.

We called this distance x, so we have:

$L^2=(H+x)^2+(B-2x)^2=H^2+2Hx+x^2+B^2-4Bx+4x^2\\\\L^2=(H^2+B^2)+5x^2+(2H-4B)x\\\\L^2=L^2+5x^2+(2H-4B)x\\\\0=5x^2+(2H-4B)x\\\\5x+(2H-4B)=0\\\\x=\dfrac{4B-2H}{5}=\dfrac{4*8-2*6}{5}=\dfrac{32-12}{5}=\dfrac{20}{5}=4$

The new height (H+x) is

$H'=H+x=6+4=10$

The base travels 2x=8, so the new base B' is 0.

This means that the ladder is all against the wall (L=H').

6 0

3 years ago

What is the answer to -6+5b=6b-7

ratelena [41]

Remember
ou can do anything to an equaiotn as long as you do it to both sides
try to isolate variable and get 1 of it

-6+5b=6b-7
subtract 5b from both sides
-6=b-7
add 7
1=b

8 0

4 years ago

Read 2 more answers

Use the slope formula to find the slope of the line through the points (-7,3) and (7.-7)

Sav [38]

<em> $answer \\ - \frac{5}{7} \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps$ </em>