1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
marta [7]
3 years ago
8

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

ravels toward the wall twice the distance that the top of the ladder moves up. How much higher is the top of the ladder now?

Mathematics
1 answer:
konstantin123 [22]3 years ago
6 0

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').

You might be interested in
YOU GET 10 POINTS HELP HELP HELP HELP ME ME ME ME WITH THE CORRECT ANWSERS
inessss [21]

Answer:

The third choice.

Step-by-step explanation:

This is a linear function.

The equation is y = (x - 5)(5x + 4) - 5x^2.

y = 5x^2 - 25x + 4x - 20 - 5x^2

y = 5x^2 - 5x^2 - 21x - 20

y = -21x - 20

That means this is a linear function, with a linear term of -21x and constant term of -20.

Hope this helps!

7 0
3 years ago
Read 2 more answers
The following table shows the length and width of two rectangles:
zhannawk [14.2K]

Answer:

10x - 8 or 2( 5x - 4)

Step-by-step explanation:

Perimeter of a rectangle = 2( Length + Width)

<u>Rectangle A </u>

Length = x + 8,

Width  = x - 1

Perimeter_A = 2((x + 8) + ( x - 1))\\\\

                 = 2(x + 8 + x - 1) \\\\= 2(2x + 7)\\\\=4x + 14

<u>Rectangle B</u>

Length = 4x + 5

Width = 3x - 2

Perimeter _B= 2((4x + 5) + (3x-2))\\\\

                 =2(4x + 5 + 3x - 2)\\\\=2(7x + 3)\\\\=14x + 6

Perimeter_B - Perimeter_A = (14x +6)-(4x + 14) \\\\

                                       =14x + 6 - 4x - 14\\\\=10x -8\\\\or \\\\=2(5x - 4)

4 0
3 years ago
If x+y=12and x-y=8, what is the value of 2x-xy?
slamgirl [31]

Answer:

2x - xy = 0

Step-by-step explanation:

We need to solve the equations simultaneously to find the values of x and y:

x + y = 12

x - y = 8 - we need to add the equations together

2x = 20

x = 10

Then we substitute x into one of the equations to find y:

10 + y = 12

12 - 10 = y

y = 2

Now we substitute x and y into the final expression:

2(10) - 2(10)

20 - 20 = 0

8 0
3 years ago
Please help me with these questions please I need help? I'm confused with these questions can somebody explain me please.
san4es73 [151]
Rationals are whole numbers no negative numbers or decimals or fractions and Intergers are only negativd numbers. Absolute Value is a negative number changed into a whole number. Hope this helps.
5 0
3 years ago
I have trouble understanding word problems. May I please have help with number 15? Thank you very much!
guapka [62]
Basically you do fractions side by side. so, 6/3=15/h and then cross multiply to get your answer so that would give you 3h=80, then divide 80÷3
5 0
3 years ago
Other questions:
  • Which pair of angles must be supplementary
    12·2 answers
  • Harry rolls 2 fair dice. Probability of both dice showing a factor of 12
    15·1 answer
  • I need this right to pass please helpp
    9·1 answer
  • PLEASE help, I will give BRAINLIEST if you answer/get it correct.
    6·1 answer
  • A graph creates a triangle with the x-axis, the line 3x-2y=0, and the line x+2y=10. Find the area of the triangle formed in squa
    7·1 answer
  • Use the method of disk or washer to set up, but do not evaluate, an integral for a volume of the solid obtained by rotating the
    5·1 answer
  • Given the circle below find the value of arc AB.<br> (13x + 2)<br> A<br> B.<br> 48<br> D
    7·1 answer
  • If 3a = 4b , then a : b= ....<br>(a) 3:4<br>(b) 4:3<br>(c) 3:7<br>(d) 4:7​
    12·2 answers
  • What is the length of YX¯¯¯¯¯¯? Enter your answer as a decimal in the box. Round your final answer to the nearest hundredth. m C
    11·1 answer
  • HELP ASAP PLZ<br> find the perimeter of the figures shown below.
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!