A ladder of length 2x+1 feet is positioned against a wall such that bottom is x-1 feet away from a wall. The distance between the floor and top of the ladder is 2x. Assume that a right angle is formed by wall and the floor.
Answers
bottom edgre=x-1
wall edge=2x
so therefor, since this is a right triangle, use pythagorean theorem
a^2+b^2=c^2
c=hypotonues=longest side
b and a=sides touching the right angle
so x-1 and 2x are a and b
2x+1=c
subsitute
(x-1)^2+(2x)^2=(2x+1)^2
x^2-2x+1+4x^2=4x^2+4x+1
add like terms
5x^2-2x+1=4x^2+4x+1
subtract 1 from both sdies
5x^2-2x=4x^2+4x
subtract 4x from both sdies
5x^2-6x=4x^2
subtract 4x^2 from both sides
x^2-6x =0
factor out the x using distributive property which is
ab+ac=a(b+c)
x^2-6x=x(x-6)
(x)(x-6)=0
if xy=0 then assume x and/or y=0
x=0
we remember that one of the side legnths is 2x and if x=0 then the side legnth=0 which is not possible, so we discard
x-6=0
add 6 to both sides
x=6
subsitute and solve
legnth of ladder=2x+1
x=6 subsitute
2(6)+1=12+1=13
legnth of ladder =13 feet
height=2x
2(6)=12
height=12 feet
base=x-1
6-1=5
legnth of ladder=13 feet
height=12 feet
base=5 feet
c^2 = a^2 + b^2
c = 2x+1
a = 2x
b = x-1
plug in and get:
(2x+1)^2 = (2x)^2 + (x-1)^2
4x^2 + 4x + 1 = 4x^2 + x^2 - 2x + 1 [distributed]
4x^2 + 4x + 1 = 5x^2 - 2x + 1 [added like terms]
x^2 - 6x = 0 [subtracted 4x^2 and 4x and 1]
x(x-6)=0 [factored out x]
x can equal 0 or 6
0 would not make any sense physically
therefore x = 6
plug this back into the length of the ladder 2x+1
2(6)+1 = 12 + 1 = 13
therefore the ladder is 13 feet long
Related Questions
Simplify. (8a^3 - 3b^2) - (a^3 + b^2)
Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = -1.
For the function y = 9x, what is the output value if 5 is the input value?y = 4y = 14y = 45y = 95
A motorcycle and a car leave an intersection at the same time. the motorcycle heads north at an average speed of 20 miles per hour, while the car heads east at an average speed of 48 miles per hour. find an expression for their distance apart in miles at the end of t hours.
Answers
150/100= 1.5
As you're looking for 6.5%, you've got to multiply 1.5 by 6.5
1.5*6.5= 9.75
You've then got to add 9.75 and 150 together
150+9.75= $159.75
Therefore, after the sales tax, the cost of the necklace is $159.75
Hope this helps :)
Answers
Answer:
245
Step-by-step explanation:
49 = 20%
2.45 = 1%
245 = 100%
Answers
2 eggs are used in each batch
1.5 amps
7.5 amps
3.3 amps
Answers
So to apply for this values in the formula we have to find total resistance in the cuircuit.
So,
3 + 2 = 5 ohms
Now, lets plug in the equations
1.5 =
5 * 1.5 = I
7.5 = I
So correct option is C
I = 7.5 amps
Answer:
0.3
Step-by-step explanation:
The equation you use is I=
V=volts
R=ohms
I=amps
You add up the ohms since there are more than one
3+2=5
so 5 ohms
the volts are 1.5
Plug in the numbers:
I=
Solve it-
1.5 divided by 5 equals 0.3
Sooooooo...
The answer is: 0.3
Answers
all you have to do is subtract the first number from the second number which is 9. then you add 9 to the last number to get your answer
Answers
So quotient means that you're dividing, so put a ÷
Next, it says the dividend, or the part being divided is -8, so now you have this: -8 ÷
Lastly, it says the divisor, or the part doing the dividing, is a quantity equal to the sum of "some number" (we'll use x) and 3. Since the divisor is one quantity collectively, you have to put it in parentheses.
This gives you: (x + 3)
When you put it all together, you get -8 ÷ (x + 3).
This can also be written as a fraction by putting -8 over (x+3).
The algebraic expression represents the phrase “The quotient of negative eight and the sum of a number and three” as –8 / (x + 3).
What is Algebra?
Algebra is the study of graphic formulas, while logic is the interpretation among those signs.
The algebraic expression represents the phrase is given below.
“The quotient of negative eight and the sum of a number and three”
Let x be the number.
Then the sum of a number and three. Then the expression will be
⇒ x + 3
Then the quotient of negative eight and the sum of a number and three. Then the expression will be given as,
⇒ –8 / (x + 3)
Thus, the quotient of negative eight and the sum of a number and three will be –8 / (x + 3).
More about the Algebra link is given below.
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