Which is greater 205.1000 or 0.205

Since the ladder is 10 ft long and its top is 6 feet high(above the ground), we find the distance of its base from the wall since these three (the ladder, wall and ground) form a right angled triangle. Let d be the distance from the wall to the ladder.

So, by Pythagoras' theorem,

10² = 6² + d² (the length of the ladder is the hypotenuse side)

d² = 10² - 6²

d² = 100 - 36

d² = 64

d = √64

d = 8 ft

Since the ladder is moved so that the base of the ladder travels toward the wall twice the distance that the top of the ladder moves up.

Now, let x be the distance the top of the ladder is moved, the new height of top of the ladder is 6 + x. Since the base moves twice the distance the top of the ladder moves up, the new distance for our base is 8 - 2x(It reduces since it gets closer to the wall).

Now, applying Pythagoras' theorem to the ladder with these new lengths, we have

10² = (6 + x)² + (8 - 2x)²

Expanding the brackets, we have

100 = 36 + 12x + x² + 64 - 32x + 4x²

collecting like terms, we have

100 = 4x² + x² + 12x - 32x + 64 + 36

100 = 5x² - 20x + 100

Subtracting 100 from both sides, we have

100 - 100 = 5x² - 20x + 100 - 100

5x² - 20x = 0

Factorizing, we have

5x(x - 4) = 0

5x = 0 or x - 4 = 0

x = 0 or x = 4

The top of the ladder is thus 4 ft higher

7 0

3 years ago

How do you do this please help

nadezda [96]

You can create the equation 1.20x + 2.50y = 300
Where 1.20 is the price of each vinca flower, x is how many vinca you will buy, 2.50 is the price of each phlox flower, y is how many plhox you will buy and 300 is how much money you have.

To get three combinations of how many plhox and vinca flowers you ( or the gardner can buy) with 300, you can just take a random value for x or y, apply it to the equation and then solve the equation for the other
variable ( x or y).
This means:
Pick a number of how many flower you will get of ONE type of flower ( ONLY ONE)
The gardner will not get any Vinca flowers, then x = 0
( as x = how many vinca flower the gardner will get)
now apply 0 to x ( this means substitute x with 0)

(1.20)(0) + 2.50y = 300
Since any number x 0 is 0, the equation will be
0 + 2.50y = 300 or just 2.50y = 300

Now to solve an equation we just need to isolate the variable (y) on one side of the equation and the value on the other.
We can do that by dividing both sides of the equation, so 2.50y turns into 2.50/2.50 times y which is just y.

2.50/2.50 y = 300/2.50
y = 120
And since we chose the value for how many vincas we would buy, we have the x value as well ( 0)
x = 0

So 1 combination can be: 0 Vinca and 120 Plhox

Combination #2 ( I ll stop explaining the steps since I already explained how to do it)

y = 0 ( I chose not to buy any Plhox)

1.20x + (2.50)(0) = 300
1.20x = 300
1.20/120x = 300/120x
x = 25
y= 0
Combination 2: 25 Vincas and 0 plhox

Combination #3:
x = 100 ( I chose to buy 10 vincas)
(1.20)(100) + 2.50y = 300
120 + 2.50y = 300
( I didnt explain thow to isolate a variable in this situation so ill explain it: to isolate this esquation we can subtract 12 from both sides of the equation so 12 cancels out. We need to do it on both sides because otherwise the first side wouldnt be equal to the other sode, and that wouldnt be an equation)

120 - 120 + 2.50y = 300 - 120
2.50y = 180
y = 72
x = 100

Combination 3: 100 Vinca and 72 Plox

I know this is long but I hope it was helpful to you if you didnt know how to solve equations :)

3 0

3 years ago

Help please ?

grandymaker [24]

Answer:

i think it may be "A" but i may be wrong sorry if im wrong

Step-by-step explanation:

5 0

3 years ago

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