Answer:
B. In general, the shoe size of a student does not affect the number of books collected.
Step-by-step explanation:
Answer:
From the Pythagorean Theorem we know:
hypotenuse^2 = side^2 + side^2
hypotenuse^2 = 36 + 36
hypotenuse = square root (72)
hypotenuse = 8.48528... feet
Step-by-step explanation:
To determine whether the corresponding terms of 2 arithmetic sequence's added will give new arithmetic sequence or not, Let' take 2 Arithmetic sequences.
In one first term is a1 and common difference is d1, in the other first term is a2 and common difference is d2.
Now nth term for first sequence = a1+(n-1) d1
nth term for second sequence = a2+(n-1) d2
Now add the 2 terms: a1+(n-1)d1 +a2 +(n-1)d2
= a1+a2 + (n-1)(d1+d2)
This is again new arithmetic sequence with first term a1+a2 and common difference d1+d2.
Hence if we add corresponding terms of 2 arithmetic sequence, we will again get an arithmetic sequence.
OK. You asked for it. Here we go.
First, let's gather up the tools we might use ...
some things that we know about triangles:
-- Every triangle: Area = (1/2) x (length of the base) x (the height)
-- Isosceles triangle: It has two sides that are the same length.
-- Right triangle: It has one right angle in it.
The sides that meet at the right angle are called the "legs".
They form a corner there, like this _| .
-------------------------------------------
Now we can start using these tools to hack away at the problem.
Farmer Ted has an isosceles right triangle garden.
The problem asks us to figure out how long the legs are.
Before he changes anything, it looks like this _| and both of
those sides are the same length. Call it 'x' until we figure out
what it really is.
Notice that one of them is the base of the triangle, and the other one
is the height. So the area of this triangle is
(1/2) (x) (x) or (1/2) x² .
-------------------------------
Farmer Ted is never satisfied. Suddenly, one day without warning, he
comes along and makes the garden bigger. He makes one of the legs
7 ft longer, and he makes the other one 5 ft longer.
Now the length of one leg is (x + 7) and the other one is (x + 5) .
They're still the base and height of the triangle, so the area of the
bigger garden is
(1/2) (x + 7) (x + 5).
The problem says that this area is 55 square feet more than the original
area, so look out, here comes the <em>equation </em>:
new area = old area + bigger
(1/2) (x + 7) (x + 5) = (1/2) x² + 55
Locked in the mysterious shadowy crevices of this equation is
everything we need in order to figure out the original length of the legs ...
what we called 'x'.
At this point, we can forget about Farmer Ted, forget about the garden,
and just go back to our laboratory with this equation and solve it to find 'x'.
Let's take it slow and easy, one little step at a time:
<u>(1/2) (x + 7) (x + 5) = (1/2) x² + 55</u>
Multiply each side by 2 : (x + 7) (x + 5) = x² + 110
Expand (FOIL) the left side: x² + 12x + 35 = x² + 110
Subtract x² from each side: 12x + 35 = 110
Subtract 35 from each side: 12x = 75
Divide each side by 12 : <em>x = 6.25 feet</em>
==============================================
OK. That's a very nice number. How do we know whether it's correct ?
Let's check it out, and see if it fits the story:
Original area = (1/2 x base x height) = (0.5 x 6.25 x 6.25) = 19.53125 sq ft
One new leg = (6.25 + 7) = 13.25 ft
Other new leg = (6.25 + 5) = 11.25 ft
New area = (1/2 x base x height) = (0.5 x 13.25 x 11.25) = 74.53125 sq ft
How much bigger is the new area ?
74.53125 - 19.53125 = <em>55 sq ft </em> yay !
When we start with legs that are 6.25-ft and go through the whole story,
the new area is exactly what the problem says it was. So 6.25-ft is the
correct original length of the legs, before Farmer Ted messed with it.
Length=2x
width=x
Perimeter of a rectangle=2(lenght)+2(width)
The first is to find out the measures of this rectangle, that is to say, you have to find the length and width of these rectangle.
We can suggest this equation:
24=2(2x)+2(x)
4x+2x=24
6x=24
x=24/6
x=4
2x=2(4)=8
The lenght will be 8 in, and the length will be 4 in.
The second; you have to calculate the area of this rectangle.
area of a rectangle= lenght x width
area=(8 in)(4 in)=32 in²
answer: the area of Marshall´s rectangular poster would be 32 in²
