Answer:
4.625 gallons
Step-by-step explanation:
1. 11 pints plus 13 quarts is 18.5 quarts
2. 18.5 quarts is equal to 4.625 gallons
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 _| .
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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 .
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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.
Answer:
Option B 
Step-by-step explanation:
we know that
The area of the rectangle room, is equal to
where
L is the length
W is the width
we have
Remember that
1 yard= 3 feet
Convert yards to feet
The area is equal to
Answer:
The y-intercept of f(x) is equal to 2 times the y-intercept of g(x).
Step-by-step explanation:
Answer: The correct answer is option B: 19%
Step-by-step explanation: The bar graph according to the question has the following set of data;
Cereal ----------34
Eggs and Bacon ----------21
Pastries ----------39
Bagels ----------48
Waffles ----------38
The total from this set of data is 180 (that is the summation of all the observed data). The portion taken up by cereals can be derived as follows;
Cereal = (34/180) x 360
Cereal = 68 degrees
Note that we have used degrees as the unit since the data would be transferred to a pie chart. Hence on the pie chart it occupies 68 degrees of the entire 360 degrees.
In order to find out what percentage this represents we can now express 68 degrees as a percentage as follows;
Cereal = (68/360) x 100
Cereal = 18.8888888
Cereal ≈ 19
Therefore cereal occupies 19 percent of the pie chart.
