The watch costed $400 before the discount.
76 * 100 = 7,600
7,600 / 19 = 400
Since they mowed
of the lawn in two equal parts, we need to split the pieces that were mowed into two equal groups. We know that in total they mowed 8 out of the total 9 pieces of lawn, so two equal groups that make 8 would be of size 4, since
. Then they each mowed
of the lawn.
Answer:
k = - 14
Step-by-step explanation:
given that (x - 5) is a factor of the polynomial then x = 5 is a root and
x³ - x² + kx - 30 = 0 for x = 5, that is
5³ - 5² + 5k - 30 = 0
125 - 25 + 5k - 30 = 0
70 + 5k = 0 ( subtract 70 from both sides )
5k = - 70 ( divide both sides by 5 )
k = - 14
The Law of Sines may be written as
b/sin(B) = c/sin(C)
Multiply each side by sin(B).
b = (c*sin(B))/sin(C)
The correct answer is C.
Answer: C. (c*sin B)/sin C
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.
