Use the multiplier method to decrease £262 by 39%You must show your working.
2 answers:
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<h2>Steps:</h2>
So for this, we will be completing the square to solve for m. Firstly, subtract 8 on both sides:
Next, divide both sides by 2:
Next, we want to make the left side of the equation a perfect square. To find the constant of this perfect square, divide the m coefficient by 2, then square the quotient. In this case:
-8 ÷ 2 = -4, (-4)² = 16
Add 16 to both sides of the equation:
Next, factor the left side:
Next, square root both sides of the equation:
Next, add 4 to both sides of the equation:
Now, while this is your answer, you can further simplify the radical using the product rule of radicals:
- Product rule of radicals: √ab = √a × √b
√12 = √4 × √3 = 2√3.
In exact form, your answer is
In approximate form, your answers are (rounded to the hundreths)
Answer
a) C
b) B
c) C, E
d) 15.5
e) 0.7
f) 67.7
Step-by-step explanation
a) A linear equation can be written as where
is the slope and
is the intercept on the
-axis. The slope describes how
changes when
changes. A negative value means the it is a decreasing change. In our case,
is
and
is
. Thus, the slope of the equation is
. This means that the area of glacier is decreasing by
every year since 2000.
b) The -intercept (= 16.2
) represents the area covered when
. But
starting from year 2000. This intercept then represents the area covered by glacier in the year 2000. Therefore, the area covered by glacier in 2000 was 16.2
.
c) means the area covered after year 2000. Setting it to 12 means the area covered after
years is 12
).
is therefore the number of years since 2000 that the total area covered will be 12
).
d) to 1 decimal place.
e) The term involving represents the disappearing area. In 12 years, the disappeared area is
to 1 decimal place.
f)
years to 1 decimal place.