Answer:
29
Step-by-step explanation:
7 1/4 + 9 3/4 = 17
6 1/4 + 5 1/2 = 12
17 + 12 = 29
Answer:
5x^2 + 12x -3 =0 ---------> solve by quadratic formula
x^2 -4x = 8 ----------> solve by completing the square
4x^2 -25 = 0 ----------> solve by square root method
x^2-5x+ 6 = 0 -----------> solve by factoring
Step-by-step explanation:
1. 5x^2 + 12x -3 =0
The best way to solve this equation is quadratic formula as all the terms in the equation have coefficients it will be convenient to solve it through quadratic formula.
2. x^2 -4x = 8
The best way to solve this equation is by completing the square as the factors cannot be made directly.
3. 4x^2 -25 = 0
the best way to solve this equation is to solve by square root method as the 25 and 4 are perfect squares.
4. x^2-5x+ 6 = 0
The best way to solve this equation is to solve by factoring as it can clearly be seen that it is convenient to make factors ..
Answer:
250
Step-by-step explanation:
If Bulan's team rows their boat at a rate of
2
minutes per
500
meters, they row at a rate of
1
minute per
250
meters. We know this because
1
minute is
1
2
of
2
minutes, and in this time, they will have to have rowed
1
2
the distance they would row in
2
minutes (
500
m).
1
2
of
500
is
250
.
So, we now have the rate in min/m.
If, every
1
minute, Bulan's team rows
250
meters, this means that every
250
meters, they have rowed for
1
minute.
Bulan's team's rowing rate in m/min is
250
m/
1
min.
1/3 ln(<em>x</em>) + ln(2) - ln(3) = 3
Recall that 
, so
ln(<em>x</em> ¹ʹ³) + ln(2) - ln(3) = 3
Condense the left side by using sum and difference properties of logarithms:
Then
ln(2/3 <em>x</em> ¹ʹ³) = 3
Take the exponential of both sides; that is, write both sides as powers of the constant <em>e</em>. (I'm using exp(<em>x</em>) = <em>e</em> ˣ so I can write it all in one line.)
exp(ln(2/3 <em>x</em> ¹ʹ³)) = exp(3)
Now exp(ln(<em>x</em>)) = <em>x </em>for all <em>x</em>, so this simplifies to
2/3 <em>x</em> ¹ʹ³ = exp(3)
Now solve for <em>x</em>. Multiply both sides by 3/2 :
3/2 × 2/3 <em>x</em> ¹ʹ³ = 3/2 exp(3)
<em>x</em> ¹ʹ³ = 3/2 exp(3)
Raise both sides to the power of 3:
(<em>x</em> ¹ʹ³)³ = (3/2 exp(3))³
<em>x</em> = 3³/2³ exp(3×3)
<em>x</em> = 27/8 exp(9)
which is the same as
<em>x</em> = 27/8 <em>e</em> ⁹
Let's find out how much she spent every month.
4000 (starting money) - 2800 (remaining money) = 1200 spent over 3 months
1200/3 = 400 per month was spent
So if she continues to spend 400 a month?
How many months are left? 12 (months of the year) - 3 (months she already spent) = 9
So 9 (remaining months) * 400 (amt per month) = 3600 she'll spend at the going rate over 9 months.
But she only has 2800 left.
2800 (remaining) - 3600 (estimated total of spending) = -800
So she will be 800$ in debt at the end of the year at the current rate.
