Answer:
20 minutes
Step-by-step explanation:
Melissa works as fast as two Bettys, so working together, they get the job done at the rate 3 Bettys could do it. That time is (60 minutes)/3 = 20 minutes.
Working together, Betty and Melissa can mow the lawn in 20 minutes.
_____
You can also think in terms of mowing rates as lawns per minute. The total mowing rate is ...
Betty's rate + Melissa's rate = (1/60 lawns/min) +(1/30 lawns/min)
= (1/60 +2/60) lawns/min = 1/20 lawns/min
The inverse rate is then ...
20/1 min/lawn
Together, they take 20 minutes to mow 1 lawn.
Answer:
Equation: y = x²
Equation: f(x) = 2(x + 1)² - 1
Step-by-step explanation:
Equation: y = x²
- when x = -2, y = (-2)² = 4 ⇒ (-2, 4)
- when x = 0, y = (0)² = 0 ⇒ (0, 0)
- when x = 2, y = (2)² = 4 ⇒ (2, 4)
Equation: f(x) = 2(x + 1)² - 1
f(-2) = 2(-2 + 1)² - 1
= 2(-1)² - 1
=2(1) - 1
= 1
Therefore, (-2, 1)
f(0) = 2(0 + 1)² - 1
= 2(1)² - 1
=2(1) - 1
= 1
Therefore, (0, 1)
f(2) = 2(2 + 1)² - 1
= 2(3)² - 1
=2(9) - 1
= 17
Therefore, (2, 17)
Answer:
y = - x² - 15x - 56
Step-by-step explanation:
y = - (x + 8)(x + 7) ← expand factors using FOIL
= - (x² + 15x + 56) ← distribute parenthesis by - 1
y = - x² - 15x - 56 ← in standard form
Answer:
x + 9
Step-by-step explanation:
Since the divisor is in the form of <em>x - c</em>, use what is called <em>Synthetic Division</em>. Remember, in this formula, -c gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:
4| 1 5 -36
↓ 4 36
----------------
1 9 0 → x + 9
You start by placing the c in the top left corner, then list all the coefficients of your dividend [x² + 5x - 36]. You bring down the original term closest to <em>c</em><em>,</em> then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have NO REMAINDER. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an x, and the 9 follows right behind it, giving you the other factor of x + 9.
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