Answer:
10 and 6
Step-by-step explanation:
Let A be the area of the rectangle, w the width and L the length
● A = w*L
The length is 4 feet more that the width so L = w+4
● A = w ×(w+4)
● A = w^2 + 4w
The area is 60 ft^2
● w^2 + 4w = 60
Substract 60 from both sides
● w^2 + 4w - 60 = 0
This a quadratic equation
We will solve it by graphing it
The solution are 6 and -10 since the graph intersect with the x-axis in those points (pictures below)
The width is 6 feet long since it is a distance and a distance is always positive.
● w = 6
● L = w + 4
● L = 6 + 4
● L = 10
The width is 6 feet and the length is 10 feet
Answer:
See below
Step-by-step explanation:
To write informal negations, change the existential quantifiers "some, there exists" for universal quantifiers "All, for every" and viceversa. Then write the informal negation of the statement after the quantifiers:
1) Some suspicions were unsubstantiated.
2) Some suspicions were substantiated.
3) All suspicions were substantiated.
4) No suspicions were unsubstantiated. Equivalently, Every suspicion was substantiated.
5) No suspicions were substantiated. Equivalently, Every suspicion was unsubstantiated.
Ln 30 + ln 2 - ln 12
ln (30 * 2) - ln 12 (when there is a + between ln you can multiply the numbers)
ln 60 - ln 12
ln (60/12) (the - sign says to divide the numbers)
ln 5 - final answer
Answer:
√34 units
Step-by-step explanation:
For this problem, you use the Pythagorean Theorum, a^2 + b^2 = c^2. So in this case, the first leg is a, 3, and the second leg is b, 5. So you plug in 3 and 5 for a and b. From there, you get 3^2 + 5^2 = c^2. That simplifies to 9 + 25 = c^2, or 34 = c^2. Take the square root of that, and you get that the hypotenuse length is √34 units.