2/5 of the students is equivalent to 394 students. The total number of students involved is thus 394*5/2.
9514 1404 393
Answer:
205 ft
Step-by-step explanation:
Let w represent the width of the rectangle. Then the length is (6w-17) and the area is ...
A = LW
7585 = (6w-17)(w)
6w² -17w -7585 = 0
Perhaps most straightforward is using the quadratic formula to solve this.
For ax² +bx +c = 0, the solution is x = (-b±√(b²-4ac))/(2a). For the above quadratic, the solution is ...

The width is 37 feet, so the length is ...
6(37) -17 = 205 . . . feet
The length of the rectangle is 205 feet.
Answer:
10.5 %
<u>Skills needed: Financial Math Essentials</u>
Step-by-step explanation:
1) First, before getting started, let's assume the price of the product is
. This variable will be used a lot throughout the problem (
).
2) Marking a price above means increasing the price in order to make money off of the purchased product. When raising something by
percent, the new price would be
.
---> In this case, the price increased by
percent.
This means that it would be: 
New price is: 
3) The shopkeeper is then offering a
percent discount off of this marked price. When offering a
percent discount price, the new price (with discount), expressed algebraically is: 
---> the expression above simplifies to 
In this case,
, 
---> 
This means that
, with discount, has been raised
.
10.5 % is the profit percent
(The profit percent being the final marked up price - purchased price)
The curve has been attached and the answer choices are:
y = 3x² – 2x + 1
y = 3x² – 6x + 3
y = 3x²<span> – 7x + 1
</span>
The attached graph has a vertex in the first quadrant. Therefore, the coordinates of the vertex would be both positive.
Let's start with first equation:
y = 3x² – 2x + 1
using the equation of axis:
x = -b/2a
x = 2/6
x = 1/3
SUbstituting the value of x in the main equation to get the y-coordinate of the vertex.
y = 3(1/3)² – 2(1/3) + 1
y = 3/9 – 2/3 + 1
y = 1/3 – 2/3 + 1
y = (1 - 2 + 3)/3
y = 2/3
Hence, the vertex would be:
(h,k) = (1/3 , 2/3)
Also, the leading coefficient is positive, so the parabola would be concave up.
Thus the final answer choice will be:
y = 3x² – 2x + 1
First, let's add 30 to both sides:
4x - 30 +30 ≥ -3x + 12+30
4x ≥ -3x + 42
Now, let's add 3x to both sides
4x +3x ≥ -3x+3x + 42
7x ≥ 42
Let's divide both by 7:
x ≥ 6