Answer:
Parking lot is 60m wide
Step-by-step explanation:
In this question. We are asked to calculate the width of the parking lot. We proceed as follows:
We know that the total length of the field and the parking lot is 300m while the total width is 200m. We should remember that the field is rectangular in nature.
Since the parking lot is x meters, the length of the field would simply be (300-2x)m while the width of the field would be (200-x). The width would also have been 200-2x but we must remember that the field is only covered on 3 sides.
Area of the field is 30,000. This means if we multiply both, we get 30,000.
Mathematically;
(300-2x)(200-x) = 30,000
60,000-300x-400x+ 2x^2 = 30,000
2x^2-700x-30,000= 0
We can see we now have a quadratic equation we need to solve.
2x^2+500x-1200x-30,000= 0
2x(x+250) -120(x+250) = 0
(2x-120)(x+250) = 0
2x-120= 0 or x+250=0
2x = 120or x = -250
x = 120/2 or x= -250
x = 60 or x=-250
We discard x = -100 as x is length and cannot be negative
Hence, x = 60m
One rose is 50 cents, so 2 roses cost $1 ( 50 cents x 2).
2 roses per dollar x 20 dollars = 40 total roses sold.
When they sell $20 dollars they make $6, so that means they pay 20-6 = $14 dollars for the 40 roses.
$14 / 40 roses = 0.35 per rose.
She pays 35 cents per rose.
The formula in order to obtain the vertex form of a
quadratic equation is given as
y=a(x-h)^2+k where (h,k) is the vertex of the quadratic
equation which is parabolic in shape and it is opening upward.
As given in the problem, y=6x^2+12x-10
Using the formula, we can transformed the quadratic equation
y=6x^2+12x-10 into its vertex form:
y=6x^2+12x-10
<span>y= (6x^2+12x)-10 (grouping)</span>
y=6(x^2+2x)-10 (factoring Common terms per
group)
y=6(x^2+2x+1)-10-6 (Completing the squares)
<span>y=6(x+1)^2-16
(Factor and Simplify) </span>
Hence, the vertex form of y=<span>6x^2+12x-10 is y=6(x+1)^2-16</span>
Answer:
The correct options are 1, 3 and 4.
Step-by-step explanation:
We need to find the expressions whose simplified form is a rational number.
Rational number: If a number is defined in the form of p/q where p and q are integers and q≠0, then it is called a rational number.
For example: 0,2, 4.3 etc.
Irrational number: If a number can not defined in the form of p/q, where p and q are integers and q≠0, then it is called an irrational number.
First expression is
12 is a rational number.
Second expression is
is an irrational number.
Third expression is
21 is a rational number.
Fourth expression is
5 is a rational number.
Therefore, the correct options are 1, 3 and 4.
The Given Sequence is an Arithmetic Sequence with First term = -19
⇒ a = -19
Second term is -13
We know that Common difference is Difference of second term and first term.
⇒ Common Difference (d) = -13 + 19 = 6
We know that Sum of n terms is given by : 
Given n = 63 and we found a = -19 and d = 6
The Sum of First 63 terms is 10521
