Standard quadratic equation .. y = a x^2 + b x + c
<span>parabola 'a' not equal to zero </span>
<span>a<0 parabola opens downward </span>
<span>a>0 parabola opens upward </span>
<span>when |a| >>0 the parabola is narrower </span>
<span>when |a| is close to zero , the parabola is flatter </span>
<span>when the constant is varied it only effects the vertical position of the parabola , the shape remains the same</span>
Given:
The inequality is:
To find:
The integer solutions to the given inequality.
Solution:
We have,
This compound inequality can be written as two separate inequalities 
and 
.
Now,
...(i)
And,
Divide both sides by 2.
...(ii)
From (i) and (ii), we get
Here, 1 is excluded and 3 is included in the solution set. There two integer values 2 and 3 in .
Therefore, the integer solution for the given inequality are 2 and 3.
In the given diagram, the value of the dashed side of rhombus OABC is 5
<h3>Distance between two points </h3>
From the question, we are to determine the length of the dashed line (OA), in rhombus OABC
In the diagram, we can observe that the length of OA is the distance between point A and the origin (O).
Using the formula for calculating distance between two points,
d =√[(x₂-x₁)² + (y₂-y₁)²]
In the diagram,
The coordinate of the origin is (0, 0)
The coordinate of point A is (3, 4)
Thus,
x₁ = 0
x₂ = 3
y₁ = 0
y₂ = 4
Putting the parameters into the formula, we get
OA =√[(3-0)² + (4-0)²]
OA =√(3² + 4²)
OA =√(9+16)
∴ OA =√25
OA = 5
Hence, in the given diagram, the value of the dashed side of rhombus OABC is 5
Learn more on Distance between two points here: brainly.com/question/24778489
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The answer is .45 minutes per mile.
To find the answer, you will set up two fractions and multiply them together, which will result in your answer, miles per minute:
(miles/hour) times (hour/minutes)
27/1 times 1/60 = 27/60 (or .45)
