Answer:
d = 13 units
Step-by-step explanation:
calculate the distance d using the distance formula
d =
let (x₁, y₁ ) = (1, 8 ) and (x₂, y₂ ) = (6, - 4 )
substitute these values into the formula for d
d =
=
=
=
= 13 units
Answer:
x = -4 is the only solution.
Step-by-step explanation:
The given equation is 2x² + 8x = x² - 16
We can find the value of x by solving the equation.
(2x² + 8x) - x² = (x² - 16) - x²
x² + 8x = - 16
(x² + 8x) + 16 = (-16) + 16
x² + 8x + 16 = 0
(x + 4)² = 0 [ Since a² + b² + 2ab = (a + b)²]
⇒ (x + 4) = 0
x = -4
Therefore, x = -4 is the only solution of the given equation.
x = four plus or minus the square root of eleven
x = negative four plus or minus the square root of five
x = four plus or minus the square root of five
Answer:
Option 2
Step-by-step explanation:
We have been given a quadratic equation
First step in completing method square is to make the coefiicient of 1
Since, in given quadratic equation coefficient of is already 1. we will proceed to the next step which is add and subtract square of the half of coefficient of x in given quadratic equation.
Here, half of coefficient of x that is 8 would be 4 so we will add and subtract in given quadratic equation we will get
Now, we will proceed to the third step that is making the whole square formula according to the terms
Here, we can see that we are geeting the formula of from
The equation will become
After simplifying we will get
After further simplification we will get
After more simplification we will get
Hence, we will get the value of x which is
The solution to the quadraticequation x² - 8x + 5 = 0, using the completing-the-square method is x = 4 ± √11
Option B is the correct answer.
We have,
To solve the quadratic equation x² - 8x + 5 = 0 using the
completing-the-square method, follow these steps:
Move the constant term (5) to the other side of the equation:
x² - 8x = -5
Take half of the coefficient of the x-term (-8) and square it:
(-8/2)² = 16
Add the squared value to both sides of the equation:
x² - 8x + 16 = -5 + 16
x² - 8x + 16 = 11
Rewrite the left side of the equation as a perfect square:
(x - 4)² = 11
Take the square root of both sides, considering both positive and negative square roots:
x - 4 = ±√11
Solve for x by adding 4 to both sides:
x = 4 ± √11
Therefore,
The solution to the quadraticequation x² - 8x + 5 = 0, using the completing-the-square method is x = 4 ± √11
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The constant of proportionality is k = 490 and the equation is y = 490x where x is the number of hours and y is the total number of miles
The time required is 12 hours
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the distance of the aircraft be = x
Let the total time taken by the aircraft be = y
Let the constant of proportionality be k
when x = 1 ,
y = 490
So , the equation will be y = kx
Substituting the values in the equation , we get
y = 490x
when x = 2
y = 490 ( 2 )
y = 980
Now , the time taken by aircraft to travel 5,880 miles is
Substitute the value of y as 5880 in the equation , we get
5880 = 490x
Divide by 490 on both sides of the equation , we get
x = 5880 / 490
x = 12
Therefore , the time taken is 12 hours
Hence , the constant of proportionality is 490
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Answer:
The constant of proportionality is 490
The jet will take 12 hours to travel 5,880 miles
Step-by-step explanation: The miles multiply by 490 each time.
490 x 12 is 5,880