Answer:
(6,3) and (2,2)
Step-by-step explanation:
y - y1 = m(x-x1)
y - 3 = 1/4(x - 6)
y = (1/4)x + 3/2
y intercept is 3/2 and slope is 1/4
Answer:
Step-by-step explanation:
It should take six hours.
Ten times three would make thirty, doing the same to the number of hours[2 hours] we multiply it by three which leaves us with six miles.
Ed runs thirty miles in six hours.
Answer:
6 hours
10 miles takes 2 hours
so 30 miles will take 6 hours
(x^2– 8)^2 + x^2 – 8 = 20
x=
The possible values of x that satisfy the equation are
x = ±√3 and x = ±2√3.
Here, we have,
To find a value of x that is a solution to the equation, we need to solve the equation for x.
Let's go through the steps:
Start with the given equation:
(x² - 8)² + x² - 8 = 20
Expand the squared term (x² - 8)²:
(x² - 8)(x² - 8) + x² - 8 = 20
Simplify:
(x⁴ - 16x² + 64) + x² - 8 = 20
Combine like terms:
x⁴ - 16x² + x² + 64 - 8 = 20
Simplify:
x⁴ - 15x² + 56 = 20
Rearrange the equation to bring all terms to one side:
x⁴ - 15x²+ 56 - 20 = 0
Simplify:
x⁴ - 15x² + 36 = 0
Now, we have a quadratic equation in terms of x².
Let's substitute y = x² to simplify further:
y² - 15y + 36 = 0
Solve the quadratic equation for y:
(y - 3)(y - 12) = 0
This gives us two possible values for y:
y - 3 = 0 --> y = 3
y - 12 = 0 --> y = 12
Substitute back y = x²:
For y = 3:
x² = 3 --> x = ±√3
For y = 12:
x² = 12 --> x = ±√12 = ±2√3
So, the possible values of x that satisfy the equation are x = ±√3 and x = ±2√3.
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Answer:
x = 2 sqrt(3) or x = -2 sqrt(3) or x = sqrt(3) or x = -sqrt(3)
Step-by-step explanation:
Solve for x:
-8 + x^2 + (x^2 - 8)^2 = 20
Expand out terms of the left hand side:
x^4 - 15 x^2 + 56 = 20
Subtract 20 from both sides:
x^4 - 15 x^2 + 36 = 0
Substitute y = x^2:
y^2 - 15 y + 36 = 0
The left hand side factors into a product with two terms:
(y - 12) (y - 3) = 0
Split into two equations:
y - 12 = 0 or y - 3 = 0
Add 12 to both sides:
y = 12 or y - 3 = 0
Substitute back for y = x^2:
x^2 = 12 or y - 3 = 0
Take the square root of both sides:
x = 2 sqrt(3) or x = -2 sqrt(3) or y - 3 = 0
Add 3 to both sides:
x = 2 sqrt(3) or x = -2 sqrt(3) or y = 3
Substitute back for y = x^2:
x = 2 sqrt(3) or x = -2 sqrt(3) or x^2 = 3
Take the square root of both sides:
Answer: x = 2 sqrt(3) or x = -2 sqrt(3) or x = sqrt(3) or x = -sqrt(3)