Answer:
The first, second, and fifth statements are correct.
Step-by-step explanation:
We are given a circle with the equation:
And we want to select the statements that are true.
First, we can convert the equation into standard form. We can group each variable:
And complete the square for the first term:
Factor and simplify:
We can rewrite our equation as:
So, this tells us that we have a circle centered on (1, 0) with a radius of 3 units.
In this case, the first statement, second statement (the point (1,0) is on the x-axis), and fifth statements are correct (the square root of 9 is also 3).
Answer: -3/5, -1/2, -7/12, -6/11
Answer:
Enter the equations.
Multiply each equation by a number to get the lowest common multiple for one of the variables.
Add or subtract the two equations to eliminate that variable .
Substitute that variable into one of the equations and solve for the other variable.
15 pounds each and 16 watermelons= 240 pounds. (15x16=240)
The line y = x + 3 has slope 1, so we look for points on the curve where the tangent line, whose slope is dy/dx, is equal to 1.
y² = x
Take the derivative of both sides with respect to x, assuming y = y(x) :
2y dy/dx = 1
dy/dx = 1/(2y)
Solve for y when dy/dx = 1 :
1 = 1/(2y)
2y = 1
y = 1/2
When y = 1/2, we have x = y² = (1/2)² = 1/4. However, for the given line, when y = 1/2, we have x = y - 3 = 1/2 - 3 = -5/2.
This means the line y = x + 3 is not a tangent to the curve y² = x. In fact, the line never even touches y² = x :
x = y² ⇒ y = y² + 3 ⇒ y² - y + 3 = 0
has no real solution for y.
