Step-by-step explanation: Just like any of your two-step equations, in this inequality, start by isolating the x term which in this case is 6x by adding 5 to both sides.

That leaves you with 6x < 60 and now just divide both sides by 2 and x < 10.

Notice that because we divide both sides of the inequality

by a positive number, not a negative, we did not change the

direction of the inequality sign.

Finally, put your answer in set notation, {x: x < 10}.

Unlike an equation which normally has one solution, the answer to an inequality must be stated as a solution set because an entire set of answers will work. In this problem, it's any number less than 10.

4 0

3 years ago

What are the coordinates of the center of the circle (x-1)²+(y-2)²=2² and y=2x+2?

defon

Answer:

Compare the given equation of the circle (x - 1)² + (y -2)² = 2²

with standard form of circle: (x - h)² + (y - k)² = r²

Here, (h, k) is the center of the circle

and r is the radius of the circle.

Thus, The center of the circle is: (1, 2)

Also, for finding the point of intersections of (x - 1)² + (y -2)² = 2² and y = 2x + 2,

Substitute the value of y from equation of line in the equation of circle.

(x - 1)² + (2x + 2 - 2)² = 2²

⇒ (x - 1)² + (2x)² = 2²

⇒ x² + 1 - 2x + 4x² = 4

⇒ 5x² - 2x - 3 = 0

Applying Middle term splitting method

5x² - 5x + 3x - 3 = 0

⇒ 5x(x - 1) + 3(x - 1) = 0

⇒ (5x + 3)(x - 1) = 0

⇒ x = $\frac{-3}{5}$ and x = 1

Thus, we get coordinates: $(\frac{-3}{5} ,\frac{4}{5} )$ and (1, 4)

6 0

3 years ago

Graph the line please help

Alex787 [66]

Here’s my answer from desmos!

3 0

3 years ago