Does the equation x² - 4x + y2 = -3 intersect the x-axis? a. yes, because the center is on the x-axis.

b. no, because the center is at (2,0) and the radius is 1

c. no, because the circle is entirely in the first quadrant.

d. yes, because the center is at (-2,0) and the radius is 3.

 a. yes, because the center is on the x-axis.

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Explanation:

The x intercepts always occur when y = 0.

Replace y with 0 and solve for x

x^2-4x+y^2 = -3

x^2-4x+0^2 = -3

x^2-4x+0 = -3

x^2-4x = -3

x^2-4x+3 = 0

(x-3)(x-1) = 0

x-3 = 0 or x-1 = 0

x = 3 or x = 1

This shows that the x intercepts are located at (3,0) and (1,0). Refer to the diagram below. The diagram shows that the roots are at points A and B. The center is the midpoint of A and B. The center is also on the x axis.

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Here's another approach:

The general template of a circle is (x-h)^2 + (y-k)^2 = r^2

Let's complete the square of the original given equation to get it into that template form above.

x^2 - 4x + y^2 = -3

(x^2-4x) + y^2 = -3

(x^2-4x+4) + y^2 = -3+4 ... add 4 to both sides

(x-2)^2 + y^2 = 1

(x-2)^2 + (y-0)^2 = 1^2

The equation is now in the template form mentioned earlier. The center is at (h,k) = (2,0) which is on the x axis.

omg what happend to your question? if you could edit this question i can

step-by-step explanation:

both the histogram and the stem and leaf plot will visually show how many shoppers were of various ages within each range of data.   the histogram does not give us the specific ages of these shoppers unlike the stem and leaf plot.a histogram does not give us a true range of the data because we do not know exactly how old the shoppers were. a stem and leaf plot will give exact ages, so we can determine the exact range along with all measures of center and the others measures of center.   with the histogram, we cannot find any of these.

step-by-step explanation: