Right triangle ABC is located at A (-1.4), B (-1, 1), and C (-5. 1) on a coordinate plane. What is the equation of a circle A with radius AC (x + 1)2 + y - 4)2 = 9
x + 5)2 + y - 1)2 = 25
(x + 5)² + (y - 12 = 16
x + 1)2 + y - 42 = 25

The equation of circle A with radius AC is , or in other words option d.

Step-by-step explanation:

If the radius of this circle is AC, then we can determine the distance between points A ( - 1, 4 ) and C ( - 5,1 ) to come to the length of the radius -

Distance between A and C =

=

= = = 5 units - Which is also the length of the radius of the circle.

So if the radius is given to be 5 in length, knowing that the general equation for a circle is ( where ( h, k ) is the center and r is the radius ) if the radius is 5, , and solution must be option b / option d.

Now if the radius is AC, the center point must be point A ( circle A ). Therefore point ( - 1, 4 ) is the center, and the equation of the circle must be the following -

= - and hence our solution is option d

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x