Answer:
steps below
Step-by-step explanation:
To construct tangent line to a circle based on two main properties of tangent line and inscriber triangle of circle
1. A line is tangent to a circle when it intersects the circle in one point. At that point, the radius of the circle forms a right angle with the tangent line. If the radius forms a right angle with the tangent line, <u>then the segment OP becomes the hypotenuse of the right triangle.</u>
2. a triangle inscribed in a circle having a diameter (OT) as one side is a right triangle.
Construction:
1. connect P and circle center "O"
2. construct perpendicular bisector of PO --- AB, Intersect M will be the center of new circle and its radius is MP
3. With the center of "M" and radius MP: construct a circle and intersect original circle at "T" and "T'"
4. PT and PT' are the tangent lines
Answer:
The coordinates of the point that divides the line internally in the given ratio is (7,3)
Step-by-step explanation:
To find this coordinates, we use the in renal division formula
we have this as;
(x,y) =( nx1 + mx2)/(m + n) , (ny1 + my2)/(m + n)
(x1,y1) = (4,-3)
(x2,y2) = (8,5)
(m,n) = (3,1)
So, substituting these values, we have ;
(x,y) = (1(4) + 3)8))/(3 + 1) , (1(-3) + 3)5)/(1 + 3)
(x,y) = (28)/4, (12/4)
(x,y) = (7,3)
Answer:
Second and last options are correct answers.
Step-by-step explanation:
Correct options are:
156 more miles.
My Work:
The Sister drove 5/4 of 156 miles. <u />The <u />"of" stands for multiplication. 5/4 * 156/1
<u />After we solve the equation, we learn that the Sister drove 195 miles, which would mean that the sister probably drove too far, leaving Nicole to drive back for them.
Because Nicole is driving the rest of the 195-156 miles, if we use the triangle sum method from elementary school, we can flip the answer to 195-156 with 156 and know that the Sister drove 156 more miles than Nicole without having to know how far Nicole drove.
Answer:
7 Hours 12 Minutes
Step-by-step explanation:
So they one of the printer increases at a rate of 1/12 and the other increases at a rate of 1/18. Since you don't know the time it actually takes, you will replace both numerators with and x. (x/12 and x/18). You want to set these up so that they are adding. (x/12 + x/18=1). Since you're adding, you want to change it to the same denominator. The lowest is 36 so you multiply x/12 by 3/3 (so you don't unbalance the equation) and x/18 by 2/2. You'll end up with 3x/36 + 2x/36= 1 which will simplify to 5x/36=1. Multiply each side by 36 to leave the variable by itself. It becomes 5x=36 and when you divide it by 5 you get 7.2. So it's seven and .2 hours, which is equivalent to7 and 1/5 of an hour or 7 hours and 12 minutes.
