On a number line, the directed line segment from q to s has endpoints q at –8 and s at 12. point r partitions the directed line segment from q to s in a 4: 1 ratio. which expression correctly uses the formula to find the location of point r?

The expression that shows the location of R is,

Step-by-step explanation:

Since, the x-coordinate of a point on the number line shows its location.

Here, the location Q and S are -8 and 12 respectively.

⇒ x-coordinates of point Q and point S are -8 and 12 respectively.

Q and S are lying on the number line,

⇒ Coordinates of Q and S are  (-8,0) and (12,0) respectively.

Now, If a point divides a line segment having end points and in the ratio m:n

Then by the section formula,

The coordinates of the point are,

Here, point R partitions the directed line segment from Q to S in a 4:1 ratio.

Thus, by the above formula, the coordinates of R

=

=  

x-coordinate of R  =  

⇒ Location of R =  

Which is the required expression.

answer: i don't understand it

step-by-step explanation: sorry

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.