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 (startfraction m over m + n endfraction) (x 2 minus x 1) + x 1 to find the location of point r? (startfraction 1 over 1 + 4 endfraction) (12 minus (negative 8)) + (negative 8) (startfraction 4 over 4 + 1 endfraction) (12 minus (negative 8)) + (negative 8) (startfraction 4 over 4 + 1 endfraction) (negative 8 minus 12) + 12 (startfraction 4 over 1 + 4 endfraction) (negative 8 minus 12) + 12

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.

Step-by-step explanation:

Given

Required

Determine the expression that correctly uses

In

and

Substitute these values in:

The expression becomes:

Solving further:

Hence, R is at 8 on the number line

Step-by-step explanation:

Given

Required

Determine the expression that correctly uses

In

and

Substitute these values in:

The expression becomes:

Solving further:

Hence, R is at 8 on the number line

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

The answer is in the image 

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg