Kelly realizes once she gets to Round Rock that she left her Art project (a major grade) at her mother's house in Plano. She would not have time to have it shipped
before it is due the next day and convinces her brother to meet her part of the way. If
the average speed limit from Plano to their meeting point (on the North side of West,
TX) is 65 miles per hour, and the average speed limit from Round Rock to their meeting
point is 75 miles per hour, how many miles will Kelly's brother have to drive before he
reaches Kelly if the driving distance between them is 196 miles and they drive the same
amount of time?

Kelly's brother has to drive 91 miles before he reaches Kelly.

Step-by-step explanation:

Since, both Kelly and her brother are traveling at the constant speed. Therefore, we will use the following formula for both:

s = v t

For Kelly:

s₁ = v₁ t₁

t₁ = s₁/v₁   equation 1

where,

t₁ = time taken by Kelly

s₁ = distance covered by Kelly

v₁ = average speed of Kelly = 75 mi/h

For Brother:

s₂ = v₂ t₂

t₂ = s₂/v₂   equation 2

where,

t₂ = time taken by Brother

s₂ = distance covered by Brother

v₂ = average speed of Brother = 65 mi/h

But it is given that both of them drive same amount of the time:

t₁ = t₂

using equation 1 and equation 2:

s₁/v₁ = s₂/v₂

s₁/s₂ = v₁/v₂

using values:

s₁/s₂ = (75 mi/h)/(65 mi/h)

s₁/s₂ = 1.15

s₁ = 1.15 s₂   equation 3

The total distance is given as:

s₁ + s₂ = 196 miles  

using equation 3:

1.15 s₂ + s₂ = 196 miles

s₂ = 196 miles/2.15

s₂ = 91 miles

Hence, Kelly's brother has to drive 91 miles before he reaches Kelly.

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.  

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq