REWRITE IN FUNCTION FORM Solve the formula for the red variable.
2y + 5 = 6
Red variable is y

Write 35 miles per gallon as a unit rate. If you missed this problem, review Example 5.11.8.

Solve 6x + 24 = 96. If you missed this problem, review Example 8.4.1.

Find the simple interest earned after 5 years on $1,000 at an interest rate of 4%. If you missed this problem, review Example 6.4.1.

Use the Distance, Rate, and Time Formula

One formula you’ll use often in algebra and in everyday life is the formula for distance traveled by an object moving at a constant speed. The basic idea is probably already familiar to you. Do you know what distance you travel if you drove at a steady rate of 60 miles per hour for 2 hours? (This might happen if you use your car’s cruise control while driving on the Interstate.) If you said 120 miles, you already know how to use this formula!

The math to calculate the distance might look like this:

distancedistance=(60miles1hour)(2hours)=120miles

In general, the formula relating distance, rate, and time is

distance=rate⋅time(9.11.1)

Definition: Distance, Rate and Time

For an object moving in at a uniform (constant) rate, the distance traveled, the elapsed time, and the rate are related by the formula

d=rt(9.11.2)

where d = distance, r = rate, and t = time.

Notice that the units we used above for the rate were miles per hour, which we can write as a ratio  mileshour . Then when we multiplied by the time, in hours, the common units ‘hour’ divided out. The answer was in miles.

Example  9.11.1 :

Jamal rides his bike at a uniform rate of 12 miles per hour for  312  hours. How much distance has he traveled?

Step-by-step explanation:

let x and 400 - x be the two numbers.  

==> 0.80x + 0.85(400 - x) = 400 - 68 from the statement of the problem.  

< ==> 0.80x + 0.85(400 - x) = 400 - 68  

==> 340 - 0.05x = 332  

< ==> -0.05x = -8 ==> x = 160, the first number ==> 400 - x = 240, the second number.

hello,

as we don't know if g(x) is continue,

answer b

f(x)=2x²-8x+1=2(x²-4x+4)+1-8=2(x-2)²-7

vertex is (2,-7) ( a minimum since coefficient of x² is > 0)