Answer:
Joe's wife must drive at a rate of 45km/hour.
Step-by-step explanation:
We are given that Joe leaves home and bikes at a speed of 30km/hour. Joe's wife leaves home five minutes later by car, and we want to determine her speed in order for her to catch up to Joe in 10 minutes.
Since Joe bikes at a speed of 30km/hour, he bikes at the equivalent rate of 0.5km/min.
Then after five minutes, when his wife leaves, Joe is 5(0.5) or 2.5 km from the house. He will still be traveling at a rate of 0.5km/min, so his distance from the house can be given by:
Where <em>t</em> represents the time in minutes after his wife left the house.
And since we want to catch up in 10 minutes, Joe's distance from the house 10 minutes after his wife left will be:
Let <em>s</em> represent the wife's speed in km/min. So, her speed times 10 minutes must total 7.5 km:
Solve for <em>s: </em>
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Thus, Joe's wife must drive at a rate of 0.75km/min, or 45km/hour.
..............................
1) 2 points:
We need to come up with a function that intersects the graph at two points, meaning has two (x,y) in common with the function. If you look at the graph of y=x^2, you see that it would be quite easy to draw a line that intersects the graph twice. In fact, there are an infinite number of functions that would satisfy this.
One easy function is y=2. This is a horizontal line in which y=2 for all values of x. In the graph y=x^2, y=2 intersects twice.
2=x^2
x^2= √2 or -√2
the shared points are (√2,2) and (-√2,2)
b) one point:
Here, we want to find an equation with only one (x,y) in common with y=x². This is a bit trickier.
One easy solution is y=-x²
Looking at a graph of the two functions, you see that y=-x² is a reflection across the x-axis of y= x². The two functions have only one point in common: (0,0).
c) no point in common
Take another look at the graph of y=x². You see that the function never crosses the x-axis. A simple function that will never intersect the graph is y=-2. Since y is negative for all values of x, it is guaranteed to never intersect y=x², a function in which y is positive for all negative or positive values of x.
Answer:
5
Step-by-step explanation:
First u minus (because of these () ) witch is 3 and 
is a fraction so u do 3× (u see that its not a ÷ sign because its a fraction) witch equals to 5
Answer:
They fall into 
tax bracket.
Step-by-step explanation:
We need to calculate their tax return jointly, which tax bracket will they fall into.
Given :-
A taxpayer had a taxable income of $42,700, and his spouse had a taxable income of $48,100.
If they wish to file their tax return jointly then
In married filling jointly table
The combine salary 
lies between 
so, the tax bracket is
Therefore, they fall into tax bracket.
