Which ordered pair is the solution to the system?

Taylor and Anya are friends who live 63 miles apart. Sometimes on a Saturday, they ride toward each other's houses on their bike

marishachu [46]

Solutions

Solution: Finding distances first

Since the bike ride took 3 hours, Taylor must have ridden 37.5 miles. Therefore Anya must have ridden 63 - 37.5 - 25.5 miles. If we divide the distance Anya rode by the amount of time it took her to ride, we will get her speed (assuming she rode at a constant speed).

25.5 miles ÷3 hours =8.5 miles per hour.

So if Anya rode at a constant speed, she was traveling 8.5 miles per hour.

Solution: Subtracting Taylor's speed from total speed

The distance between the two friends is decreasing by

63 miles ÷3 hours =21 miles per hour.

Since Taylor rides at 12.5 miles per hour, Anya's speed must be 21 - 12.5 = 8.5 miles per hour. Solutions

Solution: Finding distances first

Since the bike ride took 3 hours, Taylor must have ridden 37.5 miles. Therefore Anya must have ridden 63 - 37.5 - 25.5 miles. If we divide the distance Anya rode by the amount of time it took her to ride, we will get her speed (assuming she rode at a constant speed).

25.5 miles ÷3 hours =8.5 miles per hour.

So if Anya rode at a constant speed, she was traveling 8.5 miles per hour.

Solution: Subtracting Taylor's speed from total speed

The distance between the two friends is decreasing by

63 miles ÷3 hours =21 miles per hour.

Since Taylor rides at 12.5 miles per hour, Anya's speed must be 21 - 12.5 = 8.5 miles per hour.

Assuming Anya rode at a constant speed, she was traveling 8.5 miles per hour.

5 0

3 years ago

Find the area of the region bounded by the parabola y = 5x^2, the tangent line to this parabola at (4, 80), and the x-axis.

o-na [289]

First we have to find the tangent line:
y - y o = f ` ( x o ) * ( x - x o )
f ` ( x ) = 10 x
y - 80 = 40 ( x - 4 )
y = 40 x - 160 + 80
y = 40 x - 80
There are 2 parts of this region:
A = $\int\limits^2_0 {5 x^{2} } \, dx + \int\limits^4_2 {(5 x^{2} -40x+80)} \, dx= \\ 5 x^{3} /3 \left \{ {{2} \atop {0}} \right. +( 5 x^{3} -20 x^{2} +80x) \left \{ {{4} \atop {2}} \right.$
A = 40/3 + 320/3 - 320 + 320 - 40/3 + 80 - 160 = 320/3 - 240/3 = 80/3

4 0

3 years ago

What decimal is equivalent to 9\10

ch4aika [34]

.9 is equivalent to 9/10.
This is because 9 divided by 10 is .9.(Reciprocal)

4 0

3 years ago

Multiply.<br><br> 2/7 x 35 =

Illusion [34]

If you would like to calculate 2/7 * 35, you can do this using the following steps:

2/7 * 35 = 2 * 35/7 = 2 * 5 = 10

The correct result would be 10.

6 0

4 years ago

Which of the following does not represent an attribute of the function f(x) = [x]?

luda_lava [24]

Answer: The graph has a line of symmetry at y = 0.

Step-by-step explanation:

I suppose that this refers to the function:

f(x) = IxI

The parent absolute value function.

Remember how this works:

IxI = x if x ≥ 0

IxI = -x if x ≤ 0.

Let's analyze the sentences:

1) "The x- and y-intercepts are (0,0)"

This is true, when x = 0 we have:

y = f(0) = I0I = 0

So the point (0, 0) is the only x-intercept and the only y-intercept.

2) "Domain: (-∞,∞); Range: [0,∞)"

This is also true, we clearly do not have any restriction in the domain.

And when looking at the range, we can see that the possible values of y are always positive or zero.

3) "(0, 0) is the minimum point."

Now, as x increases in the positive range, also does the value of y.

And as x decreases in the negative range, as the absolute value changes the sign, we will also have an increase in the value of y.

Then we have that (0, 0) must be the minimum.

4) "The graph has a line of symmetry at y = 0."

This is false.

The real line of symmetry is at x = 0, y = 0 corresponds to the x-axis, and as the graph opens up, we can not have symmetry about any line parallel to the x-axis.

4 0

4 years ago

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