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Fofino [41]
3 years ago
11

Is (-5,2), (5,2), (0,-3), (3,-8), (-7,4), (-1,-1) a function

Mathematics
1 answer:
Alja [10]3 years ago
4 0
<h3>Answer: Yes it is a function</h3>

Each point listed is of the form (x,y). The x coordinate is always listed first. We dont have any repeat x values, so this is enough to conclude we have a function.

If you wanted to, you could graph each point given on the same coordinate grid. Note how none of the points stack on top of each other. Or put another way, note how it is impossible to draw a single straight line through more than one point graphed. This graph passes the vertical line test.

A function is where plugging in any x value leads to exactly one y value.

If you had two points like (5,2) and (5,7) then the input x = 5 leads to more than one output y = 2 and y = 7 at the same time, making this example not a function.

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Ben and Josh went to the roof of their 40-foot tall high school to throw their math books offthe edge.The initial velocity of Be
Taya2010 [7]

Answer

Josh's textbook reached the ground first

Josh's textbook reached the ground first by a difference of t=0.6482

Step-by-step explanation:

Before we proceed let us re write correctly the height equation which in correct form reads:

h(t)=-16t^2 +v_{o}t+s       Eqn(1).

Where:

h(t) : is the height range as a function of time

v_{o}   : is the initial velocity

s     : is the initial heightin feet and is given as 40 feet, thus Eqn(1). becomes:

h(t)=-16t^2 + v_{o}t + 40        Eqn(2).

Now let us use the given information and set up our equations for Ben and Josh.

<u>Ben:</u>

We know that v_{o}=60ft/s

Thus Eqn. (2) becomes:

h(t)=-16t^2+60t+40        Eqn.(3)

<u>Josh:</u>

We know that v_{o}=48ft/s

Thus Eqn. (2) becomes:

h(t)=-16t^2+48t+40       Eqn. (4).

<em><u>Now since we want to find whose textbook reaches the ground first and by how many seconds we need to solve each equation (i.e. Eqns. (3) and (4)) at </u></em>h(t)=0<em><u>. Now since both are quadratic equations we will solve one showing the full method which can be repeated for the other one. </u></em>

Thus we have for Ben, Eqn. (3) gives:

h(t)=0-16t^2+60t+40=0

Using the quadratic expression to find the roots of the quadratic we have:

t_{1,2}=\frac{-b+/-\sqrt{b^2-4ac} }{2a} \\t_{1,2}=\frac{-60+/-\sqrt{60^2-4(-16)(40)} }{2(-16)} \\t_{1,2}=\frac{-60+/-\sqrt{6160} }{-32} \\t_{1,2}=\frac{15+/-\sqrt{385} }{8}\\\\t_{1}=4.3276 sec\\t_{2}=-0.5776 sec

Since time can only be positive we reject the t_{2} solution and we keep that Ben's book took t=4.3276 seconds to reach the ground.

Similarly solving for Josh we obtain

t_{1}=3.6794sec\\t_{2}=-0.6794sec

Thus again we reject the negative and keep the positive solution, so Josh's book took t=3.6794 seconds to reach the ground.

Then we can find the difference between Ben and Josh times as

t_{Ben}-t_{Josh}= 4.3276 - 3.6794 = 0.6482

So to answer the original question:

<em>Whose textbook reaches the ground first and by how many seconds?</em>

  • Josh's textbook reached the ground first
  • Josh's textbook reached the ground first by a difference of t=0.6482

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How dose an incline effect speed and distance of an object?
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It makes the object move faster
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What is an equation of the line that passes through the points (-3, 8) and (4, 1)?
butalik [34]

Answer:

The equation of the line is:

y=-x+5

Step-by-step explanation:

Given the points

  • (-3, 8)
  • (4, 1)

Finding the slope between the points

\left(x_1,\:y_1\right)=\left(-3,\:8\right),\:\left(x_2,\:y_2\right)=\left(4,\:1\right)

\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

m=\frac{1-8}{4-\left(-3\right)}

m=-1

Using the point-slope form of the line equation

y-y_1=m\left(x-x_1\right)

where m is the slope

substituting the values m = -1 and the point (-3, 8)

y-y_1=m\left(x-x_1\right)

y-8=-1\cdot \left(x-\left(-3\right)\right)

y-8=-\left(x+3\right)

Add 8 to both sides

y-8+8=-\left(x+3\right)+8

y=-x+5

Therefore, the equation of the line is:

y=-x+5

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Polynomials<br><br> Multiply 5x(x2 - 4x+2)
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5x^3-20x^2+10x

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