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SOVA2 [1]
3 years ago
5

A climber is on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours he is at an altitude of 700 feet. Is the r

ate of change proportional or not?
Mathematics
1 answer:
cluponka [151]3 years ago
6 0

Answer:

  not enough information

Step-by-step explanation:

Dividing altitude by hours, we find the ratios to be 400/2 = 200 ft/h and 700/6 = 116 2/3 ft/h.

These are not the same ratio, so altitude is not proportional to time.

___

However, that's not what the question asks. It ask about rate of change. We only have enough information to determine the rate of change between hour 2 and hour 6 is 300 ft in 4 hours, or 75 ft/hour. Since we don't have any other rate of change information, we cannot determine if the rate of change is proportional to anything.

_____

<em>Comment on the question</em>

We suspect the question is simply worded poorly, and that we're supposed to determine if altitude is proportional to hours. (It is not). If that is actually the question, "rate of change" needs to be left out of the question.

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Solve x2+4x+6=0 by graphing
klemol [59]

Answer: x = -2±√2 i or no real roots. See the explanation below.

Step-by-step explanation:

If you draw the graph, you will notice that there are no common points or you can say that there are no x-intercepts.

This means that the equation doesn't have any real roots.

If there are 2 common points (2 x-intercepts) then there are 2 real roots (answers.)

If there is only one common point (vertex is on x-axis) then there is only 1 real root.

If there aren't any common points (no x-intercepts) then there are no real roots.

So first, I'm gonna convert the equation into function and convert the standard form to vertex form.

x^2+4x+6=0\\y=x^2+4x+6\\y=(x^2+4x+4)-4+6\\y=(x+2)^2+2

We notice that the vertex is at (-2,2), the graph doesn't have x-intercepts (Graph below)

So the answer is clearly complex.

If you solve this by solving the equation then it'll be.

x^2+4x+6=0\\x= \frac{-b+-\sqrt{b^2-4ac}}{2a} \\x=\frac{-4+-\sqrt{16-24} }{2}\\x=\frac{-4+-\sqrt{-8} }{2}\\\\x=\frac{-4+-2\sqrt{2}i }{2}\\\\x={-2+-1\sqrt{2}i }\\\\

The answer is complex.

However, you can find the value of x easily by graphing. For example.

x^2+6x+5=0

Factor then you get

(x+5)(x+1)=0\\x=-5,-1

Or you can convert it to vertex form then graph.

y=x^2+6x+5

y=(x^2+6x+9)-9+5\\y=(x+3)^2-4

The vertex is at (-3,-4) then graph parabola (x-intercepts determine the roots of quadratic equation. For the graph, parabola intercepts x at (-5,0) and (-1,0) that means both -5 and -1 both are the value of x.

Note:

From the standard form, y=ax^2+bx+c The graph is called Parabola, and it's Quadratic Function.

a is how the graph is, for example. If a>0, the graph is supine parabola and if a<0 then the graph is inverted parabola.

|a| is determined if the graph is wide or narrow, the more the value of a is, the more narrow it will be. The less the value of a is, the more wide it will be.

b is what determined the change of graph (likely vertex). Without b, then it'd be ax^2+k which only move y-axis and not x-axis.

c is what determined the y-intercept and y-axis. If there is no b or the value of b is 0 then the vertex is at (0,c). If there is the value of b then c is only determined the y-intercept.

4 0
3 years ago
Markita bought a roll of carpet that is 8.5 feet wide. The maximum area the carpet will cover is 136 square feet. What is the lo
kenny6666 [7]

Answer:

16 feet in length.

Step-by-step explanation:

In this situation, you are given the area and the width of the full carpet, furthermore, you must reverse the formula for area to find the length, as so:

<u>Area Formula</u>: A=<em> l • w</em>

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<em>l</em> = 16 feet

I hope this was helpful!

3 0
3 years ago
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Kobotan [32]

Answer:

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Step-by-step explanation:

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f(x-12) = (x-12)^2

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7 0
3 years ago
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What ordered pair is the solution to -7x+3y=2
goldenfox [79]

Answer:

Step-by-step explanation:

3y=7x+2

y=\frac{7x+2}{3}\\x=1,y=3\\

one pair is (1,3)

go on adding  3 in x=1,you get corresponding value of y.

x=4,y=10,(4,10)

and so on .

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Last weekend,Mandy collected 4 times as many shells as Cameron.Together how many shells did Mandy collect?write an equation and
shutvik [7]

Answer:

4x=y

Step-by-step explanation:

Mandy collects 4 times the amount that Cameron has, so Cameron's amount x 4 = Mandy's amount

6 0
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