Mathematics, 02.04.2022 14:00 pepsi08u29lll

Here is it not sure if you will spot it

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Answer from: YoungTadoe437

f(x)=-5x^2+20x

8.75 m

Step-by-step explanation:

Given ordered pairs: (0, 0) (1, 16) (2, 20) (3, 15.5) (4, 0)

From inspection, we can see that the difference in the x-values is constant (they increase by 1 each time), yet the difference in the y-values is not constant. Therefore, the relation is not linear.

As the y-values increase from 0 to 20 and then decrease back to 0, the curve is likely to be a parabola opening downwards.

The x-intercepts are at x = 0 and x = 4, so this suggests that the axis of symmetry is x = 2, and so the vertex is (2, 20).

Creating an equation using the x-intercepts:

f(x)=a(x-0)(x-4) where is some constant

$\implies f(x)=ax(x-4)$

$\implies f(x)=ax^2-4ax$

Creating an equation using the vertex form:

f(x)=a(x-2)^2+20

$\implies f(x)=ax^2-4ax+4a+20$

Equating constants to determine a:

$4a+20=0 \implies a=-5$

Therefore, equation of best fit: f(x)=-5x^2+20x

When x = 0.5:

$\implies f(0.5)=-5(0.5)^2+20(0.5)$

=-1.25+10

=8.75

Therefore, an estimate for the height of the rocket 0.5 s after it's launched is 8.75 m

Answer from: Quest

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

$4/2 = 2\\7/3.5=2\\8/4=2\\10/5=2$

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

$y=\frac{x}{2}$

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

Answer from: Quest

42.4

step-by-step explanation:

convert to decimal

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