Mathematics, 27.10.2021 07:40, ashl3yisbored

PLEASE help me need solution please

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answered: u8p4

9514 1404 393

A. f(x) = x^2 -3x -10

Step-by-step explanation:

You can easily determine the correct equation by looking at a couple of table values.

The y-value for x=0 is -10, which is the constant in the quadratic formula. (eliminates choices B and C)

The y-value for x=1 is -12, which is the sum of coefficients in the quadratic formula. For choice A, the sum of coefficients is 1 -3 -10 = -12. For choice D, the sum of coefficients is 1 +3 -10 = -6. The value for choice D does not match the table, but the value for choice A does.

The function that represents the table is ...

f(x) = x^2 -3x -10

_____

Additional comments

If you don't have equations to test, and you want to write your own equation, there are a couple of ways to do that. One is to look at the differences of y-values, and the differences of those.

The sequence of y-values shown is ...

30, 18, 8, 0, -6, -10, -12

The sequence of differences of these numbers, starting with 18-30 = -12 is ...

-12, -10, -8, -6, -4, -2

The sequence of differences of these numbers is ...

2, 2, 2, 2, 2

The fact that they are constant tells you a quadratic (degree = 2) will describe the table.

We can find the coefficients a, b, c in the quadratic formula f(x) = ax^2 +bx +c as follows. First, we define d1 as the first of the sequence of differences (-12), and d2 as the value of the second differences (2). And we'll let x0 and y0 be defined as the first of the x-values (-5) and y-values (30).

The formulas for the coefficients (a, b, c) can be found from ...

a = (d2)/2 = 2/2 = 1

b = (d1) -a(2·(x0) +1) = -12 -1(2·(-5) +1) = -12 +9 = -3

c = y0 -x0(a·x0 +b) = 30 -(-5)(1·(-5) +(-3) = 30 -40 = -10

As we noted above, the y-value corresponding to x=0 is also this c value. When the table includes x=0 and x=1, those can be used to simplify the finding of the formula coefficients.

These computations tell us f(x) = x^2 -3x -10, as above.

If you have to do this again, it might be useful to make a note of the expressions for 'a', 'b', and 'c' that we showed here, along with the definitions of the variables we used in them.

Another way to find the formula for f(x) is to make use of a calculator or spreadsheet capable of quadratic regression. Give it three (x, y) pairs from the table, and it can tell you the formula coefficients. This is illustrated by the attachment.

answered: Guest

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that $\frac{ab}{de}=\frac{bc}{ef}$ .

also, it is given that $\frac{ab}{de}=\frac{3}{4}$

so, from the options, we need that $\frac{bc}{ef}=\frac{3}{4}$ .

a. $\frac{bc}{ef}=\frac{6}{9}=\frac{2}{3}$

b. $\frac{bc}{ef}=\frac{4}{6}=\frac{2}{3}$

c. $\frac{bc}{ef}=\frac{8}{12}=\frac{2}{3}$

d. $\frac{bc}{ef}=\frac{12}{16}=\frac{3}{4}$

as, we can see that only option d gives the same ratio as $\frac{ab}{de}=\frac{3}{4}$ i.e. $\frac{bc}{ef}=\frac{3}{4}$ .

hence, the possible lengths are bc = 12 and ef = 16.

answered: Guest

x is greater than 5

step-by-step explanation:

2x+7 is greater than 17

-7 -7

2x is greater than 10

divide by 2 each side

x is greater than 5

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