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3 years ago

Please help with this question !!

Mathematics

1 answer:

mario62 [17]3 years ago

3 0

Answer:

Step-by-step explanation:

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A local 4-H club surveyed its members, and the following information was obtained: 14 members had rabbits, 10 had goats, 4 had b

Fiesta28 [93]

A) 68.29%
B) 34.15%
C) 24.39%

8 0

3 years ago

Describe the steps required to determine the equation of a quadratic function given its zeros and a point.

faltersainse [42]

Answer:

Procedure:

1) Form a system of 3 linear equations based on the two zeroes and a point.

2) Solve the resulting system by analytical methods.

3) Substitute all coefficients.

Step-by-step explanation:

A quadratic function is a polynomial of the form:

$y = a\cdot x^{2}+b\cdot x + c$ (1)

Where:

$x$ - Independent variable.

$y$ - Dependent variable.

$a$ , $b$ , $c$ - Coefficients.

A value of $x$ is a zero of the quadratic function if and only if $y = 0$ . By Fundamental Theorem of Algebra, quadratic functions with real coefficients may have two real solutions. We know the following three points: $A(x,y) = (r_{1}, 0)$ , $B(x,y) = (r_{2},0)$ and $C(x,y) = (x,y)$

Based on such information, we form the following system of linear equations:

$a\cdot r_{1}^{2}+b\cdot r_{1} + c = 0$ (2)

$a\cdot r_{2}^{2}+b\cdot r_{2} + c = 0$ (3)

$a\cdot x^{2} + b\cdot x + c = y$ (4)

There are several forms of solving the system of equations. We decide to solve for all coefficients by determinants:

$a = \frac{\left|\begin{array}{ccc}0&r_{1}&1\\0&r_{2}&1\\y&x&1\end{array}\right| }{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&1\\r_{2}^{2}&r_{2}&1\\x^{2}&x&1\end{array}\right| }$

$a = \frac{y\cdot r_{1}-y\cdot r_{2}}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x+x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}$

$a = \frac{y\cdot (r_{1}-r_{2})}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x +x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}$

$b = \frac{\left|\begin{array}{ccc}r_{1}^{2}&0&1\\r_{2}^{2}&0&1\\x^{2}&y&1\end{array}\right| }{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&1\\r_{2}^{2}&r_{2}&1\\x^{2}&x&1\end{array}\right| }$

$b = \frac{(r_{2}^{2}-r_{1}^{2})\cdot y}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x +x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}$

$c = \frac{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&0\\r_{2}^{2}&r_{2}&0\\x^{2}&x&y\end{array}\right| }{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&1\\r_{2}^{2}&r_{2}&1\\x^{2}&x&1\end{array}\right| }$

$c = \frac{(r_{1}^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1})\cdot y}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x + x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}$

And finally we obtain the equation of the quadratic function given two zeroes and a point.

6 0

3 years ago

Please help! I have no idea how to do this, it’s very confusing

Vsevolod [243]

I like that you left How you did it on there. When I was in school I did it the same way. I would assume you’re using is over of equals percent over 100. The problem however is that the above number is always the total which means it should be on the bottom.

X/72= 45/100. Similar to what you have written. Solve the proportion. 100x=72x45
100x= 3240
X = 32.4

3 0

3 years ago

A line that passes through the points (–4, 10) and (–1, 5) can be represented by the equation y = (x – 2). Which equations also

lyudmila [28]

The equation y=x-2 do not represents the line that passes through the two point, since for example -4-2=-6, not 10. So (-4,10) is not on the line.
Let find the equation of the line:
First compute the slope using formula:
<span> </span> $\frac{y_2-y_1}{x_2-x_1}= \frac{5-10}{-1-(-4)}= \frac{-5}{3}$
So the equation is in the form:
$y=\frac{-5}{3}x+s\text{ wherein s is another parameter. }$
For x=-4 we get the equation:
$10=\frac{-5}{3}(-4)+s$
Solving the above equation for s we get:
$s= \frac{10}{3}$
The equation then is the following:
$y=\frac{-5}{3}x+\frac{10}{3}$

The correct answer then is equation 2 and equation 3.

4 0

3 years ago

Read 2 more answers

Find the nth term of 1,4,3,16,5,36,7

MakcuM [25]

Answer:

64,9

Step-by-step explanation:

From my understanding the pattern would be:

Every other number is the next consecutive odd number,

( 1, 3, 5, 7 ) are all of the consecutive odds. (So the next odd is 9. )

That when we get to the part of where we get every other number for the remaining numbers, if you multiply the next even number by itself (square it).

4, 16, and 36 ( they are all perfect squares. )

They are the perfect squares of ( 2, 4, and 6) . So it makes sense that ( 8 ) is the next even number and you would square that and get ( 64 )

I hope this makes sense!!

3 0

3 years ago