Sally is 2 more than twice Bonnie’s age. The sum of their ages is 29, how old is each person? HELP PLSSSSS!

Write the equation of a quadratic function that contains the points (1,21), (2,18), and (-1,9)

Colt1911 [192]

Answer:

The equation of a quadratic function that contains the points (1, 21), (2,18) and (-1, 9) is $y = -3\cdot x^{2}+6\cdot x +18$ .

Step-by-step explanation:

A quadratic function is a second order 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.

From Algebra we understand that a second order polynomial is determined by knowing three distinct points. If we know that $(x_{1}, y_{1}) = (1, 21)$ , $(x_{2},y_{2}) = (2,18)$ and $(x_{3}, y_{3}) = (-1, 9)$ , then we construct the following system of linear equations:

$a+b+c = 21$ (2)

$4\cdot a + 2\cdot b + c = 18$ (3)

$a - b + c = 9$ (4)

By algebraic means, the solution of the system is:

$a = -3$ , $b = 6$ , $c = 18$

Therefore, the equation of a quadratic function that contains the points (1, 21), (2,18) and (-1, 9) is $y = -3\cdot x^{2}+6\cdot x +18$ .

7 0

2 years ago

A

blagie [28]

hope it helps.I was reading the same chapter

5 0

3 years ago

The populations and areas of four states are shown. A 3-column table has 4 rows. The first column has entries State A, State B,

faust18 [17]

Answer:

B.

Step-by-step explanation:

Just did the quiz

6 0

3 years ago

Find the equation of the straight line that passes through the point (1,1/2) and has slope 1/2. Enter the equation in the point-

Nataliya [291]

$\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ 1}}\quad ,&{{ \frac{1}{2}}})\quad 
% (c,d)

\end{array}
\\\quad \\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies\cfrac{1}{2}
\\ \quad \\
% point-slope intercept
y-{{ y_1}}={{ m}}(x-{{ x_1}})\qquad 
\begin{array}{llll}
\textit{plug in the values}\\

\end{array}\\
\qquad \uparrow\\
\textit{point-slope form}$

5 0

3 years ago

PLEASE HELP IM BEING TIMED!!! WILL MARK BRAINLIEST FOR CORRECT ANSWER!!! 100PTS!!!

amid [387]

Answer:

B and D.

Step-by-step explanation:

We know that when we added the two functions together, we get:

$h(x)=-x+9$

However, when we multiplied them together, we get:

$j(x)=-9x$

Let's first consider what we can determine from this.

If we add them together, we get a linear equation. However, this doesn't mean that our two original functions are linear since if we have, say, -x^2 and x^2-x+9, they will cancel and form a linear equation if we add them together.

However, since we know that if we multiply the two functions together, we get a linear equation, this means that both our original functions must be linear.

But, if we multiplied two linear functions, then we should get a quadratic, since x times x will yield x².

Therefore, this means that one of our linear functions is a horizontal line with no x variable. This is the only way to have a linear equation when multiplied.

Therefore, we have determined that both of our original functions are linear functions, and one (only one of them) is a horizontal line.

Let's go through each of the answer choices.

A) Both functions must be quadratic.

This is false as we determined earlier. If this was true, then the resulting function should be a quartic and not a line. A is false.

B) Both functions must have a constant rate of change.

Remember that all linear equations have a constant rate of change.

Since we determined that both our original functions are linear equation, this means that both our functions will have a constant rate of change.

So, B is true.

C) Both functions must have a y-intercept of 0.

Remember that one of our functions is a horizontal line.

If the y-intercept was 0, then the equation of our horizontal line will be:

$y=0$

And we know that anything multiplied by 0 will give us 0. However, the product of our function is -9x.

So, C cannot be true.

Rather, only our linear equation (not the horizontal line) may have a y-intercept of 0.

D) The rate of change of either f(x) or g(x) must be 0.

Remember that we determined that one of our lines must a horizontal.

Remember that horizontal lines have a slope of 0. In other words, the rate of change is 0.

So, D is true.

E) The y-intercepts of f(x) and g(x) must be opposites.

Well, since B and D is are true, this must be false since we can only select two options ;D

But, we can think about this. Note that if we multiply the two functions, we have a function without a y-intercept.

Remember that our horizontal line is not 0. So, the y-intercept of the horizontal line is a number.

So, the opposite of a number is another number.

So, if we multiply two non-zero numbers, we must get another number.

However, from our product, j(x)=-9x, we don't have another number. The y-intercept from this is 0.

Therefore, the two y-intercepts cannot be opposites of each other. If it was so, then we should have a y-intercept. So, E must be false.

In fact, this means that the y-intercept of our line (not the horizontal one) must be 0.

So, our answers are B and D.

And we're done!

Edit: Some (minor) errors in reasoning. Sorry!

4 0

3 years ago

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