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Mariana [72]
3 years ago
8

Determine the direction that is parabola opens: y = -5x^2 -10x -13

Mathematics
1 answer:
Lunna [17]3 years ago
8 0
The parabola opens down, since the 'a' value of the equation is a negative value.
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Find the number to add to x^2-18x
pentagon [3]

Answer:

A. add 81; (x-9)^2

Step-by-step explanation:

The perfect square formula

(a-b)^2=a^2-2ab+b^2

Rewrite expression x^2-18x as follows:

x^2-2\cdot 9\cdot x

So, to form a perfect square, +9^2 is missed.

When we add 9^2=81, we will get

x^2-2\cdot 9\cdot x+9^2=(x-9)^2

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3 years ago
What is the solution to the system of equations y= -5x + 30 x = 10
Arturiano [62]

Answer:

We have been given the equation:

y=-5x+30

And x=10

Substitute the given x in the given equation we get:

y=-5(10)+30

y=-50+30

On simplification we get:

y=-20

Required solution is:  x= 10 and y=-20

The solution to the system of equation is those points that satisfy the given system of equations.

3 0
3 years ago
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Solve the equation:<br><br> (x^4 - x + y)dx - xdy=0
algol [13]
Keeping in mind that "dx" is the delta x, or differential over the x-axis, whilst "dy" is the delta y or differential over the y-axis,

\bf (x^4-x+y)dx-xdy=0\implies \stackrel{\textit{distributing dx}}{x^4dx-xdx+ydx}-xdy=0&#10;\\\\\\&#10;ydx=xdy-x^4dx+xdx\implies y=\cfrac{xdy-x^4dx+xdx}{dx}&#10;\\\\\\&#10;y=\stackrel{\textit{distributing the denominator}}{x\cfrac{dy}{dx}-x^4+x}
5 0
3 years ago
What is the quadratic regression equation for the data set? ​ ​ ​ <br><br> PLEASEE HELP ME
Soloha48 [4]
You're trying to find constants a_0,a_1,a_2 such that \hat y=a_0+a_1\hat x+a_2{\hat x}^2. Equivalently, you're looking for the least-square solution to the following matrix equation.


\underbrace{\begin{bmatrix}1&6&6^2\\1&3&3^2\\\vdots&\vdots&\vdots\\1&9&9^2\end{bmatrix}}_{\mathbf A}\underbrace{\begin{bmatrix}a_0\\a_1\\a_2\end{bmatrix}}_{\mathbf x}=\underbrace{\begin{bmatrix}100\\110\\\vdots\\70\end{bmatrix}}_{\mathbf b}

To solve \mathbf{Ax}=\mathbf b, multiply both sides by the transpose of \mathbf A, which introduces an invertible square matrix on the LHS.

\mathbf{Ax}=\mathbf b\implies\mathbf A^\top\mathbf{Ax}=\mathbf A^\top\mathbf b\implies\mathbf x=(\mathbf A^\top\mathbf A)^{-1}\mathbf A^\top\mathbf b

Computing this, you'd find that

\mathbf x=\begin{bmatrix}a_0\\a_1\\a_2\end{bmatrix}\approx\begin{bmatrix}121.119\\-3.786\\-0.175\end{bmatrix}

which means the first choice is correct.
8 0
3 years ago
What is the interquartile range of the box and whisker plot
Irina18 [472]

Answer:

(IQR) interquartile range = 5

Step-by-step explanation:

Lower quartile: 48

Upper quartile: 53

Median: 52

Lowest value: 46

Highest value: 55

(IQR) interquartile range: Upper quartile - Lower quartile = final answer

(IQR) interquartile range: 53 - 48 = 5

5 0
3 years ago
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