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2 years ago

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Mathematics

1 answer:

gtnhenbr [62]2 years ago

6 0

Answer:I'm pretty sure it's A

Step-by-step explanation:

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12. Write the equation of a parabola with vertex at<br> (2, -3) and focus at (2,5),

Tatiana [17]

Step-by-step explanation:

The basic form of equation:

(x-h)²=4a(y-k),

(h,k)=coordinates of vertex

(h, k+a) = coordinate of focus

For given parabola:

axis of symmetry: x=2

(h, k) =(2,-3)

(h, k+a)=(2,5)

k+a=5

-3+a=5

a=8(distance from vertex to focus on the axis of symmetry)

equation: (x-2)²=4×8(y+3)

(x-2)²= 32(y+3)

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2 years ago

Which is equal to 10^12/10^-3

tiny-mole [99]

10^[ 12 - ( - 3 ) ] = 10^( 12 + 3 ) = 10^15 ;
We use the formula
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3 years ago

Find the slope and the y-intercept of the line determined by the given equation.

Nonamiya [84]

Slope is 2: y intercept is 7

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3 years ago

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Lisa purchases a professional racing bicycle that sells for $3,000, including tax. It requires an 18.5% down payment. How much i

matrenka [14]

Answer: 3,0080

Step-by-step explanation:

3 0

3 years ago

For waht values of x do the vectors -1,0,-1), (2,1,2), (1,1, x) form a basis for R3?

DaniilM [7]

<h2>Answer:</h2>

The values of x for which the given vectors are basis for R³ is:

$x\neq 1$

<h2>Step-by-step explanation:</h2>

We know that for a set of vectors are linearly independent if the matrix formed by these set of vectors is non-singular i.e. the determinant of the matrix formed by these vectors is non-zero.

We are given three vectors as:

(-1,0,-1), (2,1,2), (1,1, x)

The matrix formed by these vectors is:

$\left[\begin{array}{ccc}-1&2&1\\0&1&1\\-1&2&x\end{array}\right]$

Now, the determinant of this matrix is:

$\begin{vmatrix}-1 &2 & 1\\ 0& 1 & 1\\ -1 & 2 & x\end{vmatrix}=-1(x-2)-2(1)+1\\\\\\\begin{vmatrix}-1 &2 & 1\\ 0& 1 & 1\\ -1 & 2 & x\end{vmatrix}=-x+2-2+1\\\\\\\begin{vmatrix}-1 &2 & 1\\ 0& 1 & 1\\ -1 & 2 & x\end{vmatrix}=-x+1$

Hence,

$-x+1\neq 0\\\\\\i.e.\\\\\\x\neq 1$

4 0

3 years ago