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andreyandreev [35.5K]
3 years ago
10

Write the equation of a line in slope-intercept form that passes through (0, 7) and has a slope of -23.

Mathematics
1 answer:
Elodia [21]3 years ago
5 0

Answer:

y = -23x + 7

Step-by-step explanation

We are using the equation y = mx + b.

The slope (m) is -23, so it would be y = -23 + b.

b is the y-intercept, and the ordered pair that gives us the y-intercept is (0,7).

Remember that the y-intercept is what the y-coordinate is equal to when the x-coordinate is 0.

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Let [v1,v2,v3] be a set of nonzero vectors in r^m such that the (transpose of vi)*vj = 0 when i is not equal to j. show that the
babunello [35]
Let \mathbf V be the m\times3 matrix whose columns are \mathbf v_1,\mathbf v_2,\mathbf v_3, and let \mathbf c be the vector whose components are the constants c_1,c_2,c_3. Now consider the matrix equation

\mathbf V\mathbf c=\mathbf 0


Multiplying both sides by \mathbf V^\top, we have

\mathbf V^\top(\mathbf V\mathbf c)=(\mathbf V^\top\mathbf V)\mathbf c=\mathbf 0

More explicitly, we're writing

\mathbf V=\begin{bmatrix}\mathbf v_1&\mathbf v_2&\mathbf v_3\end{bmatrix}

Multiply both sides by \mathbf V^\top and the left hand side can be written as

\mathbf V^\top\mathbf V=\begin{bmatrix}{\mathbf v_1}^\top\\{\mathbf v_2}^\top\\{\mathbf v_3}^\top\end{bmatrix}\begin{bmatrix}\mathbf v_1&\mathbf v_2&\mathbf v_3\end{bmatrix}=\begin{bmatrix}{\mathbf v_1}^\top\mathbf v_1&{\mathbf v_1}^\top\mathbf v_2&{\mathbf v_1}^\top\mathbf v_3\\{\mathbf v_2}^\top\mathbf v_1&{\mathbf v_2}^\top\mathbf v_2&{\mathbf v_2}^\top\mathbf v_3\\{\mathbf v_3}^\top\mathbf v_1&{\mathbf v_3}^\top\mathbf v_2&{\mathbf v_3}^\top\mathbf v_3\end{bmatrix}

We're told that {\mathbf v_i}^\top\mathbf v_j=0 whenever i\neq j, so we're left with

\mathbf V^\top\mathbf V=\begin{bmatrix}\|\mathbf v_1\|^2&0&0\\0&\|\mathbf v_2\|^2&0\\0&0&\|\mathbf v_3\|^2\end{bmatrix}

Each of \mathbf v_1,\mathbf v_2,\mathbf v_3 are nonzero, which means their norms are nonzero, which necessarily implies that \mathbf c=0, and so the vectors \mathbf v_1,\mathbf v_2,\mathbf v_3 must necessarily be linearly independent.
6 0
3 years ago
Write an equation that expresses the following relationship: x varies directly as p and inversely as the difference between y an
dsp73
X = kp/y-c

cross multiply 

xy-xc = kp

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x(y-c) = kp

divide entire equation by x

y-c = kp/x

isolate y since we are solving for y
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y = kp/x + c
5 0
3 years ago
7 + p + 9 equals 17 solve for p​
xxTIMURxx [149]

Answer:

p=1

Step-by-step explanation:

5 0
4 years ago
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A person flying a kite has released 176 m of string. The string makes an angle of 27° with the
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7 0
3 years ago
Point R divides in the ratio 1 : 3. If the x-coordinate of R is -1 and the x-coordinate of P is -3, what is the x-coordinate of
dimaraw [331]

Answer:

C. 5

Step-by-step explanation:

Point R divides the line segment PQ internally. The x-coordinate of the point which divides the line segment in ration m:n internally can be calculated as:

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-1=\frac{x_{2}+3(-3) }{1+3} \\ \\-4=x_{2}-9\\\\ 5=x_{2}

Thus the x-coordinate of point Q will be 5

The x-coordinate of Q is 5.

7 0
4 years ago
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