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Aleksandr-060686 [28]
4 years ago
14

What are the measures of angles 1 and 2? m∠1 = °

Mathematics
1 answer:
nikdorinn [45]4 years ago
7 0
Where’s the whole page
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Estimate the square root of the imperfect square of 18.
ludmilkaskok [199]

Answer:

18 times four is 72

Step-by-step explanation:

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Please Help Fast!!! 20 points<br><br><br> Solve the system of equations: y−x=20 2x−15y=−1
andreev551 [17]
Isolate y: 2x-15(20+x)=-1
isolate x: 20-23 = -3
substitute: x = -23
answer: (-23, -3)
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What is the slope of the line
sineoko [7]

Answer:

-3/1

Step-by-step explanation:

It's decreasing so it would be negative

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3 years ago
Find a formula for the least squares solution of ax=b when the columns of a are orthonormal1 .
neonofarm [45]
Let \mathbf A be a rectangular m\times n matrix with column vectors \mathbf a_1,\ldots,\mathbf a_n, i.e.

\mathbf A=\begin{bmatrix}\mathbf a_1&\cdots&\mathbf a_n\end{bmatrix}

Then we have

\mathbf A^\top=\begin{bmatrix}\mathbf a_1&\cdots&\mathbf a_n\end{bmatrix}^\top

and the product of the two is

\mathbf A^\top\mathbf A=\begin{bmatrix}\mathbf a_1\cdot\mathbf a_1&\mathbf a_1\cdot\mathbf a_2&\cdots&\mathbf a_1\cdot\mathbf a_n\\\mathbf a_2\cdot\mathbf a_1&\mathbf a_2\cdot\mathbf a_2&\cdots&\mathbf a_2\cdot\mathbf a_n\\\vdots&\vdots&\ddots&\vdots\\\mathbf a_n\cdot\mathbf a_1&\mathbf a_n\cdot\mathbf a_2&\cdots&\mathbf a_n\cdot\mathbf a_n\end{bmatrix}

Because the columns of \mathbf A are orthonormal, we have

\mathbf a_i\cdot\mathbf a_j=\begin{cases}1&\text{for }i=j\\0&\text{for }i\neq j\end{cases}

which means \mathbf A^\top\mathbf A reduces to an n\times n matrix with ones along the diagonal and zero everywhere else, i.e.

\mathbf A^\top\mathbf A=\begin{bmatrix}1&0&\cdots&0\\0&1&\cdots&0\\\vdots&\vdots&\ddots&\vdots\\0&0&\cdots&1\end{bmatrix}=\mathbf I_n

where \mathbf I denotes the identity matrix. This means the solution to \mathbf{Ax}=\mathbf b is given by

\mathbf A^\top(\mathbf{Ax})=\mathbf A^\top\mathbf b\implies(\underbrace{\mathbf A^\top\mathbf A}_{\mathbf I})\mathbf x=\mathbf A^\top\mathbf b\implies\mathbf x=\mathbf A^\top\mathbf b
6 0
3 years ago
It cost $44.88 to buy 12 gallons of gas.What was the cost per gallon of gas?
Natali [406]

Answer:

$3.74 per gallon

Step-by-step explanation:

1. Divide $44.88 by 12

2. The answer will be 3.74

3. Each gallon will cost $3.74

4 0
4 years ago
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