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Lera25 [3.4K]
3 years ago
13

Identify the coefficients in the following expression. -7x + 8y - 3z + y - 9

Mathematics
2 answers:
tresset_1 [31]3 years ago
7 0
Coefficients are numerical quantity that are put before multiplying a variable in an expression, eg. 8 in 8x^y.
Therefore, the coefficients are:
-7
8
-3
and -9
Hope this helps!:)
irina1246 [14]3 years ago
5 0
The coefficients are -7, 8, -3, 1, and -9
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If y varies inversely as x, and y=20 as x=3, find y for the x value 4
Ratling [72]
\bf \qquad \qquad \textit{inverse proportional variation}\\\\
\textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad  y=\cfrac{k}{x}\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad  variation
\end{array}\\\\
-------------------------------\\\\
\begin{cases}
y=20\\
x=3
\end{cases}\implies 20=\cfrac{k}{3}\implies 20\cdot 3=k\implies 60=k
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thus\qquad \boxed{y=\cfrac{60}{x}}\\\\
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4 years ago
Before making invitations, Katrina counted the supplies she bought for her party.
aleksandrvk [35]
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5 0
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Read 2 more answers
Suppose that T : R3 → R2 is given by:
Ad libitum [116K]

Answer:  The required answers are

(a) T is proved to be a linear transformation.

(b) The matrix A such that T(x) = Ax is \begin{pmatrix}1 & 0 &0 \\ 0 & 1 &0 \end{pmatrix}

Step-by-step explanation:  We are given a linear transformation T : R³ → R² defined as follows :

T(a,b,c)=(a,b).

We are to

(a) prove that T is a linear transformation

and

(b) find a matrix A such that T(x) = Ax.

(a) Let s, t are any real numbers and (a, b, c), (a', b', c') ∈ R³.

Then, we have

T(s(a,b,c)+t(a',b',c'))\\\\=T(sa+ta',sb+tb',sc+tc')\\\\=(sa+ta',sb+tb')\\\\=(sa,sb)+(ta'+tb')\\\\=s(a,b)+t(a',b')\\\\=sT(a,b,c)+tT(a',b',c').

So, we get

T(s(a,b,c)+t(a',b',c'))=sT(a,b,c)+tT(a',b',c').

Therefore, T is a linear transformation.

(b) We know that B = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} is a standard basis for R³ and B' = {(1, 0), (0, 1)} is a standard basis for R².

So, we have

T(1,0,0)=(1,0)=1(1,0)+0(0,1),\\\\T(0,1,0)=(0,1)=0(1,0)+1(0,1),\\\\T(0,0,1)=(0,0)=0(1,0)+0(0,1).

So, the matrix A such that T(x) = Ax will be given by

\begin{pmatrix}1 & 0 &0 \\ 0 & 1 &0 \end{pmatrix}

Thus,

(a) T is proved to be a linear transformation.

(b) The matrix A such that T(x) = Ax is  \begin{pmatrix}1 & 0 &0 \\ 0 & 1 &0 \end{pmatrix}

4 0
3 years ago
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