Which equivalent fraction would you have to use in order to add 3/5 to 21/25

At a bargain store, Tanya bought 3 items that each cost the same amount. Tony bought 4 items that each cost the same amount, but

zmey [24]

<span>If Tanya’s three items (x) cost the same as Tony’s four items (y), 3x = 4y. Y is 2.25 less than x, so: 3x = 4x - 4 x 2.25. 3x = 4x - 9. 3x + 9 = 4x. 9 = x. Therefore, y = 9 - 2.25. x = 9 and y = 6.75. Three times 9 and four times 6.75 is 27. Tanya’s items cost $9 each and Tony’s cost $6.75.</span>

3 0

3 years ago

Assume {v1, . . . , vn} is a basis of a vector space V , and T : V ------> W is an isomorphism where W is another vector spac

Degger [83]

Answer:

Step-by-step explanation:

To prove that $w_1,\dots w_n$ form a basis for W, we must check that this set is a set of linearly independent vector and it generates the whole space W. We are given that T is an isomorphism. That is, T is injective and surjective. A linear transformation is injective if and only if it maps the zero of the domain vector space to the codomain's zero and that is the only vector that is mapped to 0. Also, a linear transformation is surjective if for every vector w in W there exists v in V such that T(v) =w

Recall that the set $w_1,\dots w_n$ is linearly independent if and only if the equation

$\lambda_1w_1+\dots \lambda_n w_n=0$ implies that

$\lambda_1 = \cdots = \lambda_n$ .

Recall that $w_i = T(v_i)$ for i=1,...,n. Consider $T^{-1}$ to be the inverse transformation of T. Consider the equation

$\lambda_1w_1+\dots \lambda_n w_n=0$

If we apply $T^{-1}$ to this equation, then, we get

$T^{-1}(\lambda_1w_1+\dots \lambda_n w_n) =T^{-1}(0) = 0$

Since T is linear, its inverse is also linear, hence

$T^{-1}(\lambda_1w_1+\dots \lambda_n w_n) = \lambda_1T^{-1}(w_1)+\dots + \lambda_nT^{-1}(w_n)=0$

which is equivalent to the equation

$\lambda_1v_1+\dots + \lambda_nv_n =0$

Since $v_1,\dots,v_n$ are linearly independt, this implies that $\lambda_1=\dots \lambda_n =0$ , so the set $\{w_1, \dots, w_n\}$ is linearly independent.

Now, we will prove that this set generates W. To do so, let w be a vector in W. We must prove that there exist $a_1, \dots a_n$ such that

$w = a_1w_1+\dots+a_nw_n$

Since T is surjective, there exists a vector v in V such that T(v) = w. Since $v_1,\dots, v_n$ is a basis of v, there exist $a_1,\dots a_n$ , such that

$a_1v_1+\dots a_nv_n=v$

Then, applying T on both sides, we have that

$T(a_1v_1+\dots a_nv_n)=a_1T(v_1)+\dots a_n T(v_n) = a_1w_1+\dots a_n w_n= T(v) =w$

which proves that $w_1,\dots w_n$ generate the whole space W. Hence, the set $\{w_1, \dots, w_n\}$ is a basis of W.

Consider the linear transformation $T:\mathbb{R}^2\to \mathbb{R}^2$ , given by T(x,y) = T(x,0). This transformations fails to be injective, since T(1,2) = T(1,3) = (1,0). Consider the base of $\mathbb{R}^2$ given by (1,0), (0,1). We have that T(1,0) = (1,0), T(0,1) = (0,0). This set is not linearly independent, and hence cannot be a base of $\mathbb{R}^2$

8 0

3 years ago

Based on the figure below, what is the equation for the relationship of x equals the number of rectangles and y equals the perim

Ad libitum [116K]

Answer:

Are you still there? Continue answering or we'll let someone else answer in: 19:35

Step-by-step explanation:

4 0

3 years ago

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What is the approximate volume of the cylinder?

OverLord2011 [107]

The answer would be 3,799.4 I don’t know how to get it to the nearest hundredth because I used my phone calculator but to find the answer you would take radiusxradiusxheightxpi so 11x11x10x3.14

4 0

3 years ago

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Corners of equal size are cut from a square with sides of length 8 meters (see figure).

AnnyKZ [126]

we know that

the area of the complete square is equal to

$As=b^{2}$