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3 years ago

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The ordered pair (4, -8) is in the 4th quadrant if we took the opposite of the x- value and the opposite of the y-value, which q

uadrant would the ordered pair be in ? PLS ANSWER I GIVE 30 POINTS

1 answer:

harina [27]3 years ago

8 0

9514 1404 393

Answer:

2nd quadrant

Step-by-step explanation:

Reversing the signs of both coordinates reflects the point across the origin. The quadrant diagonally opposite quadrant 4 is quadrant 2.

_____

You recall that quadrants are numbered 1 to 4 counterclockwise, starting from upper right.

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How do I solve proportions? Here’s my questions: <br><br> 1. x/8=5/16<br> 2. 5/12=15/x

Flura [38]

Proportions are very simple once you get the hang of them! What you do is cross multiple. :)

1. x/8=5/16

You first start by multiplying x and 16

Then multiply 5 and 8

So now you have 16x=40

Finally divide 16 from each side

You get: x+0.4!

2. 5/12=15/x

Remember to cross-multiply!

Now we have 5x=180

Next divide 5 from each side

You get: x=36!

7 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

2m^2 - 4m/ 2(m - 2) simplified

egoroff_w [7]

Answer:

=2m²-4m/2(m-2)

=2m(m-2)/2(m-2)

=m is the correct answer

5 0

2 years ago

Read 2 more answers

What are the possible rational zeros for f(x)=3x^4+x^3-13x^2-2x+9?

zaharov [31]

Answer:

Option 4 (±1, ±1/3, ±3, ±9) is the correct option.

Step-by-step explanation:

The given expression is $f(x)=3x^{4}+x^{3}-13x^{2}-2x+9$

We have to find the possible rational zeros for the function.

So by the rational zero theorem factors will be

=±(Factors of constant term 9)/±factors of coefficient of $x^{4}$

=±(Factors of 9)/±(Factors of 3)

=±(1, 3, 9)/±(1, 3)

=±(1, 3, 9, 1/3)

So option 4 is the correct answer.

4 0

3 years ago

Joey wants to build a rectangular garden. He plans to use a side of a river for one side of the garden, he will not place fencin

NikAS [45]

We let x and y be the measures of the sides of the rectangular garden. The perimeter subtracted with the other side should be equal to

2x + y = 92

The value of y in terms of x is equal to,

y = 92 – 2x

The area is the product of the two sides,

A = xy

Substituting,

A = x (92 – 2x) = 92x – 2x2

Solving for the derivative and equating to zero,

0 = 92 – 4x ; x = 23

Therefore, the area of the garden is,

<span> A = 23(92 – 2(23)) = 1058 yard<span>2</span></span>

5 0

3 years ago