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3 years ago

use the quadratic formula to solve the equation. If necessary, round the nearest hundredth. 2a^2-30a+108=0

1 answer:

7 0

We know that

the formula to solve the quadratic equation is
x={-b(+/-)√[b²-4ac]}/2a

we have
2a²-30a+108=0
where
a=2
b=-30
c=108

x={30(+/-)√[30²-4*2*108]}/(2*2)
x={30(+/-)√[36]}/(4)
x={30(+/-)6}/(4)
x1=(30+6)/4----> 36/4----> 9
x2=(30-6)/4----> 24/4----> 6

the answer is
the values of a are
a1=9
a2=6

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1. Is the square root of 2 between 1.3 and 1.4? How do you know?

VikaD [51]

Answer:

Step-by-step explanation:

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2 years ago

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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 $\mathbb{R}^2$

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3 years ago

Its math and struggling with it

svlad2 [7]

Answer: Solve for m m by simplifying both sides of the equation, then isolating the variable. m=15

Step-by-step explanation: Reducing to lowest terms On both sides

8 0

2 years ago

Options: y= -2x - 6 y= 2/3x + 6 y= -2/3x + 6 y=2x + 6

melisa1 [442]

Answer:

y = - $\frac{2}{3}$ x + 6

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (0, 6) and (x₂, y₂ ) = (6, 2) ← 2 points on the line

m = $\frac{2-6}{6-0}$ = $\frac{-4}{6}$ = - $\frac{2}{3}$

The line crosses the y- axis at (0, 6) ⇒ c = 6

y = - $\frac{2}{3}$ x + 6 ← equation of line

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2 years ago

Can someone give me work for the estimate

pogonyaev

If a rational number after dot "like 5.52") is smaller than 5(half) , then you assume the first number before that dot stuff :p
For example:

-》11,2 =11
-》 4.19= 4
-》2,2 = 2
etc

But if it's bigger than 5 or equals 5 , u assume the first number before that dot stuff +1
For example :
-》5.5 =6
-》3.9=4
-》225.7= 226
etcetc

so the answer is:;;

5.52 --》 52 is bigger than a half (50) so ur gonna assume like 6

1,6 --》(it equals with 1.60 too)
6 is bigger than 5 so ur gonna assume 2

6÷2 =3

Hope it helps! :))
#MissionExam001

7 0

3 years ago