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3 years ago

PLEASE HURRY

Mathematics

1 answer:

Delvig [45]3 years ago

4 0

Answer:

Answer 2) When dividing by -5, he did not change the $\leq$ to $\geq$ .

Step-by-step explanation:

If you divide or multiply a negative, you ALWAYS change the sign to its opposite.

Hope this helps! :)

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Chose all the properties that were used to simplify the following problem

timofeeve [1]

(a+b) + c = a + (b + c)

re-arrange the numbers - associative property of addition

Answer

Associative property of addition

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3 years ago

Solye for x. 8(x + 1) - 3[X + 4) = 7(2 - x)

kramer

Answer:

3/2

Step-by-step explanation:

distribute 8,-3,7

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3 years ago

Question 10 (5 points)

11Alexandr11 [23.1K]

I think the answer is A

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3 years ago

Read 2 more answers

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of

Tema [17]

Answer:

Small box weighs 13.75 kg & large box weighs 15.75 kg

Step-by-step explanation:

We can write 2 simultaneous equation and solve for weight of each box.

Let weight of large box be l and small box be s.

"3 large boxes and 5 small boxes has a total weight of 116 kilograms":

$3l+5s=116$

and

"9 large boxes and 7 small boxes has a total weight of 238 kilograms":

$9l+7s=238$

Now we can solve for l in the 1st equation and put it into 2nd equation and get s:

$3l+5s=116\\3l=116-5s\\l=\frac{116-5s}{3}$

now,

$9l+7s=238\\9(\frac{116-5s}{3})+7s=238\\3(116-5s)+7s=238\\348-15s+7s=238\\348-238=15s-7s\\110=8s\\s=\frac{110}{8}=13.75$

now we plug in 13.75 into s into equation of l to find s:

$l=\frac{116-5s}{3}\\l=\frac{116-5(13.75)}{3}\\l=15.75$

5 0

3 years ago

Consider the linear transformation T from V = P2 to W = P2 given by T(a0 + a1t + a2t2) = (2a0 + 3a1 + 3a2) + (6a0 + 4a1 + 4a2)t

Svet_ta [14]

Answer:

$[T]EE=\left[\begin{array}{ccc}2&3&3\\6&4&4\\-2&3&4\end{array}\right]$

Step-by-step explanation:

First we start by finding the dimension of the matrix [T]EE

The dimension is : Dim (W) x Dim (V) = 3 x 3

Because the dimension of P2 is the number of vectors in any basis of P2 and that number is 3

Then, we are looking for a 3 x 3 matrix.

To find [T]EE we must transform the vectors of the basis E and then that result express it in terms of basis E using coordinates and putting them into columns. The order in which we transform the vectors of basis E is very important.

The first vector of basis E is e1(t) = 1

We calculate T[e1(t)] = T(1)

In the equation : 1 = a0

$T(1)=(2.1+3.0+3.0)+(6.1+4.0+4.0)t+(-2.1+3.0+4.0)t^{2}=2+6t-2t^{2}$

$[T(e1)]E=\left[\begin{array}{c}2&6&-2\\\end{array}\right]$

And that is the first column of [T]EE

The second vector of basis E is e2(t) = t

We calculate T[e2(t)] = T(t)

in the equation : 1 = a1

$T(t)=(2.0+3.1+3.0)+(6.0+4.1+4.0)t+(-2.0+3.1+4.0)t^{2}=3+4t+3t^{2}$

$[T(e2)]E=\left[\begin{array}{c}3&4&3\\\end{array}\right]$

Finally, the third vector of basis E is $e3(t)=t^{2}$

$T[e3(t)]=T(t^{2})$

in the equation : a2 = 1

$T(t^{2})=(2.0+3.0+3.1)+(6.0+4.0+4.1)t+(-2.0+3.0+4.1)t^{2}=3+4t+4t^{2}$

Then

$[T(t^{2})]E=\left[\begin{array}{c}3&4&4\\\end{array}\right]$

And that is the third column of [T]EE

Let's write our matrix

$[T]EE=\left[\begin{array}{ccc}2&3&3\\6&4&4\\-2&3&4\end{array}\right]$

T(X) = AX

Where T(X) is to apply the transformation T to a vector of P2,A is the matrix [T]EE and X is the vector of coordinates in basis E of a vector from P2

For example, if X is the vector of coordinates from e1(t) = 1

$X=\left[\begin{array}{c}1&0&0\\\end{array}\right]$

$AX=\left[\begin{array}{ccc}2&3&3\\6&4&4\\-2&3&4\end{array}\right]\left[\begin{array}{c}1&0&0\\\end{array}\right]=\left[\begin{array}{c}2&6&-2\\\end{array}\right]$

Applying the coordinates 2,6 and -2 to the basis E we obtain

$2+6t-2t^{2}$

That was the original result of T[e1(t)]

8 0

3 years ago