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2 years ago

Find the solution to the system of equations below. 2y = 2x - 8 2x + y = 5

Mathematics

1 answer:

ladessa [460]2 years ago

8 0

Answer:

The solution to the system of equations is:

(x, y) = (3, -1)

The graph is attached below.

Step-by-step explanation:

Given the system of equations

$2y = 2x - 8$

$2x + y = 5$

Let us solve the system of equations using the elimination method

$\begin{bmatrix}2y=2x-8\\ 2x+y=5\end{bmatrix}$

Arrange equation variables for elimination

$\begin{bmatrix}2y-2x=-8\\ y+2x=5\end{bmatrix}$

Multiply y + 2x = 5 by 2: 2y + 4x = 10

$\begin{bmatrix}2y-2x=-8\\ 2y+4x=10\end{bmatrix}$

subtracting the equations

$2y+4x=10$

$-$

$\underline{2y-2x=-8}$

$6x=18$

solve 6x = 18 for x

$6x=18$

Divide both sides by 6

$\frac{6x}{6}=\frac{18}{6}$

simplify

$x=3$

For 2y - 2x = -8 plug in x = 3

$2y-2\cdot \:3=-8$

$2y-6=-8$

Add 6 to both sides

$2y-6+6=-8+6$

Simplify

$2y=-2$

Divide both sides by 2

$\frac{2y}{2}=\frac{-2}{2}$

Simplify

$y=-1$

Therefore, the solution to the system of equations is:

(x, y) = (3, -1)

The graph is attached below.

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Which of the following expressions has a coefficient of 10 and a constant of 5

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Third option is correct

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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

Write the numbers 57,000,000,000 and 19,000 in scientific notation. Then show how to divide 57,000,000,000 by 19,000 using prope

LenaWriter [7]

Answer:

the first number is 57 to the ninth power and the second is 19 to the third power, not to sure about the dividing but a quick google search should do the trick

Step-by-step explanation:

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3 years ago

Please answer correctly !!!!!!!! Will mark brainliest answer !!!!!!!!!!!!!

spin [16.1K]

Answer & Step-by-step explanation:

Since you looking for the width and you are given the length and the area, then you will divide the area by the length.

(10x² + 5x) ÷ 5x

You can also turn this into a fraction so you can know what you are dividing.

$\frac{10x^2+5x}{5x}$

So, your width is 2x + 1

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3 years ago

Read 2 more answers

The mean number of hours of study time per week for a sample of 562 students is 23. If the margin of error for the population me

Vadim26 [7]

Answer:

The 98% confidence interval for the mean number of hours of study time per week for all students is (20.9, 25.1).

Step-by-step explanation:

Confidence interval:

Sample mean plus/minus the margin of error.

In this question:

Mean of 23.

Margin of error 2.1.

Then

23 - 2.1 = 20.9

23 + 2.1 = 25.1

The 98% confidence interval for the mean number of hours of study time per week for all students is (20.9, 25.1).

3 0

2 years ago