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2 years ago

A plane travels 342 miles in 6 hours. At a constant rate how many miles did the plane travel in 1 hour?

Mathematics

1 answer:

miss Akunina [59]2 years ago

7 0

Answer:

<u>57 miles</u>

Step-by-step explanation:

342÷6= 57

<em>I hope this helped you out, if it did please mark my answer as brainliest. I will be so grateful. </em>

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Given: A, B, and C What is the value of X in the matrix equation AX + B = C?

Ksju [112]

Answer:

Option (2)

Step-by-step explanation:

Given expression is, AX + B = C

$A=\begin{bmatrix}-3 & -4\\ 1 & 0\end{bmatrix}$

$B=\begin{bmatrix}-7 & -9\\ 4 & -1\end{bmatrix}$

$C=\begin{bmatrix}-42 & -20\\ 5 & 4\end{bmatrix}$

AX + B = C

AX = C - B

C - B = $\begin{bmatrix}-42 & -20\\ 5 & 4\end{bmatrix}-\begin{bmatrix}-7 & -9\\ 4 & -1\end{bmatrix}$ = $\begin{bmatrix}-42+7 & -20+9\\ 5-4 & 4+1\end{bmatrix}$

C - B = $\begin{bmatrix}-35 & -11\\ 1 & 5\end{bmatrix}$

Let $X=\begin{bmatrix}a & b\\ c & d\end{bmatrix}$

AX = $\begin{bmatrix}-3 & -4\\ 1 & 0\end{bmatrix}\times \begin{bmatrix}a & b\\ c & d\end{bmatrix}$

= $\begin{bmatrix}(-3a-4c) & (-3b-4d)\\ a & b\end{bmatrix}$

Since AX = C - B

$\begin{bmatrix}(-3a-4c) & (-3b-4d)\\ a & b\end{bmatrix}=\begin{bmatrix}-35 & -11\\ 1 & 5\end{bmatrix}$

Therefore, a = 1, b = 5

(-3a - 4c) = -35

3(1) + 4c = 35

3 + 4c = 35

4c = 32

c = 8

And (-3b - 4d) = -11

3(5) + 4d = 11

4d = -4

d = -1

Therefore, Option (2). X = $\begin{bmatrix}1 & 5\\ 8 & -1\end{bmatrix}$ will be the answer.

7 0

3 years ago

Last month you purchased 6 individual songs and 1 albums for a total of $21.99.

Annette [7]

Answer:

Song =$1.50 Album =$12.99

Step-by-step explanation:

Lets assume Individual songs = x

albums=y

6x + y = 21.99-------- y= 21.99- 6x

4x + 3y= 44.97

Replace y in the second equation

4x+ 3(21.99-6x) = 44.97

4x +65.97- 18x = 44.97

14x= 21

x = 1.50

y= 21.99- (6*1.50)

= 12.99

7 0

3 years ago

Use slopes and y-intercepts to determine if the lines y=−x2+14 and 3x−4y=−1 are parallel.

Keith_Richards [23]

Answer: the lines are not parallel.

Explanation: if you isolate the x in 3x^2-4y=-1, the equation is y=3/4x^2+1/4

So, they are not parallel because the slope is not the same.

7 0

2 years ago

The amount Lin's sister earns at her part-time job is proportional to the number

gulaghasi [49]

Answer:

$y = 9.6x$