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Art [367]
3 years ago
15

A pair of linear equations is shown:

Mathematics
1 answer:
fenix001 [56]3 years ago
6 0

Answer: option D is the correct answer.

Step-by-step explanation:

The given pair of linear equations is

y = -x + 1

y = 2x + 4

We would compare both equations with the slope intercept form equation of a straight line which is expressed as

y = mx + c

Where

m represents slope

c represents y intercept.

Comparing the first equation,

Slope = - 1

y intercept = 1

Comparing the second equation,

Slope = 2

y intercept = 4

Therefore, the statement that best explains the steps to solve the pair of equations graphically is

D. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.

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The distance between two towns is 120 kilometers.There are approximately 8 kilometers in 5 miles.which measurement is closer to
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a. The water in the second tank decreases at a faster rate than the water in the first tank. The initial water level in the first tank is greater than the initial water level in the second tank.

Step-by-step explanation:

Step 1:

It is given that the time remaining in first tank is given by the equation y = -10x + 80. We can get the total water in the tank by substituting x = 0 in the equation. The total volume of water in first tank is 80 litres.

Step 2:

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As per the given table for the second tank, 60 litres of water remains when x =0. So the total volume of water in the second tank = 60 litres.

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Step 5:

The initial volume of water in first tank is higher. The water in  second tank decreases at a faster rate than the first tank.

Step 6:

The only correct option is:

a. The water in  second tank decreases at a faster rate than the water in the first tank. The initial water level in  first tank is greater than the initial water level in the second tank.

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Step-by-step explanation:


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Type the correct answer in each box.If matrix C represents (A − B) + A, the value of the entry represented by c41 is and the cor
strojnjashka [21]

Given the matrices A and B:

\begin{gathered} A=\begin{bmatrix}{-5} & {3} & {8} & {} \\ {3} & {6} & {-5} & {} \\ {5} & {-9} & {0} & {} \\ {7} & {3} & {4} & {}\end{bmatrix} \\  \\ B=\begin{bmatrix}{-7} & {-8} & {-5} & {} \\ {7} & {9} & {2} & {} \\ {2} & {5} & {-7} & {} \\ {2} & {8} & {-7} & {}\end{bmatrix} \end{gathered}

We know that:

C=(A-B)+A=2A-B

Then, using the matrices A and B:

\begin{gathered} C=2\cdot\begin{bmatrix}{-5} & {3} & {8} & {} \\ {3} & {6} & {-5} & {} \\ {5} & {-9} & {0} & {} \\ {7} & {3} & {4} & {}\end{bmatrix}-\begin{bmatrix}{-7} & {-8} & {-5} & {} \\ {7} & {9} & {2} & {} \\ {2} & {5} & {-7} & {} \\ {2} & {8} & {-7} & {}\end{bmatrix} \\  \\ C=\begin{bmatrix}{-10} & {6} & {16} & {} \\ 6 & {12} & {-10} & {} \\ 10 & {-18} & {0} & {} \\ 14 & 6 & 8 & {}\end{bmatrix}+\begin{bmatrix}{7} & {8} & {5} & {} \\ -{7} & -{9} & -{2} & {} \\ -{2} & {-5} & {7} & {} \\ {-2} & -{8} & {7} & {}\end{bmatrix} \\  \\ \therefore C=\begin{bmatrix}{-3} & 14 & 21 & {} \\ -1 & {3} & {-12} & {} \\ 8 & {-23} & 7 & {} \\ 12 & -2 & 15 & {}\end{bmatrix} \end{gathered}

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C_{41}=12

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B_{41}=2

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