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brilliants [131]
3 years ago
14

Grace is three times as old as Hans, but in 5 years she will be twice as old as Hans is then. How old are they now? Set up an th

en solve a system of linear equations. please show step by step
Mathematics
1 answer:
frosja888 [35]3 years ago
5 0

Answer:

3x - y = 0; 2x - y = -5

Step-by-step explanation:

Let x be the present age of Hans and y be the present age of Grace,

Since, in present Grace is three times as old as Hans,

⇒ y = 3x

⇒ 3x - y = 0

Now, after 5 years,

The age of Hans = x + 5,

And, the age of Grace = y + 5

Also, in 5 years Grace will be twice as old as Hans is then,

⇒ y + 5 = 2 ( x + 5 )

⇒ y + 5 = 2x + 10

⇒ 2x - y = -5

Hence, the required system of linear equations is,

3x - y = 0; 2x - y = -5

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Suppose A is a matrix and k is a positive integer. What does the notation Ak mean?
Butoxors [25]

Answer:

Scalar product

Step-by-step explanation:

The scalar product of a matrix refers to the product of a matrix and a number. The scalar is used to multiply each element in the matrix to get the final vector. In the question the scalar is k which is a constant and the matrix is A.

in the example below 2 is the scalar

2*\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right]

the final matrix will be

\left[\begin{array}{ccc}2&4&6\\8&10&12\\14&16&18\end{array}\right]

7 0
3 years ago
WILL MARK BRAINLIEST Given a the line y=2.5x+4, find line whose graph: b intersects with the graph of the given line.
valentina_108 [34]
Your equation will be y=4x-1 and the intersection point will be (2,9). Hope this helps!

7 0
3 years ago
Total tax: 0.05(50 + 40)
Elenna [48]

Answer:

i think it's 4.5

7 0
3 years ago
What is the value of n in this equation?<br><br> n - 409 = 732
Natalija [7]

Answer:

n = 1141

Step-by-step explanation:

To find the value of n you add 732 and 409 giving you 1141.

8 0
3 years ago
Read 2 more answers
Which equation can you use to solve for x? x + 56 = 180 x + 146 = 180 180−x=146 x + 56 = 146 The figure contains a pair intersec
Harlamova29_29 [7]
The correct question is
<span>Which equation can you use to solve for x? x + 56 = 180 x + 146 = 180 180−x=146 x + 56 = 146 The figure contains a pair intersecting lines. One of the four angles formed by the intersecting lines is labeled 146 degrees. The angle opposite and not adjacent to this angle is broken into two smaller angles by a ray that extends from the point where the two lines intersect. One of these smaller angles is labeled 56 degrees, and the other smaller angle is labeled x degrees.

see the picture attached to better understand the problem

we know that
angle 146</span>° and angle (56°+x°) area equal -----> by vertical angles
so
146=56+x
therefore

the answer is
<span>x + 56 = 146</span>

3 0
3 years ago
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