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3 years ago

Translate to a system of equations:

Mathematics

1 answer:

omeli [17]3 years ago

3 0

Answer:

m + n = 15

m - 3 = n

The numbers are 9 and 6

Step-by-step explanation:

From the question,

The sum of two numbers is fifteen; the first number is m and the second number is n. To translate to a system of equations, we can write that

m + n = 15 ..... (1)

Also, from the question,

One number is three less than the other,

Also, to translate to a system of equations, we can write that

m - 3 = n ...... (2)

If desired, we can determine m and n

From equation (1)

m + n = 15

Then,

m = 15 - n ...... (3)

Put the value of m in equation (3) into equation (2)

m - 3 = n

Then

15 - n - 3 = n

15 - 3 = n + n

12 = 2n

n = 12/2

∴ n = 6

For m, put the value of n into equation 3

m = 15 - n

m = 15 - 6

m = 9

∴ m = 9 and n = 6

Hence, the numbers are 9 and 6

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vagabundo [1.1K]

Answer:

The Amin's score in math was 46.

Step-by-step explanation:

The question is:

The average math score for Amin, azman and aziz is 73. Azman marks 35 more than Amin while aziz is twice that of Amun. What is Amin's sign?

Solution:

Let us denote that:

x = Amin's score in math

y = Azman's score in math

z = Aziz's score in math.

The average of x, y and z is, 73.

That is:

$\frac{x+y+z}{3}=73\\\\\Rightarrow x+y+z = 219$

Now it is provided that:

$y=x+35...(i)\\z=2x...(ii)$

Use the equations (i) and (ii) to determine the value of x as follows:

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Thus, the Amin's score in math was 46.

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3 years ago

Vanessa draws one side of equilateral ΔABC on the coordinate plane at points A(–2, 1) and B(4,1). What are the possible coordina

grandymaker [24]

Important question. No menu of choices given so we'll just have to figure it out.

It's not possible in two dimensions for all three vertices of an equilateral triangle to be lattice points, i.e. points with integer coordinates.

Since A(-2,1) and B(4,1) have integer coordinates, our other point won't. There will be a √3 involved, the algebraic tell that there's a 30/60/90 triangle lurking somewhere in the problem.

Here the given side is parallel to the x axis which makes things easier.

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The x coordinate of the third vertex will be the same as that of the midpoint of AB, let's call it M,

M = ( (-2 + 4) / 2, (1 + 1)/2 ) = (1, 1)

We're making some progress. Whatever our height h is our two candidates for the third vertex C are (1, 1 ± h).

Since |AB|=6, we get |AB|=|BC|=|AC|=6 because it's an equilateral triangle.

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3² + h² = 6²

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h² = 27

h = 3√3

Answer: C is (1, 1 + 3√3) or (1, 1 - 3√3)

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Answer:

Step-by-step explanation:

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Step-by-step explanation:

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