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insens350 [35]
3 years ago
10

The sum of the digits of a two-digit number is 5. If the number is multiplied by 3, the result is 42. Write and solve a system o

f equations to find the number.
Mathematics
1 answer:
Elenna [48]3 years ago
6 0
A two digit number has a tens digit and a ones digit.
Let's say x = tens digit and y = ones digit

"The sum of the digits is 5"
x + y = 5

The next phrase is "the number multiplied by 3 is 42" but we need to represent the number using the digits. So they need to be multiplied first by their place value and added together. [Example: 34 = 3(10) + 4(1)]

The number is: 10x + y
3(10x + y) = 42

The system of equations: (two equations for two unknowns)
x + y = 5
30x + 3y = 42

Then you can use substitution or elimination to combine and solve.
I'll use elimination, multiply the entire top equation by -3 and add the equations together. y will cancel out

-3x - 3y = -15
30x + 3y = 42
------------------
27x + 0 = 27
x = 1

then plug x = 1 into either equation to find y

1 + y = 5
y = 4

remember the x and y represent digits so the number xy is 14
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Answer:

x\geq 6\text{ or } x

Step-by-step explanation:

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A circle has a sector with area 33 pi and a central angle of 11/6 pi radians. What is the area of a circle?
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36π

Step-by-step explanation:

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where α = central angle in radians

Since \pi r^2 is the area of a circle, A, this implies that:

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A circle has a sector with area 33 pi and a central angle of 11/6 pi radians.

Therefore, the area of the circle, A, is:

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Step-by-step explanation:

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Use phytagoras theorem to find the base of the triangle:

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