The product of two positive numbers is 48. the larger number is 13 more than the smaller. Find both numbers [Only an algebraic solution will be accepted.]

Larger number:

16

Smaller number

3

Step-by-step explanation:

Larger number: 16

Smaller number: 3

Explanation:

Suppose the larger number is

a

and the smaller number is

b

.

You solve the following system of equations:

a⋅b=48

a−13=b

Since b is a −13, you can plug that into a⋅b=48, so...a⋅(a−13)=48

a 2−13a=48

a2−13a−48=0

Factor the polynomial:

(a−16)(a+3)=0

a=16 or a=−3a is positive so a=16.

We can now solve for b by plugging in a, so...16−13=b3=b We have a=16 and b=3, meaning that the larger number is 16 and the smaller number is 3.

Step-by-step explanation:

One side of a triangle is four centimeters longer than the shortest side. The third side of the triangle is twice as long as the shortest side. Find the length of all the sides if the perimeter is 40 centimeters.

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Answer by orca(409) About Me  (Show Source):

You can put this solution on YOUR website!

Let x be the length of the shortest side.

Then the lengths of the other two sides are x + 4 and 2x.

The perimeter of the triangle is x + (x + 4) + 2x.

As the perimeter is 40, we have

x + (x + 4) + 2x = 40

Solving for x, we have

x+ x + 4 + 2x = 40

4x + 4 = 40

4x = 36

x = 9

So the length of the shortest side is 9 cm.

The lengths of the other two sides are:

x + 4 = 9 + 4 = 13 cm

2x = 2*9 = 18 cm