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Anit [1.1K]
3 years ago
8

The product of two positive numbers is 48. the larger number is 13 more than the smaller. Find both numbers [Only an algebraic s

olution will be accepted.]
Mathematics
1 answer:
Valentin [98]3 years ago
5 0

Answer:

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.

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Answer:

Equation → 5y = 3y + 6

Value of ST = 15

Step-by-step explanation:

From the picture attached,

In right triangles ΔVST and ΔVUT,

Acute angles ∠SVT ≅ ∠UVT [Given]

TV ≅ TV [By reflexive property of congruence]

ΔVST ≅ ΔVUT [Hypotenuse angle congruence of right triangles]

Therefore, corresponding parts of the congruent triangles are congruent.

Therefore, ST ≅ TU

5y = 3y + 6

5y - 3y = 6

2y = 6

y = 3

Therefore, ST = 5y

ST = 5(3)

     = 15

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