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tigry1 [53]
3 years ago
14

The sum of all three numbers is 12. The sum of twice the first number, 4 times the second number, and 5 times the third number i

s 35. The difference between 8 times the first number and the second number is 52. What are the three numbers?
Mathematics
1 answer:
grigory [225]3 years ago
5 0

Answer:

The numbers are 7, 4 and 1

Step-by-step explanation:

Let the numbers =x, y, z.

The sum of all three numbers is 12, x+y+z=12--------i

The sum of twice the first number, 4 times the second number, and 5 times the third number is 35, 2x+4y+5z=35-------ii

The difference between 8 times the first number and the second number is 52, 8x-y=52---------iii

Now, from (i),z =1-x-y--------iv

substitute (iv) in (ii),

2x+4y+5(12-x-y)=35

2x+4y+60-5x-5y=35

collect like terms

-3x-y=-25

that is, 3x-y=25--------v

solving (iii) and (v) simultaneously (add iii and v), we have

11x=77

divide both sides by 11 to obtain x=7

Put x=7 in (v)

3(7)+y=25

21+y=25

implies y=25-21=4

put x=7 and y=4 in (iv)

z=12-7-4=1

Hence, the numbers are 7, 4 and 1.

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Alex73 [517]

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3 years ago
Find the value of the discriminant for <img src="https://tex.z-dn.net/?f=7x%5E%7B2%7D%20%2B5x%2B1%3D0" id="TexFormula1" title="7
kondor19780726 [428]

Answer:

No real roots

Step-by-step explanation:

Given

7x² + 5x + 1 = 0 ← in standard form

with a = 7, b = 5, c = 1

To determine the nature of the roots use the discriminant

Δ = b² - 4ac

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• If b² - 4ac = 0 then roots are real and equal

• If b² - 4ac < 0 then the roots are not real

Here

b² - 4ac = 5² - (4 × 7 × 1) = 25 - 28 = - 3

Thus the 2 roots are not real

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