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Marrrta [24]
3 years ago
12

The sum of two numbers is 35. Three times the larger number is the same as 4 times the smaller number. Find the smaller number

Mathematics
1 answer:
nikitadnepr [17]3 years ago
3 0
If 35-x is the smaller number and x is the larger number, we can take that 3*x=4*(35-x)=140-4x. Subtracting 3x from both sides, we get 140-7x=0. Adding 7x to both sides, we get 140=7x. Lastly, we can divide both sides by 7 to get x=20
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3 years ago
The square of a number plus three times the number is 70. find the numbers.
Harrizon [31]

Answer:

Step-by-step explanation:

The equation for that is

x^2+3x=70

If we subtract over the 70, we have a quadratic that we can factor to solve for the values of x that will make that equation true.

x^2+3x-70=0

Now we need the factors of 70 that will either add or subtract to give us the linear term of 3. The factors of 70 that will work are 10 and 7. 10 times 7 is 70, and 10 - 7 = 3:

x^2+10x-7x-70=0 and now we will factor by grouping:

(x^2+10x)-(7x-70)=0 and factor out what's common:

x(x+10)-7(x+10)=0

The factor (x + 10) is common, so we will now factor that out:

(x+10)(x-7)=0

By the Zero Product Property, either x + 10 = 0 or x - 7 = 0, so x = -10 or 7

Those are the 2 numbers that will work.

(-10)^2+3(-10)=70 simplifies to

100 - 30 which does in fact equal 70. OR

(7)^2+3(7)=70 which simplifies to

49 + 21 which also equals 70.

So you're done!

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\bf \begin{cases}
(f\circ g)(x)=x^2-6x+8\\\\
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