Mathematics, 19.09.2019 17:30 eemorales5100

Which two numbers add up to 14 and multiply to 8?

Answers: 2

Show answers

Answers

For now, let's call the numbers A and B .

You gave us two clues about the numbers.
You said:
-- (A + B) = 14
-- (A · B) = 8 .

There are a couple of different ways to go about this.
Here's my way:

I'm going to use 'substitution' to solve this pair of equations.

-- Take the first equation and solve it for B:

A + B = 14

Subtract A from each side:    B = 14 - A

-- Take that and write it in place of B in the second equation:

   A · B = 8

   A · (14 - A) = 8

Eliminate parentheses: 14A - A² = 8

Subtract 8 from each side: 14A - A² - 8 = 0

Multiply each side by -1 : -14A + A² + 8 = 0

Re-arrange the terms: A² - 14A + 8 = 0

There's your nice familiar quadratic equation to solve.
A quadratic equation always has two solutions.
The two solutions to this one are the two numbers you're looking for.

Looking at the left side, it's pretty obvious that there's no easy way
to factor it. So you'll just have to use the quadratic formula.

When you solve the quadratic equation, you get these two solutions:

A = 7 + √41 = 13.4031 ... (rounded)
and
A = 7 - √41 =    0.5969 ...   (rounded)

When you compare these numbers to Destanyhale's numbers
in the first answer, you'll find that they're completely different.

Don't get scared ! Destanyhale's method of solution was completely
right, and the two numbers over there are perfectly correct, but
there are two 'minor' problems with that
-- Destanyhale didn't explain how to find the solution.
-- Destanyhale swapped the sum and the product in the question.
That is, s/he said they add up to 8 and multiply to 14.

But, after mis-reading the question, the rest of that solution is well done.

Answer from: Quest

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2

Answer from: Quest

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

Another question on Mathematics

Mathematics, 21.06.2019 17:50

F(x) = x2 − 9, and g(x) = x − 3 f(x) = x2 − 4x + 3, and g(x) = x − 3 f(x) = x2 + 4x − 5, and g(x) = x − 1 f(x) = x2 − 16, and g(x) = x − 4 h(x) = x + 5 arrowright h(x) = x + 3 arrowright h(x) = x + 4 arrowright h(x) = x − 1 arrowright

Answers: 2

Answer

Mathematics, 21.06.2019 18:30

The measure of one angle of an octagon is two times smaller that of the other seven angles. what is the measure of each angle?

Answers: 3

Answer

Mathematics, 21.06.2019 21:30

Noel is hoping to make a profit (in $) on the school play and has determined the function describing the profit to be f(t) = 8t – 2654, where t is the number of tickets sold. what does the number 8 tell you?

Answers: 1

Answer

Mathematics, 21.06.2019 21:30

Iwill give brainliest. suppose tommy walks from his home at (0, 0) to the mall at (0, 5), and then walks to a movie theater at (6, 5). after leaving the theater tommy walks to the store at (6, 0) before returning home. if each grid square represents one block, how many blocks does he walk?