One number is 7 more than twice another. If their difference is 22, what is the larger number?

Mathematics

2 answers:

Salsk061 [2.6K]3 years ago

7 0

Answer:

its 37

Step-by-step explanation:

Vaselesa [24]3 years ago

5 0

Answer:

Step-by-step explanation:

We'll write each one of these statements into an algebraic equation. The word "is" means "=", the words "more than" mean "+", and "difference" means subtraction. x will be one number, and y will be the other number. The first sentence, then, in an algebraic equation, is

x = 2y + 7

The second equation, then, is

x - y = 22

Since we know from the first equation what x is equal to, we will sub in what x equals into the second equation in place of x:

2y + 7 - y = 22 and

y + 7 = 22 so

y = 15.

Sub that in for y to solve for x:

x - 15 = 22 so

x = 37

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Solve 2x2 − 4x − 5 = 0 by completing the square.

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For this case we have the following polynomial:
$2x ^ 2 - 4x - 5 = 0
$
Rewriting we have:
$2x ^ 2 - 4x = 5

x ^ 2 - 2x = 5/2$
Then, completing squares we have:
$x ^ 2 - 2x + (-2/2) ^ 2 = 5/2 + (-2/2) ^ 2
$
Rewriting:
$x ^ 2 - 2x + (-1) ^ 2 = 5/2 + (-1) ^ 2

x ^ 2 - 2x + 1 = 5/2 + 1

(x-1) ^ 2 = 7/2$
$x-1 = +/- \sqrt{7/2} x = 1 +/- \sqrt{7/2}$
Then, the solutions are:
$x1 = 1 + \sqrt{7/2} x2 = 1 - \sqrt{7/2}$
Answer:
$x1 = 1 + \sqrt{7/2} 

x2 = 1 - \sqrt{7/2}$