In this exercise, you're required to find two numbers by translating the word problem into an algebraic expression and then solving for the unknown variables (x and y).

Translating the word problem into an algebraic expression, we have;

Two numbers differ by 8:

$x-y=8$ ....equation 1.

The product of the two numbers is 713:

$xy=713$ ....equation 2.

To calculate the sum of the two numbers:

First of all, we would solve for each of the unknown variables (x and y).

From eqn. 1, we have:

$x=8+y$ ....equation 3.

Substituting eqn. 3 into eqn. 2, we have:

$y(y+8)=713\\\\y^2+8y=713\\\\y^2+8y-713=0$

Solving the quadratic equation by factorization, we have:

$y^2-31y +23y-713=0\\\\y(y-31)+23(y-31)=0\\\\(y+23)(y-31)=0$

y = -23 or 31.

For the value of x, when y = 31:

$x=8+31$

x = 39

Now, we can calculate the sum of the two numbers:

$x+y=39+31=70$

Read more on word problems here: brainly.com/question/13170908

4 0

3 years ago

Anyone needs help with an assignments

hoa [83]

Answer:

Not right now, but thank you! :)

Explanation:

8 0

2 years ago

Unit 2 Quiz

Karolina [17]

Answer: C. They will have more time to manage his mother's care.

Explanation:

A single income option means that only one of them will be working and only one source of income will be used to maintain all three of them including Daniel's mother. This will most definitely result in them having less disposable income and less financial income in general.

Also the scenario painted made no mention of a baby so option D is incorrect. The most likely option in C which makes sense because with one of them staying home to take care of the mother, they will have time to be able to take care of her better.

4 0

3 years ago