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anastassius [24]
3 years ago
9

What two positive numbers whose difference is 7 and whose product is 294

Mathematics
1 answer:
Aloiza [94]3 years ago
7 0

Answer:

Step-by-step explanation:

We will use x and y as our positive numbers.  We need to write 2 equations from this information.  The first is that the difference between the numbers is 7:

x - y = 7 is the equation for that.

The second is that the product of the 2 numbers is 294:

xy = 294

Let's begin by solving the first equation for x:

x = 7 + y

Now sub that in for x in the second equation:

(7 + y)y = 294 and

7y+y^2=294

This is a quadratic, so let's put it into standard form, setting it equal to 0:

y^2+7y-294=0

We have to factor this now to find out what values of y satisfy this equation.

Think: "what 2 number multiply to equal -294 and add to equal 7.  To find these numbers we find all the factors of 294, which are:

1, 294

2, 147

3, 98

6, 49

7, 42

14, 21

It looks like 14 and 21 will work.  If we make the 14 negative, then 21 - 14 = 7.  And if the 14 is negative, then -14 * 21 = -294.  So the signs are correct.  The equation rewritten using those values in place of 7y is:

y^2+21y-14y-294 = 0 and we factor by grouping:

(y^2+21y)-(14y-294)=0

Out of the first set of parenthesis we can pull out a y, and from the second set we can pull out a 14:

y(y + 21) - 14(y + 21) = 0

What's common now is the factor (y + 21).  So factor THAT out, and you're left with:

(y + 21)(y - 14) = 0

Set each of these expression equal to 0 and solve for y:

y + 21 = 0 so

y = -21 and

y - 14 = 0 so

y = 14

Since we were told that both of the numbers are positive, then y has to be 14.  

Sub in y = 14 to find x:

x = 7 + 14 so

x = 21

There you go!

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Solve the following: -3x + 7(x + 5) = 5x + 38<br><br> please explain!
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The president of a certain university receives a salary that is three times the salary of one of the department heads. The total
marissa [1.9K]

Answer:

Salary of President =   $180,000

Salary of Dept. Head =  $60,000

Step-by-step explanation:

The question is to find the salary of president and department head.

We let the salary of one of department heads be "x"

Since, the salary of president is THREE (3) TIMES a department head, we can say:

Salary of President = 3x

Now, we know the total of these 2 salaries is 240,000. Thus, we can write:

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Now, we can solve for x:

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And now the president is "3x", so his salary is:

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3 years ago
What is 0.7 written as a fraction?
alexgriva [62]
7/10 is the fraction for 0.7 





7 0
2 years ago
Read 2 more answers
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