1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
QveST [7]
3 years ago
13

One number is 10 more than another number. If the product of the two numbers is -21 find both numbers

Mathematics
1 answer:
sergeinik [125]3 years ago
8 0

Answer:

The Two numbers are 7 and -3.

Step-by-step explanation:

For this problem, the first thing we need to do is rewrite what we are given in mathematical terms, or equations that we can use to solve our problem at hand. We can say that:

X = <em>"one number" </em>

and

X+10 = <em>"our other number".</em>

then with our given information and newly defined mathematical terms, we would then combine both of them and formulate it into an equation that we can use to find the two numbers:

= x(x+10) = -21   (Next, we expand this equation to:) --->

=  X2+10x-21=0  (Side Note: the "x2" is x squared.).

= X2+10x-21 = 0  (add 21 to the other side to get)

= X2+10x +21 = 0  (this is the equation that we will use to find the two numbers)

Next step is to solve by factoring the equation X2+10x+21=0

An easy way to approach factoring an equation of this format is to think..

"<em>What two numbers can add up to equal ten? (10x) and also multiply to equal 21 (+21) ? "</em>

In our case, our two numbers are 7 and 3. (Because 7 plus 3 equals ten, and also 7 times 3 equals 21.)

So, with that information, : X2+10x+21 factored equals  

(x+3)(x+7) = 0.

Next, we set both X+3 and X+7 equal to zero and solve for x to find the two numbers

= ( x+3) = 0   (3-3 = 0   0-3 = -3), so,  X= -3        

= (x+7) = 0 (7-7 = 0  0-7 = -7), so, X = -7

So with the work above we found the two numbers we need, However, the question specifically stated that the product of the two numbers is negative 21, and we currently have positive 21 (Because neg 7 times neg 3 = positive 21).

So, with this, our last step is to use one of the two numbers that we found (X= -3 or X= -7) in the second equation that we made in the beginning to find the last number that we need.

We know that a negative number times a positive number equals a negative number, so with this fact in mind, we revisit one of our first equations while keeping our original question in mind that:

<em>"one number is </em><em>10</em><em> more than another number "</em>

With that in mind, the only combination that has the highest chance of working in accordance to the question we have is:

X=-3

So based on that observation, we have assumed that -3 is our first number. We need to <em>prove</em> that it is the right number by plugging it into the equation below:

So, if we plug in -3 in our equation that we made in the beginning (X+10 = "our other number"), then we find:

= -3+10 = 7  which is our second and final number!

Therefore, the two numbers are 7 and -3 because 7 is 10 more than -3,

and the product of both numbers are -21.

 

I hope this helps,  Thanks for your time!  

You might be interested in
What fraction of 3 is 2 2/5
Yuki888 [10]

Answer: 2 2/5 is 4/5 of 3

Step-by-step explanation:

We can view that as what do we multiply 3 by to get 2 2/5 and call that value x

3x = 2 2/5

x = (2 2/5)/3

Let's turn 2 2/5 into an improper fraction... 2 2/5 = 12/5

So we have

x = (12/5)/3 = (12/5)(1/3) = 4/5

Thus 2 2/5 is 4/5 of 3

Verify:  3(4/5) = 12/5 = 2 2/5

5 0
2 years ago
Find the rate of change on the table
Aneli [31]

Answer:

51

Step-by-step explanation:

8 0
2 years ago
Nine less than The quotient of two and a number x
aleksley [76]
2/x-9. You must divide 2 by x first to follow the order of operations then subtract by nine.

4 0
3 years ago
Read 2 more answers
The value of a car decreases by 1/6 every year. What type of function represents this patten
PolarNik [594]

Answer:

Exponential decay

Step-by-step explanation:

the answer is not linear decrease cause the price doesn't decrease the same every year

.. ..

4 0
3 years ago
What is the value of a?
pantera1 [17]

Answer:

a=25

Step-by-step explanation:

since angle T is 60, and angle Y is the exact same as T, it would make sense that a=25 [3(25)-15]

4 0
2 years ago
Read 2 more answers
Other questions:
  • what plan would great a two house legislature with representation decided only by a states population
    15·1 answer
  • Round to the nearest hundredth?(geometry?)
    14·1 answer
  • Solve the inequality (picture)
    15·1 answer
  • suppose a financial investment account is defined by A(t) = 5500(1.12)^t,where A(t) is in dollar and t is the number of years th
    12·1 answer
  • Two times Antonio’s age plus three times Sarah’s age equals 34. Sarah’s age is also five times Antonio’s age. How old is Sarah?
    6·1 answer
  • A herd of 37 horses has 33 white and some black horses. What is the ratio of black horses to white horses?​
    10·1 answer
  • Write a polynomial function with the given zeros. multiply the terms (write in standard form).
    10·1 answer
  • −6x+14&lt;−28 OR 9x+15≤−12
    6·2 answers
  • Help me please with this problem
    11·1 answer
  • 100 point for free giving it away bc I want to be nice
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!