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
lions [1.4K]
3 years ago
12

The Johnson twins were born five years after their older sister. This​ year, the product of the three​ siblings' ages is exactly

2998 more than the sum of their ages. How old are the​ twins?
Mathematics
1 answer:
Mamont248 [21]3 years ago
8 0

Answer:

13 years.

Step-by-step explanation:

Suppose, today, the Johnson twins' age is x years. Then the age of their elder sister will be (x + 5) years old. It is given that product of the three​ siblings' ages is exactly 2998 more than the sum of their ages. Therefore:

x + x + x + 5 + 2998 = (x)(x)(x + 5).

3x + 3003 = x^3 + 5x^2.

x^3 + 5x^2 - 3x - 3003 = 0.

To solve the question, factor theorem will be used. It states if any number c satisfies the equation f(c) = 0, then c is the factor of f(x). By observation, it can be seen that x = 13 can be a possible candidate for the factor of f(x). To verify, check f(13).

f(13) = 13^3 + 5(13^2) - 3(13) - 3003 = 2197 + 845 - 39 - 3003 = 0.

Since f(13) = 0, therefore x = 13 is the factor of f(x).

Now applying synthetic division:

Column 1       2       3       4            5

     13    |         1       5      -3        -3003  (Row 1)

______|______<u>  _13__234___3003</u>   (Row 2)

            |         1       18      231          0    (Row 3)

The method requires to write the coefficients of all the powers in the Row 1 on the right hand side of the table. Put the factor x = 13 on the left hand side of the table (Row 1 Column 1). The first step involves the second column elements to be added. Since there is only 1, thus there will be 1 below the line. Next step involves multiplying 1 with the factor (which is 13) and this will be the element for row 2 column 3. The add the elements of the column 3. The answer comes out to be -3. Repeat the above steps for the columns 4 and 5. The sum of the column 5 (the last column) should be 0, which is the case. The elements of the last row are actually the coefficients of the quadratic equation which is resultant from dividing f(x) by (x - 13). Thus:

x^2 + 18x + 231 = 0.

Using completing the square:

x^2 + 18 = -231.

(x)^2 + 2*(x)*(9) + (9)^2 = -231 + (9)^2.

(x + 9)^2 = -231 + 81.

(x + 9)^2 = -150.

Taking square root on both sides shows that rest of the 2 answers of this polynomial will be complex roots since square root of -150 does not exist in real numbers. Therefore, since the age is a real quantity and not a complex quantity, the age of the twins is 13 years!!!

You might be interested in
Byron bought a keyless entry door lock that has the digits 0 through 9 on the keypad. He wants to choose a three-digit
kolbaska11 [484]

Answer:

the answer is 10,000

Step-by-step explanation:

thats what i put on the test and got it right

5 0
2 years ago
Read 2 more answers
Victor was having a hard time deciding which new vehicle he should buy. He decided to make the final decision based on the gas e
Amanda [17]

Answer:

Victor should buy Legend because it has a better unit rate

<em></em>

Step-by-step explanation:

See attachment for complete question.

To determine which car has more gas efficiency, we have to calculate the slope of each car.

Vehicle 1: Legend

Take any two corresponding points from the table

(x_1,y_1) = (4,72)

(x_2,y_2) = (12,216)

The slope is then calculated using;

m = \frac{y_2 - y_1}{x_2 - x_1}

m = \frac{216 - 72}{12 - 4}

m = \frac{144}{8}

m = 18

<em>This implies that this vehicle (legend) travels 18 miles per gallon of gas</em>

Vehicle 2: Supreme

Take any two corresponding points from the graph

(x_1,y_1) = (0,0)

(x_2,y_2) = (15,250)

The slope is then calculated using;

m = \frac{y_2 - y_1}{x_2 - x_1}

m = \frac{250 - 0}{15 - 0}

m = \frac{250}{15}

m = 16.7

This implies that this vehicle (supreme) travels 16.7 miles per gallon of gas

<em>Base on the calculations above, Victor should buy Legend because it has a better unit rate</em>

6 0
2 years ago
The coordinates of △ABC△ABC are A(12,8), B(10,18), C(4,16)A(12,8), B(10,18), C(4,16). After a dilation, the coordinates are A'(6
mixer [17]
The scale factor is 1/2 because when you multiply the x and y-coordinates of each point by 1/2, you will get the coordinates of the new dilated points.
7 0
3 years ago
Read 2 more answers
If a ticket at the movie theater called $7.50 and popcorn cost $3.50 and the drink cost $1.50 and the cab cost $12 for up to fiv
pentagon [3]
This is me cab/ticket,popcorn,drink 7.50+ 3.5+1.50+12.= 24.50

Friends if I take 3

Popcorn,drink,ticket
12.50 ×3= 37.50

So now me plus 3 friends
24.50 +37.5=62.00


8 0
3 years ago
What does it mean by domain and range and how would I use that to fill out the table?​
Sav [38]

The domain is the set of all allowed x values. In this case, we consider the whole numbers between 0 and 10. So we have x = 0, x = 1, x = 2, ... all the way up to x = 10.

To find the y values, you replace each x with the numbers mentioned and simplify.

For instance, if x = 2, then,

f(x) = 3.50x

f(2) = 3.50*2

f(2) = 7

This tells us that x = 2 packages cost y = 7 dollars.

5 0
3 years ago
Read 2 more answers
Other questions:
  • 5x-2y+3z-2x-y+4z solve
    13·2 answers
  • PLEASE THINS IS DUE BY 1 P.M TODAY. PLEASE HELP ME
    7·1 answer
  • David currently has $270 in his bank account and
    9·2 answers
  • Helps? PLEASE I NEED ANSWER
    11·2 answers
  • -5.12z = 40.96<br>z = [?]​
    15·1 answer
  • Arrange the numbers in increasing order 5.049, 5.069, 5.49, 5.09
    6·2 answers
  • How many samples of size 2 can be formed from population of size 5
    9·1 answer
  • This is one of the least few I promise.
    8·1 answer
  • If f(1) = 10 and f(n) = f(n = 1) – 4 then find the value of f(5).
    15·1 answer
  • Will mark brainliest! Questions are in the picture!
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!