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
yawa3891 [41]
3 years ago
8

Find 4 consecutive even integers such that the sum of the first and three times the fourth is equal to 48 more than the sum of 2

nd and 3rd integers
Mathematics
1 answer:
serious [3.7K]3 years ago
3 0

Answer:

18 , 20 , 22 and 24.

Step-by-step explanation:

Let the numbers be n , n + 2, n + 4 and n + 6.

So we have the following equation:

n + 3(n + 6) =  48 + n + 2 + n + 4

n + 3n + 18 = 48 + 2n + 6

4n + 18 = 2n + 54

2n = 36

n = 18

So the numbers are 18 , 20 , 22 and 24.

You might be interested in
Use Cramer Rule to solve the following system: 8x−5y=70 and 9x+7y=3
nlexa [21]

Answer:

(x,y) = (5,-6)

Step-by-step explanation:

\underline{\textbf{Determinant of a matrix.}}\\\\\text{For a}~ 2 \times 2 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2\\b_1&b_2 \end{vmatrix} = a_1b_2 - a_2b_1\\\\\\\text{For a}~ 3 \times 3 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2&a_3\\ b_1&b_2&b_3\\ c_1&c_2&c_3 \end{vmatrix} = a_1\begin{vmatrix} b_2&b_3\\c_2&c_3 \end{vmatrix} - a_2 \begin{vmatrix} b_1&b_3\\c_1&c_3 \end{vmatrix}+ a_3 \begin{vmatrix} b_1&b_2\\c_1&c_2 \end{vmatrix}\\\\\\

                     ~~~~~~~~~~~~~~~~~~=a_1(b_2c_3-b_3c_2) -a_2(b_1c_3-b_3c_1) +a_3(b_1c_2-b_2c_1)

\underline{\textbf{Cramer's Rule to solve a system of two equations.}}\\\\\text{Consider the system of two equations:}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_1x + b_1 y= c_1\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_2x +b_2 y = c_2\\\\\text{Here,}\\\\x = \dfrac{D_x}{D}= \dfrac{\begin{vmatrix} c_1&b_1\\c_2&b_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\\\ y= \dfrac{D_y}{D}= \dfrac{\begin{vmatrix} a_1&c_1\\a_2&c_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\

\underline{\textbf{Solution:}}\\\\~~~~~~~~~~~~~~~~~~~~~~~8x-5y = 70~~~~~~...(i)\\\\~~~~~~~~~~~~~~~~~~~~~~~9x +7y = 3~~~~~~~...(ii)\\\\\text{Applying Cramer's rule:}\\\\x = \dfrac{D_x}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 70& -5 \\3&7 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{70(7) -(-5)(3)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{490+15}{56+45}\\\\\\~~=\dfrac{505}{101}\\\\\\~~=5

y = \dfrac{D_y}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 8& 70 \\9&3 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{(8)(3) -(70)(9)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{24-630}{56+45}\\\\\\~~=-\dfrac{606}{101}\\\\\\~~=-6

\textbf{Hence, the solution to the system of equation is}~ (x,y) = (5,-6)

7 0
2 years ago
15. The cost of beverages in a vending machine is shown.
Alja [10]

Answer:

I can't understand what you have written and what to find

5 0
3 years ago
Simplify <br><br>1/4 (8 m-4 n) + 1/3 (6 m+ 3 n).<br><br>answers<br><br>-4m<br><br>1/4m<br><br>4m​
hammer [34]
1/4(8m - 4n) + 1/3(6m + 3n)=

Distribute the fractions through the parentheses

2m - n + 2m + n =

Combine like terms

2m + 2m - n + n = 4m

The answer is 4m
3 0
2 years ago
How would you write 20% as a fraction
givi [52]
For 20% out of 100% it would be 1/5 as you need 5 20s for 100
6 0
3 years ago
Read 2 more answers
Answer ASAP plz I have 2 minutes
earnstyle [38]
250+25= 275 is your answer
5 0
3 years ago
Other questions:
  • A 273,000-gallon shipment of fuel is 2.3 percent
    15·1 answer
  • What is the value of m in the equation m-n= 16, when n=8?<br> O 20<br> O 32<br> O 44<br> O 48
    10·1 answer
  • What is the greatest factorization for 24 and 28 to fine their greatest common factor
    15·1 answer
  • Simplify (4/5)^-2. Show your work!<br> PLEASE HELP ASAP! 40 POINTS!
    12·1 answer
  • PLS HELP I WILL GIVE BRAINLIST
    5·2 answers
  • A variety of energy bar regularly sells for $1.35, but for one week they were on sale for $0.95.
    13·2 answers
  • Plss help me with this:(((​
    9·1 answer
  • Help my little brother I don’t feel like helping him
    10·1 answer
  • Need help with questions 32-33
    11·2 answers
  • Please help me and don’t troll
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!