The solution to the algebraic expression is: 23e - 21g - 14j + 32
What are algebraic expressions?
Algebraic expressions are mathematical expressions that contain variables, coefficients, and arithmetic operations such as addition, subtraction, division, and multiplication.
Solving algebraic expressions are an important part of mathematics as it helps to improve the aptitude and solving skills of the students.
From the given information, we have;
23j - 21g + 20e - 13 + 52e - 37j + 45 - 49e
let's rearrange by taking the like terms to the same sides;
= 23j -37j - 21g + 20e + 52e - 49e - 13 + 45
= -14j - 21g + 23e + 32
= 23e - 21g - 14j + 32
Therefore, we can conclude that the solution to the algebraic expression is: 23e - 21g - 14j + 32
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The system is:
i) <span>2x – 3y – 2z = 4
ii) </span><span>x + 3y + 2z = –7
</span>iii) <span>–4x – 4y – 2z = 10
the last equation can be simplified, by dividing by -2,
thus we have:
</span>i) 2x – 3y – 2z = 4
ii) x + 3y + 2z = –7
iii) 2x +2y +z = -5
The procedure to solve the system is as follows:
first use any pairs of 2 equations (for example i and ii, i and iii) and equalize them by using one of the variables:
i) 2x – 3y – 2z = 4
iii) 2x +2y +z = -5
2x can be written as 3y+2z+4 from the first equation, and -2y-z-5 from the third equation.
Equalize:
3y+2z+4=-2y-z-5, group common terms:
5y+3z=-9
similarly, using i and ii, eliminate x:
i) 2x – 3y – 2z = 4
ii) x + 3y + 2z = –7
multiply the second equation by 2:
i) 2x – 3y – 2z = 4
ii) 2x + 6y + 4z = –14
thus 2x=3y+2z+4 from i and 2x=-6y-4z-14 from ii:
3y+2z+4=-6y-4z-14
9y+6z=-18
So we get 2 equations with variables y and z:
a) 5y+3z=-9
b) 9y+6z=-18
now the aim of the method is clear: We eliminate one of the variables, creating a system of 2 linear equations with 2 variables, which we can solve by any of the standard methods.
Let's use elimination method, multiply the equation a by -2:
a) -10y-6z=18
b) 9y+6z=-18
------------------------ add the equations:
-10y+9y-6z+6z=18-18
-y=0
y=0,
thus :
9y+6z=-18
0+6z=-18
z=-3
Finally to find x, use any of the equations i, ii or iii:
<span>2x – 3y – 2z = 4
</span>
<span>2x – 3*0 – 2(-3) = 4
2x+6=4
2x=-2
x=-1
Solution: (x, y, z) = (-1, 0, -3 )
Remark: it is always a good attitude to check the answer, because often calculations mistakes can be made:
check by substituting x=-1, y=0, z=-3 in each of the 3 equations and see that for these numbers the equalities hold.</span>
Answer:
52 pounds
Step-by-step explanation:
1 pound=16oz.
240/16=15
15+37=52
Answer:
Step-by-step explanation:
(7/12) of 840 attended the concert:
(7/12)*(840) = 490 students attended the Spring Concert.
(840 - 490) = 350 did not attend
(350/840) is the fraction of students who did not attend. This can be reduced to (35/84)
(350/840) = 0.4167 or 41.67% did not attend.
