A system of equations only has a unique solution if all the equations are linearly independent (this means that we have two or more equations representing the same curve).
Here we have the system:
a*x + 2*y + 4*z = b
2*x + y + 3*z = a + 1
5*x - 2*y + (a + 1)*z = 3
Now we want to show that if a = -5 or a = 2, then the system does not have a unique solution.
To see this, we can just replace a by these values and see that the equations are not linearly independent.
for a = 2 we get:
2*x + 2*y + 4*z = b
2*x + y + 3*z = 2 + 1
5*x - 2*y + (2 + 1)*z = 3
Simplifying this:
2*x + 2*y + 4*z = b
2*x + y + 3*z = 3
5*x - 2*y + 3*z = 3
From the second and third equation we can write:
2*x + y + 3*z = 3 = 5*x - 2*y + 3*z
2*x + y + 3*z = 5*x - 2*y + 3*z
2*x + y = 5*x - 2*y
3*y = 3*x
y = x
now that we know this, we can rewrite the equations as:
4*(x + z) = b
3*(x + z) = 3
Now we can take the quotient of the two equations to get:
(4*(x + z))/3*(x + z) = (4/3) = b/3
b = 4
Then the equations become:
4*(x + z) = 4
3*(x + z) = 3
Here we can divide te above one by 4 and the below one by 3 to get:
(x + z) = 1
(x + z) = 1
So both equations represent the same line, thus, the system does not have a unique solution.
Now for a = -5:
-5*x + 2*y + 4*z = b
2*x + y + 3*z = -5 + 1
5*x - 2*y + (-5 + 1)*z = 3
Simplify it:
-5*x + 2*y + 4*z = b
2*x + y + 3*z = -4
5*x - 2*y - 4*z = 3
Now we can rewrite the first equation as:
-5*x +2*y - b = -4*z
and the third one as:
-4*z = 3 - 5*x + 2*y
Then we can write:
-5*x +2*y - b = -4*z = 3 - 5*x + 2*y
-5*x +2*y - b = 3 - 5*x + 2*y
Now we can remove the -5*x in both sides to get:
+2*y - b = 3 + 2*y
Now we can remove the 2*y in both sides to get:
-b = 3
b = -3
Replacing this in our system we get:
-5*x + 2*y + 4*z = -3
2*x + y + 3*z = -4
5*x - 2*y -4*z = 3
Now we can multiply the first equation by -1:
-1*(-5*x + 2*y + 4*z)= -1*(-3)
5*x - 2*y - 4*z = 3
This is the same as the third equation, so here we can see that the first and third equations represent the same line, thus, the system of equations does not have a unique solution.
If you want to learn more, you can read:
https://brainly.com/question/12895249
Over a period of 1 1/4
-
years
5/
16
in. of tread has worn off a tire. What was the average tread wear per year?
What is the equation of a circle with center -4, 7 and radius 6
Answer:
[tex]( x + 4 )^2 + ( y - 7 )^2 = 36[/tex]
Step-by-step explanation:
Use the circle equation, [tex]( x - h )^2 + ( y - k )^2 = r^2[/tex]
Plug in the center and radius:
[tex]( x + 4 )^2 + ( y - 7 )^2 = 6^2[/tex]
Simplify:
[tex]( x + 4 )^2 + ( y - 7 )^2 = 36[/tex]
So, the equation is [tex]( x + 4 )^2 + ( y - 7 )^2 = 36[/tex]
find the distance between each pair of points if necessary round to the nearest tenth.
17. A(6,7),B(-1,7)
18. C(5,-5),D(5,3)
19. E(-1,0),F(12,0)
20. Q(2,-6),T(10,0)
21. H(20,-4),I(-4,3)
22. J(-5,5),K(-3,-2)
I will give brainliest please help and show work
Step-by-step explanation:
q17
[tex]d = \sqrt{ {(7 - 7)}^{2} + {(6 - ( - 1))}^{2} } = 7[/tex]
q18
[tex]d = \sqrt{ {(5 - 5)}^{2} + {(3 - ( - 5))}^{2} } = 8[/tex]
q19
[tex]d = \sqrt{ {(12 - ( - 1))}^{2} + {(0 - 0)}^{2} } = 12[/tex]
q20
[tex]d = \sqrt{ {(10 - 2)}^{2} + {(0 - ( - 6))}^{2} } = 10[/tex]
q21
[tex]d = \sqrt{ {(3 - ( - 4))}^{2} + {(( - 4) - 20)}^{2} } = 25[/tex]
q22
[tex]d = \sqrt{ {(( - 3) - ( - 5))}^{2} + {(( - 2) - 5)}^{2} } = 7.1[/tex]
Complete the equation. (x-2)(x^2 + 2x + 4) = ( , )
Answer:
Step-by-step explanation:
x(x² + 2x + 4)-2((x² + 2x + 4)
x³+2x²+4x -2x²-4x-8
x³-8
What is the equation of the line that passes through the point (8,−3) and has an undefined slope?
Answer:
[tex]x = 8[/tex]
Step-by-step explanation:
Recall that horizontal lines have a slope of zero, while vertical lines have an undefined slope.
Therefore, the line must be vertical.
And since it is vertical, we will only need to consider the x-coordinate of our point.
The x-coordinate of (8, -3) is 8.
Hence, the equation of the line that passes through (8, -3) with an undefined slope is:
[tex]x = 8[/tex]
Answer: x= 8
Step-by-step explanation:
It is a vertical line that passes through point 8 on the x axis.
Which represents a function?
Answer:
B
Step-by-step explanation:
For a function to be a function, every x value can only equal a single y value. A has two y values for one x value, and so does C and D. This leaves only B.
Please help and please give explanation
Answer: -5 i guess i might b wrong i dont know -5
Step-by-step explanation:
Help!!!!!!!!!!!!!!
2x+3=x-7
Answer:
x = - 10Step-by-step explanation:
2x+3=x-7
=> 2x - x = - 7 - 3
=> x = -10 (Ans)
You are wrapping a gift box that is 16 inches long,
7 inches wide, and 9 inches tall. Find the amount of
wrapping paper you need to wrap the gift box to the
nearest square inch.
Answer:
1008 inches
Step-by-step explanation:
Evaluate:
45
O 256
O 625
0 1024
o I don't know
Answer:
A. 256
Step-by-step explanation:
4×4×4×4=256
I hope this helps!
pls ❤ and mark brainliest pls!
answer : 1024
100% correct ;)
Help!!!!! Pleaseee I don’t understand
Answer:
Question 22: x = 3Question 23: AB = 10Question 24: BD = 14Question 25: CE = 17Concept:
Here, we need to know the idea of the segment addition postulate.
The Segment Addition Postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.
If you are still confused, you may tell me or refer to the attachment below for a graphical explanation.
Solve:
Question 22. If AC = 16, what is x?
Given information
AC = 16
AB = x + 7
BC = 2x
Given expression deducted from the segment addition postulate
AB + BC = AC
Substitute values into the expression
x + 7 + 2x = 16
Combine like terms
x + 2x + 7 = 16
3x + 7 = 16
Subtract 7 on both sides
3x + 7 - 7 = 16 - 7
3x = 9
Divide 3 on both sides
3x / 3 = 9 / 3
[tex]\boxed {x=3}[/tex]
Question 23. What is AB?
Given information
x = 3
Given expression deducted from the segment addition postulate
AB = x + 7
Substitute values into the expression
AB = (3) + 7
[tex]\boxed {AB=10}[/tex]
Question 24. What is BD?
Given information
BC = 2x
CD = 3x - 1
x = 3
Given expression deducted from the segment addition postulate
BD = BC + CD
Substitute values into the expression
BD = 2x + 3x - 1
BD = 2(3) + 3(3) - 1
BD = 6 + 9 - 1
BD = 15 - 1
[tex]\boxed {BD=14}[/tex]
Question 25. What is CE?
Given information
CD = 3x - 1
DE = 2x + 3
x = 3
Given expression deducted from the segment addition postulate
CE = CD + DE
Substitute values into the expression
CE = 3x - 1 + 2x + 3
CE = 3(3) - 1 + 2(3) + 3
CE = 9 - 1 + 6 + 3
CE = 8 + 6 + 3
CE = 14 + 3
[tex]\boxed {CE=17}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
|72| ÷ |-12| =
?????????
Answer:
6
Step-by-step explanation:
|72| ÷ |-12|
Absolute value of 72 = 72
Absolute value of -12 = 12
72 ÷ 12 = 6
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
i need help this question?
5x2 + 7% -2x2 - 10x + 5
Answer:
[tex] \frac{1107}{100} - 10x[/tex]
Step-by-step explanation:
[tex]5x2 + 7\% - 2 \times 2 - 10x + 5[/tex]
➡️ [tex]10 + 7\% - 2 \times 2 - 10x + 5[/tex]
➡️ [tex]10 + \frac{7}{100} - 2 \times 2 - 10x + 5[/tex]
➡️ [tex]10 + \frac{7}{100} - 4 - 10x + 5[/tex]
➡️ [tex]11 + \frac{7}{100} - 10x[/tex]
➡️ [tex] \frac{1107}{100} - 10x[/tex]
what is 6% of 3125
Answer:
187.5
Step-by-step explanation:
6% of 3125
=> 6/100 x 3125
=> 18750/100
=> 187.5
Show Work! There are 380 students, teachers, and chaperones going on school buses for a field trip. Each school bus can hold 68 passengers. Everyone will ride on a school bus. How many school buses does this group need?
Answer:
6 buses
Step-by-step explanation:
i believe you just have to divide 380/68
then it'll give you 5.5 and then have to round to the nearest integer
Determine a quadratic equation that has 7 and -4 as solutions.
Answer:
(x+x1)(x-x2)
let x1=7 and x2=-4
(x+7)(x-(-4))
(x+7)(x+4)
x^2+4x+7x+28
x^2+11x+28
Which statement is true regarding the graphed functions?
euf
12
40
B
4
914
2
1 2
3
4.
5
B
X
I f 5 4 3 2 12)
-4
B
be
10
2
141
f(4) = g(4)
f44) = (1-2)
Help meeeeeeeeeeeeeeeee
Answer:
x-3
Step-by-step explanation:
the inverse is x-3
this is the answer
1. Which is an example of an algebraic expression?
Answer:
3-a
Step-by-step explanation:
it involves variables like x, y, z
in this case a
Emily Bought the Following items for Christmas gifts for her Friends: 5 Hannah Montana calendars, 3 DVDs, 2 books, 1 Monopoly game, 8 CDs, 1 Box of Candy, and 2 gift Cards to Walmart.What is the Ratio of DVDs to the total number of Gifts.
Answer:
Ig its 22:3
Step-by-step explanation:
First we add all the gifts and put it in the ratio and the other is 3 dvds
1109,1116,1123 what’s next
Answer:
C. 1130
BRAINLIEST, PLEASE!
Step-by-step explanation:
1109 + 7 = 1116
1116 + 7 = 1123
1123 + 7 = 1130
The value of the missing number is 1130.
Missing numberThe missing number in the series can be determined by finding the common difference or pattern of the numbers.
let the common difference = d
1109 + 7 = 1116
1116 + 7 = 1123
1123 + 7 = 1130
Thus, the value of the missing number is 1130.
Learn more about missing numbers here: https://brainly.com/question/1241542
write and simplify an expression for the area of the triangle
(show step by step)
Answer:
Step-by-step explanation:
The area of the triangle is
B*h/2
Where B=x+5 and h=x-2 so if we substitute
(x+5)*(x-2)/2 =
(x^2 +3*x -10)/2=
x^2/2 + 3/2 *x -5
0.2 kg
2m
9.8g
Pls help quick
Which of the following is the best example of kinetic energy?
A book sitting on a bookshelf
A golfer preparing to putt the ball
A race car in position at the start line
A satellite orbiting the Earth
Answer:
i had this question a little while back and the right answer was
d. a satellite orbiting the Earth.
(:
Which of the following is a true statement of the figure
Answer:
The last one
Step-by-step explanation:
8. Is it possible to have an object that does not have 360° rotational symmetry? Explain your reasoning.
Add the Following Fractions:
\large \frac{3}{8}+\frac{2}{8}=?
a. 5/16
:b. 5/8
c. 6/8
d. 1/8
Answer:
B. [tex]\frac{5}{8}[/tex]
Explanation:
Because the denominators (bottom numbers) of both fractions are the same, we simply just add the numerators (top numbers) and keep 8 as the denominator.
One positive number is 2 more than twice another. If their product is 1012, find the numbers.
Answer:
46 and 22
Step-by-step explanation:
22 x 2 = 44
44 is 2 less than 46
46 x 22 = 1012
Simplify
5(x + 8) - 2x = 7(x + 10)
Answer:
-15/2
Step-by-step explanation:
5(x + 8) - 2x = 7(x + 10)
=> 5x + 40 - 2x = 7x + 70
=> 3x + 40 = 7x + 70
=> 3x - 7x = 30
=> -4x = 30
=> x = -30/4
=> x = -15/2
what is the answer to this problem (40+35+2(30+25))/5
Answer:
37
Step-by-step explanation:
Answ 925
Step-by-step explanation: