A linear system in three variables has infinitely many solutions when the equations are dependent on each other and represent the same line or plane. To determine if a system has infinitely many solutions, we can solve the system and check if any of the equations can be derived from the others or if they represent the same line or plane.
Explanation:When a linear system in three variables has infinitely many solutions, it means that the three equations are dependent on each other and represent the same line or plane. This happens when the coefficients of the variables in the equations are proportional to each other. To determine if a system has infinitely many solutions, we can solve the system and check if any of the equations can be derived from the others or if they represent the same line or plane.
Let's take the system of equations given in the question:
7y = 6x + 84y = 8y + 7 = 3xWe can start by solving equations (1) and (2) for y:
7y = 6x + 8 (equation 1)4y = 8 (equation 2)Simplifying equation (2), we get:
y = 2
Substituting y = 2 into equation (1), we have:
7(2) = 6x + 8
14 = 6x + 8
6x = 14 - 8
6x = 6
x = 1
Now, let's substitute the values of x and y into equation (3):
y + 7 = 3x
2 + 7 = 3(1)
9 = 3
This equation is not true. Therefore, the system of equations is inconsistent and does not have infinitely many solutions. The system does not represent the same line or plane.
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What is the equation of the line, in point-slope form, that passes through the points (-3, -1) and (-6, 8)? open study?
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Hello : let A(-3,-1) B(-6,8)
the slope is : (YB - YA)/(XB -XA)
(8+1)/(-6+3) =9/(-3)
the slope is: -3
The data set shows the weights of pumpkins, in pounds, that are chosen for a photograph in a farming magazine. 18 22 14 30 26 (a) What is the mean, x , of the data set? (b) What is the sum of the squares of the differences between each data value and the mean? Use the table to organize your work. (c) What is the standard deviation of the data set? Use the sum from Part (b) and show your work. (d) A second group of pumpkins, with weights of 32, 35, 33, 34, and 36 pounds, are chosen for another photograph. Will the standard deviation of these weights be greater or less than the standard deviation found in Part (c)? Answer this without doing a calculation and explain your reasoning.
Determine the relationship between the lines that pass through the given points: line
a.(-3, 5) and (0, 7) line
b.(6, 2) and (9, 4)
5. 41°F equals how many degrees Celsius?
The angle of elevation to the sun is 24°. What is the length of the shadow cast by a person 1.82 m tall?
The length of the shadow cast by a person 1.82 m tall is; 4.09m
Angle of ElevationThe angle of Elevation to the sub is 24°.
On this note, the shadow cast on the floor represents the adjacent of the angle of Elevation.
Hence, the length of the shadow cast can be calculated from Tangent identify as follows;
Tan 24° = 1.82/ll = 1.82/Tan 24l = 1.82/0.445Length of shadow = 4.09m
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the area of the a rectangular painting is 4902 cm squared. if the length of the painting is 86 cm, what is it’s width?
Find a equation for the line, in point-slope form, that contains (5,1) and is perpendicular to 6x − 3y = 2.
Three eggs are required to make two dozen muffins. how many eggs are needed to make 12 dozen muffins using a proportion
PLEASE HURRY!! 30 POINTS
Simplify
73+3(23−13)2
Answer:
1976
Step-by-step explanation:
Find the values of x and y that make these triangles congruent by the HL Theorem
A. X=5, y=6
B. X= -5, y=6
C. X=5, y= -6
D. X=6, y=5
Solve the equation 1-|1/3q-5| = -6
2007 divided by j = 223
The sum of 2 consecutive numbers is 97. Find the numbers
Write an equation of the line passing through point P(−8, 0) that is perpendicular to the line 3x−5y = 6
To find the equation of a line perpendicular to another line, we need to find the negative reciprocal of the slope. Substituting the values into the point-slope form, we can find the equation of the perpendicular line.
Explanation:To find the equation of a line that is perpendicular to another line, we need to find the negative reciprocal of the slope of the given line. The given line has the equation 3x - 5y = 6, so its slope is 3/5. The negative reciprocal of 3/5 is -5/3, so the slope of the line perpendicular to the given line is -5/3.
Since we know a point on the perpendicular line is P(-8, 0), we can use the point-slope form of a line to find the equation. The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Substituting -8 for x1, 0 for y1, and -5/3 for m, we get y - 0 = -5/3(x - (-8)).
Simplifying the equation gives y = -5/3x - 40/3, which is the equation of the line passing through point P(-8, 0) and perpendicular to the line 3x - 5y = 6.
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Show work on simply 2+(3g-4)-(8g+3)
Study the products shown. Is there a pattern?
(x + 3)2 = x2 + 6x + 9
(x + 4)2 = x2 + 8x + 16
(x + 5)2 = x2 + 10x + 25
(x + 6)2 = x2 + 12x + 36
Each product is in the form ax2 + bx + c.
Which of the following describes the relationship between b and c?
c is 1.5 times that of b.
c is double b.
c is the square of half of b.
c is the square of b.
Answer:
The correct option is 3. c is the square of half of b.
Step-by-step explanation:
The given equations are
[tex](x+3)^2=x^2+6x+9[/tex]
[tex](x+4)^2=x^2+8x+16[/tex]
[tex](x+5)^2=x^2+10x+25[/tex]
[tex](x+6)^2=x^2+12x+36[/tex]
These are the perfect square. According to this pattern,
[tex](x+y)^2=x^2+2xy+y^2[/tex] .... (1)
Each product is in the form
[tex](x+y)^2=ax^2+bx+c[/tex] .... (2)
From (1) and (2), we get
[tex]b=2y[/tex]
[tex]c=y^2[/tex]
[tex]c=(\frac{b}{2})^2[/tex] [tex][\because b=2y][/tex]
It means c is the square of half of b.
Therefore the correct option is 3.
solve for x. 3x-r=r(-3+x)
Olivia's work and solution to the equation -6x + 11=43 is shown. Identify each error in Olivia,s work ad epxplian what she would have done instead.
-6x + 11=43
+11 +11
-6x = 54
-6x/6 = 54/6
X = 9
Felicity's insurance company pays for 65% of her elbow surgery, after she pays a $500 deductible.
How much will Felicity pay for her elbow surgery if it costs $9400?
A. $3290
B. $3465
C. $3615
D. $3790
Which expression is equivalent to 32⋅32⋅32⋅32 ? (Also All The 32s Are Fractions, The Lines Just Wont Come Up.)
Answer:
If this is 1/32 for all of them the answer would be (1/32)^4 or (1/32) to the 4th power. if this is 3/2 it would be (3/2)^4 or (3/2) to the 4th power.
Step-by-step explanation:
If this is 1/32 for all of them the answer would be (1/32)^4 or (1/32) to the 4th power. if this is 3/2 it would be (3/2)^4 or (3/2) to the 4th power. I hope this helps : )
Which equation illustrates the commutative property of addition?
The plate is rotated 90° about the origin in the counterclockwise direction. In the image trapezoid, what are the coordinates of the endpoints of the side congruent to side FG?
Find three consecutive integers with a sum of -36
What is the reciprocal of 6 3/7?
45/7 is the correct answer
16x^2 = 49 help find x.
Simplify: (sin θ − cos θ) − (sin θ + cos θ)2 (5 points)
What is the total surface area of this composite solid ?
Sydney read 50 pages and 40 minutes she reads at a constant rate how many pages can Sydney read per minute
Sydney can read 5/4 or 1.25 pages in one minute
Data;
number of pages = 50time taken = 40 minuterate = ?What is RateThis can be defined as the measure of one unit against another unit.
If it take Sydney 40 minutes to read 50 pages, let's calculate how many pages she will read in one minute to determine her rate.
[tex]40 pages = 50 minutes\\x pages = 1 minute[/tex]
Let's cross multiply both sides and solve for x
[tex]50 pages = 40 minute\\x pages = 1 minute\\x = \frac{50*1}{40}\\x = 1.25 page[/tex]
From the calculations above, Sydney can read 5/4 or 1.25 pages in one minute.
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Please help me out!! ☮✌
a linear pair would equal 180 degrees
so 180-28 = 152
Triangles are congruent if they have the same ______________.