Which value of b results in infinitely many solutions for the system?

9x+6y=b
3x+2y=1

6
1
5
3

Answer:

A)positive

Step-by-step explanation:

All quantities greater than zero will be positive, although zero itself is not considered negative or positive. Also, debt means that something would be owed. This would mean the number is negative and therefore not correct.

Answer:

y = x - 23

Step-by-step explanation:

9514 1404 393

Answer:

  (81/43, -31/43) ≈ (1.884, -0.7209)

Step-by-step explanation:

The orthocenter is the intersection point of the altitudes of the triangle. Since this is not a right triangle, you need to find the equations of the altitude lines, then find where those intersect.

If we call the points A, B, C in the order given, the attached figure shows the altitude lines from B perpendicular to AC, and from C perpendicular to AB.

We can find the equation of the perpendicular line using the form ...

  ∆x·x +∆y·y = c

where ∆x and ∆y are the differences in coordinates between the points on the "side" and the value of constant 'c' is determined by evaluating the expression using x and y as the coordinates of the opposite vertex.

__

For line AC, we have ...

  (∆x, ∆y) = C - A = (2, -1) -(-3, 0.5) = (2+3, -1-0.5) = (5, -1.5)

Then the equation of the first altitude line is ...

  5x -1.5y = 6(3) -1.5(3) = 10.5

Multiplying by 2 puts this in standard form:

  10x -3y = 21

__

For line AB, we have ...

  (∆x, ∆y) = B - A = (3, 3) -(-3, 0.5) = (3+3, 3-0.5) = (6, 2.5)

Then the equation of the second altitude line is ...

  6x +2.5y = 6(2) +2.5(-1) = 9.5

Multiplying by 2 puts this in standard form:

  12x +5y = 19

__

Then the orthocenter is the solution to the system of equations ...

  10x -3y -21 = 0

  12x +5y -19 = 0

This set of equations can be solved a number of ways. One is the "cross-multiplication" method.

  1/(10·5 -12·(-3)) = x/(-3·(-19) -5·(-21)) = y/(-21(12) -(-19)(10))

  x = 162/86 = 81/43

  y = -62/86 = -31/43

The orthocenter is (81/43, -31/43) ≈ (1.884, -0.7209).

_____

Additional comment

The "cross multiply method" is based on cross products when the equations  are written in standard form:

  ax +by +c = 0

  dx +ey +g = 0

Usually, the coefficients are written in two rows of four, with the first column repeated at the end:

  a  b  c  a

  d  e  g  d

Then cross products are formed, where diagonal down is positive and diagonal up is subtracted from that:

  p1 = (ae -db), p2 = (bg -ec), p3 = (cd -ga)

These give the solution to the equations when put in the form ...

  1/p1 = x/p2 = y/p3   ⇒   x = p2/p1   and   y = p3/p1

If you look at videos of this "cross multiply method," they will put the 1/p1 at the end of the string of equalities, and they will use the coefficients in the order starting with b instead of a. I find the arrangement here easier to remember, so less likely to get confused.

Further comment

You can, of course, find the slopes of the lines, and their opposite reciprocals, then use a point-slope form or some other method for writing the equations of the altitude lines. The solution to the equations can proceed by substitution or elimination. No doubt these methods are somewhat familiar. The method used here tries to get to the answer much more quickly with a lot less writing. (Unfortunately, it takes a bit of writing to explain it all.)

Answer:

Plant A is y=2x+6

Step-by-step explanation:

Slope: 2

Y-intercept: 6

Answer:

x = 1, y = 2

Step-by-step explanation:

-5x + y = -3, we get y = 5x - 3.

Then plugs into the second equation, we get

-x - 5 (5x-3) = -11.

-x - 25x + 15 = -11,

-26x = -26

x = 1,

plugs x = 1 to y = 5x - 3, we get y = 2.

Answer:

From eq (1)

[tex]{:}\longrightarrow[/tex][tex]\sf -5x+y=-3 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf y=-3+5x [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf y=5x-3\dots\dots (3) [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf -x-5 (5x-3)=-11 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf -x-25x+15=-11 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf -26x=-11-15 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf -26x=-26 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf x={\dfrac {-26}{-26}}[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf x=1[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf y=5x-3 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf y =5 (1)-3 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf y=5-3 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf y=2 [/tex]

[tex]\therefore[/tex](x,y)=(1,2)

Answer:

46

Step-by-step explanation:

So, the plan

monthly =40 + 1.50x

and he orders 4 movies in a month your problem to solve now looks like this

1 month = 40+1.50x4

Then, 1 month= 40 + 6

1 month= 46

Answer:Around 50 pints

Step-by-step explanation:

$35=$40

$47=$50

$57=$60

$40+$50+$60=$150/3=50

Answer:

Step-by-step explanation:

7a^4 + 3a^4 is 10a^4

Answer:

A

Step-by-step explanation:

for the two of them, the first answer is the answer

Answer:

#1 - First option: y + 7 =  [tex]\frac{-1}{4}[/tex](x -4)

#2 - First option: y = 2x - 5

Step-by-step explanation:

#1

Given: (x1,y1) = (4,-7) and m = [tex]\frac{-1}{4}[/tex];

To find the point slope form which is

y - y1 = m(x - x1); substitute (x1,y1) and m

y - (-7) = [tex]\frac{-1}{4}[/tex](x -4)

y + 7 =  [tex]\frac{-1}{4}[/tex](x -4)

#2

Given: points (x1,y1) = (0, -5) and (x2,y2)=(4,3)

To find the slope we use

m = [tex]\frac{(y2-y1)}{(x2-x1)}[/tex] = [tex]\frac{(3-(-5))}{(4-0)}[/tex] = [tex]\frac{8}{4}[/tex] = 2

Now pick a number to find b

y = mx + b

y1 = mx1 + b

-5 = 2(0) + b

b = -5

now plug into y = mx + b; which is

y = 2x - 5

Answer: 2/9

Step-by-step explanation:

Step-by-step explanation:

5x+2y=29

5x-2y=41

add the equations

10x=70

divide both sides by ten

x=7

substitute 7 in the first equation

5(7)+2y=29

simplify

35+2y=29

subtract 35 from both sides

2y=-6

simplify

y=-3 x=7

3x+2y=9

5x+2y=12

subtract the equations

-2x=-3

simplify

x=1.5

substitute

3(1.5)+2y=9

simplify

4.5+2y=9

subtract 4.5 from both sides

2y=4.5

simplify

y=2.25 x=1.5

5x+2y=-9

2x-3y=4

multiply first equation by three and second by two

15x+6y=-27

4x-6y=8

add equations

19x=-19

simplify

x=-1

substitute

15(-1)+6y=-27

simplify

-15+6y=-27

add 15 to both sides

6y=-12

simplify

y=-2 x=-1

Answer:

Friction is a force between two surfaces that are sliding, or trying to slide, across each other.

Step-by-step explanation:

For example, when you try to push a book along the floor, friction makes this difficult.

Answer:

Friction is the force that opposes motion between any surfaces that are in contact. There are four types of friction: static, sliding, rolling, and fluid friction. Static, sliding, and rolling friction occur between solid surfaces. Fluid friction occurs in liquids and gases.

Step-by-step explanation:

Answer:

10. I feel bad for him.

Step-by-step explanation:

Answer:

slope=2 ie m=2

y=2x+b

and to solve b, we put in 4 and 9 into the equation

9=2*4+b, so b=9-8=1

hence y=2x+1

Step-by-step explanation:

Answer:

Student your question is not too clear, please complete the question

Answer:

sorry bro ion know it i just need points for my testg.

Step-by-step explanation:

Answer:

$2.80

Step-by-step explanation:

17-3=14

14 divided by 5=

2.8

Add 0 since it's about money.

$2.80

Answer:

identity

Step-by-step explanation:

it states that any number times 1 is equal to itself. so when u have 14y, you can multiply it by 1 and it will remain the same.

Answer:

identity

Step-by-step explanation:

Answer:

3x + 21

Step-by-step explanation:

3(x+7)

3 * x + 3 * 7

3x + 21

HOPE THIS HELPS

PLZZ MARK BRAINLIEST

Answer:

3x + 21

Step-by-step explanation:

3(x + 7)

3(x + 21)

3x + 21

Answer:

15.36%

Step-by-step explanation:

Answer:

20x^2 - 107x - 10.

Step-by-step explanation:

8x - 108x - 10 - (9x^2 + 7x -29x^2)

simplifying:

-100x - 10 - (7x - 20x^2)

20x^2-100x - 7x - 10

20x^2 - 107x - 10

Answer:

−9x

2

+x−8

Step-by-step explanation:

Answer: y=-8/5x-4

Step-by-step explanation:

8x+5y=-20

-8x         -8x

5y=-8x-20

/5     /5

y=-8/5x-4

Answer:

−5

Step-by-step explanation:

By substituting the value of x in f(x) with -4,

(-4)^2+4(-4)-5

=16+(−16)−5

=0−5

=-5

Your welcome :D  

Answer:

-2

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

Answer:

Step-by-step explanation:

C. Solve for y

Answer:

False

Step-by-step explanation:

Answer:

y=2 x=5

Step-by-step explanation:

3x-2y=11

2x-3y=4

you multiply both equations to cancel one variable out. in this case you multiply the first equation by 2 and the second by -3

     6x-4y=22

+    -6x-9y=12

--------------------------

0x+5y=10

y=2

you plug that in either equation

3x-2(2)=11

3x-4=11

3x=15

x=5

Answer:

x = 6

Step-by-step explanation:

Given

3x - 11 = - 2x + 19 ( add 2x to both sides )

5x - 11 = 19 ( add 11 to both sides )

5x = 30 ( divide both sides by 5 )

x = 6

Answer:

C I think

Step-by-step explanation: