For What Value Of M Does 3x + 4 = Mx + 4 Have An Infinite Number Of Solutions? (2024)

Mathematics High School

Answers

Answer 1

Answer:

3

Step-by-step explanation:

Solve for m.

3x + 4 = mx + 4 subtract 4 from each side

3x + 4 - 4 = mx + 4 - 4 the 4’s on both sides will cancel

3x = mx divide each side by x

3x/x = mx/x The x cancels and you’re left with

3 = m

If m = 3 then

3x + 4 = mx + 4 will become

3x + 4 = 3x + 4 subtract 4 from each side

3x + 4 - 4 = 3x + 4 - 4 the 4’s on both sides will cancel

3x = 3x divide each side by 3

3x/3 = 3x/3 The 3s cancel and you’re left with

x = x

So for any value of x, positive or negative, they will equal each other. Therefore there are an infinite number of solutions when m = 3

Related Questions

1. & 2. In the diagram below, points A, B, and C are collinear. Answer each of the following questions. The figure shown below is not drawn to scale, meaning you cannot determine your answers by using your ruler.​

Answers

Answer:

a. 8 in

b. 9¾ in

Step-by-step explanation:

a. Given:

AC = 5 in

CB = 3 in

Since points A, C and P are collinear, therefore,

AC + CB = AB (segment addition postulate)

5 + 3 = AB (substitution)

8 = AB

AB = 8 in

b. Given:

AC = 6¼ in

CB = 3½ in

AC + CB = AB (segment addition postulate)

6¼ + 3½ = AB (substitution)

9¾ = AB

AB = 9¾ in

Hi guys my little brother needs help to Do his homework And I’m doing mine so I can’t help him can anyone help plzz

Answers

The answer is 91.77

22.89 x 2 =45.78

45.78 + 45.99 = 91.77

You are building a shelf that fits in a corner. In the figure, the entire shelf is △LMN. Each unit in the coordinate plane represents one inch.

Find the area A of the shelf.
A= __ in.2

Answers

Answer: 50in'2

Step-by-step explanation:

First you would do: |25-(5)| since they share the same x value. Which would be 20

Next: |5-10|= 5, since N and M share the same y value

Lastly you would plug in those values to find the area of a triangle: 5*20*1/2= 50 in

Help please!!!!!!!!!!!!!!!!!!!!!!!!

Answers

i think its B not sure tho sorry

What is the next number in the following pattern?
4,- 6, 8,- 10, 12, ...

Answers

Answer:

-14

Step-by-step explanation:

im not really sure

Answer: -14

Step-by-step explanation: its basically counting by 2, but going from positive to negative

Help me with segment addition postulate

Answers

Answer:the answer is 15

Which expression represents the phrase? "The product of 5 and 6 reduced by t." A) 5 – 6t B) 5(6 – t) C) 5(6 + t) D) 5 + 6t

Answers

Answer:

B. 5(6-t)

Step-by-step explanation:

5(6-t)

means that 5*6 reduced by t

Tao wants to check that the expression 3(4x – 6) simplifies to 12x – 18. What is the value when 2 is substituted for x into both expressions?


(Sin4x+2Sin3x+Sin2x)/
Sinx=
2Sin3xCotx/2​

Answers

Answer:

Consider the given equation.

4sinxsin2xsin4x=sin3x

2(2sin2xsinx)sin4x=sin3x

We know that

2sinAsinB=cos(A−B)−cos(A+B)

Therefore,

2[cos(2x−x)−cos(2x+x)]sin4x=sin3x

2[cosx−cos3x]sin4x=sin3x

2sin4xcosx−2sin4xcos3x=sin3x

We know that

2sinAcosB=sin(A+B)+sin(A−B)

Therefore,

sin(4x+x)+sin(4x−x)−[sin(4x+3x)+sin(4x−3x)]=sin3x

sin(5x)+sin(3x)−[sin(7x)+sin(x)]=sin3x

sin(5x)−sin(7x)=sin(x)

We know that

sinC−sinD=2cos(

2

C+D

)sin(

2

C−D

)

Therefore,

2cos(

2

5x+7x

)sin(

2

5x−7x

)=sinx

2cos(

2

12x

)sin(

2

−2x

)=sinx

2cos(6x)sin(−x)=sinx

−2cos(6x)sin(x)=sinx

cos6x=−

2

1

6x=2nπ±

3

x=

3

±

9

π

Hence, the value is

3

±

9

π

.

sorry mate don't know the answer

Are these inverses of one another?
Yes
No
No way to tell

Answers

It should be (Yes) because the graph is really cleanse that it is inverses of one another.

filiate
Consider the line MU for M(-1, 1) and U(4, 5).
what’s the distance from M to U ?

Answers

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ \sqrt{41} \: \: units}}}}}[/tex]

Step-by-step explanation:

Let M ( -1 , 1 ) be ( x₁ , y₁ ) and U ( 4 , 5 ) be ( x₂ , y₂ )

Finding the distance from M to U

[tex] \boxed{ \sf{distance = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }}[/tex]

[tex] \longrightarrow{ \sf{ \sqrt{ {(4 - ( - 1))}^{2} + {(5 - 1)}^{2} } }}[/tex]

[tex] \longrightarrow{ \sf{ \sqrt{ {(4 + 1)}^{2} + {(5 - 1)}^{2} } }}[/tex]

[tex] \longrightarrow{ \sf{ \sqrt{ {(5)}^{2} + {(4)}^{2} } }}[/tex]

[tex] \longrightarrow{ \sf{ \sqrt{25 + 16}}} [/tex]

[tex] \longrightarrow{ \sf{ \sqrt{41} }}[/tex] units

The distance from M to U is [tex] \sf{ \sqrt{41} \: \: units}[/tex]

Hope I helped!

Best regards! :D

Answer:

The answer is

[tex]\sqrt{41} \: \: or \: \: 6.403 \: \: \: units[/tex]

Step-by-step explanation:

The distance between two points can be found by using the formula

[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

M(-1, 1) and U(4, 5)

The distance from M to U is

[tex] |MU| = \sqrt{ ({ - 1 - 4})^{2} + ( {1 - 5})^{2} } \\ = \sqrt{ ({ - 5})^{2} + ( { - 4})^{2} } \\ = \sqrt{25 + 16} [/tex]

We have the final answer as

[tex] \sqrt{41} \: \: or \: \: 6.403 \: \: \: units[/tex]

Hope this helps you

8. The endpoints of ST are $(-3, 2) and T(5,8). Find the coordinates of
the midpoint of ST. Then find ST.

Answers

Answer:

Option (A)

Step-by-step explanation:

If the extreme ends of a segment are [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex],

Coordinates of the mid-point will be = [tex][\frac{(x_1+x_2)}{2},\frac{(y_1+y_2)}{2}][/tex]

And the length of the segment is = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Coordinates of the extreme ends of the ST are S(-3, 2) and T(5, 8).

Therefore, coordinates of the midpoint of ST will be = [tex](\frac{-3+5}{2},\frac{2+8}{2})[/tex]

= [tex](1,5)[/tex]

Length of ST = [tex]\sqrt{(5+3)^2+(8-2)^2}[/tex]

= [tex]\sqrt{64+36}[/tex]

= 10 units

Option (A) will be the answer.

how much is it 320,000×_=32,000,000​

Answers

Answer:

100.

Step-by-step explanation:

320,000×100=32,000,000​

100

since 32,000,000 is two place values greater than 320,000

so

320,000 * 100 = 32,000,000

: 9(p + 2) = 3(3p – 5)

Find the inequality with its graph

Answers

Answer:

NKKNKND FG

Step-by-step explanation:

What is the slope of the line shown?

A : slope = -1/3

B : slope = 8

C : slope = 3

D : slope -3

Answers

Answer is D slope -3

Yes the answer is d -3

I am somewhat confused on how to do this, can someone explain? thanks!

Answers

Answer:

(3x-1)×2=12-x

Step-by-step explanation:

AC = 3x - 1
AD = 12 - x
AD = AC + CD
After putting the values given above,
12 - x = 3x - 1 + CD
12 - x - 3x + 1 = CD
13 - 4x = CD

If C is the midpoint of AD then
AC = CD
3x - 1 = -4x + 13
3x + 4x = 13 + 1
7x = 14
X = 14 / 7
X = 2

CD = - 4x + 13
CD = - 4(2) + 13
CD = - 8 + 13
CD = 5

Which list correctly orders A, B, and c from lеаѕt tо greatest whеn A = -8, B = |-6| and c = |11|
А. В. С
С. А. В
В, А, С
С, В, А

Answers

Answer:

Correct order: C, B, A

The last answer : )

Step-by-step explanation:

A = -8

B = -6

C = 11

Correct order: C, B, A

The last answer : )

*Hope this helps!! : )*

The order of the expressions from least to greatest is A, B, C

How to order the numbers?

The equation of the numbers are given as:

A = -8, B = |-6| and c = |11|

Evaluate the absolute value expressions

A = -8, B = 6 and c = 11

Order the expressions from least to greatest

A = -8, B = 6 and c = 11

Hence, the order of the expressions from least to greatest is A, B, C

Read more about order at:

https://brainly.com/question/1094377

Factor the equation.
x^2 + 7x = 3x + 12

Answers

Answer:

3489.9583

Step-by-step explanation:

but htts its s

Autum school holding a voleturing challeng. Students are encouraged to volunteer for at least 1 1/2 hours per week. Volenteers abou the same amount each week. During a 3- week period she volunteers for 6 3/4 hours. Autumn wants to compare her volunteers rate with the challenge rate

Answers

Given :

Challenge given is to volunteer for about 1 1/2 hours per week .

Autum did at a rate of 6 3/4 hours per week .

To Find :

The comparison ( ratio ) her volunteers rate with the challenge rate .

Solution :

Simplifying challenge rate in in normal fraction , [tex]1\dfrac{1}{2}=\dfrac{2+1}{2}=\dfrac{3}{2}[/tex] .

Also , simplifying her rate , [tex]6\dfrac{3}{4}=\dfrac{(6\times 4)+3}{4}=\dfrac{27}{4}[/tex] .

Now , ratio of his work by challenge is :

[tex]R=\dfrac{\dfrac{27}{4}}{\dfrac{3}{2}}\\\\\\R=\dfrac{27\times 2}{4\times 3}\\\\R=\dfrac{9}{2}[/tex]

Therefore , the ratio is 9/2 or 4 1/2 .

Hence , this is the required solution .

Autumn volunteered 3/4 hours per week more than the least hours per week of volunteering.

Given that,
Autumn school holding a valeting challenge. Students are encouraged to volunteer for at least 1 1/2 hours per week. Volunteers about the same amount each week. During a 3- week period she volunteers for 6 3/4 hours.

What is the rate of change?

Rate of change is defined as the change in value with respect to time is called rate of change.

Here,
Autumn wants to compare her volunteer rate with the challenge rate,
So
Extra hours of volunteering = 6 3/4 - 3 [ 1 1/2] = 2 1/4
Rate of volunteering per week = [2 1 / 4] / 3 = 3 / 4

Thus, Autumn volunteered 3/4 hours per week more than the least hours per week of volunteering.

Learn more about the rate of change here:

https://brainly.com/question/13103052

#SPJ5

Find the value of ‘x’ for each of the following
7. X=
8.X=
9.X=
10.x=

Answers

Answer:

7. x=9

8. x=12

9. x=[tex]\sqrt{85}[/tex]

10. x=[tex]\sqrt{45}[/tex]

a proportional relationship can be shown in two different ways:​

Answers

What are u asking ? I’m don’t get it

i will give brainliest!!

Answers

Answer:

[tex] \huge{ \boxed{ \sf{70}}}[/tex]

Step-by-step explanation:

[tex] \underline{ \sf{Given}} : [/tex]

[tex] \sf{ \angle \:FGJ \: = \: 30° \:, } \: \: \angle \: JGH \: = \: 40° \: , \: \angle \: FGH= x[/tex]

Finding the value of x°

[tex] \sf{ \angle \: FGH= \angle \: FGJ \: + \: \angle \: JGH\:}[/tex]

Plug the values

[tex] \mapsto{ \sf{x = 40 + 30}}[/tex]

Add the numbers

[tex] \mapsto{ \sf{x = 70}}[/tex]

The value of x° is 70°

Hope I helped!

Best regards! :D

~[tex] \text{TheAnimeGirl}[/tex]

A woman wants to send a framed photograph of her family to her parents. The frame is 9 in long and 7 in wide. Will the frame lay flat in a box that has a square​ base, height ​6 in., and volume 546 in.³ ​?

Answers

Step-by-step explanation:

V=l*b*h , it's square, so l=b

V=l*h

l=V/h

l=546/6

l=91 in

So, if length of base is 91 in, the frame will be easily lay flat

Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. He spent a total of
$47.65. If Hugh bought 3 magazines, how many books did he buy?
The equation that models the problem is 3.95m + 8.95b = 47.65, where m is the number of magazines and b is the
number of books?

Answers

Answer:

Step-by-step explanation:

The equation is 3.95m + 8.95b = 47.95 where m is the amount of magazines bought and b is the amount of books bought. 47.95 is the total spent. We know that he bought 3 magazines, so we can switch m with 3. 3.95 multiplied by 3 is 11.85. The equation is now 11.85 + 8.95b = 47.65. Subtract 11.85 from both sides to get b by itself. 8.95b = 35.8. Divide both sides by 8.95 to get b by itself. b = 4

Hugh bought 4 books.

I hope this helped!

Answer:

m=3 b=4

Step-by-step explanation:

3.95 x 3 = 11.85

47.65 - 11.85 = 35.8

35.8 ÷ 8.95 = 4

m=3 b=4

The sum of two numbers is 12
and their product is 32.
What are the two numbers ?

Answers

Answer:

8 and 4

Step-by-step explanation:

8 x 4= 32

8+4 = 12

Using the expression 10xy + 6, what are the
variables?

Pleasee huryyy!!

Answers

Answer:xy

Step-by-step explanation:

Hey! This is my first question! The equation is relatively simple but something makes me not understand it. Your help would be greatly appreciated. :)

Answers

Answer:101°

Step-by-step explanation:

79 + 101=180

Answer:

101 = LHK

Step-by-step explanation:

GHK = GHL + LHK

GHK is a straight line so it equals 180

180 = 79+ LHK

Subtract 79 from each side

180-79 = 79-79+ LHK

101 = LHK

PLEASE PLEASE HELP ME WITH THIS!!

Answers

Answer:

A

Step-by-step explanation:

The square root of 5/3 is irrational because it cannot be expressed as the ratio of two integers (which is the definition of irrational numbers). If you were to put this into a calculator the answer would go on forever and never repeat, similar to pi, a famous irrational number.

V=1/3nr^2h ; solve for r

Answers

Answer: r=3v/2nh

Step-by-step explanation:

please help its due today!!!​

Answers

Answer:

line a and b are perpendicular as well as c and b

i think if not then none of them are because its hard to tell since they are sideways

Step-by-step explanation:

For What Value Of M Does 3x + 4 = Mx + 4 Have An Infinite Number Of Solutions? (2024)

FAQs

How do you know if there is an infinite number of solutions? ›

Some equations have infinitely many solutions. In these equations, any value for the variable makes the equation true. You can tell that an equation has infinitely many solutions if you try to solve the equation and get a variable or a number equal to itself.

How do you find infinite many solutions? ›

An infinite solution can be produced if the lines are coincident and they must have the same y-intercept. The two lines having the same y-intercept and the slope, are the exact same line. In simpler words, we can say that if the two lines are sharing the same line, then the system would result in an infinite solution.

Which equation has an infinite number of solutions? ›

If we end up with the same term on both sides of the equal sign, such as 4 = 4 or 4x = 4x, then we have infinite solutions.

What is the solution to 3x 4 ≤ 2 or 2x 11 ≥ 1? ›

The solution to the inequalities 3x - 4 ≤ 2 or 2x + 11 ≥ -1 is x ≤ 2 or x ≥ -6. This includes all real numbers because any value of x will satisfy at least one of the inequalities.

When can you have infinite solutions? ›

The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept.

How do you know if a number is infinite? ›

Infinity Meaning

A set of numbers can be defined as infinite if there exists a one-to-one correspondence between that set and a proper subset of itself. Let us consider an example x+ 1 = x, this is only possible when x is an infinite number. The addition of 1 won't result in the change on the original number.

How to tell if an equation has one, none, or infinite solutions? ›

If we can solve the equation and get something like x=b where b is a specific number, then we have one solution. If we end up with a statement that's always false, like 3=5, then there's no solution. If we end up with a statement that's always true, like 5=5, then there are infinite solutions.. Created by Sal Khan.

What is the condition for infinite number of solutions? ›

Condition for Infinite Solution

An infinite solution could be made if the given lines do coincide and then they have to be at the same y-intercept. The two lines which are having a similar y-intercept and also the slope is the exactly same line.

Does 0 0 mean infinite solutions? ›

If you get an equation that is always true, such as 0 = 0, then there are infinite solutions.

What is an equation that has an infinite number of solutions called? ›

If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.

When three equations have infinitely many solutions? ›

When linear systems in three variables have infinite solutions, this means that linear equations are coinciding. In other words, they produce the exact same equation and lie on top of one another. This means that every single x, y, and z value will satisfy all three equations.

Which equation has no solution? ›

The last type of equation is known as a contradiction, which is also known as a No Solution Equation. This type of equation is never true, no matter what we replace the variable with. As an example, consider 3x + 5 = 3x - 5. This equation has no solution.

What is the answer to 2 3x 1 ≥ 4x 6? ›

Summary: The value of x in the solution set of 2(3x - 1) ≥ 4x - 6 is (-2, ∞).

What is the solution of inequality 3 4x ≤ 11? ›

To find the solution of the inequality 3 - 4x ≤ 11, Solve for x. Now divide both sides of the inequality by -4. Therefore, The solution to the inequality is x ≥ -2.

What is 2x to the power of 2? ›

We can use this rule to evaluate 2x squared, or (2x)2, because we are raising the product 2x to the power of 2. We see that (2x)2 is equal to 4x2.

How do you know if a matrix has infinite solutions or no solutions? ›

Hence, a matrix has an infinite solution if the number of variables is more than the number of nonzero rows in the reduced row-echelon form of the matrix.

How do you know that this system has in fact infinitely many solutions? ›

If a consistent linear system of equations has a free variable, it has infinite solutions. If a consistent linear system has more variables than leading 1s, then the system will have infinite solutions. A consistent linear system with more variables than equations will always have infinite solutions.

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