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kipiarov [429]
3 years ago
13

How many solutions does the equation have?

Mathematics
2 answers:
stich3 [128]3 years ago
8 0

Answer:  The correct option is

(B) 1 solution.

Step-by-step explanation:  We are given to find the number of solutions that the following equation has :

2x+3=4x+2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

To find the number of solutions, we must try to solve the given equation first.

The solution of equation (i) is as follows :

2x+3=4x+2\\\\\Rightarrow 4x-2x=3-2\\\\\Rightarrow 2x=1\\\\\Rightarrow x=\dfrac{1}{2}.

Since we can find only one value of x from the equation, so there will be only one solution.

Option (B) is CORRECT.

Alex17521 [72]3 years ago
4 0

Answer:

x = 1/2

Step-by-step explanation:

2x + 3 = 4x + 2

-2x        -2x

3 = 2x + 2

-2          -2

1 = 2x

Divide both sides by 2x

x = 1/2

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Part 1

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Part 2

7-8\div4(3^2-1)=7-8\div4(9-1) \\  \\ =7-8\div4(8)=7-8\div32=7- \frac{1}{2} \\  \\ =6  \frac{1}{2} = \frac{13}{2}



Part 3

2-2(2-5)^2+3^2=2-2(-3)^2+9 \\  \\ =2-2(9)+9=2-18+9=-7



Part 4

(5^2-9\cdot3)^2-11=(25-27)^2-11 \\  \\ =(-2)^2-11=4-11=-7



Part 5

[(2-3)^2-5]\cdot4=[(-1)^2-5]\cdot4 \\  \\ =(1-5)\cdot4=-4\cdot4=-16



Part 6

12-11\cdot2+16\div8=12-22+2 \\  \\ =-8



Part 7

-5+1\cdot3-(7-2^3)=-5+3-(7-8) \\  \\ =-2-(-1)=-2+1=-1



Part 8

8+2\cdot3-14\div7=8+6-2 \\  \\ =12



Part 9

(8-2)^2+\frac{1}{4}[4-3(6-10)]=6^2+\frac{1}{4}[4-3(-4)] \\  \\ =36+\frac{1}{4}[4-(-12)]=36+\frac{1}{4}(4+12)=36+\frac{1}{4}(16) \\  \\ =36+4=40



Part 10

7+(2-3^2)\cdot5=7+(2-9)\cdot5 \\  \\ =7+(-7)\cdot5=7+(-35)=7-35 \\  \\ =-28



Part 11

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Part 12

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8 0
3 years ago
Tree factories build the same widget. Th number of widgets produced in each factory are shown in the table.
masya89 [10]

Answer:

1 8 9 6

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Step-by-step explanation:

8 0
3 years ago
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The table includes points on a quadratic function used to model the shape of a hole for one support beam at a new building site.
erastovalidia [21]

The hole is 8 feet deep at ground level ⇒ 3rd answer

Step-by-step explanation:

The form of the quadratic function is y = ax² + bx + c, where

  • a is the coefficient of x²
  • b is the coefficient of x
  • c is the y-intercept (at x = 0)

The vertex point of the quadratic is (h , k), where h=\frac{-b}{2a}

and k is the value of y when x = h

The table:

→  x  :  -2   ,  0  ,  2

→  y  :  -6   , -8  ,  -6

∵ x represents distance from hole's center in feet

∵ y represents the depth from level ground

∴ The quadratic function is y = ax² + bx + c

∵ c is the value of y at x = 0 ⇒ y-intercept

- From the table at x = 0 ⇒ y = -8

∴ c = -8

- Substitute its value in the function model

∴ y = ax² + bx - 8

- To find the values of a and b substitute x and y in the model by

   the coordinates of the point in the table

∵ x = -2 and y = -6

∴ -6 = a(-2)² + b(-2) - 8

∴ -6 = 4a - 2b - 8

- Add 8 to both sides

∴ 2 = 4a - 2b

- Switch the two sides

∴ 4a - 2b = 2 ⇒ (1)

∵ x = 2 and y = -6

∴ -6 = a(2)² + b(2) - 8

∴ -6 = 4a + 2b - 8

- Add 8 to both sides

∴ 2 = 4a + 2b

- Switch the two sides

∴ 4a + 2b = 2 ⇒ (2)

Now we have a system of equation to solve it

Add equations(1) and (2) to eliminate b

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∴ a = 0.5

- Substitute value of a in equation (1) or to to find b

∵ 4(0.5) + 2b = 2

∴ 2 + 2b = 2

- Subtract 2 from both sides

∴ 2b = 0

- Divide both sides by 2

∴ b = 0

Substitute the values of a and b in the function model

∴ y = 0.5x² + (0)x - 8

∴ y = 0.5x² - 8

∵ y represents the depth from level ground

∵ The vertex of the function model is (h , k)

∴ The deep of the hole at ground level is the value of k

∵ h=\frac{-b}{2a}

∴ h=\frac{-(0)}{2(0.5)}

∴ h = 0

∵ k is the value of y when x = h

- From the table at x = 0 ⇒ y = -8

∴ k = -8

- Ignore the sign (-) because the k represents the depth of the

  hole in feet

∴ The deep of the hole at ground level is 8 feet

The hole is 8 feet deep at ground level

Learn more:

You can learn more about the quadratic function in brainly.com/question/1332667

#LearnwithBrainly

4 0
3 years ago
What are the intercepts of y=4x-2
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I think that the intercepts are (0.5,0) and (0,2) which is the first choice.
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3 years ago
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