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At the beginning of the month, a song on a streaming service already had 1,000 listens, and was getting 38 new listens each day. Meanwhile, a different song already had 900 listens, and was getting 40 new listens each day. Write an equation to show the number of days it would take for the two songs to have the same number of listens. Use x as your variable.(1 point) please help me!

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To find the number of days it takes for the two songs to have the same number of listens, we can set up equations based on the initial listens and the daily increase in listens.

  1. For the first song:
  • Initial listens: 1,000
  • Daily increase: 38 listens
  • After \( x \) days, the total listens for the first song will be: \[ 1000 + 38x \]
  1. For the second song:
  • Initial listens: 900
  • Daily increase: 40 listens
  • After \( x \) days, the total listens for the second song will be: \[ 900 + 40x \]

Now we can set these two expressions equal to each other to find the number of days \( x \) when the two songs have the same number of listens: \[ 1000 + 38x = 900 + 40x \]

Now you can solve for \( x \).

what is x

To solve the equation \(1000 + 38x = 900 + 40x\), we can start by isolating \(x\):

  1. Subtract \(38x\) from both sides: \[ 1000 = 900 + 2x \]

  2. Next, subtract 900 from both sides: \[ 1000 - 900 = 2x \] \[ 100 = 2x \]

  3. Finally, divide both sides by 2: \[ x = \frac{100}{2} = 50 \]

So, \(x = 50\). It will take 50 days for the two songs to have the same number of listens.

An ice skating rink has two ways you can use the facility. The first option is to pay $10 per visit. The second option is to pay $32 per month, and $6 per visit. Write and solve an equation to show the number of visits it would take for the cost of the two plans to be equal.(1 point) Responses 10=32+6x ; x=−3 10 equals 32 plus 6 x ; x equals negative 3 10x=32+6x ; x=4 10 x equals 32 plus 6 x ; x equals 4 10x=32+6x ; x=8 10 x equals 32 plus 6 x ; x equals 8 10x=32−6x ; x=2 10 x equals 32 minus 6 x ; x equals 2

To find the number of visits at which the total costs of the two payment options are equal, we can set up the equations based on the given pricing plans.

  1. First option: \(10\) dollars per visit.

    • Total cost for \(x\) visits = \(10x\)

  2. Second option: \(32\) dollars per month plus \(6\) dollars per visit.

    • Total cost for \(x\) visits = \(32 + 6x\)

Now we can set these two costs equal to each other: \[ 10x = 32 + 6x \]

Now, we can solve for \(x\):

  1. Subtract \(6x\) from both sides: \[ 10x - 6x = 32 \] \[ 4x = 32 \]

  2. Divide both sides by 4: \[ x = \frac{32}{4} = 8 \]

Thus, the number of visits at which the costs of the two plans are equal is \(x = 8\).

From the provided options, the correct response is:
\(10x = 32 + 6x; x = 8\).

At the beginning of the month, a song on a streaming service had 700 listens, and it was getting 52 new listens each day. Meanwhile, a different song had 600 listens, and it was getting 56 new listens each day. When will the two songs have the same number of listens?(1 point) The songs will have the same number of listens after days.

To find out when the two songs will have the same number of listens, we can set up equations based on the information provided.

  1. First song:

    • Initial listens: 700
    • Daily increase: 52 listens
    • After \(x\) days, the total listens will be: \[ 700 + 52x \]

  2. Second song:

    • Initial listens: 600
    • Daily increase: 56 listens
    • After \(x\) days, the total listens will be: \[ 600 + 56x \]

Now, we can set these two expressions equal to each other: \[ 700 + 52x = 600 + 56x \]

Now, let's solve for \(x\):

  1. Subtract \(52x\) from both sides: \[ 700 = 600 + 4x \]

  2. Next, subtract 600 from both sides: \[ 700 - 600 = 4x \] \[ 100 = 4x \]

  3. Finally, divide both sides by 4: \[ x = \frac{100}{4} = 25 \]

Thus, the two songs will have the same number of listens after 25 days.

Miguel’s car has a 20-gallon capacity, and Christina’s car has a 16-gallon capacity. Miguel uses 1.5 gallons of gas per week, and Christina uses 1 gallon of gas per week. When will Miguel and Christina have the same amount of gas in their tanks?(1 point) Responses After 8 weeks they will have the same amount of gas in their tanks. After 8 weeks they will have the same amount of gas in their tanks. After 18 week they will have the same amount of gas in their tanks. After Start Fraction 1 over 8 End Fraction week they will have the same amount of gas in their tanks. After 1.6 weeks they will have the same amount of gas in their tanks. After 1.6 weeks they will have the same amount of gas in their tanks. After −8 weeks they will have the same amount of gas in their tanks.

To determine when Miguel and Christina will have the same amount of gas in their tanks, we can set up an equation based on their starting amounts and their gas usage per week.

  1. Miguel's car:

    • Capacity: 20 gallons
    • Uses: 1.5 gallons per week
    • Amount of gas after \( x \) weeks: \[ \text{Gas remaining for Miguel} = 20 - 1.5x \]

  2. Christina's car:

    • Capacity: 16 gallons
    • Uses: 1 gallon per week
    • Amount of gas after \( x \) weeks: \[ \text{Gas remaining for Christina} = 16 - 1x \]

Now, we can set these two expressions equal to find out when they will have the same amount of gas: \[ 20 - 1.5x = 16 - x \]

Now, let's solve for \( x \):

  1. Add \( 1.5x \) to both sides: \[ 20 = 16 - x + 1.5x \] \[ 20 = 16 + 0.5x \]

  2. Subtract 16 from both sides: \[ 20 - 16 = 0.5x \] \[ 4 = 0.5x \]

  3. Finally, divide both sides by 0.5: \[ x = \frac{4}{0.5} = 8 \]

Thus, Miguel and Christina will have the same amount of gas in their tanks after 8 weeks.

The correct response is: After 8 weeks they will have the same amount of gas in their tanks.

Which of the following equations has exactly one solution?(1 point) Responses 3x−8=3x+8 3 x minus 8 equals 3 x plus 8 −3x+8=−3x−8 negative 3 x plus 8 equals negative 3 x minus 8 −8x+3=−8x+3 negative 8 x plus 3 equals negative 8 x plus 3 −3x−8=3x−8

To determine which equation has exactly one solution, we will analyze each provided equation.

  1. \(3x - 8 = 3x + 8\): \[ 3x - 3x = 8 + 8 \Rightarrow 0 = 16 \quad \text{(no solution)} \]

  2. \(-3x + 8 = -3x - 8\): \[ -3x + 3x = -8 - 8 \Rightarrow 0 = -16 \quad \text{(no solution)} \]

  3. \(-8x + 3 = -8x + 3\): \[ -8x + 8x = 3 - 3 \Rightarrow 0 = 0 \quad \text{(infinitely many solutions)} \]

  4. \(-3x - 8 = 3x - 8\): \[ -3x - 3x = -8 + 8 \Rightarrow -6x = 0 \Rightarrow x = 0 \quad \text{(one solution)} \]

The equation \(-3x - 8 = 3x - 8\) has exactly one solution, which is \(x = 0\).

Thus, the correct answer is: \(-3x - 8 = 3x - 8\).