NaHCO3+HC2H3O2→NaC2H3O2+H2O+CO2
A student mixes baking soda (NaHCO3) and acetic acid (HC2H3O2) to produce a chemical reaction shown. Which statement about the reaction is correct?
(1 point)
Responses
Atoms of Na are destroyed during the reaction.
Atoms of Na are destroyed during the reaction.
Some atoms gain mass after the reaction.
Some atoms gain mass after the reaction.
The atoms of the reactants are regrouped during the reaction.
The atoms of the reactants are regrouped during the reaction.
There are more H atoms after the reaction.
The atoms of the reactants are regrouped during the reaction.
Use the chemical reaction to answer the question.
2H2+O2→2H2O
There are four atoms of hydrogen (H) before the reaction. How many atoms of hydrogen are present after the reaction?
(1 point)
Responses
5
5
8
8
2
2
4
There are four atoms of hydrogen (H) before the reaction, and after the reaction, there are still four atoms of hydrogen.
Students are called by their teacher at the beginning of the year. Expectations are reviewed by the teacher to help set the students up for success. Lessons should be completed by students on the day they appear on the planner.
Use the passage to complete the following questions.
Rewrite the paragraph so that all the sentences are in active voice.
The teacher calls the students at the beginning of the year and reviews expectations with them to help set them up for success. The students should complete lessons on the day they appear on the planner.
The dancer (to practice) for many hours each day before a performance. She (to move) to the rhythm of music. She (to dance) across the stage, (to hear) the applause, and (to take) her final curtsy.
Use the passage to complete the following questions.
Rewrite the paragraph using the verbs provided to make the subject and verb agree.
The dancer practices for many hours each day before a performance. She moves to the rhythm of music. She dances across the stage, hears the applause, and takes her final curtsy.
What does it mean to solve an equation, have the variables cancel out, and have the answer be 3=3, for example?
*
1 point
When an equation is solved, it means that the value of the unknown variable(s) in the equation is determined. In the case where the variables cancel out and the answer is 3=3, it means that the equation is true for all values of the variable(s). In other words, any value of the variable(s) that satisfies the equation will result in both sides of the equation being equal to each other.
What does it mean to solve an equation, have the variables cancel out, and have the answer be 3=3, for example?
*
1 point
one solution
infinite solutions
no solution
Having the variables cancel out in an equation and resulting in the answer 3=3 means that the equation has infinitely many solutions. This means that any value substituted for the variable(s) in the equation will yield a true statement. In this case, the equation is always true, regardless of the value of the variable(s).
what do i choose
In this case, the correct answer is "infinite solutions."
Solve for x: 2x + 4 + 3x = 39
1 point
x = 13
x = 7
x = 39
To solve for x in the equation 2x + 4 + 3x = 39, we can combine like terms first:
2x + 3x + 4 = 39
5x + 4 = 39
Next, we can isolate the variable x by subtracting 4 from both sides:
5x = 35
Finally, we can solve for x by dividing both sides by 5:
x = 7
Therefore, the solution to the equation is x = 7.
What are the order of operations?
*
1 point
The order of operations is a set of rules that determines the sequence in which mathematical operations should be performed in an expression.
The order of operations is as follows:
1. Parentheses/Brackets: Any operations inside parentheses or brackets should be done first.
2. Exponents: Perform any operations involving exponents or powers.
3. Multiplication and Division: Perform multiplications and divisions from left to right.
4. Addition and Subtraction: Perform additions and subtractions from left to right.
This order ensures that mathematical expressions are evaluated correctly and consistently.
If there is no number before a variable, is there a coefficient and what would it be?
*
1 point
0
1
If there is no number explicitly written before a variable, the coefficient is understood to be 1. This is because when a number is not explicitly written before a variable, it is assumed to be multiplied by 1. Therefore, the coefficient of a variable without a number before it is 1.
Solve the equation: 6(x-2) -2x = 4x
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1 point
x= -12
x = 0
-12=0 no solution
To solve the equation, let's simplify the left side of the equation first:
6(x-2) -2x = 4x
6x - 12 - 2x = 4x
Combine like terms:
4x - 12 = 4x
Now, let's move all terms with x to one side:
4x - 4x = 12
Simplify, and we are left with:
0 = 12
Since this equation is not true (0 is not equal to 12), there is no solution to the equation.
Therefore, the correct answer is -12=0, no solution.
Solve for x.
−5x=−30(1 point)
To solve for x in the equation −5x = −30, we can isolate the variable x by dividing both sides of the equation by -5:
−5x / -5 = −30 / -5
This simplifies to:
x = 6
Therefore, the solution to the equation is x = 6.
Solve for x.
12−x/9=11(1 point)
To solve for x in the equation 12 - x/9 = 11, we can start by isolating the variable x by subtracting 12 from both sides:
12 - x/9 - 12 = 11 - 12
Simplifying further:
-x/9 = -1
To eliminate the fraction, we can multiply both sides of the equation by 9:
9 * (-x/9) = 9 * (-1)
Simplifying:
-x = -9
Finally, to solve for x, we can multiply both sides of the equation by -1 to isolate x:
(-1) * (-x) = (-1) * (-9)
Simplifying:
x = 9
Therefore, the solution to the equation is x = 9.
Solve for x.
−20=−5+3x(1 point)
To solve for x in the equation −20 = −5 + 3x, we can start by isolating the variable x by moving the constant term (-5) to the other side:
−20 + 5 = 3x
Simplifying:
−15 = 3x
Next, to solve for x, we divide both sides of the equation by 3:
−15 / 3 = x
Simplifying further:
x = -5
Therefore, the solution to the equation is x = -5.
20=5−38x(1 point)
To solve for x in the equation 20 = 5 - 38x, we can start by isolating the variable x by moving the constant term (5) to the other side:
20 - 5 = -38x
Simplifying,
15 = -38x
Next, to solve for x, we divide both sides of the equation by -38:
15 / -38 = x
Simplifying further,
x ≈ -0.3947
Therefore, the solution to the equation is x ≈ -0.3947.
Solve for x.
20=5−3/8x(1 point)
To solve for x in the equation 20 = 5 - (3/8)x, we can start by isolating the variable x.
First, let's simplify the right side of the equation:
20 = 5 - (3/8)x
To get rid of the fraction, we can multiply both sides of the equation by 8:
8 * 20 = 8 * 5 - 8 * (3/8)x
160 = 40 - 3x
Next, we can move the constant term (40) to the other side:
160 - 40 = 40 - 40 - 3x
120 = -3x
To solve for x, we divide both sides of the equation by -3:
120 / -3 = -3x / -3
-40 = x
Therefore, the solution to the equation is x = -40.
Solve for x.
7(4x−15)=63
To solve for x in the equation 7(4x - 15) = 63, we will start by simplifying the left side of the equation:
28x - 105 = 63
Next, we will isolate the term with x by moving the constant term to the other side:
28x = 63 + 105
28x = 168
Finally, we can solve for x by dividing both sides of the equation by 28:
x = 168/28
Simplifying:
x = 6
Therefore, the solution to the equation is x = 6.
Solve for x: −2(3x−15)−25=35.(1 point)
To solve for x in the equation −2(3x - 15) - 25 = 35, we will start by simplifying the left side of the equation:
-6x + 30 - 25 = 35
-6x + 5 = 35
Next, we will isolate the term with x by moving the constant term to the other side:
-6x = 35 - 5
-6x = 30
Finally, we can solve for x by dividing both sides of the equation by -6:
x = 30 / -6
Simplifying:
x = -5
Therefore, the solution to the equation is x = -5.
Solve for x: 12x+5=10x−11.(1 point)
To solve for x in the equation 12x + 5 = 10x - 11, we will start by isolating the variable x by moving the constant term to the other side and the term with x to the left side of the equation:
12x - 10x = -11 - 5
Simplifying:
2x = -16
Next, to solve for x, we will divide both sides of the equation by 2:
(2x) / 2 = (-16) / 2
Simplifying further:
x = -8
Therefore, the solution to the equation is x = -8.
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)
Let's set up an equation to represent the number of days it would take for the two songs to have the same number of listens.
For the first song:
Number of listens = 1,000 + 38x (where x represents the number of days)
For the second song:
Number of listens = 900 + 40x (where x represents the number of days)
Setting them equal to each other, we have:
1,000 + 38x = 900 + 40x
Now we can solve for x in order to find the number of days it would take 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
Let's set up an equation to represent the number of visits it would take for the cost of the two plans to be equal.
For the first option:
Cost = $10 per visit
For the second option:
Cost = $32 per month + $6 per visit
Setting the two costs equal to each other, we have:
10x = 32 + 6x
Now we can solve for x to find the number of visits it would take for the cost of the two plans to be equal.
To simplify the equation, let's subtract 6x from both sides:
10x - 6x = 32
Simplifying further:
4x = 32
To isolate x, we can divide both sides by 4:
4x / 4 = 32 / 4
Simplifying further:
x = 8
Therefore, it would take 8 visits for the cost of the two plans to be equal.
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)
Let's set up an equation to represent the number of days it would take for the two songs to have the same number of listens.
For the first song:
Number of listens = 700 + 52x (where x represents the number of days)
For the second song:
Number of listens = 600 + 56x (where x represents the number of days)
Setting them equal to each other, we have:
700 + 52x = 600 + 56x
Now we can solve for x in order to find the number of days it would take for the two songs to have the same number of listens.
To simplify the equation, let's subtract 52x from both sides:
700 + 52x - 52x = 600 + 56x - 52x
Simplifying further:
700 = 600 + 4x
Next, let's subtract 600 from both sides:
700 - 600 = 600 + 4x - 600
Simplifying further:
100 = 4x
To isolate x, we can divide both sides by 4:
100 / 4 = 4x / 4
Simplifying further:
25 = x
Therefore, 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)
To determine when Miguel and Christina will have the same amount of gas in their tanks, we will set up an equation using their respective gas usage.
Let's assume x represents the number of weeks needed for them to have the same amount of gas in their tanks.
The gas amount in Miguel's tank after x weeks will be: 20 (gallons) - 1.5 (gallons/week) * x (weeks)
The gas amount in Christina's tank after x weeks will be: 16 (gallons) - 1 (gallon/week) * x (weeks)
Setting these two amounts equal, we have the equation:
20 - 1.5x = 16 - x
To solve for x, we'll isolate the variable terms on one side and the constant terms on the other side:
20 - 16 = -x + 1.5x
4 = 0.5x
Next, we'll divide both sides by 0.5 to solve for x:
4 / 0.5 = x
x = 8
Therefore, Miguel and Christina will have the same amount of gas in their tanks after 8 weeks.
Which of the following equations has exactly one solution?(1 point)
Responses
−3x+8=−3x−8
negative 3 x plus 8 equals negative 3 x minus 8
3x−8=3x+8
3 x minus 8 equals 3 x plus 8
−8x+3=−8x+3
negative 8 x plus 3 equals negative 8 x plus 3
−3x−8=3x−8
The equation that has exactly one solution is:
−8x + 3 = −8x + 3
This equation shows that the variable term (-8x) cancels out on both sides, leaving only the constant term (3) on both sides. Therefore, it has no dependence on the value of x and will always be true regardless of the value of x. This means that the equation has infinitely many solutions.
Solve for x to determine if the equation has one, none, or infinite solutions.
11x=3(7x−1)−10x(1 point)
Responses
The equation has one solution: x=−1.
The equation has one solution: x equals negative 1 .
The equation has no solution.
The equation has no solution.
The equation has one solution: x=−3.
The equation has one solution: x equals negative 3 .
The equation has infinite solutions.
The equation has infinite solutions.
To determine if the equation 11x = 3(7x - 1) - 10x has one, none, or infinite solutions, we will solve for x:
First, distribute the 3 to simplify the right side of the equation:
11x = 21x - 3 - 10x
Combining like terms:
11x = 21x -