Andrew picks three words from a dictionary every week and has listed 24 words. He has been doing this for 8 weeks.
Which of the following can be represented by the equation 3x = 24
3
𝑥
=
24
?(1 point)
Responses
A survey was conducted to determine the favorite subject of seventh grade students. One-third of all surveyed, or 24 students, said math is their favorite subject. How many students were surveyed?
A survey was conducted to determine the favorite subject of seventh grade students. One-third of all surveyed, or 24 students, said math is their favorite subject. How many students were surveyed?
The cost of a pair of shoes is three times the cost of a shirt. If the cost of the shirt is $24, how much does the pair of shoes cost?
The cost of a pair of shoes is three times the cost of a shirt. If the cost of the shirt is $24, how much does the pair of shoes cost?
Andrew picks three words from a dictionary every week and lists them in his notebook. So far, he has listed 24 words. How many weeks has Andrew been doing this?
Andrew picks three words from a dictionary every week
just the answer
11 answers
The temperature dropped by 12°
12
°
in 5 hours. The temperature dropped the same amount every hour. Complete the equation that represents the amount of change, x
𝑥
, of temperature every hour and solve this equation.(1 point)
5x=
5
𝑥
=
The temperature decreased by °
°
every hour.
12
°
in 5 hours. The temperature dropped the same amount every hour. Complete the equation that represents the amount of change, x
𝑥
, of temperature every hour and solve this equation.(1 point)
5x=
5
𝑥
=
The temperature decreased by °
°
every hour.
To solve for the amount of change in temperature, \( x \), every hour, we start with the equation that represents the total drop in temperature over 5 hours:
\[ 5x = 12 \]
Now, to solve for \( x \):
-
Divide both sides by 5:
\[ x = \frac{12}{5} \]
-
Simplifying \( \frac{12}{5} \) gives:
\[ x = 2.4 \]
Thus, the temperature decreased by \( 2.4° \) every hour.
Which of the following equations has a solution of −7
−
7
?(1 point)
Responses
5x+11=−24
5
𝑥
+
11
=
−
24
5 x plus 11 equals negative 24
−3x−8=−29
−
3
𝑥
−
8
=
−
29
negative 3 x minus 8 equals negative 29
4x−23=5
4
𝑥
−
23
=
5
4 x minus 23 equals 5
−x+3=−4
−
7
?(1 point)
Responses
5x+11=−24
5
𝑥
+
11
=
−
24
5 x plus 11 equals negative 24
−3x−8=−29
−
3
𝑥
−
8
=
−
29
negative 3 x minus 8 equals negative 29
4x−23=5
4
𝑥
−
23
=
5
4 x minus 23 equals 5
−x+3=−4
To determine which equation has a solution of \( x = -7 \), we will substitute \( -7 \) into each equation and see if it satisfies them.
-
For \( 5x + 11 = -24 \): \[ 5(-7) + 11 = -35 + 11 = -24 \quad \text{(True)} \]
-
For \( -3x - 8 = -29 \): \[ -3(-7) - 8 = 21 - 8 = 13 \quad \text{(False)} \]
-
For \( 4x - 23 = 5 \): \[ 4(-7) - 23 = -28 - 23 = -51 \quad \text{(False)} \]
-
For \( -x + 3 = -4 \): \[ -(-7) + 3 = 7 + 3 = 10 \quad \text{(False)} \]
The only equation that has a solution of \( x = -7 \) is:
\( 5x + 11 = -24 \).
Which of the following equations has a solution different from the rest? (1 point)
Responses
12x−3=12
1
2
𝑥
−
3
=
1
2
Start Fraction 1 over 2 End Fraction x minus 3 equals Start Fraction 1 over 2 End Fraction
34x+5=−14
3
4
𝑥
+
5
=
−
1
4
Start Fraction 3 over 4 End Fraction x plus 5 equals negative Start Fraction 1 over 4 End Fraction
−0.35x−0.52=1.93
−
0.35
𝑥
−
0.52
=
1.93
negative 0.35 x minus 0.52 equals 1.93
−17x−34=14
Responses
12x−3=12
1
2
𝑥
−
3
=
1
2
Start Fraction 1 over 2 End Fraction x minus 3 equals Start Fraction 1 over 2 End Fraction
34x+5=−14
3
4
𝑥
+
5
=
−
1
4
Start Fraction 3 over 4 End Fraction x plus 5 equals negative Start Fraction 1 over 4 End Fraction
−0.35x−0.52=1.93
−
0.35
𝑥
−
0.52
=
1.93
negative 0.35 x minus 0.52 equals 1.93
−17x−34=14
To find which equation has a solution different from the rest, we will solve each equation individually.
-
For \( 12x - 3 = 12 \): \[ 12x = 12 + 3 \ 12x = 15 \ x = \frac{15}{12} = \frac{5}{4} = 1.25 \]
-
For \( \frac{3}{4}x + 5 = -\frac{1}{4} \): \[ \frac{3}{4}x = -\frac{1}{4} - 5 \ \frac{3}{4}x = -\frac{1}{4} - \frac{20}{4} \ \frac{3}{4}x = -\frac{21}{4} \ x = -\frac{21}{4} \cdot \frac{4}{3} \ x = -7 \]
-
For \( -0.35x - 0.52 = 1.93 \): \[ -0.35x = 1.93 + 0.52 \ -0.35x = 2.45 \ x = \frac{2.45}{-0.35} \approx -7 \]
-
For \( -17x - 34 = 14 \): \[ -17x = 14 + 34 \ -17x = 48 \ x = \frac{48}{-17} \approx -2.82 \]
Summary of Solutions:
- \( 12x - 3 = 12 \) gives \( x = 1.25 \)
- \( \frac{3}{4}x + 5 = -\frac{1}{4} \) gives \( x = -7 \)
- \( -0.35x - 0.52 = 1.93 \) gives \( x \approx -7 \)
- \( -17x - 34 = 14 \) gives \( x \approx -2.82 \)
Conclusion:
The equation that has a solution different from the rest is \( 12x - 3 = 12 \), which yields \( x = 1.25 \). All the other equations result in solutions around \( -7 \) or \( -2.82 \).
Lindsay practices the guitar 50 minutes on Saturday and 30 minutes on most weekdays. Last week she practiced 140 minutes. How many weekdays did she practice? Write an equation in the form px+q=r
𝑝
𝑥
+
𝑞
=
𝑟
to represent this problem.(2 points)
x
𝑥
+ =
𝑝
𝑥
+
𝑞
=
𝑟
to represent this problem.(2 points)
x
𝑥
+ =
To write an equation in the form \( px + q = r \) where \( x \) represents the number of weekdays Lindsay practiced, we start by identifying the variables and constants involved in the problem.
Let:
- \( x \) = number of weekdays Lindsay practiced
- 30 minutes = amount of time she practices on each weekday
- 50 minutes = amount of time she practices on Saturday
- 140 minutes = total practice time for the week
Lindsay's total practice time for the week can be expressed as: \[ \text{Total Practice Time} = \text{Saturday Practice} + \text{Weekday Practice} \]
This can be formulated as: \[ 50 + 30x = 140 \]
In this equation:
- \( p = 30 \) (the number of minutes she practices each weekday),
- \( q = 50 \) (the minutes spent practicing on Saturday),
- \( r = 140 \) (the total practice time).
Thus, the equation representing this problem is: \[ 30x + 50 = 140 \]
You can solve this equation to find the number of weekdays she practiced.
A baby elephant weighs 150 pounds when born. It gains 2 pounds per day during the first year. How many days will it take the elephant to weigh a total of 224 pounds?(1 point)
days
days
To determine how many days it will take for the baby elephant to reach a weight of 224 pounds, we can set up the following equation.
- Initial weight of the elephant: 150 pounds
- Weight gain per day: 2 pounds
- Target weight: 224 pounds
Let \( d \) represent the number of days the elephant gains weight. The total weight after \( d \) days can be expressed as:
\[ \text{Weight after } d \text{ days} = 150 + 2d \]
We want this weight to equal 224 pounds, so we set up the equation:
\[ 150 + 2d = 224 \]
Now, we can solve for \( d \):
-
Subtract 150 from both sides: \[ 2d = 224 - 150 \] \[ 2d = 74 \]
-
Divide both sides by 2: \[ d = \frac{74}{2} = 37 \]
Thus, it will take the elephant 37 days to weigh a total of 224 pounds.