To determine if 1/2 is a solution to -4b + 9 = 7, we substitute 1/2 in for b in the equation and solve:
-4(1/2) + 9 = 7
-2 + 9 = 7
7 = 7
Since both sides of the equation are equal when b = 1/2, 1/2 is a solution to the equation.
Determine if the given value is a solution to the equation.
−4b+9=7;
1
2
29 answers
Is b=
1
2 a solution of the equation −4b+9=7?
No
Yes
1
2 a solution of the equation −4b+9=7?
No
Yes
Yes, b = 1/2 is a solution to the equation -4b + 9 = 7.
An athlete trains for 70 min each day for as many days as possible. Write an equation that relates the number of days d that the athlete spends training when the athlete trains for 560 min.
To write the equation, we can use the fact that the athlete trains for 70 minutes each day.
Let d represent the number of days the athlete trains.
Since the athlete trains for 70 minutes each day, the total amount of training time is the product of 70 and d, which can be represented as:
70d = 560
This equation relates the number of days (d) to the total training time (560 minutes).
Let d represent the number of days the athlete trains.
Since the athlete trains for 70 minutes each day, the total amount of training time is the product of 70 and d, which can be represented as:
70d = 560
This equation relates the number of days (d) to the total training time (560 minutes).
Enter an equation where any numbers represent numbers of minutes
Let m represent the number of minutes of training time and t represent the total number of minutes the athlete spends training.
The equation can be written as:
t = m * d
In this equation, d represents the number of days and m represents the number of minutes of training each day. The total training time, t, is equal to the product of m and d.
The equation can be written as:
t = m * d
In this equation, d represents the number of days and m represents the number of minutes of training each day. The total training time, t, is equal to the product of m and d.
An athlete trains for 85 min each day for as many days as possible. Write an equation that relates the number of days d that the athlete spends training when the athlete trains for 765 min.
Question content area bottom
Part 1
Enter an equation where any numbers represent numbers of minutes.
Question content area bottom
Part 1
Enter an equation where any numbers represent numbers of minutes.
Let d represent the number of days the athlete trains.
Since the athlete trains for 85 minutes each day, the total amount of training time is the product of 85 and d, which can be represented as:
85d = 765
This equation relates the number of days (d) to the total training time (765 minutes).
Since the athlete trains for 85 minutes each day, the total amount of training time is the product of 85 and d, which can be represented as:
85d = 765
This equation relates the number of days (d) to the total training time (765 minutes).
Use mental math to find the solution of the equation.
19+d=24
19+d=24
To find the solution to the equation 19 + d = 24, we can use mental math.
Subtract 19 from both sides of the equation to isolate the variable d:
d = 24 - 19
Simplifying,
d = 5
Therefore, the solution to the equation 19 + d = 24 is d = 5.
Subtract 19 from both sides of the equation to isolate the variable d:
d = 24 - 19
Simplifying,
d = 5
Therefore, the solution to the equation 19 + d = 24 is d = 5.
Use a table to find the solution of the equation.
6a−7=11
6a−7=11
To find the solution to the equation 6a - 7 = 11 using a table, we can create a table with values for a and the corresponding values for 6a - 7, until we find the value that satisfies the equation.
Let's start with some values for a:
a = 0, 1, 2, 3, 4
Now we can substitute these values for a into the equation 6a - 7 = 11 and compute the corresponding values for 6a - 7:
For a = 0:
6(0) - 7 = -7
For a = 1:
6(1) - 7 = -1
For a = 2:
6(2) - 7 = 5
For a = 3:
6(3) - 7 = 11
For a = 4:
6(4) - 7 = 17
Now we can see that when a = 3, the equation 6a - 7 = 11 is satisfied.
Therefore, the solution to the equation is a = 3.
Let's start with some values for a:
a = 0, 1, 2, 3, 4
Now we can substitute these values for a into the equation 6a - 7 = 11 and compute the corresponding values for 6a - 7:
For a = 0:
6(0) - 7 = -7
For a = 1:
6(1) - 7 = -1
For a = 2:
6(2) - 7 = 5
For a = 3:
6(3) - 7 = 11
For a = 4:
6(4) - 7 = 17
Now we can see that when a = 3, the equation 6a - 7 = 11 is satisfied.
Therefore, the solution to the equation is a = 3.
Use a table to find the solution of the equation. If the solution lies between two consecutive integers, identify those integers.
3.9=2n−3
3.9=2n−3
To find the solution to the equation 3.9 = 2n - 3 using a table, we can create a table with values for n and the corresponding values for 2n - 3, until we find the value that satisfies the equation.
Let's start with some values for n:
n = 0, 1, 2, 3, 4
Now we can substitute these values for n into the equation 2n - 3 and compute the corresponding values:
For n = 0:
2(0) - 3 = -3
For n = 1:
2(1) - 3 = -1
For n = 2:
2(2) - 3 = 1
For n = 3:
2(3) - 3 = 3
For n = 4:
2(4) - 3 = 5
Now we can see that when n = 2, the equation 3.9 = 2n - 3 is approximately satisfied.
Therefore, the solution to the equation is n = 2. However, if we consider only integers, we can see that the solution lies between the integers 1 and 2.
Let's start with some values for n:
n = 0, 1, 2, 3, 4
Now we can substitute these values for n into the equation 2n - 3 and compute the corresponding values:
For n = 0:
2(0) - 3 = -3
For n = 1:
2(1) - 3 = -1
For n = 2:
2(2) - 3 = 1
For n = 3:
2(3) - 3 = 3
For n = 4:
2(4) - 3 = 5
Now we can see that when n = 2, the equation 3.9 = 2n - 3 is approximately satisfied.
Therefore, the solution to the equation is n = 2. However, if we consider only integers, we can see that the solution lies between the integers 1 and 2.
Use a table to find the solution of the equation. If the solution lies between two consecutive integers, identify those integers.
27.8=5n−2
Question content area bottom
Part 1
If the solution is an integer, type this integer. Otherwise, type the two consecutive integers between which the solution lies.
27.8=5n−2
Question content area bottom
Part 1
If the solution is an integer, type this integer. Otherwise, type the two consecutive integers between which the solution lies.
To find the solution to the equation 27.8 = 5n - 2 using a table, we can create a table with values for n and the corresponding values for 5n - 2, until we find the value that satisfies the equation.
Let's start with some values for n:
n = 0, 1, 2, 3, 4
Now we can substitute these values for n into the equation 5n - 2 and compute the corresponding values:
For n = 0:
5(0) - 2 = -2
For n = 1:
5(1) - 2 = 3
For n = 2:
5(2) - 2 = 8
For n = 3:
5(3) - 2 = 13
For n = 4:
5(4) - 2 = 18
Now we can see that when n = 3, the equation 27.8 = 5n - 2 is approximately satisfied.
Therefore, the solution to the equation is n = 3. As the solution is an integer, we can conclude that the solution is n = 3.
Let's start with some values for n:
n = 0, 1, 2, 3, 4
Now we can substitute these values for n into the equation 5n - 2 and compute the corresponding values:
For n = 0:
5(0) - 2 = -2
For n = 1:
5(1) - 2 = 3
For n = 2:
5(2) - 2 = 8
For n = 3:
5(3) - 2 = 13
For n = 4:
5(4) - 2 = 18
Now we can see that when n = 3, the equation 27.8 = 5n - 2 is approximately satisfied.
Therefore, the solution to the equation is n = 3. As the solution is an integer, we can conclude that the solution is n = 3.
Tell whether the equation has the ordered pair as a solution.
y=3x; (4,12)
Question content area bottom
Part 1
Is (4,12) a solution of the given equation?
y=3x; (4,12)
Question content area bottom
Part 1
Is (4,12) a solution of the given equation?
To determine if the ordered pair (4, 12) is a solution to the equation y = 3x, we substitute the values of x and y from the ordered pair into the equation.
When x = 4, the equation becomes:
y = 3(4)
y = 12
Since the value of y is equal to 12, which matches the given value of y in the ordered pair, (4, 12) is indeed a solution to the equation y = 3x.
When x = 4, the equation becomes:
y = 3(4)
y = 12
Since the value of y is equal to 12, which matches the given value of y in the ordered pair, (4, 12) is indeed a solution to the equation y = 3x.
Tell whether the equation has the ordered pair as a solution.
y=3x; (−6,−24)
Question content area bottom
Part 1
Is (−6,−24) a solution of the given equation?
Yes
Yes
y=3x; (−6,−24)
Question content area bottom
Part 1
Is (−6,−24) a solution of the given equation?
Yes
Yes
To determine if the ordered pair (-6, -24) is a solution to the equation y = 3x, we substitute the values of x and y from the ordered pair into the equation.
When x = -6, the equation becomes:
y = 3(-6)
y = -18
The value of y is not -24, which does not match the given value of y in the ordered pair (-6, -24). Therefore, (-6, -24) is NOT a solution to the equation y = 3x.
When x = -6, the equation becomes:
y = 3(-6)
y = -18
The value of y is not -24, which does not match the given value of y in the ordered pair (-6, -24). Therefore, (-6, -24) is NOT a solution to the equation y = 3x.
Decide whether the ordered pair (−4,8) is a solution of the equation.
y=−2x
Question content area bottom
Part 1
Is (−4,8) a solution to y=−2x?
Yes
y=−2x
Question content area bottom
Part 1
Is (−4,8) a solution to y=−2x?
Yes
To determine if the ordered pair (-4, 8) is a solution to the equation y = -2x, we substitute the values of x and y from the ordered pair into the equation.
When x = -4, the equation becomes:
y = -2(-4)
y = 8
The value of y is 8, which matches the given value of y in the ordered pair (-4, 8). Therefore, (-4, 8) is indeed a solution to the equation y = -2x.
When x = -4, the equation becomes:
y = -2(-4)
y = 8
The value of y is 8, which matches the given value of y in the ordered pair (-4, 8). Therefore, (-4, 8) is indeed a solution to the equation y = -2x.
Question content area top
Part 1
Use a table, an equation, and a graph to represent the relationship below.
Ty is 7 years younger than Bea.
Question content area bottom
Part 1
Complete the table below.
Ty's and Bea's Ages (years)
Ty's Age
1
2
3
4
5
Bea's Age
enter your response here
enter your response here
enter your response here
enter your response here
enter your response here
Part 1
Use a table, an equation, and a graph to represent the relationship below.
Ty is 7 years younger than Bea.
Question content area bottom
Part 1
Complete the table below.
Ty's and Bea's Ages (years)
Ty's Age
1
2
3
4
5
Bea's Age
enter your response here
enter your response here
enter your response here
enter your response here
enter your response here
To complete the table, we need to determine Bea's age for each of the given ages of Ty. We know that Ty's age is 7 years younger than Bea's age.
Using the given ages for Ty, we can calculate Bea's age for each row:
Ty's Age | Bea's Age
-------------------
1 | 8
2 | 9
3 | 10
4 | 11
5 | 12
Therefore, the completed table is:
Ty's and Bea's Ages (years)
Ty's Age | Bea's Age
1 | 8
2 | 9
3 | 10
4 | 11
5 | 12
Using the given ages for Ty, we can calculate Bea's age for each row:
Ty's Age | Bea's Age
-------------------
1 | 8
2 | 9
3 | 10
4 | 11
5 | 12
Therefore, the completed table is:
Ty's and Bea's Ages (years)
Ty's Age | Bea's Age
1 | 8
2 | 9
3 | 10
4 | 11
5 | 12
Let x represent Ty's age and y represent Bea's age. Choose the correct equation below.
The correct equation is y = x + 7.
This equation represents the relationship where Ty's age (x) is 7 years younger than Bea's age (y). We add 7 to Ty's age (x) to get Bea's age (y).
This equation represents the relationship where Ty's age (x) is 7 years younger than Bea's age (y). We add 7 to Ty's age (x) to get Bea's age (y).
Use the table at the right. How long will the jet take to travel 3870 mi?
Passenger Jet Travel
Hours, h
1
2
3
4
Miles, m
430
860
1290
1720
Question content area bottom
Part 1
The jet will take enter your response here hours to travel 3870 mi.
Passenger Jet Travel
Hours, h
1
2
3
4
Miles, m
430
860
1290
1720
Question content area bottom
Part 1
The jet will take enter your response here hours to travel 3870 mi.
To determine how long the jet will take to travel 3870 miles, we can use the information from the table.
From the table, we can see that after 4 hours, the jet has traveled 1720 miles. Since the jet is traveling at a constant rate, we can calculate the hourly rate by dividing the total distance traveled by the total number of hours:
Hourly rate = 1720 miles / 4 hours = 430 miles per hour
To find how long it will take the jet to travel 3870 miles, we can divide the total distance by the hourly rate:
Time = 3870 miles / 430 miles per hour ≈ 9 hours
Therefore, the jet will take approximately 9 hours to travel 3870 miles.
From the table, we can see that after 4 hours, the jet has traveled 1720 miles. Since the jet is traveling at a constant rate, we can calculate the hourly rate by dividing the total distance traveled by the total number of hours:
Hourly rate = 1720 miles / 4 hours = 430 miles per hour
To find how long it will take the jet to travel 3870 miles, we can divide the total distance by the hourly rate:
Time = 3870 miles / 430 miles per hour ≈ 9 hours
Therefore, the jet will take approximately 9 hours to travel 3870 miles.