Solve for x to determine if the equation has one, none, or infinite solutions.
4x=3(x+5)−15(1 point)
Responses
The equation has no solution.
The equation has no solution.
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=0.
The equation has one solution: x equals 0 .
The equation has one solution: x=−10.
The equation has one solution: x equals negative 10 .
To solve the equation 4x = 3(x + 5) - 15, we can start by distributing the 3 on the right side:
4x = 3x + 15 - 15
Simplifying further, we have:
4x = 3x
Now, subtracting 3x from both sides, we get:
x = 0
Therefore, the equation has one solution: x = 0.
Solve for x to determine if the equation has one, none, or infinite solutions.
5(2x+2)−7x=3x+6(1 point)
Responses
The equation has no solution.
The equation has no solution.
The equation has one solution: x=6.
The equation has one solution: x equals 6 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=10.
To solve the equation 5(2x + 2) - 7x = 3x + 6, we can start by distributing the 5 on the left side:
10x + 10 - 7x = 3x + 6
Combining like terms, we get:
3x + 10 = 3x + 6
Now, subtracting 3x from both sides, we have:
10 = 6
This is a contradiction because 10 is not equal to 6.
Therefore, the equation has no solution.
Solve the inequality 6x+1<5x−8.(1 point)
x
a
To solve the inequality 6x + 1 < 5x - 8, we can start by isolating the x term on one side of the inequality.
Subtracting 5x from both sides, we get:
6x - 5x + 1 < -8
Simplifying further, we have:
x + 1 < -8
Now, subtracting 1 from both sides:
x < -8 - 1
x < -9
Therefore, the solution to the inequality is x < -9.
Shantel offers online tutorial services. She charges $25.00 an hour per student. Her budget tracker reflects a total of $3,200.00 monthly expenses. How many hours must Shantel work each month to earn a monthly profit of at least $600.00?(1 point)
at least
hours
To determine how many hours Shantel must work each month to earn a monthly profit of at least $600, we need to set up an equation.
Let's let x represent the number of hours Shantel works each month.
She charges $25.00 per hour per student, so her total earnings from tutoring each month can be calculated as 25x.
Her monthly expenses are $3,200.00.
To find the monthly profit, we subtract the expenses from the earnings:
Profit = Earnings - Expenses
Profit = 25x - 3200
We want the profit to be at least $600, so we can set up the following inequality:
25x - 3200 ≥ 600
Adding 3200 to both sides of the inequality, we get:
25x ≥ 3800
Dividing both sides by 25, we find:
x ≥ 152
Therefore, Shantel must work at least 152 hours each month to earn a monthly profit of at least $600.
La’Shondra solves the inequality 6+3x≤24. She begins by subtracting 6 from both sides of the inequality and then divides both sides of the equivalent inequality by a number. What is the number?(1 point)
To solve the inequality 6 + 3x ≤ 24, La'Shondra begins by subtracting 6 from both sides:
6 + 3x - 6 ≤ 24 - 6
Simplifying further:
3x ≤ 18
To isolate x on one side of the inequality, La'Shondra needs to divide both sides by a number. In this case, the number is 3.
Dividing both sides by 3, we get:
(3x) / 3 ≤ 18 / 3
Simplifying:
x ≤ 6
Therefore, the number that La'Shondra divides both sides of the inequality by is 3.
Solve the inequality Rx>10, where R is a number greater than 0.(1 point)
x
over R
To solve the inequality Rx > 10, where R is a number greater than 0, we need to isolate x.
We can do this by dividing both sides of the inequality by R:
(Rx) / R > 10 / R
Simplifying:
x > 10 / R
Since R is a number greater than 0, dividing 10 by R will result in a positive number. However, without knowing the specific value of R, we cannot simplify the expression further.
Therefore, the solution to the inequality is x > (10 / R), where R is a number greater than 0.
Solve the inequality Ay+3<12, where A is a number greater than 0.(1 point)
y
over A
To solve the inequality Ay + 3 < 12, where A is a number greater than 0, we can begin by isolating the variable y.
First, subtract 3 from both sides:
Ay + 3 - 3 < 12 - 3
This simplifies to:
Ay < 9
To isolate y, we need to divide both sides by A:
(Ay) / A < 9 / A
Simplifying further:
y < 9/A
Since A is a number greater than 0, dividing 9 by A will result in a positive number. However, without knowing the specific value of A, we cannot simplify the expression further.
Therefore, the solution to the inequality is y < 9/A, where A is a number greater than 0.
Jorelle is planning a 5-day vacation. The trip will cost him $1,300.00 for airfare, food, and itineraries. He plans to stay in a hotel room for $80.00 per night. He only has $950.00 in savings, but he earns $25.00 per hour from his online tutoring services. Create a linear inequality in one variable that would best translate the problem. Determine the minimum number of hours Jorelle must tutor so he can have enough money for the trip.(1 point)
Let's say the number of hours Jorelle needs to tutor is represented by the variable h.
Given that Jorelle earns $25.00 per hour from his online tutoring services, his earnings from tutoring can be expressed as 25h.
The total cost of the trip, including airfare, food, itineraries, and hotel expenses, is $1300.00.
Jorelle only has $950.00 in savings.
To determine the minimum number of hours Jorelle must tutor so he can have enough money for the trip, we need to set up an inequality.
His earnings from tutoring must be greater than or equal to the total trip cost minus his savings:
25h ≥ 1300 - 950
Simplifying further:
25h ≥ 350
Therefore, the linear inequality that best translates the problem is 25h ≥ 350, where h represents the number of hours Jorelle needs to tutor.
Jorelle is planning a 5-day vacation. The trip will cost him $1,300.00 for airfare, food, and itineraries. He plans to stay in a hotel room for $80.00 per night. He only has $950.00 in savings, but he earns $25.00 per hour from his online tutoring services. Create a linear inequality in one variable that would best translate the problem. Determine the minimum number of hours Jorelle must tutor so he can have enough money for the trip.(1 point)
Responses
950+25x≤1,700; at most 30 hours
950 plus 25 x less-than-or-equal-to 1,700 ; at most 30 hours
950+25x≥1,300; at least 14 hours
950 plus 25 x greater-than-or-equal-to 1,300 ; at least 14 hours
950+25x≥1,700; at least 30 hours
950 plus 25 x greater-than-or-equal-to 1,700 ; at least 30 hours
950+25x≤1,300; at most 14 hours
To determine the minimum number of hours Jorelle must tutor so he can have enough money for the trip, we need to create a linear inequality that represents the problem.
Jorelle's expenses for the trip, including airfare, food, and itineraries, total $1,300.00.
Jorelle has $950.00 in savings.
Jorelle earns $25.00 per hour from his tutoring services.
Jorelle plans to stay in a hotel room for 5 nights, costing $80.00 per night.
The expenses for the hotel room for 5 nights can be calculated as 5 * $80.00 = $400.00.
To have enough money for the trip, the total expenses (including the hotel room) should be less than or equal to the sum of Jorelle's savings and his earnings from tutoring:
400 + 25x ≤ 950 + 25x ≤ 1300
Simplifying further:
950 + 25x ≤ 1300
Therefore, the linear inequality that best translates the problem is 950 + 25x ≤ 1300, where x represents the number of hours Jorelle must tutor.
To determine the minimum number of hours Jorelle must tutor, we need to solve the inequality:
950 + 25x ≤ 1300
Subtracting 950 from both sides:
25x ≤ 350
Dividing both sides by 25:
x ≤ 14
So, the minimum number of hours Jorelle must tutor is at most 14 hours.
Mary Ann solves the inequality −3x≥12. Justify the steps Mary Ann takes to find the solution set.(1 point)
Responses
Mary Ann adds −3 to both sides of the inequality and changes the inequality symbol to ≤ to get x≤9.
Mary Ann adds negative 3 to both sides of the inequality and changes the inequality symbol to less-than-or-equal-to to get x less-than-or-equal-to 9 .
Mary Ann adds −3 to both sides of the inequality to get x≥9.
Mary Ann adds negative 3 to both sides of the inequality to get x greater-than-or-equal-to 9 .
Mary Ann divides both sides of the inequality by −3 and changes the inequality symbol to ≤ to get x≤−4.
Mary Ann divides both sides of the inequality by negative 3 and changes the inequality symbol to less-than-or-equal-to to get x less-than-or-equal-to negative 4 .
Mary Ann divides both sides of the inequality by −3 to get x≥−4.
To solve the inequality -3x ≥ 12, Mary Ann wants to isolate the variable x.
First, she can start by dividing both sides of the inequality by -3. However, since she is dividing by a negative number, the inequality symbol needs to be flipped. Dividing both sides by -3 gives:
(-3x) / -3 ≤ 12 / -3
Simplifying, we get:
x ≤ -4
Therefore, the steps Mary Ann takes are: Mary Ann divides both sides of the inequality by -3 and changes the inequality symbol to ≤ to get x ≤ -4.
Kirk solves the inequality 5<12y−7. Which statement explains the steps he uses to find the solution set of the inequality?(1 point)
Responses
Kirk adds 7 to both sides of the inequality and then multiplies both sides of the equivalent inequality by 12 to get 144<y.
Kirk adds 7 to both sides of the inequality and then multiplies both sides of the equivalent inequality by 12 to get 144 less than y .
Kirk adds 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get 1<y.
Kirk adds 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get 1 less than y .
Kirk adds −7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get (−16)<y.
Kirk adds negative 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get left parenthesis negative Start Fraction 1 over 6 End Fraction right parenthesis less than y .
Kirk adds 7 to both sides of the inequality, then divides both sides of the equivalent inequality by 12 and reverses the inequality symbol to get 1>y.
To solve the inequality 5 < 12y - 7, Kirk wants to find the solution set. Here are the steps he uses:
1. Kirk adds 7 to both sides of the inequality:
5 + 7 < 12y - 7 + 7
12 < 12y
2. Kirk divides both sides of the inequality by 12:
12 / 12 < 12y / 12
1 < y
Therefore, the statement that explains Kirk's steps to find the solution set of the inequality is: Kirk adds 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get 1 < y.
Which of the following shows how to solve the linear inequality with a letter coefficient Hy<7, where H is a number greater than 0?(1 point)
Responses
y<7H
y less than 7 upper H
y<7H
y less than Start Fraction 7 over upper H End Fraction
Hy<7
upper H y less than 7
y<7
y less than 7
To solve the linear inequality Hy < 7, where H is a number greater than 0, we can divide both sides of the inequality by H.
(Hy) / H < 7 / H
Simplifying further, we have:
y < 7/H
Therefore, the solution to the inequality is y < 7/H.
Which term in the following inequality is a letter coefficient? Bx+72<12(1 point)
Responses
B
upper B
x
x
Bx
upper B x
72
The term in the inequality that is a letter coefficient is Bx.
How did rivers affect the locations of early settlements in Georgia? (1 point)
Responses
People often settled near shoals where it was easier to cross the river
People often settled near shoals where it was easier to cross the river
People often settled away from rivers and other bodies of water
People often settled away from rivers and other bodies of water
People typically settled near rivers where the rapids were high
People typically settled near rivers where the rapids were high
People usually settled in areas where riverbeds were even and shallow
People often settled near rivers where the rapids were high.
Choose the correct answer from the drop down menu. (1 point)
The
acts as the boundary between South Carolina and Georgia
Savannah River
True or false: Rivers determined Georgia’s original boundaries and affected the location of its settlements. (1 point)
Responses
True
Which of Georgia’s Rivers flows into the Gulf of Mexico and forms the border between Georgia and Alabama? (1 point)
Responses
Savannah River
Savannah River
Chattahoochee River
Chattahoochee River
Flint River
Flint River
Ocmulgee River
Chattahoochee River
Why do many Georgia rivers begin in the Blue Ridge region? Select TWO.(2 points)
Responses
The Blue Ridge region receives the most rainfall
The Blue Ridge region receives the most rainfall
The hot climate in the Blue Ridge region
The hot climate in the Blue Ridge region
The Blue Ridge region has the highest elevation
The Blue Ridge region has the highest elevation
The Blue Ridge region is mostly flat so it's easier for rivers to flow