A student claims that the gravitational force between two objects depends upon the mass of the objects and the distance between them. Which argument best supports the student's claim?
a- If the distance between two objects increases, the gravitational force between the objects will decrease.
b- If the distance between two objects increases, the gravitational force between the objects will increase.
c- If the distance between two objects decreases, the gravitational force between the objects will disappear.
d- If the distance between two objects decreases, the gravitational force between the objects will not change
a- If the distance between two objects increases, the gravitational force between the objects will decrease.
The sum of two numbers is 22. Three times one number increased by five is 35. What are the two numbers?
Responses
10
12
6
16
11
7
15
The two numbers are 10 and 12.
Explanation:
Let's call the two numbers x and y.
From the first sentence, we know that:
x + y = 22
From the second sentence, we know that:
3x + 5 = 35
Simplifying this equation, we have:
3x = 30
x = 10
Now that we know x is 10, we can substitute it into the first equation:
10 + y = 22
y = 12
So the two numbers are 10 and 12.
At Barnes and Noble, Sylvia purchased a journal and a cookbook that cost a total of $54, not including tax. If the price of the journal, j, is $3 more than 2 times the price of the cookbook, c, which system of linear equations could be used to determine the price of each item?
1. The equation for the total cost
2. The equation for the price of the journal
3. You can choose any method to solve this system: graphing, substitution, or elimination. Choose a method and solve for the price of the journal and the cookbook.
The price of the journal is
The price of the cookbook is
1. The equation for the total cost:
j + c = 54
2. The equation for the price of the journal:
j = 2c + 3
To solve, we can use substitution. Substitute the second equation into the first equation for j:
(2c + 3) + c = 54
Simplify and solve for c:
3c + 3 = 54
3c = 51
c = 17
Now that we know the price of the cookbook is $17, we can use the second equation to find the price of the journal:
j = 2(17) + 3
j = 37
So the price of the journal is $37 and the price of the cookbook is $17.
Samuel currently has 18 rocks in his collection and gains 4 each week. Lewis currently has 30 rocks in his collection and gains 3 each week.
Set up a system of equations to show how many rocks each has in their collection.
Samuel has y=Response areax+Response area.
Lewis has Response areax+Response area.
After how many weeks will Samuel and Lewis have the same number of rocks in their collections? Response area weeks
How many rocks will Samuel and Lewis have when the amount of rocks in their collection is equal? They will each have Response area rocks in their collection.
Samuel has y = 4x + 18 rocks in his collection after x weeks.
Lewis has y = 3x + 30 rocks in his collection after x weeks.
To find when they will have the same number of rocks, we need to set the two equations equal to each other and solve for x:
4x + 18 = 3x + 30
x = 12
So it will take 12 weeks for Samuel and Lewis to have the same number of rocks in their collections.
To find how many rocks they will each have, we can substitute x = 12 into either equation:
Samuel: y = 4(12) + 18 = 66 rocks
Lewis: y = 3(12) + 30 = 66 rocks
So they will each have 66 rocks in their collection when the amount of rocks is equal.
Which graph represents the solution for the equation -5/2x -1 = 4x +2
To solve for x:
-5/2x - 1 = 4x + 2
-5/2x - 4x = 2 + 1
-13/2x = 3
x = -6/13
So the solution is a single point, (-6/13, 0).
The correct graph would be a point, not a line.
Billy is 6 years younger than Amy. The sum of their ages is 22. How old will each of them be in 8 years?
Amy will be Response area and Billy will be Response area.