GEOMETRY!!!!!!!!!!!!!

A drawer contains quarters and nickels. There are 200 total coins valuing $30.00. Think about a system of equations that can be

Margaret [11]

Answer:

100

Step-by-step explanation:

Let n and q represent the numbers of nickels and quarters, respectively. A suitable system of equations is ...

n + q = 200 . . . . . . there are 200 coins in the drawer

5n +25q = 3000 . . .their value is $30.00

For mixture problems like this, it is often a good idea to substitute for the variable representing the contributor of lower value. That is, we want to write an expression for n that we can use for substitution.

Using the first equation to solve for n, ...

n = 200 - q

Substituting this into the second equation gives ...

5(200 -q) +25q = 3000

1000 +20q = 3000 . . . . . . simplify

20q = 2000 . . . . . . . . . . . . subtract 1000

q = 100 . . . . . . . . . . . . . . . . divide by 20

n = 200 -q = 100 . . . . . . . . the number of nickels, as we want

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Comment on the solution

We solved for q, then had to do an extra step to find the value of n that the problem asks for. Had we written q = 200-n and used that for substitution, we would have ended with the equation -20n = -2000. This would give the answer for n directly (with no additional steps required).

Sometimes working with negative numbers is uncomfortable or results in errors, so we chose to use the solution method that would avoid negative numbers.

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Comment on the problem statement

We are told about coins in a drawer, and we are asked about coins in a jar. There is not enough information to answer the question asked. We have had to assume that both refer to the same quantity of coins—an assumption that is not supported by anything in the problem statement.

8 0

3 years ago

Read 2 more answers

-4x + 7 is greater than or equal to 83 (sorry, i couldn't get the sign for it)

bezimeni [28]

Answer:

-19

Step-by-step explanation:

you first substract 7 from 83 since its the inverse operation

then you divide it by -4 which give you -19

4 0

2 years ago

from the top of a tree the angle of depression of a rock on the ground is 49 degrees. If the tree is 18.5 m tall, how far is the

Rashid [163]

Answer:

Step-by-step explanation:

If you were to sit in the very top of said tree and look directly straight, your line of vision would be parallel to the ground. The angle of depression is in between your line of vision and the rock. When you look down at the rock, your line of vision to the rock is a transversal between the 2 parallel lines. With this being the case, the angle of depression is alternate interior with the angle made on the ground from the rock to the top of the tree. See the illustration I attached below.

We are looking for the distance on the ground between the tree and the rock, which we will call x. The side opposite the reference angle is the height of the tree and the side adjacent to the reference angle is x. Side opposite over side adjacent is the tangent ratio. Therefore,

$tan(49)=\frac{18.5}{x}$ and