Answer:
$330
Step-by-step explanation:
If we let Q be the number of quarters and N be number of nickels, this is the formula we would use:
[1] 25Q + 5N = 635 (using cents instead of dollars)
We also know something about Q and N.
[2] Q + N = 51
So multiply both sides of the second equation by 5. The reason we do this is because we're going to need to cancel out one of the variables (either Q or N) to solve for the other one. If we multiply times 5, we'll have 5N in both equations.
5Q + 5N = 255
Now we have two equations, and the second one can be subtracted from the first.
25Q + 5N = 635
-(5Q + 5N) = -255
---------------------
20Q = 380
so
Q = 19
There are 19 quarters.
And since there are 51 coins in all, 51-19 = 32 nickels.
Answer:
x = 3
Step-by-step explanation:
Angle S and Angle T are consecutive interior angles. Therefore, we know that T + S = 180°.
First, we need to solve for T, and since angles S and T are consecutive interior angles, we know that T + S = 180°. If we reorganize the equation to include the things we know (S = 105°), then we get 180° - 105° = 75°. So T is 75°.
Now, we use T = 75° and the information given to us in the picture to set up an equation. 75 = 24x + 3. Now, we can find x by isolating it. Do this by:
1) Subtracting 3 from both sides to give you 72 = 24x. We do this to get rid of the 3 from the "x side", but we must also do it to the other to keep the equation true. This moves the 3 from the "x side" to the other since we're trying to isolate x.
2) Divide 24 by both sides to get 3 = x. We use the same logic as we did for 3, except this time we divide since that's the opposite of multiplying.
In conclusion, x = 3.
Answer:
1,001 ways for them to decide.
Step-by-step explanation:
The order in which they will visit the countries is not important, so we use the combinations formula to solve this question.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
In this question:
10 countries from a set of 14. So
1,001 ways for them to decide.
Answer: 
<u>Step-by-step explanation:</u>
When you subtract b/2a from both sides, you end up with the Quadratic Formula.
