Answer: The jar contains 40 quarters and 42 nickels.
Step-by-step explanation:
The worth of a quarter is 25 cents. Converting to dollars, it becomes
25/100 = $0.25
The worth of a nickel is 5 cents. Converting to dollars, it becomes
5/100 = $0.05
Let x represent the number of quarters that they have in the jar.
Let y represent the number of nickels that they have in the jar.
Kevin and Randy Muise have a jar containing 82 coins, all of which are either quarters or nickels. This means that
x + y = 82
The total value of the coins in the jar is $12.10. This means that
0.25x + 0.05y = 12.1 - - - - - - - - - - - 1
Substituting x = 82 - y into equation 1, it becomes
0.25(82 - y) + 0.05y = 12.1
20.5 - 0.25y + 0.05y = 12.1
- 0.25y + 0.05y = 12.1 - 20.5
- 0.2y = - 8.4
y = - 8.4/ - 0.2
y = 42
x = 82 - y = 82 - 42
x = 40
Answer:
38.3 square inches
Step-by-step explanation:
The product of length and width gives the area of a rectangle:
area = (9.00 in)·(4.25 in) = 38.2500 in²
Each contributor has 3 significant digits, so your rounding rule requires the answer be rounded to 3 significant digits:
area ≈ 38.3 in²
To find the product of (4x-5y)^2,
we can rewrite the problem as:
(4x-5y)(4x-5y) (two times because it is squared)
Now, time to use that old method we learned in middle school:
FOIL. (Firsts, Outers, Inners, and Lasts)
FOIL can help us greatly in this scenario.
Let's start by multiplying the 'Firsts' together:
4x * 4x = <em>16x^2</em>
Now, lets to the 'Outers':
4x * -5y = <em>-20xy</em>
Next, we can multiply the 'Inners':
-5y * 4x = <em>-20xy</em>
Finally, let's do the 'Lasts':
-5y * -5y = <em>25y</em>^2
Now, we can take the products of these equations from FOIL and combine like terms. We have: 16x^2, -20xy, -20xy, and 25y^2.
-20xy and -20xy make -40xy.
The final equation (product of (4x-5y)^2) is:
16x^2 - 40xy + 25y^2
Hope I helped! If any of my math is wrong, please report and let me know!
Have a good one.
Answer:
Step-by-step explanation:
The first thing that we can do is look at the equation of the line and then worry about the inequality afterwards.
This line has a y-intercept of 4 and a slope of -1.
This means that the equation of this line would be 
Now that we have the equation of the line, we just need to determine which inequality sign to use.
As the shaded region is BELOW the line, we will use a less than (<) sign.
As the line is fully shaded, I can only assume that it is meant to include the line, which would mean that would be the equation for this inequality.
Y = -6.
-2(7)-2y=-2
-14-2y=-2
you need to move -14 to the other side by canceling out -14 with +14, and add +14 to -2, giving you -2y=12. -2/12=-6
