Answer:
There would be 24 dimes and 76 quarters.
Step-by-step explanation:
In order to find this, start by defining the number of dimes by x and the number of quarters as y. Now we can create a system of equations. Make the first about the total number of coins.
x + y = 100
Make the second about the amount of money.
.10x + .25y = 21.40
Now we can solve using elimination by multiplying the second equation by -4 and adding through.
x + y = 100
-.40x - y = -85.60
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.60x = 14.4
x = 24
Now we can use the amount of dimes we have to find the number of quarters.
x + y = 100
24 + y = 100
y = 76
Answer:
A. The ordered pair (5, 3.5) represents 5 lbs. of strawberries cost $3.50.
B. The cost per pound of strawberries is shown at (1, 0.7).
C. The relationship shown in the graph is a direct variation because as the pounds of strawberries increase, the cost also increases.
Explanation:
A. The coordinate is in (x,y). The x-axis represents the pound of strawberries and the y-axis represents the cost of the strawberries.
B. The cost for one pound of strawberries can be calculated to find the exact value of y (cost) when x is 1. The graph shows 5 lbs. of strawberries cost $3.50 so divide $3.50 by 5 lbs. to find the cost per pound of strawberries. 3.5 ÷ 5 = 0.7. On the graph, the cost for one pound of strawberries is at (1, 0.7)
C. A direct variation in a graph is shown when both x and y increase or decrease together. In this case, as the pounds of strawberries increase, the cost of the strawberries also increases.
Step-by-step explanation:
hope this helps, happy learning!!!
- Solve 2m + n = 2 and 3m - 2n = 3 using substitution.
We can use the substitution method to solve linear equations of this form. Let's solve for m & n.
To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.
Choose one of the equations and solve it for m by isolating m on the left-hand side of the equal sign.
Subtract n from both sides of the equation.
Divide both sides by 2.
Multiply 1/2 times -n+2.
Substitute 
for m in the other equation, 3m-2n=3.
Multiply 3 times .
Add 
to -2n.
Subtract 3 from both sides of the equation.
Divide both sides of the equation by 
, which is the same as multiplying both sides by the reciprocal of the fraction.
Substitute 0 for n in 
. Because the resulting equation contains only one variable, you can solve for m directly.
The system is now solved.
<h3>
Answer: 2x^2 + 6x - 4</h3>
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Work Shown:
f(x) - g(x) = [ f(x) ] - [ g(x) ]
f(x) - g(x) = ( 3x^2+x-3) - ( x^2-5x+1 )
f(x) - g(x) = 3x^2+x-3 - x^2+5x-1
f(x) - g(x) = (3x^2-x^2) + (x+5x) + (-3-1)
f(x) - g(x) = 2x^2 + 6x - 4
