1 answer:
Answer:
11 pennies
33 nickels
7 quarters
Step-by-step explanation:
Let x be the number of pennies, then the number of nickels is 3x.
There are 51 coins in total, so the number of quarters is 51 - x - 3x = 51 - 4x.
Amounts:
- in pennis - x cents;
- in nickels - 5(3x) = 15x cents;
- in quarters - 25(51 - 4x) cents.
Tota amount = $3.51 = 351 cents.
Hence,
11 pennies
33 nickels
7 quarters
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Answer:
Solution (1.8,1.61)
Step-by-step explanation:
Let us do it one by one.
Graph 1 :
y=-3x+7
Let us find some random coordinates to graph this equation
x = 0 ; y = -3(0)+7 = 7
(0,7)
x=1 ; y=-3(1) + 7 = -3+7=4
(1,4)
Plotting these coordinates on graph , and joining them will give us the line on the graph.
Graph 2 :
y = Sqrt ( 2x-1)
let us find random cordinates for some values of x
x=1, y = sqrt (2(1)-1) = sqrt (1) = 1
(1,1)
x=0.5 , y = sqrt (2(0.5)-1) = sqrt (0) = 0
(0.5,0)
Hence we have two coordinates , now we also see that , after comparing it from standard form of an square root function,
the square root function is upper half of parabola opening towards right and the point of origin is (0.5,0)
Let us find the solution , for that we need to put y=-3x+7 in y=sqrt (2x-1)
and we get
-3x+7=sqrt (2x-1)
squaring on both sides we get
9x^2+49-42x=2x-1
9x^2-44x+50=0
solving it with quadratic formula
x=[-b+sqrt(b^2-4ac)]/2a
we get x = 1.8 and replacing it in first equation we get y = 1.61
Hence the solution will be (1.8,1.61)
Answer:
Lavania observed 39 fruit flies after 6 days of observation
Step-by-step explanation:
Let x be the number of fruit flies on the first day of Lavania's study.
After 6 days she had nine more than five times as many fruit flies as when she began the study.
Five times as many fruit flies as when she began the study = 5x
Nine more than five times as many fruit flies as when she began the study=5x+9
The expression to find the population of fruit flies Lavania observed after 6 days is 5x+9
If she observes 20 fruit flies on the first day of the study, then x=6, then