Mathematics, 20.01.2020 08:31 ibarral37102

Nicole has a collection of 29 nickels and dimes worth $2.30. how many of each does she have?

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You have two unknowns, so you need two equations to solve them. If n = the number of nickles, and d = the number of dimes, then we can say that n + d = 29. Furthermore, we can say that .05n + .1d = 2.30, i.e. the value of a nickel times the number of nickels plus the value of a dime times the number of dimes must equal the total value of the coins. We call this a system of equations. Both equations must work with correct answers. We can solve the system in more than one way. The easiest to understand is probably substitution. Given that n + d = 29, we can subtract d and say that n = 29 - d. Now we substitute (29 - d) into the other equation for n: .05(29-d) + .1d = 2.30 now distribute1.45 - .05d + .1d = 2.3 now combine like terms.05d = .85 now divided = 17 dimes now use this with the first equation n + 17 = 29
n = 12

Hope this helps! Good luck!

Answer from: Quest

Add them all together then u will get your answer
Which expression is equivalent to the one that is modeled? a) 3x + 4 b) 3(3x + 4) c) 3(x + 4) d)

Answer from: Quest

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

= 2×(-2)+(-8)×(6)+(-8)×(-5)

= -4-48+40

= -12

hence, v.w= -12

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