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zlopas [31]
2 years ago
7

Solve the system of equations - 6x + 5y = 0 and -5x + 5y = -5 by combining

Mathematics
1 answer:
Anna [14]2 years ago
7 0

9514 1404 393

Answer:

  (x, y) = (-5, -6)

Step-by-step explanation:

The coefficients of y are the same, so we can eliminate y by subtracting one equation from the other. Here, we choose to subtract the first from the second, so that the coefficient of x ends up positive.

  (-5x +5y) -(-6x +5y) = (-5) -(0)

  x = -5 . . . . . . simplify

  -6(-5) +5y = 0 . . . . . . substitute x into the first equation

  6 +y = 0 . . . . . . . . . .  divide by 5

  y = -6 . . . . . . subtract 6

The solution to the system of equations is (x, y) = (-5, -6).

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Area of fountain is 147.58 and area of path is 28.26
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Miguel an 2 of his friends share 7 rice cakes equally.
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7 ÷ 2 = 3.5 or 3 and 1/2
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Jordan invests $9,500 into an account that earns 3.25% annual interest. How much will
balandron [24]

The amount of money that Jordan will earn at the end of 10 years = $12,587.5

<h3>Calculation of compounded interests</h3>

The principal amount invested(P) = $9,500

The annual compounded daily interest rate(R) of the account = 3.25%

The time given (T) = 10 years

Simple interest (SI) = P×T × R/100

SI = 9,500×10×3.25/100

SI= 308750/100

SI= $3087.50

Therefore the total amount that would be in the account after 10 years = $9,500 + $3,087.50

= $12,587.5

Learn more about compound interest here:

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4 0
2 years ago
julia puts her stickers into arrays in an album. some of her stickers are animal stickers. there are a different number of stick
lina2011 [118]

The total number of stickers :

Page 1 : 28

Page 2 : 24

Page 3 : 72

Page 4 : 48

<h3>Further explanation </h3>

There are several properties in integer multiplication operations

  • 1. closed property

Multiplication between integers will produce integers too

  • 2. commutative property

a x b = b x a

  • 3. associative property

ax (bxc) = (axb) xc

  • 4. identity

ax1 = 1 x a = a

  • 5. distributive  property

* addition

ax (b + c) = axb + axc

* substraction

ax (b-c) = axb - axc

We can use facts to solve multiplication problems

for example :

6 x 7 = (5 x 7) + ( 1 x 7) = 42

we can break facts with 6 into  5s and 1s facts from multiplication above

julia puts her stickers into arrays in an album

From picture (attached) we can find the total number of stickers on each page with 1s,2s,3s and 5s facts

  • Page 1 : 4 x 7 = (2 x 7) + ( 2 x 7) = 14 + 14 = 28
  • Page 2 : 4 x 6 = (1 x 6) + (3 x 6) = 6 + 18 = 24
  • Page 3 : 8 x 9 = ( 3 x 9) + (5 x 9) = 27 + 45 = 72
  • Page 4 : 8 x 6 = (3 x 6) + (5 x 6) = 18 + 30 = 48

<h3>Learn more</h3>

the multiplicative identity property

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Keywords : stickers, arrays, album, page, Julia

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5 0
3 years ago
Sand falls onto a conical pile at the rate of 10 cubic feet per minute. The radius of the pile is always equal to one half it al
Andreas93 [3]

Answer:

Either one of these.

Step-by-step explanation:

volumepile=1/3 (PI r^2)h

but r=h/2, so

volume=1/12 PI h^3

dv/dt=10 ft^3/min

but dv/dt=1/12 PI 3h^2 dh/dt

solve for dh/dt

This assumes you mean by "altitude" the height. If you mean altitude as slant height, you have to adjust the fromula

_______________________________________________

given: r = h/2

V = (1/3)π r^2 h

= (1/3)π (h/2)^2 (h)

= (1/12) π h^3

dV/dt = (1/4)π h^2 dh/dt

for the given data ...

10 = (1/4)π(25)dh/dt

dh/dt = 10(4)/((25π) = 1.6/π feet/min

3 0
3 years ago
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