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Semenov [28]
4 years ago
15

Mrs. Hyde is the art teacher at Washington Elementary School. She is hanging her students' artwork on one of the walls in the sc

hool hallway. Use the clues to determine in which order the artwork is being hung, from left to right. The third graders are to the left of the fourth graders. The second graders are between the fifth graders and the third graders. The fifth graders' artwork is hung first.
Mathematics
1 answer:
Irina-Kira [14]4 years ago
8 0

1. The fifth graders' artwork is hung first.

2.  The second graders are between the fifth graders and the third graders. Since the fifth graders' artwork is hung first, then the second graders' artwork is hung second and the third graders' artwork is hung third.

3. The third graders are to the left of the fourth graders. This means that the fourth graders' artwork is hung fourth.

Answer: 5th draders' artwork, 2nd graders' artwork, 3rd graders' artwork, 4th graders' artwork (from the left to the right).

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Step-by-step explanation:

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3 years ago
The sum of squares of two consecutive positive even integers is 52 more than their product. Find these numbers.
natulia [17]

Answer:

The first set of consecutive even integers equals (8 , 6)

The second set is ( - 8 and - 6) which also works.

Step-by-step explanation:

Equation

(x)^2 + (x + 2)^2 = (x)(x + 2) + 52            Remove the brackets on both sides

Solution

x^2 + x^2 + 4x + 4 = x^2 + 2x + 52        Collect the like terms on the left

2x^2+ 4x+ 4 = x^2 + 2x + 52                  Subtract right side from left

2x^2 - x^2 + 4x - 2x + 4 - 52  =  0          Collect the like terms

x^2 + 2x - 48 = 0                                     Factor

(x + 8)(x - 6) = 0

Answer

Try the one you know works.

x - 6 = 0

x = 6

Therefore the two integers are 6 and 8

6^2 + 8^2 = 100

6*8 + 52  = 100

So 6 and 8 is one set of  consecutive even numbers that works.    

========================

What about the other set.

x + 8 = 0

x = - 8

x and x + 2

- 8  and -8 + 2 = - 8, - 6

(- 8 )^2 + (- 6)^2 = 100

(-8)(-6) + 52 = 100

Both sets of consecutive numbers work.


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