Answer:
(0,5)
Step-by-step explanation:
The numbers are: 36 and 11 .
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Explanation:
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Let us represent the TWO (2) numbers with the variables;
"x" and "y" .
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x + y = 47 .
y − x = 25.
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Since: " y − x = 25 " ;
Solve for "y" in terms of "x" ;
y − x = 25 ;
Add "x" to each side of the equation:
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y − x + x = 25 + x ;
to get:
y = 25 + x .
Now, since:
x + y = 47 ;
Plug in "(25 + x)" as a substitution for "y"; to solve for "x" :
x + (25 + x) = 47 ;
x + 25 + x + 47 ;
2x + 25 = 47 ;
Subtract "25" from each side of the equation:
2x + 25 − 25 = 47 − 25 ;
2x = 22 ;
Divide EACH SIDE of the equation by "2" ;
to isolate "x" on one side of the equation; and to solve for "x" ;
2x / 2 = 22 / 2 ;
x = 11 ;
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x + y = 47<span> ;
</span>Plug in "11" for "x" into the equation ; to solve for "y" ;
11 + y = 47 ;
Subtract "11" from EACH SIDE of the equation;
to isolate "y" on one side of the equation; and to solve for "y" ;
11 + y − 11 = 47 − 11 ;
y = 36 .
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So: x = 11 , y = 36 ;
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Let us check our work:
y − x = 25 ;
36 − 11 =? 25 ? Yes!
x + y = 47 ;
36 + 11 =? 47 ? Yes!
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The numbers are: 36 and 11 .
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First factorise the top = -(w+6)
The first factorise the bottom: (w^2 + 4w -12) = (w+6) (w-2)
Therefore the two (w+6) cancels out and you are left with -1 / w-2
Answer:
C. 17, 12, 7
Step-by-step explanation:
In a triangle, the sum of the lengths of any two sides must be greater then the length of the third side. If you can show any two segments, the sum of whose lengths is less than the length of the third segment, that cannot form a triangle.
In choices A, B, and D, there is at least one sum of the lengths of two segments that is less then the length of the third segment. That shows that choices A, B, and D cannot form triangles.
A. 8 + 7 = 15 < 16 No
B. 9 + 7 = 16 = 16 No
D. 11 + 5 = 16 < 17 No
C.
17 + 12 = 29 > 7
12 + 7 = 19 > 17
17 + 7 = 24 > 12
Yes
<h3>
Answer: x = (
y-2)^2 +
5</h3>
In other words, y-2 goes in the first box and 5 goes in the second box.
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Work Shown:
y^2 - 4y - x + 9 = 0
y^2 - 4y + 9 = x
x = y^2 - 4y + 9
x = y^2 - 4y + 4 + 5 .... rewrite 9 as 4+5
x = (y^2-4y+4) + 5
x = (y-2)^2 + 5 .... apply the perfect square factoring rule
So we'll have y-2 go in the first box and 5 goes in the second box
note: One version of the perfect square factoring rule says (a-b)^2 = a^2-2ab+b^2.
