Factor (Reverse Distribute): 5x−5y
1 answer:
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Answer:
<em>Cathy was born in 1980 and she was 18 years old in 1998</em>
Step-by-step explanation:
<u>Equations</u>
This is a special type of equations where all the unknowns must be integers and limited to a range [0,9] because they are the digits of a number.
Let's say Cathy was born in the year x formed by the ordered digits abcd. A number expressed by its digits can be calculated as
In 1998, Cathy's age was
And it must be equal to the sum of the four digits
Rearranging
We are sure a=1, b=9 because Cathy's age is limited to having been born in the same century and millennium. Thus
Operating
If now we try some values for c we notice there is only one possible valid combination, since c and d must be integers in the range [0,9]
c=8, d=0
Thus, Cathy was born in 1980 and she was 18 years old in 1998. Note that 1+9+8+0=18
Answer:
DE = 6 cm
Step-by-step explanation:
Let DE = x cm.
Since DE is parallel to AB therefore by the alternate interior angles theorem, m∠BAD = m∠ADE and m∠ABE = m∠DEB ............(1)
As AD is an angle bisector of ∠A, therefore m∠EAD = m∠DAB ; Since BE is an angle bisector of ∠B ⇒ m∠ABE = m∠EBD.
Therefore, from (1) We get , m∠EAD = m∠ADE and m∠EBD = m∠BED.
So, the triangles ADE and EDB are then isosceles with AE = ED and ED = DB.
So AE = DE = DB = x, and since the perimeter of ABDE is 30 cm, then
12 + x + x + x = 30
⇒ 12 + 3x = 30
⇒ x = 6
Hence, the length of DE is 6 cm.
The Correct option is D). y=1x+1 And y=2x+2
Step-by-step explanation:
The equation of a line is given as y=mx+c.
where m=slope of line and c=y intercept
The slope of line is given as m=
Solving for Redline:
From the given graph, redline passes through (-1,0) and (0,1)
The slope of Redline is m=
The slope of Redline is m=
The slope of Redline is m=(1)
And Y-intercept is 1
The equation of a Redline is given as y=1x+1
Solving for Blue-line:
From the given graph, Blue-line passes through (-1,0) and (0,2)
The slope of Blue-line is m=
The slope of Blue-line is m=
The slope of Blue-line is m=(2)
And Y-intercept is 2
The equation of a Blue-line is given as y=2x+2
The Correct option is D). y=1x+1 And y=2x+2