First write out all the two digit square numbers
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
Next divide all of them by 7
16/7 = 2 2/7 or 2 and 2 remainders
25/7 = 3 4/7 or 3 and 4 remainders
36/7 = 5 1/7 or 5 and 1 remainder
49/7 = 7
64/7 = 9 1/7 or 9 and 1 remainder
81/7 = 11 4/7 or 11 and 4 remainders
This tells us that the only possible remainders for a two digit square number divided by 7 are 1, 2 and 4
If Doris got 6 and Horace got 3, they must have made a mistake.
Harris has 60-y dollars left. Hope this helps!
Answer:
32 and 35
Step-by-step explanation:
I am going to use x for the smaller number and y for the larger one.
The sum of both these numbers is 67, so the equation should be:x+y=67
Since the smaller number is three less than the larger number, that means 3 has to be added to the smaller number to make it equal in size to the larger number.
x+3=y
To solve the equation, simply plug in
x+3 for the y variable in the first equation.x+x+3=67→ Rewrite the first equation2x=64→
Subtract 3 from each side, combine like termsx=32→
Divide each side by 2The smaller number is 32, so we plug that in to the second equation to find the larger number.
32+3=yy=35
The two numbers are 32 and 35
Answer:
25y^2
Step-by-step explanation:
The area of a square is A=s*s where s is the side length. Here s=5y. So the area is A = s*s = 5y*5y = 25y^2
Step-by-step explanation:
To start, every term has an
x
in common, so we can factor that out. Doing this, we get
x
(
x
2
+
x
−
42
)
=
0
What I have in blue can be factored by a thought experiment. What two numbers have a sum of
1
and a product of
−
42
?
After some trial and error, we arrive at
−
6
and
7
. Thus, this business can be factored as
x
(
x
−
6
)
(
x
+
7
)
=
0
We can leverage the zero product property here, setting all three terms equal to zero. As our zeroes, we get
x
=
0
,
x
=
6
, and
x
=
−
7
