x
4
+
50
x
2
+
625Rewrite
625
as
25
2
.
u
2
+
50
u
+
25
2
Check the middle term by multiplying
2
a
b
and compare this result with the middle term in the original expression.
2
a
b
=
2
⋅
u
⋅
25
Simplify.
2
a
b
=
50
u
Factor using the perfect square trinomial rule
a
2
+
2
a
b
+
b
2
=
(
a
+
b
)
2
, where
a
=
u
and
b
=
25
.
(
u
+
25
)
2
Replace all occurrences of
u
with
x
2
.
(
x
2
+
25
)
2
Answer:
[-4, 2½]
Step-by-step explanation:
The quickest way to do this is to calculate how far apart each corresponding coordinate is, then take HALF of that range:
From -4 to -4 → 0
From 3 to -8 → 11
-3 + 5½ = 2½ [y-coordinate] → [-4, 2½]
** Just in case you were wondering why I did not calculate zero, zero is neutral, so it stays zero.
I am joyous to assist you anytime.
Answer:
$0.75 per lemon
Step-by-step explanation:
Express the ratio on the left as a decimal:
$3/(4 lemons) = $?/lemon
0.75 $/lemon = ? $/lemon
0.75 = ?
The unit rate is $0.75 per lemon.
This is a linear equation in x.
x + 6 = 2x-7
Adding -2x to both sides we obtain,
x +6 - 2x = -7
Now let's again add -6 to both sides of the equation, This implies that:
x-2x = -7-6
Let us simplify further to obtain,
-x = - 13
Let's multiply through by -1 to obtain
x = 13
CHECK
13 +6 = 2(13) - 7
13 + 6 = 26 -7
19 = 17
10*3=30. Next, you add 30+3 which gives you 33. Then divide 33/10 which will give you 3.3. Move the decimal place to the left.