Distributive property is in the form of:<span>
a (b+c) = ab + bc</span>
<span>
In this case, we try writing 47 as:</span>
47 = 50-3 or 47 = 40+7
Therefore:<span>
11 x 47 = 11 x (50-3) = 11 x 50 - 11 x 3 = 550 - 33 =
517
or
<span>11 x 47 = 11 x (40+7) = 11 x 40 + 11 x 7 = 440 + 77 =
517</span></span>
Answer:
Step-by-step explanation:
Move 729 to the left side of the equation by subtracting it from both sides. x 3 − 729 = 0 Factor the left side of the equation. Rewrite 729 as 9
3
. x
3
−
9
3
=
0
. Since both terms are perfect cubes, factor using the difference of cubes formula, a
3
−
b
3
=
(
a
−
b
)
(
a
2+ab+b2). Where a
=x and b=9. (x−9)(x2+x⋅9+92)=0
. Simplify. Move 9 to the left of x
. (x−9)(x2+9x+92)=0. Raise 9 to the power of 2
. (x
−9
)(
x
2
+
9
x
+81
)=0
. Set x
−9 equal to 0 and solve for x. Set the factor equal to 0. x−
9=
0. Add 9 to both sides of the equation. x=9
. Set x2+
9
x
+
81 equal to 0 and solve for x
. Set the factor equal to 0
. x2+9x+81=0. Use the quadratic formula to find the solutions. −b±√b2−4(ac) 2a. Substitute the values a=1, b=9, and c=81 into the quadratic formula and solve for x. −9±√92−4⋅ (1⋅81
) 2⋅
1 Simplify. Simplify the numerator. Raise 9 to the power of 2. x=−9±√81−4⋅(1⋅81) 2⋅1. Multiply
81
by
1
.
x
=
−
9
±
√
81
−
4
⋅
81
2
⋅
1
Multiply
−
4
by
81
.
x
=
−
9
±
√
81
−
324
2
⋅
1
Subtract
324
from
81
.
x
=
−
9
±
√
−
243
2
⋅
1
Rewrite
−
243
as
−
1
(
243
)
.
x
=
−
9
±
√
−
1
⋅
243
2
⋅
1
Rewrite
√
−
1
(
243
)
as
√
−
1
⋅
√
243
.
x
=
−
9
±
√
−
1
⋅
√
243
2
⋅
1
Rewrite
√
−
1
as
i
.
x
=
−
9
±
i
⋅
√
243
2
⋅
1
Rewrite
243
as
9
2
⋅
3
.
Tap for fewer steps...
Factor
81
out of
243
.
x
=
−
9
±
i
⋅
√
81
(
3
)
2
⋅
1
Rewrite
81
as
9
2
.
x
=
−
9
±
i
⋅
√
9
2
⋅
3
2
⋅
1
Pull terms out from under the radical.
x
=
−
9
±
i
⋅
(
9
√
3
)
2
⋅
1
Move
9
to the left of
i
.
x
=
−
9
±
9
i
√
3
2
⋅
1
Multiply
2
by
1
.
x
=
−
9
±
9
i
√
3
2
Factor
−
1
out of
−
9
±
9
i
√
3
.
x
=
−
1
9
±
9
i
√
3
2
Multiply
−
1
by
−
1
.
x
=
1
−
9
±
9
i
√
3
2
Multiply
−
9
±
9
i
√
3
by
1
.
x
=
−
9
±
9
i
√
3
2
The final answer is the combination of both solutions.
x
=
−
9
−
9
i
√
3
2
,
−
9
+
9
i
√
3
2
The solution is the result of
x
−
9
=
0
and
x
2
+
9
x
+
81
=
0
.
x
=
9
,
−
9
−
9
i
√
3
2
,
−
9
+
i
√
3
2
Answer:
Step-by-step explanation:
Split it into two:
Y<3x
Y<5
X = 1
Y = 3
(1,3)
X = 2
Y = 6
(2, 6)
Plot the line up to y = 4.999999999999999999999 and not higher.
Answer:
Step-by-step explanation:
1a. 25/50 =x/100
25*100= 2500/50= 50
A= 50%
1b. 35/40 = x/100
35*100= 3500/40= 87.5
A=87.5%
2a. 15/20= x/100
20*5= 100; 15*5= 75
A=75%
2b. 25/70= x/100
25*100= 2500/70= 35.71
A=35.71
3a. 15/80= x/100
15*100= 1500/80=18.75
A=18.75%
3b. 30/60= x/100
30/60= 1/2;1/2=0.5;0.5= 50%
A=50%
4a. 70/80 =x/100
70*100=7000/80 =87.5
A=87.5
4b.30/60 = 50% ( same as question #3b)
Answer:
Time of murder = 10:39 am
Step-by-step explanation:
Let the equation of exponential function representing the final temperature of the body after time 't' is,
f(t) = 
Here, a = Initial temperature
n = Constant for the change in temperature
t = Duration
At 11:30 am temperature of the body was 91.8°F.
91.8 = 
--------(1)
Time to reach the body to the morgue = 12:30 pm
Duration to reach = 12:30 p.m. - 11:30 a.m.
= 1 hour
Therefore, equation will be,
84.4 = 
eⁿ = 
ln(eⁿ) = ln(0.9194)
n = -0.08403
From equation (1),
91.8 = 
![ln[(e)^{0.08403t}]=ln[\frac{98.6}{91.8}]](https://tex.z-dn.net/?f=ln%5B%28e%29%5E%7B0.08403t%7D%5D%3Dln%5B%5Cfrac%7B98.6%7D%7B91.8%7D%5D)
0.08403t = 0.07146
t = 0.85 hours
t ≈ 51 minutes
Therefore, murder was done 51 minutes before the detectives arrival.
Time of murder = 11:30 - 00:51
= 10:90 - 00:51
= 10:39 am
