Answer:
The dimensions of the yard are W=20ft and L=40ft.
Step-by-step explanation:
Let be:
W: width of the yard.
L:length.
Now, we can write the equation of that relates length and width:
(Equation #1)
The area of the yard can be expressed as (using equation #1 into #2):
(Equation #2)
Since the Area of the yard is 
, then equation #2 turns into:
Now, we rearrange this equation:
We can divide the equation by 5 :
We need to find the solution for this quadratic. Let's find the factors of 160 that multiplied yields -160 and added yields -12. Let's choose -20 and 8, since 
and 
. The equation factorised looks like this:
Therefore the possible solutions are W=20 and W=-8. We discard W=-8 since width must be a positive number. To find the length, we substitute the value of W in equation #1:
Therefore, the dimensions of the yard are W=20ft and L=40ft.
1) 16 X 16= 256
2) 17 x 17 = 289
3) 18 x 18 = 324
4) 19 x 19 = 361
the answer is 2 because it's the largest number that is smaller than 300.
Answer:
The ratio is;
3/7 : 1
Step-by-step explanation:
Here, we want to express the given ratio in the form n:1 where n is a fully simplified fraction
Mathematically, we have this by dividing both numbers by 14
That would be ;
6/14 : 14/14
= 3/7 : 1
Answer:3
x
−
2
y
=
7
Explanation:
Write the standard form of the line that goes through
(
3
,
1
)
and is perpendicular to
y
=
−
2
3
x
+
4
.
The equation
y
=
−
2
3
x
+
4
is in slope intercept form
y
=
m
x
+
b
where
m
= slope and
b
= the
y
intercept.
The slope of this line is then
m
=
−
2
3
A perpendicular slope is the opposite sign reciprocal. So, we change the sign of
−
2
3
and switch the numerator and denominator.
Perpendicular slope
m
=
3
2
To find the equation of the new line, use the point slope equation
y
−
y
1
=
m
(
x
−
x
1
)
where
m
=
slope and
(
x
1
,
y
1
)
is a point.
The slope is
3
2
and the point is the given point
(
3
,
1
)
.
y
−
1
=
3
2
(
x
−
3
)
a
a
a
Distribute
y
−
1
=
3
2
x
−
9
2
Standard form is
a
x
+
b
y
=
c
where
a
,
b
and
c
are integers and
a
is positive.
a
a
2
(
y
−
1
=
3
2
x
−
9
2
)
a
a
a
Multiply the equation by
2
a
a
a
a
a
2
y
−
2
=
3
x
−
9
−
3
x
a
a
a
a
a
a
a
−
3
x
a
a
a
Subtract
3
x
from both sides
−
3
x
+
2
y
−
2
=
−
9
a
a
a
a
a
a
a
a
+
2
a
a
a
+
2
a
a
a Add 2 to both sides −
3
x
+
2
y
=
−
7
−
1
(
−
3
x
+
2
y
=
−
7
)
a
a
a
Multiply the equation by −
1
3
x
−
2
y
=
7
