If you notice the picture below
the composite figure is just a trapezoid sitting on top of a rectangle
and then, the rectangle has a triangular hole in it
so.. get the area of the trapezoid
then get the area of the rectangle, which is just a 12x14
and then get the area of the triangle, which surely you know is 1/2 bh
then, subtract the triangle's area from the rectangle's area
and whatever is left, namely the difference, add that to the area of the trapezoid, and that's the composite's area
namely the area of the trapezoid plus the rectangle's, minus the triangle's
A - 3b = 4
a = b -2
(b - 2) - 3b = 4
b - 2 - 3b = 4
-2b = 4 + 2
-2b = 6
b = 6/-2
b = -3
a = b - 2
a = -3 -2
a = -5
to check: a = -5 ; b = -3 ⇒ (-5,-3)
a - 3b = 4
-5 - 3(-3) = 4
-5 + 9 = 4
4 = 4
Answer:
The mean, because the data distribution is symmetrical.
Step-by-step explanation:
Without even knowing the mean or median this can be solved. The data isn't skewed to the left nor right, so it is symmetrical. The mean is the central value of numbers so it should represent the center well.
Answer:
13 and 77 degrees
Step-by-step explanation:
Complementary = 90 degrees
Set an angle to x
x+(x+64)=90
2x+64=90
2x=26
x=13
angle measures: 13, 77 degrees
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
