The legs of an isosceles triangle are congruent; they have the same length, so if one leg measures 2 m, the other leg also measures 2 m.
2m + 2m + b = 7.5 m
b + 4 m = 7.5 m
b = 3.5 m
The length of the base is 3.5 m.
Okay. An obtuse triangle is any triangle that has 1 angle that measures more than 90°. As we can see, angle QRS measures 76° and angle PRQ measures 104°. 104 > 90. Triangle PQR is a closed figure, and a triangle measures 180° total. There can only be 1 obtuse angle in any triangle. PRQ is an obtuse angle. Therefore, triangle PQR is an obtuse triangle.
Answer:
18.2 cubic meters.
Step-by-step explanation:
From the measurements they give us, we assume that the shed has the shape of a rectangular prism, however, to calculate the amount of storage, we must calculate the volume.
The volume would be:
V = height * width * length
According to the statement height = 2, width = 2 and length = 3.25
V = 2 * 2 * 3.25
V = 13
That is, the volume of the shed is 13 cubic meters, but then they mention that the roof line to the peak is 0.8 meters high, which means that the volume can increase, the new volume would be changing the height = 2 + 0.8 = 2.8, the other values remain the same:
V = 2.8 * 2 * 3.25
V = 18.2
That is to say that when adding that part, the volume that is to say total amount of storage is 18.2 cubic meters.
Answer: The equation of an ellipse:
(
x
−
h
)
2
a
2
+
(
y
−
k
)
2
b
2
=
1
;
a
>
b
Has vertices at
(
h
±
a
,
k
)
Has foci at
(
h
±
√
a
2
−
b
2
,
k
)
Use the vertices to write 3 equations:
k
=
4
[1]
h
−
a
=
−
6
[2]
h
+
a
=
10
[3]
Use equations [2] and [3] to solve for h and a:
2
h
=
4
h
=
2
a
=
8
Use the focus to write another equation:
8
=
h
+
√
a
2
−
b
2
Substitute values for h and a:
8
=
2
+
√
8
2
−
b
2
6
=
√
64
−
b
2
36
=
64
−
b
2
b
2
=
64
−
36
b
2
=
28
b
=
√
28
Substitute the values into the standard form:
(
x
−
2
)
2
8
2
+
(
y
−
4
)
2
(
√
28
)
2
=
1
Forks :
20 x 12 = 240
Spoons:
10 x 12 = 120
Knives :
5 x 10 = 50
Paper plates :
175
Total :
175 + 50 + 120 + 240 = 585
585 picnic items were donated
