<u>Given</u>:
Given that ABC is a right triangle.
The length of AB is 7 units.
The measure of ∠A is 65°
We need to determine the length of AC
<u>Length of AC:</u>
The length of AC can be determined using the trigonometric ratio.
Thus, we have;
Where the value of 
is 65° and the side adjacent to the angle is AC and the side hypotenuse to the angle is AB.
Substituting the values, we have;
Substituting AB = 7, we have;
Multiplying both sides by 7, we get;
Rounding off to the nearest hundredth, we get;
Thus, the length of AC is 2.96 units.
This is a hexagonal prism: Volume = Area of Base (hexagon) x Height:
There are 6 equal equilateral triangles in a hexagone.
The apothem (or altitude of each triangle) = side x (√3)/2 =12(√3)/2 = 6√3
Area of ONE equilateral triangle = (side x altitude)/2:
Area of ONE equilateral triangle = (12 x 6√3)/2 = 36√3 ft²
Area of the SIX equilateral triangles = 36√3 x 6 = 216√3 ft²
VOLUME = BASE X HEIGHT = 216√3 x 15 = 3240√3 ft³
OR VOLUME = 5612 ft³
Answer:
D.
Step-by-step explanation:
All other equations have x or y to the power of one so they are linear. D. has x or y to the power of two, so it's not linear. Quadratics and any variable to the power of 2 and above is not linear (numbers on their own are also always linear, so ignore any powers on them)
Given: Yu, Nailah, and Elena each bought between 7 and 9 yards of ribbon Yu bought 3 pieces of ribbon. Nailah bought 5 pieces of ribbon. Elena bought 6 pieces of ribbon.
To find: Who can buy which ribbon
Solution:
Ribbon Sizes
1 2/3 = 5/3 yard
4/5 yard
3 1/2 = 7/2 Yard
Yu, Nailah, and Elena each bought between 7 and 9 yards of ribbon
Yu bought 3 pieces of ribbon
=> 3 * 5/3 = 5
3 * 4/5 = 2.4
3 * 7/2 = 10.5
Nailah bought 5 pieces of ribbon
=> 5 * 5/3 = 8.33
5 * 4/5 = 4
5 * 7 /2 = 17.5
Elena bought 6 pieces of ribbon
=> 6 * 5/3 = 10
6 * 4/5 = 4.8
6 * 7 /2 = 21
Only value between 7 & 9 is 5 * 5/3 = 8.33
hence Nailah only can buy 1 2/3 = 5/3 yard ribbon
or there is some mistake in the data
