Answer: 294√3
Explanation:
1) The described hexagon has these featrues:
a) 6 congruent equilateral triangles whose side lengths measure 14
b) height of each triangle = apotema = a
c) the area of each triangle is base × a / 2 = 14 × a / 2 = 7a
2) a is one leg of a right triangle whose other leg is 14 / 2 = 7, and the hypotenuse is 14.
3) Then you can use Pythagorean theorem fo find a:
14² = 7² + a² ⇒ a² = 14² - 7² = 147 ⇒ a = √ 147 = 7√3
4) Therefore, the area of one triangle is: 14 × 7√3 / 2 = 49√3
5) And the area of the hexagon is 6 times that: 6 × 49√3 = 294√3
Answer:
y = 0.25x + 1.5
Step-by-step explanation:
its starts at 1.5 on the y-axis
goes up 0.25 units
Answer:
RS = 4.8
OT = 3.6
From the Pythagorean Theorem we know:
OR^2 = ST^2 + OT^2
OR^2 = 4.8^2 + 3.6^2
OR ^2 = 23.04 + 12.96
OR^2 = 36
OR = 6
Step-by-step explanation:
1.
An expression of the form

is called a "compound fraction"
Compound fractions can be written as simple fractions by multiplying c to a, and then adding the product to c as follows:

for example,

can be written as:

2.
when we subtract or add a fraction

from an integer k,
we first write k as a fraction with denominator n. We can do this as follows:

for example, if we want to subtract

from 8,
we first write 8 as a fraction with denominator 2:

3.
Thus,

4.
The simple fraction 7/2 is not an option, so we write it as a compound fraction as follows:

(So write 7 as the sum of the largest multiple of 2, smaller than 7 + what is left. In our case these numbers are 6 and 1, then proceed as shown)
5. Answer: D