What is the range of possible sizes for side x? _ < x < _

2.8 < x < 5.8

Step-by-step explanation:

We must apply the Triangle Inequality Theorem which states that for any triangle with sides a, b, and c:

a + b > c

b + c > a

c + a > b

Here, let's arbitrarily denote a as 4.1, b as 1.3, and c as x. So, let's plug these values into the 3 inequalities listed above:

a + b > c  ⇒  4.1 + 1.3 > x  ⇒  5.8 > x

b + c > a  ⇒  1.3 + x > 4.1  ⇒  x > 2.8

c + a > b  ⇒  x + 4.1 > 1.3  ⇒  x > -2.8

Look at the last two: clearly if x is greater than 2.8 (from the second one), then it will definitely be greater than -2.8 (from the third), so we can just disregard the last inequality.

Thus, the range of possible sizes for x are:

2.8 < x < 5.8

~ an aesthetics lover

There are two cases: either x is the largest value or 4.1 is the largest value.

First case: x is largest so that means x < 4.1 + 1.3 which becomes x < 5.8

Second case: 4.1 is largest so that means x + 1.3 > 4.1 which becomes x > 2.8

Answer is 2.8 < x < 5.8.

rectangle: 9 1/8 x 4 1/9 = 37 37/72in

parallelogram: b times h= 10.3 x 6.2 = 63.86

trapezoid: a+b/2 times h= 42.5

volume of prism: l times w times h= 36

d (5 x (-20)) * (100 x (0.7))

step-by-step explanation:

5÷1/100 * -.7 *-20

copy dot flip

5*100 * -.7 *-20

rearrange

5*-20   * 100 *-.7

-100   *-70

7000