Given: x + 2 < -5. Choose the solution set.


the answer is as following:

Fruit juice:6

Lemonade:18

the answer has to equal 1/3 so the answer is 6 for fruit juice and 18 for lemonade

Answer:

SA=158cm²

Step-by-step explanation:

To find surface area, you find the area for all the surfaces and add them together. Let's start with the red rectangular prism first.

The top has measurements of 5 and 2. The area of that is 10.

The bottom is the same so it's area is also 10 but we don't want to add it since it's not on the surface.

The side facing us has measurements of 4 and 2, the area is 8.

The side opposite to this is the same so it's area is also 8

Now the right face of this shape is 4 and 4 so 16.

The left face will have the same area. It'll also be 16.

The surface area of the red shape is 10+8+8+16+16= 58

Now the orange shape.

The side facing us is 5 and 3 so area=15

The side opposite to this will have the same area.= 15

The right face is also 5 and 3 so 5x3=15

The opposite face to this will also have an area of 15

Now the top face, it's 5 and 5 = 25. We have to subtract the area covered by the red shape. So 25 - 10 = 15

The bottom face's area will be 25.

The surface area of this shape will be : 15+15+15+15+25=100

Now add the areas of both shapes

58+100 = 158

SA=158cm²

Hope this helps :)

Given:

Given that the two sides of the triangle are x, 4.0 and 5.6

We need to determine the range of possible sizes for the side x.

Range of x:

The range of x can be determined using the triangle inequality theorem.

The triangle inequality theorem states that, "if any side of a triangle must be shorter than the other two sides added together".

Thus, applying the theorem, we have;

Also, the the triangle inequality theorem states that, "the third side must be also larger than the difference between the other two sides".

Thus, we have;

Thus, the range of possible values for x are

Final answer:

In accordance with the triangle inequality theorem, the range for the length of the third side (x) in a triangle with sides of 4.0 and 5.6 is greater than 1.6 but less than 9.6.

Explanation:

In the field of Mathematics, specifically geometry, to find the range of possible lengths of a side of a triangle, you need to understand the triangle inequality theorem. The triangle inequality theorem states that the length of a side of a triangle must be less than the sum of the lengths of the other two sides, but more than the absolute difference.

Given you have two sides, 4.0 and 5.6, the possible length for side x should be less than (4.0 + 5.6 = 9.6) and greater than the absolute difference (5.6 - 4.0 = 1.6). So, the range for side x should be 1.6 < x < 9.6.

Learn more about Triangle Inequality Theorem

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