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pochemuha
2 years ago
11

Which of the expressions below have exactly 3 terms? Select all that apply.

Mathematics
1 answer:
Fynjy0 [20]2 years ago
7 0

Answer:

C. 6x + 9 - 3x^2

Step-by-step explanation:

We have 4 expressions and are being asked which has 3 terms.

When it comes to terms, terms are numbers that are different, it could be separated through a variable, square root, symbol, e.t.c.

So when looking for an answer, we need 3 numbers with different variables or symbols, let's look

A. only has two, 10x and 8. Therefore it is wrong.

B. has 4 terms, 3x^3, 6x^2, 9x, and 12. Therefore it is wrong.

<u>C. is correct because it has 3 terms, 6</u><u>x</u><u>, </u><u>9</u><u>, and 3x</u><u>^2</u><u>.</u>

D. has 2 terms, 833 and 12x, though 16 is there, it is the same as 833, therefore not counting it as its own term.

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2.  18 cubic cm.

3. 27 cubic cm

5. 90 cubic m

Step-by-step explanation:

2. Triangular prism

So, we have a triangular prism with a width of 3 cm, a height of 1.5 cm and a length of 4.  We'll take the triangle shape as the base.

Like for any prism, the volume is the base multiplied by the height.

So, the area of the base is found with the regular formula: base x height:

so, 3 x 1.5 = 4.5 sq cm for the base.

Then we multiply the base by the length to get the volume: 4.5 x 4 = 18 cubic cm.

3. Trapezoidal prism

Again, first step is to calculate the area of the trapezoid shape, then multiply by its depth.

The area of a trapezoid is calculated with the formula:

A = h/2 * (a + b) where a and b represent the short and long sides respectively.

So, for our given trapezoid:

A = 1.5/2 * (2+4) = 0.75 * 6 = 4.5 sq cm.

Then we multiply the base area by the height to get the volume:

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5. Triangular prism 2

The best way to approach this one is to consider it's a triangle prism with a height of 3 cm, and use the triangle shape (with sides of 13 and 5) as the base.

But to calculate the area of that triangle we need to find out the missing length. Using Pythagore's theorem, we can easily find the length of the other side with the hypotenuse formula:

hypotenuse² = sideA² + sideB²

In our case, we have:

13² = x² + 5²

169 = x² + 25

x² = 144

x = 12

Now we can calculate the area of the triangle easily:

A = (b x h)/2 = (5 x 12)/2 = 30 sq m

Then multiply by the thickness of the prism....

V = 30 x 3 = 90 cubic m

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