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2 years ago

Factor: 9x^2 + 15x.

Mathematics

1 answer:

slega [8]2 years ago

6 0

Answer:

3(3x^2 + 5)

Step-by-step explanation:

step 1: find out the greatest common factor (GCF) of the number 9 and 15

ex: 9x^2 + 15x (3 * 3x^2 + 3 * 5)

step 2: factor out the common term 3

ex: 3 * 3x^2 + 3 * 5 (3 * 3x^2 + 5)

step 3: simplify the equation

3 * 3x^2 + 5 [3(3x^2 + 5)]

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a. What is the name of the 3D shape?

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b. What is the formula for total surface area for this shape?

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$S=2A_{b}+P_{b}h$

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The surface area of the figure is 144 cm²

Step-by-step explanation:

a. What is the name of the 3D shape?

The 3D shape has two congruent and parallel faces (triangles) and the other faces are parallelograms, then the 3D shape is a prism

b. What is the formula for total surface area for this shape?

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where:

Area of the base of the prism: Ab

Perimeter of the base: Pb

Height of the prism: h

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The base of the prism is a triangle. Then to calculate the area of the base, we must use the formula to calculate the area of a triangle:

$A_{b}=\frac{bh}{2}\\ A_{b}=\frac{(4 cm)(3 cm)}{2}\\ A_{b}=\frac{12cm^{2} }{2}\\ A_{b}=6cm^{2}$

The perimeter of the base is the perimeter of the triangle, equal to the sum of the sides of the triangle:

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h: Height of the prism is the distance between the bases of the prism (the triangle), then h=11 cm

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