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2 years ago

How do you factor this expression: x^3 + 9x^2 + 27x + 27. Thanks! :)

Mathematics

1 answer:

soldier1979 [14.2K]2 years ago

5 0

Answer:

(x + 3)³

Step-by-step explanation:

Use rational root test to check for possible rational roots.

Factors of 27 are 1, 3, 9, and 27.

Factors of 1 are 1.

Possible rational roots are:

±1/1, ±3/1, ±9/1, ±27/1

Checking each one, we find that -3 is a root. So x + 3 is a factor.

Knowing that, we can use grouping to factor.

x³ + 9x² + 27x + 27

x³ + 9x² + 18x + 9x + 27

x (x² + 9x + 18) + 9 (x + 3)

x (x + 6) (x + 3) + 9 (x + 3)

(x + 3) (x (x + 6) + 9)

(x + 3) (x² + 6x + 9)

(x + 3) (x + 3)²

(x + 3)³

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Vince bought 6 boxes of worms to use as bait while fishing with his friends. If each person uses exactly 3/8 of a box of worms,

tia_tia [17]

We are given the following information:

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<em>each person uses 3/8 a box</em>

<em>there are 6 boxes</em>

Because each box is $\frac{8}{8}$ , and there are 6 boxes, we know that 1 person is $\frac{3}{8*6}$ , or $\frac{3}{48}$ .

In order to find how many people can use the 6 boxes, we can divide it by 3 (for each use):

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<em>Hope this helps! :)</em>

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3 years ago

The perimeter of the original rectangle is 16 feet. A small rectangle has a length of 6. 2 feet and width of 1. 8 feet. A larger

ankoles [38]

The perimeter of the enlarged rectangle is 32 ft and the width of the larger rectangle is 3.6 ft.

<h3>What is perimeter of plane?</h3>

The measure of the boundary of a plane or shape is called its perimeter. The perimeter of a plane or shape is the sum of all the sides.

A small rectangle has a length of 6.2 feet and width of 1.8 feet. The parameter of this triangle is,

$P_s=6.2+1.8\\P_s=8\rm\; ft$

The small rectangle has a length of 6.2 and the larger rectangle has a length of 12.4 feet. Thus the scale factor of enlargement is,

$r=\dfrac{12.4}{6.2}\\r=2$

The perimeter of the original rectangle is 16 feet and scale factor is 2. Thus, the perimeter of the enlarged rectangle is,

$P_l=2\times16\\P_l=32\rm\; ft$

The small rectangle has width of 1.8 feet and scale factor is 2. Thus, the width of the larger rectangle is,

$w_l=1.8\times2\\w_1=3.6\rm\; ft$

Hence, the perimeter of the enlarged rectangle is 32 ft and the width of the larger rectangle is 3.6 ft.

Learn more about the perimeter of plane here;

brainly.com/question/1662271

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1 year ago

What other information do you need in order to prove the triangles congruent using the SAS congruence postulate

iren [92.7K]

AC is perpendicular to BD.

<h3>Further explanation</h3>

We observe that both the ABC triangle and the ADC triangle have the same AC side length. Therefore we know that $\boxed{ \ \overline{AC} \cong \overline{AC} \ }$ is reflexive.
The length of the base of the triangle is the same, i.e., $\boxed{ \ \overline{BC} = \overline{CD} \ }$ .
In order to prove the triangles congruent using the SAS congruence postulate, we need the other information, namely $\boxed{ \ AC \bot BD \ }$ . Thus we get ∠ACB = ∠ACD = 90°.

Conclusions for the SAS Congruent Postulate from this problem:

$\boxed{ \ \overline{BC} = \overline{CD} \ }$
∠ACB = ∠ACD
$\boxed{ \ \overline{AC} = \overline{AC} \ }$

- - - - - - - - - -

The following is not other or additional information along with the reasons.

∠CBA = ∠CDA no, because that is AAS with ∠ACB = ∠ACD and $\boxed{ \ \overline{AC} \cong \overline{AC} \ }$
∠BAC = ∠DAC no, because that is ASA with $\boxed{ \ \overline{AC} \cong \overline{AC} \ }$ and ∠ACB = ∠ACD.
$\boxed{ \ \overline{BC} = \overline{CD} \ }$ no, because already marked.

- - - - - - - - - -

Notes

The SAS (Side-Angle-Side) postulate for the congruent triangles: two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle; the included angle properly represents the angle formed by two sides.
The ASA (Angle-Side-Angle) postulate for the congruent triangles: two angles and the included side of one triangle are congruent to two angles and the included side of another triangle; the included side properly represents the side between the vertices of the two angles.
The SSS (Side-Side-Side) postulate for the congruent triangles: all three sides in one triangle are congruent to the corresponding sides within the other.
The AAS (Angle-Angle-Side) postulate for the congruent triangles: two pairs of corresponding angles and a pair of opposite sides are equal in both triangles.

<h3>Learn more</h3>

Which shows two triangles that are congruent by ASA? brainly.com/question/8876876
Which shows two triangles that are congruent by AAS brainly.com/question/3767125
About vertical and supplementary angles brainly.com/question/13096411

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2 years ago

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Step-by-step explanation:

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1 year ago