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2 years ago

How many permutations can be formed from the letters of the word tennessee ?

1 answer:

8 0

<span>3780 If you consider every letter in the word "tennessee" to be unique there is 9!, or 362880 different ways to arrange the letters. So let's use that as a starting point. Now there's 4 e's, which we really don't care how they're arranged. So divide by 4!, or 24. Giving us 362880/24 = 15120 different ways to arrange the letters. There's also 2 n's. So divide by 2!, giving us 15120/2 = 7560 different ways. Don't forget the s's either. So another division by 2!, giving 7560/2 = 3780 different ways. And there's no more duplicate letters, so the final figure is 3780 different ways to arrange the letters in the word "tennessee".</span>

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The equation of the graphed line 2x + 3y = -6 written in standard form is, $\rm y= -\frac{2}{3}x -2$ and for line 2x + 3y = 6 will be, $\rm y = \frac{-2}{3}x+2$

<h3>What is the equation?</h3>

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

a) 2x + 3y = -6

The line in which the standard form is found as;

Ax + By + C = 0

The typical form of a slope intercept is

y = mx+c

where m denotes the slope and b the line's y-intercept.

$3y= -6-2x\\\\ y=\frac{-6-2x}{3}\\\\ y= -\frac{2}{3}x -2$

To obtain the slope standard form, we rewrite. The obtained equation is in the form of the slope-intercept.

b) 2x + 3y = 6

The line in which the standard form is found as;

Ax + By + C = 0

The typical form of a slope intercept is

y = mx+c

where m denotes the slope and b the line's y-intercept.

$\rm 3y= 6-2x \\\\ y= \frac{6-2x}{3} \\\\ y = \frac{-2}{3}x+2$

Hence, The equation of the graphed line 2x + 3y = -6 written in standard form is, $\rm y= -\frac{2}{3}x -2$

To learn more, about equations, refer;

brainly.com/question/10413253

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What is the equation of the graphed line written in standard form?

2x + 3y = -6, 2x + 3y = 6

Summary:

a. The equation of the graphed line 2x + 3y = -6 written in standard form is y= -2/3 x -2.

b. The equation of the graphed line 2x + 3y = 6 written in standard form is y= -2/3 x +2.

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The answer is b). GH good luck

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3 years ago

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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
$\boxed{ \ \overline{AC} = \overline{AC} \ }$

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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.

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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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