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3 years ago

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What is the sum of the geometric sequence 1,-6,36... if there are 6 terms

1 answer:

zalisa [80]3 years ago

7 0

$a_1=1;\ a_2=-6;\ a_3=36;\ ...\\\\r=a_2:a_1\to r=-6:1=-6\\\\S_n=\dfrac{a_1(1-r^n)}{1-r}\\\\a_1=1;\ r=-6;\ n=6\\\\subtitute\\\\S_6=\dfrac{1(1-(-6)^6)}{1-(-6)}=\dfrac{1-46656}{1+6}=\dfrac{46655}{7}=6665$

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Give an example for a pair of alternate interior angles, a pair of corresponding angles, and a pair of alternate exterior angles

erastovalidia [21]

Step-by-step explanation:

Consider the provided information.

Consider the figure 1:

We need to give an example of a pair of alternate interior angles, a pair of corresponding angles, and a pair of alternate exterior angles.

Alternate interior angles: If a transversal cuts two parallel line then pair of angles on the inner side of lines but on opposite sides of the transversal are know as the alternate interior angle:

For example: ∠3 and ∠6 are alternate interior angle another pair are ∠4 and ∠5.

Corresponding angles: If a transversal cuts two parallel line then the angles in same corner are called corresponding angles.

For example: ∠1 and ∠5 are corresponding angle another pair are ∠4 and ∠8.

Alternate exterior angles: If a transversal cuts two parallel line then the pair of angles on the outer side of lines but on opposite sides of the transversal are known as the alternate exterior angles.

For example: ∠1 and ∠8 are alternate exterior angle another pair are ∠2 and ∠7.

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3 years ago

The expression (x⁴)(x-12) is equivelent to x^n. what is the value to n?

Kobotan [32]

I attached the work/steps for my answer.

5 0

2 years ago

SU and VT are chords that intersect at point R.

vovikov84 [41]

Answer:

<h2>The length of the line segment VT is 13 units.</h2>

Step-by-step explanation:

We know that SU and VT are chords. If the intersect at point R, we can define the following proportion

$\frac{RS}{RT} =\frac{RV}{RU}$

Where

$RS=SR=x+6\\RT=x+4\\VR=RV=x+1\\RU=x$

Replacing all these expressions, we have

$\frac{x+6}{x+4} =\frac{x+1}{x}$

Solving for $x$ , we have

$x(x+6)=(x+4)(x+1)\\x^{2} +6x=x^{2} +x+4x+4\\6x-5x=4\\x=4$

Now, notice that chord VT is form by the sum of RT and RV, so

$VT=VR+RT\\VT=x+1+x+4\\VT=2x+5$

Replacing the value of the variable

$VT=2(4)+5\\VT=8+5\\VT=13$

Therefore, the length of the line segment VT is 13 units.

5 0

2 years ago

Read 2 more answers

I need help? can anyone help

erica [24]

I think it’s 5 but don’t get mad if it’s wrong

7 0

3 years ago

Rewrite each fraction in simplest form using the GCF of the numerator and denominator.

Elanso [62]

Answer:

$\sf 6. \quad \dfrac{7}{10}$

$\sf 7. \quad \dfrac{5}{17}$

Step-by-step explanation:

<h3><u>Question 6</u></h3>

To find the greatest common factor (GCF), first list the prime factors of each number:

42 = 2 × 3 × 7
60 = 2 × 2 × 3 × 5

42 and 60 share one 2 and one 3 in common.

Multiply them together to get the GCF: 2 × 3 = 6.

Therefore, 6 is the GCF of 42 and 60.

Divide the numerator and the denominator by the found GCF:

$\implies \sf \dfrac{42 \div 6}{60 \div 6}=\dfrac{7}{10}$

<h3><u>Question 7</u></h3>

To find the greatest common factor (GCF), first list the prime factors of each number:

80 = 2 × 2 × 2 × 2 × 5
272 = 2 × 2 × 2 × 2 × 17

80 and 272 share four 2s in common.

Multiply them together to get the GCF: 2 × 2 × 2 × 2 = 16.

Therefore, 16 is the GCF of 80 and 272.

Divide the numerator and the denominator by the found GCF:

$\implies \sf \dfrac{80 \div 16}{272 \div 16}=\dfrac{5}{17}$

5 0

1 year ago

Read 2 more answers