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4 years ago

The sum of the first 7 terms of a geometric sequence is 16383.

Mathematics

1 answer:

gogolik [260]4 years ago

4 0

UNFINISHED ANSWER - PRESSED ENTER TOO EARLY. SORRY

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If vector u = (5, 3) and vector v = (-1, 4), what is the component form of vector u + v?

Mrac [35]

I think this is the answer
$\binom{5}{3} + \binom{ - 1}{4} = \binom{ 4}{7}$

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3 years ago

WILL GIVE 100 POINTS AND BRAINLIEST! Prove that the square of the second number out of three consecutive odd numbers is four gre

Ad libitum [116K]

Answer:

Let's choose the three odd consecutive numbers 1, 3, and 5.

3^2=9

1•5=5

9-5=4

Let's try the same thing, but with the numbers 101, 103, and 105.

103^2=10609

101•105=10605

10609-10605=4

So, yes, the square of the second number out of three consecutive odd numbers is four greater than the product of the first and the third numbers.

4 0

3 years ago

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In JKL, mJ = 90, mK = 30, and mL = 60. Which of the following statements about JKL are true?

kumpel [21]

The <em><u>correct answers</u></em> are:

KL = 2*JL; JK = (√3)JL; and JK = ((√3)/2)KL

Explanation:

This is a 30-60-90 right triangle. This type of triangle has a special relationship among the sides. Let the smallest side, across from the 30° angle, be t. This means JL = t.

The hypotenuse of the triangle is two times the length of the smallest side; this means that KL = 2t, which means that KL = 2*JL.

The side of the triangle opposite the 60° angle will be the "medium sized" side; it is equal to √3 times the smallest side, or √3t; this gives us that JK = √3t = (√3)JL.

Comparing JK to KL, we have

$\frac{t\sqrt{3}}{2t}$

The t on top and bottom cancel out, leaving us with the ratio (√3)/2. This means that JK = ((√3)/2)KL.

8 0

3 years ago

Read 2 more answers

1/1×3 + 1/3×5 + ... + 1/47×49 HELP PLZ

Natalka [10]

Answer:

24/49

Step-by-step explanation:

Let's add the terms and see if there's a pattern

$\dfrac{1}{1\times 3}+\dfrac{1}{3\times 5}=\dfrac{5+1}{1\times 3\times 5}=\dfrac{2}{5}\quad\text{sum of 2 terms}\\\\\dfrac{2}{5}+\dfrac{1}{5\times 7}=\dfrac{14+1}{5\times7}=\dfrac{3}{7}\quad\text{sum of 3 terms}$

Suppose we say the sum of n terms is (n/(2n+1)), the next term in the series will be 1/((2n+1)(2n+3)) and adding that to the presumed sum gives ...

$\dfrac{n}{2n+1}+\dfrac{1}{(2n+1)(2n+3)}=\dfrac{n(2n+3)+1}{(2n+1)(2n+3)}=\dfrac{2n^2+3n+1}{(2n+1)(2n+3)}\\\\=\dfrac{(2n+1)(n+1)}{(2n+1)(2n+3)}=\dfrac{n+1}{2n+3}\text{ matches }\dfrac{(n+1)}{2(n+1)+1}$

Then it appears the sum of n terms is (n/(2n+1)). So, the sum of 24 terms is ...

$S_{24}=\dfrac{24}{2\times24+1}=\boxed{\dfrac{24}{49}}$

3 0

3 years ago

HELP ASAP ITS WORTH 22 POINTS PLZ.

Anarel [89]

Answer:

J---

Step-by-step explanation:

If she made 1 Dozen (12) and he kids ate 3, (12-3= 9), she needs to make how many more cupcakes, and since we can use a variable, c + 9 = 24 (Because she promised to bring 24------She would need to make 15 more cupcakes)

7 0

3 years ago

Read 2 more answers