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1 year ago

Help. I will give brainliest if correct. A. -4/3 B. -3/4 C. 10/17 D. 17/10

Mathematics

1 answer:

mel-nik [20]1 year ago

4 0

The correct option is option B.

The common difference between given data is -3/4.

<h3>What is Sequence?</h3>

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Here, given points;

x₁ = 1 , x₂ = 2 and y₁ = -3.75 , y₂ = -4.5

Now,

d = (y₂ - y₁)/(x₂-x₁)

d = (-4.5 - (-3.75))/(2 - 1)

d = -0.75 / 1

d = - 75/100

d = -3/4

Thus, The correct option is option B. The common difference between given data is -3/4.

Learn more about Sequence from:

brainly.com/question/21961097

#SPJ1

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Which expressions have a value of 16/81? Check all that apply.

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Which expression have a value of 16/81? check all that apply. (2/3)^4, (16/3)^4, (4/81)^2, and (4/9)^2

Answer:

First and last option is correct.

$(\frac{2}{3})^{4}=\frac{16}{81}$

$(\frac{4}{9})^{2}=\frac{16}{81}$

Step-by-step explanation:

Given:

There are four options.

(2/3)^4, (16/3)^4, (4/81)^2, and (4/9)^2

We need to check all given options for value of 16/81.

Solution:

Using rule.

$(\frac{a}{b})^{n}=\frac{a^{n}}{b^{n}}$

Solve for option $(\frac{2}{3})^4$ .

$(\frac{2}{3})^{4}=\frac{2^4}{3^4}=\frac{2\times 2\times 2\times 2}{3\times 3\times 3\times 3}=\frac{16}{81}$

Solve for option $(\frac{16}{3})^4$ .

$(\frac{16}{3})^{4}=\frac{16^4}{3^4}=\frac{16\times 16\times 16\times 16}{3\times 3\times 3\times 3}=\frac{65536}{81}$

Solve for option $(\frac{4}{81})^2$ .

$(\frac{4}{81})^{2}=\frac{4^2}{81^2}=\frac{4\times 4}{81\times 81}=\frac{16}{6561}$

Solve for option $(\frac{4}{9})^2$ .

$(\frac{4}{9})^{2}=\frac{4^2}{9^2}=\frac{4\times 4}{9\times 9}=\frac{16}{81}$

Therefore, expression $(\frac{2}{3})^4$ and $(\frac{4}{9})^2$ have a value of $\frac{16}{81}$ .

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