Mathematics: Iwill give brainliest and 5 stars to correct answer and if you show your work

Option D y = is the equation representing proportional relationship. Solution: For the proportional relationship, for all values of x, must be a constant value. Let’s check option A.Divide both the sides by x.For x = 1, For x = 2, So is different for x = 1 and x = 2. So option A do not represent proportional relationship. Similarly for option B and C also there is constant term in the equation. So option B and C will also have different values of for two values of x. For option D So for all value...

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Ответ:

dbn4everloved

13.01.2022

Mathematics

We see that:

$a_2-a_1=-4-1=\boxed{-5}\\\\
a_3-a_2=-9-(-4)=-9+4=\boxed{-5}\\\\
a_4-a_3=-14-(-9)=-14+9=\boxed{-5}\\\\\ldots$

So this is an arithmetic sequence with common difference d = -5. We can calculate the sum of that sequence as:

Sum = (first term + last term) * number of terms/2

first term = 1
number of terms = 12

last term = a₁₂ = ?

We know that:

$a_{n} = a_1+(n-1)\cdot d$

so:

$a_{12}=a_1+(12-1)\cdot d=1+11\cdot(-5)=1-55=\boxed{-54}$

And sum:

$S_{n}=(a_1+a_{n})\cdot\frac{n}{2}\\\\\\
S_{12}=\big(1+(-54)\big)\cdot\frac{12}{2}\\\\\\
S_{12}=-53\cdot6\\\\\\\boxed{S_{12}=-318}$

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Ответ:

wrightstephanie193

01.03.2023

Mathematics

Option D

y = $\frac{1}{3}$ is the equation representing proportional relationship.

Solution:

For the proportional relationship, for all values of x, $\frac{y}{x}$ must be a constant value.

Let’s check option A.

$y=x+\frac{1}{3}$

Divide both the sides by x.

$\frac{y}{x}=1+\frac{1}{3 x}$

For x = 1,

$\frac{y}{x}=1+\frac{1}{3 \times 1}=\frac{4}{3}$

For x = 2,

$\frac{y}{x}=1+\frac{1}{3 \times 2}=6$

So $\frac{y}{x}$ is different for x = 1 and x = 2.

So option A do not represent proportional relationship.

Similarly for option B and C also there is constant term in the equation.

So option B and C will also have different values of $\frac{y}{x}$ for two values of x.

For option D

$y=\frac{1}{3} x$

So for all value of x in above case y/x will be 1/3 .hence D is correct option , that is y = (1/3)x is the equation represents proportional relationship.

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