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3 years ago

Write the equation of a line

Mathematics

1 answer:

Gre4nikov [31]3 years ago

8 0

Answer:

Answer: Option D.

Step-by-step explanation:

Hey there!!

Here, To find the equation of a st.line passing through point (3,1) is :

$(y - 1) = m1(x - 3)$

It is the first equation.

Given, Another equation is:

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

It is 2nd equation.

Comparing the 2nd equation with y = mx+c we get,

Slope (m2) = 2/3.

As per the condition of parallel lines,

m1 = m2 = 2/3.

Putting, the value of m1 in equation 1st we get,

$(y - 1) = \frac{2}{3} (x - 3)$

or, 3 (y-1) = 2(x-3)

or, 3y - 3 = 2x - 6

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

$y = \frac{2}{3} x - 1$

Diving-3/3 = -1.

Therefore, y = 2/3 x - 1 is the required equation.

Hope it helps.

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Mr. Moran chose 10 different test scores out of 50, and they are shown below. For the following set of data, find the mean test

frozen [14]

Answer:

39.5

Step-by-step explanation:

5 0

2 years ago

Lee wants to collect 22 of a certain type of action figure. He had 11 of the figures, then got 3 more for his birthday. What dec

Shalnov [3]

To solve this problem, we must first find the fraction of action figures that Lee has gotten so far. To do this, we will represent the number of action figures that Lee currently has in the numerator divided by the denominator, the total number of action figures that Lee is attempting to collect.

First, we must recognize that Lee currently has 11 action figures plus the 3 that he got for his birthday. To find the total number of action figures that Lee has, we must add together these two parts.

11+3 = 14

Therefore, Lee has 14 action figures (this will become the numerator of the fraction). The denominator of the fraction is the total number of action figures, which we are given is 22.

Thus, our fraction is 14/22.

To convert this into a decimal, we can simply divide the numerator of the fraction by the denominator of the fraction, which gives us:

14/22 = 0.636363636

Therefore, your answer is approximately 0.636.

Hope this helps!

6 0

3 years ago

MATH HELP!!! 100PTS!!!

Lostsunrise [7]

Answer:

$x =\dfrac{20 +\sqrt{454}}{18}, \quad \dfrac{20 -\sqrt{454}}{18}$

Step-by-step explanation:

Given functions:

$p(x)=2x-4$

$r(x)=\dfrac{6x-1}{9x+1}$

Solve for p(x) = r(x):

$\begin{aligned}p(x) & = r(x)\\\implies 2x-4 & = \dfrac{6x-1}{9x+1}\\(2x-4)(9x+1)&=6x-1\\18x^2+2x-36x-4&=6x-1\\18x^2-40x-3&=0\end{aligned}$

As the found quadratic equation cannot be factored, use the Quadratic Formula to solve for x:

Quadratic Formula

$x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0$

Therefore:

$a=18, \quad b=-40, \quad c=-3$

Substitute the values of a, b and c into the quadratic formula and solve for x:

$\begin{aligned}\implies x & =\dfrac{-(-40) \pm \sqrt{(-40)^2-4(18)(-3)} }{2(18)}\\\\& =\dfrac{40 \pm \sqrt{1816}}{36}\\\\& =\dfrac{40 \pm \sqrt{4 \cdot 454}}{36}\\\\& =\dfrac{40 \pm \sqrt{4}\sqrt{454}}{36}\\\\& =\dfrac{40 \pm2\sqrt{454}}{36}\\\\& =\dfrac{20 \pm\sqrt{454}}{18}\end{aligned}$