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Citrus2011 [14]
3 years ago
9

What is an equation of the line that passes through the points (3,1) and (6,6)?

Mathematics
1 answer:
koban [17]3 years ago
5 0
<h3>The equation of the line that passes through the points (3,1) and (6,6) is:</h3>

y = \frac{5}{3}x -4

<em><u>Solution:</u></em>

Given that,

We have to find the equation of the line that passes through the points (3,1) and (6,6)

<em><u>Find the slope of line</u></em>

m = \frac{y_2-y_1}{x_2-x_1}

From given,

(x_1, y_1) = (3, 1)\\\\(x_2, y_2) = (6, 6)

Substituting the values we get,

m = \frac{6-1}{6-3}\\\\m = \frac{5}{3}

<em><u>The slope intercept form of line is given as:</u></em>

y = mx + c ------ eqn 1

Where,

m is the slope

c is the y intercept

Substitute m = 5/3 and (x, y) = (3, 1) in eqn 1

1 = \frac{5}{3} \times 3 + c\\\\1 = 5 + c\\\\c = -4

Substitute m = 5/3 and c = -4 in eqn 1

y = \frac{5}{3}x -4

Thus the equation of line in slope intercept form is found

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In a class test of 15 questions, (+4) marks are given for every correct answer, (– 2) marks are
romanna [79]

If he answered 3 questions correctly, then the number of questions is got wrong is 7 and the number of questions that he did not attempt is 5.

<h3>What is the linear system?</h3>

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

In a class test of 15 questions, (+4) marks are given for every correct answer, (– 2) marks are given for every incorrect answer, and 0 marks are given for questions that are not attempted. Punit scored (– 2) marks.

If he answered 3 questions correctly, then the number of the question are got wrong and the number of the question that he did not attempt.

Let x be the correct question and y be the incorrect question, z be the number of questions that he did not attempt, and A be the number of the total score. Then we have

4x – 2z = A

x + y + z = 15

If A = -2 and x = 3, then we have

4 × 3 – 2z = -2

      12 + 2 = 2z

              z = 7

Then the value of y will be

3 + y + 7 = 15

           y = 5

More about the linear system link is given below.

brainly.com/question/20379472

#SPJ1

3 0
2 years ago
If ΔABC is dilated by a scale factor of 2 with a dilation center of A, what will be the coordinates of point B'?
ryzh [129]
They are (0,6) because if the center of dilation is point A which means it does not change, while both other points increase their distance from point A by a factor of two (double)
5 0
3 years ago
Find all solutions of the given system of equations (If the system is infinite many solution, express your answer in terms of x)
lisov135 [29]

Answer:

(a) The system of the equations \left \{ {2x-3y\:=3} \atop {4x-6y\:=3}} \right. has no solution.

(b) The system of the equations \left \{ {4x-6y\:=10} \atop {16x-24y\:=40}} \right. has many solutions y=\frac{2x}{3}-\frac{5}{3}

Step-by-step explanation:

(a) To find the solutions of the following system of equations \left \{ {2x-3y\:=3} \atop {4x-6y\:=3}} \right. you must:

Multiply 2x-3y=3 by 2:

\begin{bmatrix}4x-6y=6\\ 4x-6y=3\end{bmatrix}

Subtract the equations

4x-6y=3\\-\\4x-6y=6\\------\\0=-3

0 = -3 is false, therefore the system of the equations has no solution.

(b) To find the solutions of the system \left \{ {4x-6y\:=10} \atop {16x-24y\:=40}} \right. you must:

Isolate x for 4x-6y=10

x=\frac{5+3y}{2}

Substitute x=\frac{5+3y}{2} into the second equation

16\cdot \frac{5+3y}{2}-24y=40\\8\left(3y+5\right)-24y=40\\24y+40-24y=40\\40=40

The system has many solutions.

Isolate y for 4x-6y=10

y=\frac{2x}{3}-\frac{5}{3}

3 0
2 years ago
Need help with this one !
nika2105 [10]

Answer:

r=5

Step-by-step explanation:

5x5x5=125

6 0
3 years ago
Let $r$ and $s$ be the roots of $3x^2 + 4x + 12 = 0.$ Find $r^2 + s^2.$ Pls help.
nirvana33 [79]

Answer:

-56/9

Step-by-step explanation:

By Vieta's formulas,

$r + s = -\frac{4}{3}$ and $rs = \frac{12}{3} = 4.$ Squaring the equation $r + s = -\frac{4}{3},$ we get

$r^2 + 2rs + s^2 = \frac{16}{9}.$ Therefore,

$r^2 + s^2 = \frac{16}{9} - 2rs = \frac{16}{9} - 2 \cdot 4 = -\frac{56}{9}}$

5 0
2 years ago
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