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WITCHER [35]
3 years ago
15

What is the equation of the line that passes through (6, 1) and is perpendicular to the line y 3x+2? CI) At what angle do the li

nes y= 6x +4 and y-2x+3 cross?
Mathematics
1 answer:
Andrews [41]3 years ago
8 0

Answer with explanation:

The equation of any line with slope 'm' and passing through any point (x_1,y_1) is given by

y=mx+(y_1-mx_1)

As we know that the general equation of a line with slope 'm' is y=mx+c

Comparing with the given equation y=3x+2 we can conclude slope of the given line is m_1=3

Now we know that the product of slopes of perpendicular lines is -1

Mathematically we can write for perpendicular lines

m_1\times m_2=-1

Thus the slope of the required line is obtained from the above relation since it is given that they are perpendicular

3\times m_{2}=-1\\\\\therefore m_{2}=\frac{-1}{3}

Hence using the given and the obtained values the equation of the required line is

y=-\frac{1}{3}x+(1-\frac{-1}{3}\times 6)}\\\\y=\frac{-x}{3}+3

Part b)

The angle of intersection between 2 lines with slopes m_{1},m_2 is given by

\theta =tan^{-1}(\frac{m_2-m_1}{1+m_1m_2})

Comparing the equations of given lines

y=6x+3\\\\y=2x+3

with the standard equation we get

m_{1}=6\\\\m_{2}=2

Thus the angle of intersection becomes

\theta =tan^{-1}(\frac{2-6}{1+2\times6})=17.10

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What is the solution to the system of equations l? y= 1/2x-6 x=-4
alina1380 [7]

Answer:

<h2>x = -4 and y = -8 → (-4, -8)</h2>

Step-by-step explanation:

y=\dfrac{1}{2}x-6\\\\x=-4\\\\\text{Put the value of x to the first equation:}\\\\y=\dfrac{1}{2}(-4)-6\\\\y=-2-6\\\\y=-8

4 0
2 years ago
Find the product of all positive integer values of $c$ such that $3x^2+7x+c=0$ has two real roots. I will award a lot of points
Agata [3.3K]

Answer:  24

<u>Step-by-step explanation:</u>

Let's find one solution:

3x² + 7x + c = 0

a=3 b=7  c=c

First, let's find c so that it has REAL ROOTS.

⇒ Discriminant (b² - 4ac) ≥ 0

                         7² - 4(3)c ≥ 0

                         49 - 12c ≥ 0

                               -12c  ≥ -49

                                c\leq\dfrac{-49}{-12}\quad \rightarrow c\leq \dfrac{49}{12}      

Since c must be a positive integer, 1 ≤ c ≤ 4

Example: c = 4

3x² + 7x + 4 = 0

(3x + 4)(x + 1) = 0

x = -4/3, x = -1         Real Roots!

<em>You need to use Quadratic Formula to solve for c = {1, 2, 3}</em>

<em />

Valid solutions for c are: {1, 2, 3, 4)

Their product is: 1 x 2 x 3 x 4 = 24

<em />

7 0
3 years ago
Describe the transformations from the parent function f(x)=x^2 to the function g(x+2)^2+5
jolli1 [7]

Answer:

The parent function is the simplest form of the type of function given.

g

(

x

)

=

x

2

The transformation being described is from  

g

(

x

)

=

x

2

to  

f

(

x

)

=

x

2

.

g

(

x

)

=

x

2

→

f

(

x

)

=

x

2

The horizontal shift depends on the value of  

h

. The horizontal shift is described as:

f

(

x

)

=

f

(

x

+

h

)

- The graph is shifted to the left  

h

units.

f

(

x

)

=

f

(

x

−

h

)

- The graph is shifted to the right  

h

units.

In this case,  

h

=

0

which means that the graph is not shifted to the left or right.

Horizontal Shift: None

The vertical shift depends on the value of  

k

. The vertical shift is described as:

f

(

x

)

=

f

(

x

)

+

k

- The graph is shifted up  

k

units.

f

(

x

)

=

f

(

x

)

−

k

- The graph is shifted down  

k

units.

In this case,  

k

=

0

which means that the graph is not shifted up or down.

Vertical Shift: None

The graph is reflected about the x-axis when  

f  (

x

)

=

−

f

(

x

)

.

Reflection about the x-axis: None

The graph is reflected about the y-axis when  

f

(

x

)

=

f

(

−

x

)

.

Reflection about the y-axis: None

Compressing and stretching depends on the value of  

a

.

When  

a

is greater than  

1

: Vertically stretched

When  

a

is between  

0

and  

1

: Vertically compressed

Vertical Compression or Stretch: None

Compare and list the transformations.

Parent Function:  

g

(

x

)

=

x

2

Horizontal Shift: None

Vertical Shift: None

Reflection about the x-axis: None

Reflection about the y-axis: None

Vertical Compression or Stretch: None

image of graph

5 0
3 years ago
Please help will mark as brainliest pls show work
Darya [45]

9514 1404 393

Answer:

  y = 1/5x +8

Step-by-step explanation:

The slope of the perpendicular line will be the opposite reciprocal of the slope of the given line:

  m = -1/(-5) = 1/5

The y-intercept (b) can be found from this and the given point:

  b = y -mx

  b = 9 -(1/5)(5) = 8

Then the slope-intercept equation can be written ...

  y = mx +b . . . . . . line with slope m and y-intercept b

  y = 1/5x +8

_____

<em>Additional comment</em>

Since the question asks for "an equation," the problem can be solved even more quickly using the point-slope form of the equation of a line.

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -9 = 1/5(x -5) . . . . . an equation for line j

6 0
2 years ago
The slope of the line below is - Write a point-slope equation of the line
Rainbow [258]

Answer:

D.

Step-by-step explanation:

pint slope form:

(y-y1)=m(x-x1)

do just olug in the point and the slope into the equation

(y-4)= -8/7 (x-4)

3 0
3 years ago
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