Find the slope intercept form and the point slope the line perpendicular to 4x-7y=2 going through (-6,1)

Answers

Answer 1

Answer:

Slope-intercept form: [tex]y=-\frac{7}{4}x-\frac{19}{2}[/tex]

Point-slope-form: [tex]y-1=-\frac{7}{4}(x+6)[/tex]

Step-by-step explanation:

Hi there!

We want to find the equation of the line perpendicular to the line 4x-7y=2 that goes through (-6, 1) in slope-intercept form, as well as the point-slope form

Slope-intercept form is defined as y=mx+b, where m is the slope and b is the y intercept

Point-slope form is defined as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point

Meanwhile, perpendicular lines have slopes that are negative and reciprocal. When they are multiplied together, the result is -1

So let's find the slope of the line 4x-7y=2

The equation of the line is in standard form, which is ax+by=c, where a, b, and c are integer coefficients a is non-negative, and a and b aren't 0

So let's find the slope of the line 4x-7y=2

One way to do that is to convert the equation of the line from standard form to slope-intercept form

Our goal is to isolate y onto one side

Subtract 4x from both sides

-7y=-4x+2

Divide both sides by -7

y=[tex]\frac{4}{7}x-\frac{2}{7}[/tex]

So the slope of the line 4x-7y=2 is [tex]\frac{4}{7}[/tex]

Now, we need to find the slope of the line perpendicular to it

Use this formula: [tex]m_1*m_2=-1[/tex]

[tex]m_1[/tex] in this case is [tex]\frac{4}{7}[/tex]

[tex]\frac{4}{7}m_2=-1[/tex]

Multiply both sides by [tex]\frac{7}{4}[/tex]

m=[tex]-\frac{7}{4}[/tex]

Let's see the equation of the perpendicular line so far in slope-intercept form:

y=[tex]\frac{-7}{4}x[/tex]+b

We need to find b now

The equation of the line passes through (-6,1), so we can use it to solve for b.

Substitute -6 as x and 1 as y

[tex]1=-\frac{7}{4}*-6+b[/tex]

Now multiply

1=[tex]\frac{42}{4}+b[/tex]

Subtract 42/4 from both sides to isolate b

-19/2=b

Substitute -19/2 as b into the equation

The equation in slope-intercept form y=[tex]\frac{-7}{4}x-\frac{19}{2}[/tex]

Now, here's the equation in point-slope form

Recall that the slope is [tex]\frac{-7}{4}[/tex] , our point is (-6, 1), and point-slope form is [tex]y-y_1=m(x-x_1)[/tex]

Let's label the value of everything to avoid any confusion

[tex]m=-\frac{7}{4} \\x_1=-6\\y_1=1[/tex]

Now substitute those values into the equation

[tex]y-1=-\frac{7}{4}(x--6)[/tex]

We can simplify the x--6 to x+6

[tex]y-1=-\frac{7}{4}(x+6)[/tex]

Hope this helps!


Related Questions

simplify:-a). (-5a²)²(6ab²)(-3ab²)​

Answers

First you would combine that like terms then add them all together, and your answer would be 2a^2 + b^2 +c^2

if a(b+c)=d and a, b, c and d are all integer, then which of the following must be true?
A. ab+c=d
B. ab+ac=d
C. a(b+c)>10
D. ab

Answers

Answer:

B. ab+ac=d

Step-by-step explanation:

Answer:

ab + ac = d

Step-by-step explanation:

a(b+c)=d

Distribute the a

ab + ac = d

3c + 2 = -22
whats c?

Answers

3c+  2=  -22

⇔3c = -22 -2

⇔3c = -24

⇔c=  -24/3

⇔c=- 8

Answer:

3c= -22-2

3c= -24

c= -24/3

c= -8

Step-by-step explanation:

What value of x will make the equation true?

(Square Root of 5) (square root of 5)=x

Answers

Answer:

(2.236067978)(2.236067978)

=5 ans.

If this is incorrect forgive me

I hope this will help you

stay safe

Please help me with this, i need help

Answers

Answer:

woa

i  n

Step-by-step explanation:

This table shows the relationship of the total number of pieces of fruit to the number of bananas.
Why is StartFraction 6 Over 5 EndFraction not equivalent to Three-halves?

Answers

Given:

The table that shows the relationship of the total number of pieces of fruit to the number of bananas.

To find:

Why is [tex]\dfrac{6}{5}[/tex] not equivalent to [tex]\dfrac{3}{2}[/tex].

Solution:

If a, b, c are real numbers, then

[tex]\dfrac{a}{b}=\dfrac{a\times c}{b\times c}[/tex]

The given fraction is [tex]\dfrac{3}{2}[/tex]. It can be written as:

[tex]\dfrac{3\times 2}{2\times 2}=\dfrac{6}{4}[/tex]

The number 3 is multiplied by 2 to get 6. So, the 2 should also be multiplied by 2. The ratio should be [tex]\dfrac{6}{4}[/tex], not [tex]\dfrac{6}{5}[/tex].

Therefore, the correct option is A.

Answer two questions about Equations A and B:
A. 3(x+2) = 18
B.
r + 2 = 6
1) How can we get Equation B from Equation A?

Answers

Step-by-step explanation:

3x+6=18

3x=18-6

3x=12

x=4

Find the equation of the line that passes through (1,6) and (3,10).
y=2x+4
y=-2x+4
y=-24-4
Oy-23-4

Answers

Answer:

m = (y2 - y1) / (x2 - x1) = (10 - 6) / (3 - 1) = 2    slope of line

y = m x + b standard form of straight line

y = 2 x + b      where b is the intercept at x = 0

b = y - 2 x

b = 6 - 2 = 4    from our first equation

Also, b = 10 - 6 = 4       check from second equation

y = 2 x + 4    is our equation

Check if y = 6 and x = 1 then

y = 2 * 1  + 4 = 6   verifying the first point given

Anybody knows the answers to the monomial functions ?

Answers

Step-by-step explanation:

A monomial function is an expression with only one term. ... For example, a polynomial function is the sum of many monomial functions; If there's only one term in a polynomial function, then it is a monomial function [2]. Monomial functions can take many forms: A monomial (a number by itself is a “monomial”).

As displayed on a production possibilities curve, what will an increase in technology allow a society to do? a. Produce more, as long as the resources are also available. c. It will not affect society’s production. b. Produce less, because more resources are spent on developing technology. d. The society will spend more on the same level of production. Please select the best answer from the choices provided A

Answers

Answer:

a. Produce more, as long as the resources are also available

Step-by-step explanation:

from brainly itself

scouteo

Ace

The correct answer is A) produce more, as long as the resources are also available.

As displayed on a production possibilities curve, an increase in technology will allow a society to produce more, as long as the resources are also available.

A production possibilities graph is a valid representation of the available ways an economy is able to use the resources. In this case, an increase in technology will allow a society to produce more, as long as the resources are also available means that as long there are enough resources in the market, technology in a country helps with the production of more things to be consumed or traded.  

When solving a quadratic in the form a x squared + b x + c = 0 we are really finding the x–intercepts. These x–intercepts are also called roots. What is another term for roots or x-intercepts? a. exponents c. zeros b. quadratics d. variables Please select the best answer from the choices provided A B C D

Answers

C. Zeros
This is because you plug 0 into X to get the Y answer which is your x-intercept

Can someone help please and thank you

Answers

Answer:

b

Step-by-step explanation:

C and D are complementary angles. Which of the following measures cannot be true
Om C= 30° and m D = 60°
Om C= 60° and m2D = 30°
Om C= 65° and m D = 35°
Om C = 55° and m D = 35°

Answers

Answer:

C= 65° and m D = 35°

this cannot be true

Step-by-step explanation:

a complementary angle adds up to 90°

65°+35°=100

90° =/= 100°

Consider the following 8 numbers, where one labelled x
is unknown.
27, 20, 34,
x, 7, 47, 26, 41
Given that the range of the numbers is 63,
work out 2 values of x

Answers

Answer:  70  and -16

==========================================================

Explanation:

For now, we'll assume x is the largest value (aka the max)

Let's sort the values from smallest to largest.

7, 20, 26, 27, 34, 41, 47, x

We see that 7 is the smallest item, so,

range = max - min = x - 7

Set this equal to 63 and solve for x

x-7 = 63

x = 63+7

x = 70

So x could be equal to 70.

---------------------------

Next, we'll assume that x is the smallest value

That means the min is x and 47 is now the max

max - min = range

47 - x = 63

-x = 63-47

-x = 16

x = -16

So if x is the smallest value, then it must be -16

----------------------------

Finally, we'll let x be somewhere between 7 and 47

Unfortunately, we can't pin down a specific value here since we could have lots of possible values. Three such examples are x = 8, x = 9, and x = 10. There are many others.

If your teacher is looking for 2 values only, then I would refer to the previous two sections and ignore this section entirely.

Find sin 0
A. 16/20
B. 12/16
C. 12/20
D. 16/12

Answers

Answer:

16/20

Step-by-step explanation:

Since this is a right triangle

sin theta = opp side / hypotenuse

sin theta = 16/20

Answer:

A.

[tex]{ \tt{ \sin( \theta) = \frac{opposite}{hypotenuse} }} \\ \\ { \tt{ \sin( \theta) = \frac{16}{20} }}[/tex]

Solve the equation by completing the square. Round to the nearest hundredth if necessary. x^2 - x = 25​

Answers

from completing the square, x = 5.52 and -4.52

Answer:

[tex]x1 = - 4.525[/tex]

[tex]x2 = 5.525[/tex]

Step-by-step explanation:

[tex]x1 = \frac{1 - \sqrt{101} }{2} [/tex]

[tex]x2 = \frac{1 + \sqrt{101} }{2} [/tex]

Identify the equation of the circle that has its center at (9, 12) and passes through the origin.

Answers

Answer:

(x-9)^2 +(y-12)^2 = 225

Step-by-step explanation:

First find the length of the radius

If is the distance from the center to the point

d = sqrt( (x2-x1)^2 + (y2-y1)^2 )

   = sqrt( (0-9)^2 + (0-12)^2)

   = sqrt ( 81+144)

  = sqrt(225)

  = 15

The equation for a circle is

( x-h) ^2+ (y-k)^2 = r^2

(x-9)^2 +(y-12)^2 = 15^2

(x-9)^2 +(y-12)^2 = 225

Evaluate:
18 (5n - 4) = [?]

Answers

Answer:

90n-72=0

Step-by-step explanation:

18×5n-18×4=0

An acute angle of a right triangle measures 30°, and the length of the triangle's hypotenuse is 10 ft. Find the missing angle measure and side lengths.

Answers

Answer:

missing angle <60 and side lengths 5, 5[tex]\sqrt{3}[/tex]

Step-by-step explanation:

we understand from the given information that  the triangle in question is a special right triangle

and since this is a special triangle the side lengths follows :

the side length that sees <90 is represented by 2x

the side length that sees <60 is represented by x[tex]\sqrt{3}[/tex]

and the side length that sees <30 is represented by x

2x = 10 so x = 5 and  x[tex]\sqrt{3}[/tex] = 5[tex]\sqrt{3}[/tex]

The range of cells in column D and rows 1 to 10 is represented as:

1:10 D1:D10 D:D

Answers

Answer:

how?

Step-by-step explanation:

I didnt get question

The probability that Dan buys a sandwich is 0.2.
The probability that Dan gets the bus is 0.9.
Assuming the events are independent, what is the probability that Dan buys a sandwich
and gets the bus?

Answers

Answer:

0.18

Step-by-step explanation:

Find the probability that both independent events occur by multiplying the individual probabilities by each other:

0.2(0.9)

= 0.18

So, the probability is 0.18

Help pleas like please ASAP

Answers

Answer:

(x+9)(x+5)

Step-by-step explanation:

find 2 numbers that add to 14 and multiply to 45

X+9 x+5 hope that helped

The function f(x) = One-sixth (two-fifths) Superscript x is reflected across the y-axis to create the function g(x). Which ordered pair is on g(x)?

Answers

Answer:

[tex](-3,4/375)[/tex]

Step-by-step explanation:

Given

[tex]f(x) = \frac{1}{6}(\frac{2}{5})^x[/tex]

Reflection: Across y-axis

Required

The ordered pair on g(x)

The rule of reflection across y-axis is:

[tex](x,y) = (-x,y)[/tex]

So, we have:

[tex]g(x) = f(-x)[/tex]

f(-x) is:

[tex]f(-x) = \frac{1}{6}(\frac{2}{5})^{-x[/tex]

Recall that:

[tex]g(x) = f(-x)[/tex]

Hence:

[tex]g(x) = \frac{1}{6}(\frac{2}{5})^{-x[/tex]

From the options (missing in the question), the ordered pair is:

[tex](-3,4/375)[/tex]

To check this, we have:

[tex]g(x) = \frac{1}{6}(\frac{2}{5})^{-x[/tex]

[tex]g(-3) = \frac{1}{6}(\frac{2}{5})^{--3[/tex]

[tex]g(-3) = \frac{1}{6}(\frac{2}{5})^{3[/tex]

Expand

[tex]g(-3) = \frac{1}{6}(\frac{8}{125})[/tex]

Simplify

[tex]g(-3) = \frac{1}{3}(\frac{4}{125})[/tex]

Open bracket

[tex]g(-3) = \frac{4}{375}[/tex]

convert into power notation -1/81​

Answers

Answer:

-1/9^2 is the power notation for your questions

Step-by-step explanations

What expression is equal to (3 x 5) x 4

Answers

Answer:

60

Step-by-step explanation:

Step 1:

3 x 5 = 15

Step 2:

15 x 4 = 60

Answer:

well 3. x 5 is 15, then multiply by 4 to get 60.

Step-by-step explanation:

Help Now Pleaseee!!!!
Find the volume of the sphere

Answers

Answer:

7235 using 3.14 for pi

7238 using the pi button

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

V = 4/3 pi (12)^3

V = 2304pi

Letting pi = 3.14

V = 7234.56 and rounding to a whole number

V = 7235

Using the pi button

V =7238.22947 and rounding to a whole number

V = 7238

Answer: 7238

Step-by-step explanation:

The formula used is 4/3πr³

Now let's substitute the radius: 12

4/3πr³

=4/3×π×12³

=4/3×π×1728

=7238.22947

but since we are rounding it to the nearest whole number the answer would be 7238

The polygons in each pair are similar. Find the missing side length

Answers

Answer:

24 is the answer because 18/3=6 6x4 is 24

Which is a y-intercept of the continuous function in the table? х – 4 -3 -2 -1 0 1 f(x) -10 0 0 – 4 -6 0 2 O (0,6) O (-2, 0) O (6,0) 0 (0, -2)
Plz Hurry​

Answers

Answer:

x:-4,-3,-2,-1,0,1

f(x):-10,0,0,-4,-6,0

from the table we can see when x=0, y=-6

Therefore the y-intercept will be (0,-6)

OAmalOHopeO

The y intercept of the continuous function in the table is given by the relation f ( 0 ) = -6

What is a function rule?

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the function be represented as A

Now , the value of A is

Let the values of x be x = { -4 , -3 , -2 , -1 , 0 }

Let the values of y be y = { -10 , 0 , 0 , -4 , -6 }

Now , the y intercept of the function is when the value of x = 0

So , when x = 0 , the value of y = -6

And , f ( 0 ) = -6

Therefore , the y intercept is ( 0 , -6 )

Hence , the y intercept of the function is ( 0 , -6 )

To learn more about function rule click :

https://brainly.com/question/3760195

#SPJ7

What is the value of X?​

Answers

Answer:

x=2

Step-by-step explanation:

A line that intersects a circle in two points is called a secant line, and this is the case for both line DE and AE.

For two secant lines that intersect outside of the circle, such as the ones here, we can say that

CE * DE = BE * AE

Therefore, we need to then define these lines.

CE is x+4, BE is x+1, AE = (BE + AB) = 11+x+1 = 12+x, and DE = (CE + DC) = 1+x+4 = 5+x

We then have

(x+4) * (5+x) = (x+1) * (12+x)

expand

5x + x² + 20 + 4x = 12x+x²+12+x

x²+9x + 20 = x²+13x+12

Next, we want to congregate all values to one side so we can solve for x. This can be done by subtracting both sides by (x²+13x+12) to get

-4x + 8 = 0

subtract 8 from both sides to isolate the x and its coefficient

-4x = -8

divide both sides by -4 to isolate the x

x = 2

Answer: A

Explanation: I just took a test on it

A running track has two semi-circular ends with radius 27m and two straights of length 90.6m as shown.
Calculate the total distance around the track rounded to 1 DP.

Answers

Answer:

350.85

Step-by-step explanation:

90.6*2 = 181.2

27*2 = 54 (diameter)

54*pi = 169.646003294

169.646003294 + 181.2 = 350.846003294

350.846003294 = 350.85

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