Find an equation in slope-intercept form of the line satisfying the specified conditions.
Through (8,-3), perpendicular to -6x + 7y=-62.

Answers

Answer 1

Answer:

[tex]y = - \frac{7}{6} x + 6 \frac{1}{3} [/tex]

Step-by-step explanation:

Slope-intercept form

y= mx +c, where m is the slope and c is the y-intercept.

-6x +7y= -62

Rewriting this equation into the slope-intercept form:

7y= 6x -62

[tex]y = \frac{6}{7} x - \frac{62}{7} [/tex]

The product of the slope of 2 perpendicular lines is -1.

Let the slope of the unknown line be m.

[tex]m( \frac{6}{7} ) = - 1[/tex]

[tex]m = - 1 \div \frac{6}{7} [/tex]

[tex]m = - \frac{7}{6} [/tex]

Substitute the value of m into the equation:

[tex]y = - \frac{7}{6} x + c[/tex]

To find the value of c, substitute a pair of coordinates into the equation.

When x= 8, y= -3,

[tex] - 3 = - \frac{ 7}{6} (8) + c[/tex]

[tex] - 3 = - \frac{28}{3} + c[/tex]

[tex]c = \frac{28}{3} - 3[/tex]

[tex]c = \frac{19}{3} [/tex]

[tex]c = 6 \frac{1}{3} [/tex]

Thus, the equation of the line is [tex]y = - \frac{7}{6} x + 6 \frac{1}{3} [/tex].


Related Questions

A yoga studio charges a $180 yearly fee for membership plus $18 for each class. What is the average total cost per class if a studio member takes 75 classes per year? Do not include the dollar sign ($) in your answer.

Answers

Answer:

Average total cost per class is 13.5

Step-by-step explanation:

A yoga studio charges a 150 yearly fee for membership plus150yearlyfeeformembershipplus12 for each class.

Yearly charge = 150 $

Charge per class = 12 $

A studio member takes 100 classes per year

Number of class attended by studio member = 100

We need to find average total cost per class for this member for a year.

Total charge = Yearly charge + Number of class attended x Charge per class

Total charge = 150 + 100 x 12

Total charge = 150 + 1200

Total charge = 1350 $

\begin{gathered}\texttt{Average total cost per class = }\frac{\texttt{Total charge}}{\texttt{Number of class attended by studio member}}\\\\\texttt{Average total cost per class = }\frac{1350}{100}=13.5\$\end{gathered}

Average total cost per class =

Number of class attended by studio member

Total charge

Average total cost per class =

100

1350

=13.5$

Average total cost per class = 13.5 $

Study hard

Brainliest please thank you!

Answer:

1,530

Step-by-step explanation:

Total charge = 180 + 75 x 18

Total charge = 150 + 1,350

Total charge = 1,530 $

PLEASE HELP
What is the volume of the cylinder?
A. 60.0 cm3
B. 120.0 cm3
O C. 188.4 cm
D. 300.0 cm3
E. 942.0 cm

Answers

Answer:

i think E.942 cm³ is answer

Volume = πr²h

so

3.14×5×5×12

= 942 cm²

Consider the sequence: -7, -2, 3, 8…. What is f(7)?

Answers

You are adding by 5 in the sequence.
If f(1) is -7
f(2) = -2
f(3)= 3
f(4)=8
f(5)=13
f(6)=18
Therefore, f(7)=23

The graph below represents data that was collected by students on the number of social media posts they made the previous day. What's the greatest number of posts a student made?

Answers

From the graph given, the greatest number of posts a student made, which is the maximum data value is: 10 posts.

Given the graph given that represents the data that was collected by students shows the following:

The lowest number of posts a student made is 0 (3 students made 0 posts).The greatest number of posts a student made is 10 (2 students made the greatest number of posts).The number of posts made by most students is 7 (6 students made 7 posts).

In summary, from the graph given, the greatest number of posts a student made, which is the maximum data value is: 10 posts.

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Help help help help help help math math

Answers

Answer:

4x+14 = 2(2x+7}

12x+6=6{2x+1}

Solution set for the equation x^2-6x+10=0

Answers

Answer:

3+2i, 3-2i

Step-by-step explanation:

no rational solutions

if you use quadratic formula you get (6±[tex]\sqrt{-4}[/tex])÷2

Find all perfect squares between 100 and 300.

Answers

Answer: The answer in the first image.

Explanation: The explanation is in the second image.

If the food bill is $38.92, then what would the tip be if you want to leave a tip of 15%?

Answers

Answer:

$5.84

Step-by-step explanation:

Which is the equivalent of 0.00000000989 in proper scientific notation?

Answers

Answer:

  9.89×10^-9

Step-by-step explanation:

  0.000 000 009 89 = 9.89×10^-9

__

We have introduced spaces in the number to make the digits easier to count. (Some technical publications will write the number with thin spaces for just that reason.) The most-significant digit is in the 9th place to the right of the decimal point, so has a place value of 10^-9.

i really need helpppppppppppppppppppppppppppppp

Answers

Answer:

it makes no sence

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

Mean x¯¯¯ 7.25

Median x˜ 7

Mode 6

Range 12

Minimum 1

Maximum 13

Count n 16

Sum 116

Quartiles Quartiles:

Q1 --> 5

Q2 --> 7

Q3 --> 10

Interquartile

Range IQR 5

Outliers none

7.25 - 7 = 0.25

?/5 =8/10 type the missing number that makes this fraction equal

Answers

Answer:

4/5 = 8/10

Step-by-step explanation:

x/5 = 8/10

x = 8/10 × 5

x = 4

As a car ages, its value decreases. The value of a particular car with an original purchase price of $27, 200 is modeled by the following function, where
c is the value at time t, in years.
c(t) - 27, 200(1 -0.21)
a. What is the value of the car when it is 4 years old?
The value of the car after 4 years is Sl
b. What is the total depreciation amount after 5 years?
After 5 yehrs, the total depreciation amount is s[

Answers

a. The value of the car when it is 4 years old is approximately $13,645.23.

b. The car has depreciated by about $16,367.54 after 5 years.

To find the value of the car when it is 4 years old, we can substitute t = 4 into the given function:

c(4) = 27,200(1 - 0.21)^4

c(4) = 27,200(0.79)^4

c(4) ≈ 13,645.23

b. To find the total depreciation amount after 5 years, we need to find the difference between the original purchase price ($27,200) and the value of the car after 5 years. Using the function given, we can find the value of the car after 5 years by setting t = 5:

c(5) = 27,200(1 - 0.21)^5

c(5) = 27,200(0.79)^5

c(5) ≈ 10,832.46

Therefore, the total depreciation amount after 5 years is:

27,200 - 10,832.46 ≈ $16,367.54

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?
58 62
28 27 13
13 15 12 11
6 7 8 4 7
4 2 5 3 1 6

Answers

Answer:

105

Step-by-step explanation:

First, adding two sequence numbers and that result become upper number

Mrs. terrance has a large bin of 236 crayons. She divides them equally among four containers.

Answers

236 / 4=59 hoped this helped

John made 357$ for 17 hours of work.
At the same rate, how many hours would he have to work to make $237???

Answers

Answer: 14 hours

Step-by-step explanation: First I found the unit rate of how much money per hour. So, 357 divided by 17 = 21. So know I know that she earns 21$ per hour. Then, I did 237 divided by 17 which would be 13 remainder 16. Since he only get paid if he works for a full hour, I think the answer would be 14.

[tex]\begin{array}{ccll} \$&hrs\\ \cline{1-2} 357&17\\ 237&x \end{array}\implies \cfrac{357}{237}=\cfrac{17}{x}\implies \implies \cfrac{119}{79}=\cfrac{17}{x}\implies 119x=1343 \\\\\\ x = \cfrac{1343}{119}\implies x = \cfrac{79}{7}\implies x = 11\frac{2}{7}\leftarrow \textit{11 hours, 17 minutes and 8 seconds}[/tex]

Simplify the expression completely.

Answers

Answer: B

Step-by-step explanation: Best way to solve this is to first take the square root of 9 which is 3. Notice in the expression there is an x^4 but once the square root of 9x^4 is taken, you get 3x^2. There is a minus sign in the middle, so answer choice C and D are out. Now, there is answer choice A or B. Now we take the square root of 12 but 12 isn't a perfect square root. But, you can think of 2 numbers that when you multiply give you 12 and one of those numbers is a perfect square root. In this case, it would be 4 because 4 times 3 = 12. Square root of 4 is 2. Again, notice there is an x^2. Once the square root of 4 is taken, you are left with 2x and square root of 3. The square root of 3 isn't a perfect square root. But, you can write the expression in the following way:

2x[tex]\sqrt{3}[/tex] - 3[tex]x^{2}[/tex]

Hope this helps.

The area of a circular cake plate is 1520 cm?. Find the diameter of the plate to the nearest cm

Answers

Answer:

Hola

tengo una pregunta

de que país

eres? ._.

Can someone help me on this math problem please

Answers

Answer:

  CPCTC

Step-by-step explanation:

In each case the half-angles resulting from bisecting the angles are corresponding parts of congruent triangles, hence congruent themselves. (CPCTC)

When a segment divides an angle into two congruent parts, it is an angle bisector.

What is the exponential expression for the numerical expression 6·6·6·6·6? ​ 5·6^5​ 5^6. ​6^5. 30^5​



32 POINTS

Answers

The answer should be 6^5

Determine if the sequence below is arithmetic or geometric and determine the common difference/ratio in simplest form.




64,16,4,…

This is a (geometric/arithmetic) sequence and the (common ratio/common difference) is equal to ____.

Answers

Step-by-step explanation:

this is clearly not a linear sequence (the terms don't have the same difference).

so, it has to be a geometric sequence.

the common ratio is r.

s2 = s1 × r

16 = 64 × r

r = 16/64 = 1/4

control :

s3 = s2×r

4 = 16 × 1/4 = 4

correct.

Common ratio is 1/4

What is geometric progression ?

A geometric progression or a geometric sequence is the sequence, in which each term is varied by another by a common ratio. The next term of the sequence is produced when we multiply a constant (which is non-zero) to the preceding term. It is represented by:

a, ar, ar2, ar3, ar4, and so on.

Where a is the first term and r is the common ratio.

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 1/4

gives the next term. In other words, [tex]a_n=a_1r^n^-^1[/tex]

Hence, common ratio r = 1/4

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Michael has 13 dollars in his wallet. His father gives him his allowance for the week. Now Michael has 18 dollars. How many dollars did Michael's father give him?

Answers

Answer: 5 Dollars

Step-by-step explanation: You only have to substract 13 of 18, the answer of that is 5.

18-13=5
Michaels after give him $5

20 POINTS AND BRAINLIST! WILL BE GIVEN!!
complete the following statements.

<1 and <5 are remote interior angles of <4.

_ and _ and are remote interior angles of <6.

_ and _ are remove interior angles of <2.

Answers

The sum of the remote interior angles are equal to the exterior angles.

The completed statements are;

∠1 and ∠3 are remote interior angles of ∠6

∠3 and ∠5 are remote interior angles of ∠2

Reasons:

Remote interior angles are the angles that are not on the same vertex as an exterior angle

The remote interior angles of ∠4 are ∠1 and ∠5

Similarly, we have;

∠1 and ∠3 are remote interior angles of ∠6

∠3 and ∠5 are remote interior angles of ∠2

Learn more about the exterior and interior angles of a triangle here:

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In a class of 30 students, 60% like math. How many students: Do not like math?

Answers

Answer:

12 students

Step-by-step explanation:

30×0.4=12.

So if 60% like math the 100-60=40, so 40% dislike math
So you take 40% ad write it as a fraction which is 40 4
—— = ——
100 10

So then you take 4 and divide by the bottom the times by the top like so…
——
10

First divide by the bottom : 30 divided by 10 = 3
Then times by the top : 3 x 4 = 12

Therefore 12 students dislike math!

Approximately what portion of the box is shaded blue?

A.2/3. B.9/10
C.3/5

Answers

the answer should be b 9/10

What is equivalent to 56 − 7 + ( 26 − 4 ) ÷ 2

Answers

Answer:

60

Step-by-step explanation:

56-7+22÷2

56-7+11

67-7=60

hope it helps thanks

Q.

x ÷ 2 = 1.000.000.000
x = ?​

Answers

x÷2=1.000.000.000

x=1.000.000.000×2

x=2.000.000.000

Check:

2.000.000.000÷2=1.000.000.000

♪Answer :

let's find the value of x

x ÷ 2 = 1.000.000.000x = 1.000.000.000*2x = 2.000.000.000

Which angle is complementary to <1?

Answers

Answer:

I don't know sorry but have a nice time answering this question

I need help asap! Pls :)

Answers

Answer:

x = 18

Step-by-step explanation:

trIangle ABC was reflated over y-axis. the coordinate of point A are(6,-4). what are the coordinate of A

Answers

Answer:

(-6,-4)

Step-by-step explanation:

Rule for reflection over the y axis (x,y) -----> (-x,y)

Explanation of rule : change the sign of the x value and keep the y value the same.

Applying rule to given coordinate

(6,-4) -----> change the sign of 6 to get -6 and keep -4 as it is -----> (-6,-4)

Refer to the attached image for more validation. Note that x=0 is the y axis

need help 5 stars and good rating for math problem

Answers

Answer: the 20 ounce box cost less per ounce

Step-by-step explanation:

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