What is the equation of the line in slope-intercept form that is perpendicular to the line y = x – 2 and passes through the point (–12, 10)?

Answers

Answer 1
Final answer:

To find the equation of a line that is perpendicular to another line, we need to consider the fact that perpendicular lines have slopes that are negative reciprocals of each other. The given line has a slope of 1, so the perpendicular line will have a slope of -1. Using the point-slope form of a line, we can find the equation of the perpendicular line by plugging in the given point and slope.

Explanation:

To find the equation of a line that is perpendicular to another line, we need to consider the fact that perpendicular lines have slopes that are negative reciprocals of each other. The given line has a slope of 1, so the perpendicular line will have a slope of -1.

Using the point-slope form of a line, y - y1 = m(x - x1), we can plug in the values of the given point (-12, 10) and the slope (-1) to find the equation:

y - 10 = -1(x - (-12))

y - 10 = -1(x + 12)

y - 10 = -x - 12

y = -x - 2

Therefore, the equation of the line that is perpendicular to y = x - 2 and passes through the point (-12, 10) is y = -x - 2.


Related Questions

Part A: Explain how to determine the value of the vertical translation, d, for the graph of g(x). (2 points)

Part B: Explain how to determine the value of the vertical translation, d, for the graph of f(x) = 2sin(θ + 120°) + 6. (3 points)

Answers

Answer:

Part A: Up 9

Part B: Up 6

Step-by-step explanation:

Part A: The graph appears to be a cosine graph since it starts at a peak on the y-axis. Normally a cosine graph starts at (0,1). This graph begins at (0,10). It has been shifted up y a translation by 9.

Part B: Each trig equation has a basic structure f(x) = a sin (x+b) + k where:

a is the vertical stretchb is the horizontal shiftk is the vertical shift

A vertical translation is a vertical shift and is represented by the value in k added outside of the function. In the equation f(x) = 2sin(θ + 120°) + 6, k = 6. The vertical translation is 6.

A circus had 40 lions. If the ratio of lions to monkeys was 4:9, how many lions and monkeys are there?

Answers

Answer:

90 monkeys

Step-by-step explanation:

If the circus has 40 lions (4*10) = 40

Lions would also multiply by 10 (9*10) = 90

Both sides must be multiplied by the same number to be consistent.

he product of ten and a number is greater than the difference of four times the number and two.

Answers

Answer:

You can use 1 as a solution.

Step-by-step explanation:

10 + 1 = 11

1 * 4 = 4

4 - 2 = 2

11 > 2

Please help me with this math homework ​

Answers

Basically you have to find the graph that goes through the middle of the line or points to it.

I know you can do it! If you have any questions just reply.

given 8y — 6x =8 :

A) transform the equation into slope-intercept form.

b) find the slope and y-intercept of the line.

c) what is the slope of a line parallel to this line?

d) what is the slope of a line perpendicular to this line ?

e) find the equation, in point-slope form, of the line that is perpendicular to this line and passes through the point (0,2).

Answers

Answer:

Step-by-step explanation:

A:  slope-intercept form:  Solve 8y — 6x =8 for y, as follows:  8y = 6x + 8, so that y = (3/4)x + 1.

B:  Slope:  3/4; y-intercept:  (0, 1)

C:  Any line parallel to this line has the same slope, namely, 3/4.

D:  Any line perpendicular to this line has a slope that is the negative reciprocal of 3/4; that is, the slope of the perp. line is -4/3.

PLEASE HELP ASAP
Evaluate the expression. 8(12 + 4)0 − 4(8 + 3)0
A) 0
B) 1
C) 2
D) 4

Answers

A I think cuz both are multiplied by 0

The answer is zero because there is a zero that you would have to multiply you sum too

Between what two consecutive integers does .... lies?

Answers

Answer: third option

Step-by-step explanation:

To solve the exercise you must apply the proccedure shown below:

- Find the value of irrational number given in the problem (By definition, an irrational number cannot be written as a simple fraction, where the numerator and the denominators are integer.

- Then the value in decimal number is the following:

[tex]\sqrt{115}=10.72[/tex]

- The number 10.72 is located between the integer 10 and the integer 11.

can someone find the volume of this pyramid?

Answers

Check the picture below.

now, let's notice the triangle on the base.... is an isosceles, two sides are twins, and therefore, the two angles they make out are also twins, so, if the central angle is 100°, the other angles are each 80°/2, namely 40°, therefore, using the law of sines,

[tex]\bf \textit{Law of sines} \\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{sin(100^o)}{2.5}=\cfrac{sin(40^o)}{r}\implies r\cdot sin(100^o)=2.5\cdot sin(40^o) \\\\\\ r=\cfrac{2.5\cdot sin(40^o)}{sin(100^o)}\implies \boxed{r\approx 1.63}[/tex]

now, let's notice the shaded triangle, namely the one with 35°, is a right-triangle, namely one angle is 35°, another 90°, so the last one must be 55°.

the opposite side to the 35° is "r", which we know is about 1.63, so again, let's use the law of sines to find the side "h",

[tex]\bf \cfrac{r}{sin(35^o)}=\cfrac{h}{sin(55^o)}\implies r\cdot sin(55^o)=h\cdot sin(35^o) \\\\\\ \cfrac{r\cdot sin(55^o)}{sin(35^o)}=h\implies \cfrac{1.63\cdot sin(55^o)}{sin(35^o)}\approx h\implies \boxed{2.33\approx h} \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a circular cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r\approx 1.63\\ h\approx 2.33 \end{cases}\implies V\approx \cfrac{\pi (1.63)^2(2.33)}{3}\implies \blacktriangleright V\approx 6.48 \blacktriangleleft[/tex]

make sure your calculator is in Degree mode.

How to solve logarithmic equations as such

Answers

[tex]\bf \textit{exponential form of a logarithm} \\\\ \log_a b=y \implies a^y= b\qquad\qquad a^y= b\implies \log_a b=y \\\\\\ \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} ~\hspace{7em} \begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{\textit{we'll use this one}}{a^{log_a x}=x} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \log_2(x-1)=\log_8(x^3-2x^2-2x+5) \\\\\\ \log_2(x-1)=\log_{2^3}(x^3-2x^2-2x+5) \\\\\\ \log_{2^3}(x^3-2x^2-2x+5)=\log_2(x-1) \\\\\\ \stackrel{\textit{writing this in exponential notation}}{(2^3)^{\log_2(x-1)}=x^3-2x^2-2x+5}\implies (2)^{3\log_2(x-1)}=x^3-2x^2-2x+5[/tex]

[tex]\bf (2)^{\log_2[(x-1)^3]}=x^3-2x^2-2x+5\implies \stackrel{\textit{using the cancellation rule}}{(x-1)^3=x^3-2x^2-2x+5} \\\\\\ \stackrel{\textit{expanding the left-side}}{x^3-3x^2+3x-1}=x^3-2x^2-2x+5\implies 0=x^2-5x+6 \\\\\\ 0=(x-3)(x-2)\implies x= \begin{cases} 3\\ 2 \end{cases}[/tex]

Subscriptions to a popular fashion magazine have gone down by a consistent percentage each year and can be modeled by the function y = 42,000(0.96)t. What does the value 42,000 represent in the function? A) The decay factor of subscribers. B) The initial number of subscribers. C) The number of time intervals. D) The number of subscribers after t years. Submit

Answers

Answer:

B) The initial number of subscribers.

Step-by-step explanation:

The given equation is:

[tex]y=42000(0.96)^{t}[/tex]

[tex]y=42000(1-0.04)^{t}[/tex]

We can compare this equation with the general model of exponential growth/decay:

[tex]y=A(1-r)^{t}[/tex]

Here A represents the initial amount, r represents the rate of decay and t represents the time in years.

Comparing both equations, we can see that 42,000 represents the Initial Quantity which in this case is the initial number of subscribers.

So option B gives us the correct answer.

Answer:

B) the initial number of subscribers

Step-by-step explanation:

HELP PLEASE 3 QUESTIONS (30 POINTS)

Answers

Answer:

1.) A

2.) B I Think

3.) B

Answer:

1. a / 2. c / 3. b

Step-by-step explanation:

the inequality 6-2/3

Answers

16 over 3 is the answer u write the numerator above the denominator 6 over 1 minus 2 over 3 6 times 3 over 1 x3 minus 2 over 3 u get 18 minus 2 over 3 and subtract 18 and 2 u get 16 over 3

Answer:

x>9

Step-by-step explanation:

       

Simplify   2/3

           (6 -  (— • x)) -  (x - 9)  < 0  

        3          

Plz help me with it

Answers

Answer:   [tex]\bold{2\sqrt[3]{15} }[/tex]

Step-by-step explanation:

[tex]\sqrt[3]{10} \cdot \sqrt[3]{12} =\sqrt[3]{2\cdot 5\cdot 2\cdot 2\cdot 3} =2\sqrt[3]{3\cdot 5} =\boxed{2\sqrt[3]{15}}[/tex]

Determine whether the table could represent a function that is linear, exponential, or neither. If the function is exponential or linear, find a function that passes through the points. If the function is neither exponential nor linear, type NONE.

x 1 2 3 4
f(x)70 40 10 -20
f(x)=

Answers

Answer:

Linear

y = -30x + 100

Step-by-step explanation:

The table has a set of inputs with matching outputs. The behavior of the outputs will determine the type of function. The outputs appear to descend at a constant subtraction rate of -30 each time.

70 - 30 = 40

40 - 30 = 10

10 - 30 = -20

etc.

A constant addition or subtraction rate is a slope. Since the function has a slope, this is a linear function.

To write the function you'll need a slope and a y-intercept. Recall, the y-intercept is where x = 0. This is not in the table but can be found by reversing the process by adding 30 + 70 = 100.

Substitute m = -30 and b = 100 into y = mx+b for the equation.

y = -30x + 100

Answer:

Step-by-step explanation:

the answer is f(x)= 100-30x

Need so much help with number 3

Answers

Answer:

Judy is 12 Years old.

Step-by-step explanation:

Add up all the ages and you get 43 years old. Subtract 55 by the 43 to get 12 meaning Judy is 12. Please mark brainliest.

Answer:

Judy's age is 12 years old

Step-by-step explanation:

to find the average you need to add all numbers up ans then divide by how many there are.

10 + 10 + 11 + 12 + 12 = 55/5 = 11

hope this helps

need help with number 29

Answers

Answer:

9c

Step-by-step explanation:

Collecting like terms

We can do 8-6 which is 2

and then 2 add 7 which is 9

Add c

Add. Write your answer as a fraction in simplest form. 9/10 +(− 4/5 )

Answers

Step-by-step explanation:

9/10 + (-4/5)

1. Use the least common denominator (LCD): 10

9/10 + (-8/10)

2. Remove the parentheses:

9/10 - 8/10

3. Simplify:

= 1/10

Hope this Helped!!

~Shane

The perimeter of a square is 76.4m calculate the length of its diagonal

Answers

Answer: About 27.01

Step-by-step explanation: The way to find the diagonal is to multiply one side of the square by the sq. rt. of 2. First, we had to find one side of the square, which would be 76.4 divided by 4, then multiply that by the square root of 2.

76.4 / 4 = 19.1

19.1 x sq. rt. of 2 = 27.0114790413, or about 27.01

Type in all the digits of Pi

I have a picture. Type in all of them. Get 30 points.

Answers

Answer:

PI= 3.1415926535897932384624338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058

Pi is a Mathematics constant that represents the ratio of a circle's circumference to its diameter. Its decimal representation is approximately 3.14.

The value of Pi is a mathematical constant that represents the ratio of a circle's circumference to its diameter.

The decimal representation of Pi is approximately 3.14159265358979323846264338327.

However, it is important to note that Pi is an irrational number, which means its decimal representation goes on infinitely without repeating.

Learn more about Mathematics here:

https://brainly.com/question/27235369

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The probable question may be:

Type in all the digits of Pi

I have a picture. Type in all of them. Get 30 points.

A slice of PI

******************

****************

3.14159265358979

323846264338327

95028841971693

9937510582097

 494459230781

  64062862089

   9862803482

     534211706

      79821480

       8651328

        230664

         70938

          4460

           955

            05

             8

‐15−8= ‐15 + __

= __

Enter numbers to evaluate ‐15−(‐8).

‐15−(‐8)= ‐15 + __

=__

Answers

Answer:

‐15−8= ‐15 + -8

‐15−(‐8)= ‐15 + 8

Step-by-step explanation:

‐15−8 = -23

‐15 + -8 = -23

‐15−(‐8) = -7

-15+8 = -7

Answer:

‐15−8= ‐15 + -8

‐15−(‐8)= ‐15 + 8

Which number is a factor of 8?

4
7
5
6

Answers

Answer:

4

Step-by-step explanation:

[tex]The\ factors\ of\ 8:\ 1,\ 2,\ 4,\ 8\\\\8=1\cdot8\\8=2\cdot\boxed4\\8=4\cdot2\\8=8\cdot1[/tex]

4 is the correct answer

What happens if you breed a patchwork fish (Bb) with a fish that only had Blue Scales (BB)?
a. What is the probability of having fish with red scales? _____%
b. What is the probability of having fish with patchwork scales?____%

Answers

Answer:

50% and 50%, they are both the same!

Final answer:

When breeding a patchwork fish (Bb) with a fish that only has Blue Scales (BB), there is a 50% chance of having fish with red scales (Bb) and a 0% chance of having fish with patchwork scales (bb).

Explanation:

When breeding a patchwork fish (Bb) with a fish that only has Blue Scales (BB), the offspring will have a 50% chance of having red scales (Bb) and a 50% chance of having blue scales (BB). This is because the blue scales are dominant over the red scales, represented by the capital 'B', and the patchwork scales are recessive, represented by the lowercase 'b'.



To calculate the probability of having fish with red scales, we divide the number of offspring with red scales (Bb) by the total number of possible offspring, and then multiply by 100. So the probability is 50%.



To calculate the probability of having fish with patchwork scales, we divide the number of offspring with patchwork scales (bb) by the total number of possible offspring, and then multiply by 100. Since the fish that only has blue scales does not carry the patchwork gene, there will be no offspring with patchwork scales. Therefore, the probability is 0%.

Learn more about breeding fish here:

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9. Consider a pattern that begins with 28 and each consecutive number is six more than the previous term. What are the first three terms of this pattern?

Answers

Answer:

The first three numbers in the pattern would be 6, 12, and 18 since the rule pattern goes by six. I'm not sure if this is what you were looking for but I hope I helped!

Factor. 49x16−16y64

Answers

Answer:

(7x8 + 4y32) • (7x8 - 4y32)

Step-by-step explanation:

P.1 (49 • (x16)) - 24y64

P.2 72x16 - 24y64

P.3 (7x8 +4y32) • (7x8 - 4y32)

What is the solution to the proportion 8/x = 4/5

Answers

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷ Since 8/x is two times the size of 4/5, you multiply by 2

4/5=8/10

X=10

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

DOGE

During the first week of a summer camp 2 out of 3 campers were boys. During the second week 3 out of 5 were boys. There were a 15 total campers each week. During which week were there more boy campers. Explain

Answers

Step-by-step explanation:

2/3=10/15 (divide 15 by 3 to get 5, then multiply both numerator and denominator by 5 to set equivalent)

3/5=9/15

10/15 is greater than 9/15, so during the 1st week there were more boy campers

Final answer:

During the first week of a summer camp, there were more boy campers.

Explanation:

To determine during which week there were more boy campers, we need to compare the fractions of boys in each week. In the first week, 2 out of 3 campers were boys, which can be written as a fraction as 2/3. In the second week, 3 out of 5 campers were boys, which can be written as a fraction as 3/5. To compare these fractions, we need to find a common denominator. In this case, the lowest common denominator is 15, which is the total number of campers each week. Multiplying the numerator and denominator of each fraction by 5 and 3 respectively, we get 10/15 for the first week and 9/15 for the second week. Therefore, during the first week, there were more boy campers.

Learn more about Comparing Fractions here:

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Find the surface area of a cylinder

Answers

A = 2•3.14•3•8 + 2•3.14•3^2 = 207.34512

Answer:

Surface area = 207.24 in²

Step-by-step explanation:

Remember to always convert the diameter into a radius.

D = 6 in (divide it by two to get the radius) R = 3 in

Radius = 3 in

Formula:

SA = 2[tex]\pi[/tex]rh + 2[tex]\pi[/tex]r²

Solution:

SA = 2[tex]\pi[/tex]rh + 2[tex]\pi[/tex]r²

SA = 2(3.14)(3)(8) + 2(3.14)(3)

SA = 2(3.14)(3)(8) + 2(3.14)(9)

SA = 150.72 + 56.52

SA = 207.24 in²

Please help find missing angle

Answers

a=1, c=25/7(3.571429) b=?
c=hypotenuse
a=side

In this case, we are finding for a SIDE and not the HYPOTENUSE.

Using Pythagoras' theorem
side²= hyp²–side²
b²= 3.57²–1²
b²= 12.7–1
b²= 11.7
b²= √11.7
b²= 3.4(correct to 1 dp)

Therefore, b= 3.4

HOPE THIS HELPS.... IF NOT I'M SO SORRY :'(
IF IT HELPS YOU PLEASE THANK ME AND GIVE ME BRAINLIEST :)

Answer:

[tex]\frac{24}{7}=b[/tex]

Step-by-step explanation:

We are given a right angled triangle.

Hypotenuse = c = [tex]\frac{25}{7}[/tex]

Base = a = 1

Now we are supposed to find the perpendicular i.e. b

So, we will use Pythagoras Theorem  :

[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]

[tex]c^2=b^2+a^2[/tex]

[tex](\frac{25}{7})^2=b^2+1^2[/tex]

[tex]\frac{625}{49}=b^2+1[/tex]

[tex]\sqrt{\frac{625}{49}-1}=b[/tex]

[tex]\frac{24}{7}=b[/tex]

Hence the missing length is [tex]\frac{24}{7}[/tex].

The volume of a cube can be found using the equation V=S3, where V is the volume and Sis the measure of one side of the cube. Match the equation for how to solve for the side length of a cube to its description.

Answers

Answer:

s = ∛729 in³

Step-by-step explanation:

Since the volume is 729 in³, our equation can be plugged into:

729 = s³.

Isolate s by cube rooting each side: ∛729 = s.

A quadrilateral has angle measures of 102°, 84°, and 77°. What is the measure of the fourth angle?

Answers

Answer:

Measure of the 4th angle = 360-(102+84+77)

= 360-263

= 97°

Hope this helps!

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