MATHEMATICS HIGH SCHOOL

What's perpendicular to:
y= x-1

And

y= -1/3x -1

Answers

Answer 1
Answer: Those are two separate lines, and they're not parallel or perpendicular
to each other.
So there's no line that's perpendicular to both of them, and you're asking
two separate questions.

For both of them, you have to remember this: 
Lines that are perpendicular have negative reciprocal slopes.

-- The slope of [ y = x - 1 ] is 1, and the negative reciprocal of 1 is -1/1 = -1 .
A line perpendicular to [ y = x - 1 ] is [ y = -x + any number ].

-- The slope of [ y = -1/3 x - 1 ] is -1/3, and the negative reciprocal of -1/3 is 3 .
A line perpendicular to [ y = -1/3 x - 1 ] is [ y = 3x + any number ].


Answer 2
Answer: k:y=m_1x+b_1;\ l:y=m_2x+b_@\n\nk\ \perp\ l\iff m_1m_2=-1\n\n========================\nk:y=x-1;\ l:y=mx+b\n\nk\ \perp\ l\iff1m=-1\to m=-1\n\nl:y=-1x+b\to y=-x+b\ (b\in\mathbb{R})\n==========================\nk:y=-(1)/(3)x-1;\ l:y=mx+b\n\nk\ \perp\ l\iff-(1)/(3)m=-1\to m=3\n\nl:y=3x+b\ (b\in\mathbb{R})

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One number is 1 more than 4 times another. Their product is 18. What are the numbers?

Answers

The numbers are 9 and 2.

One number is 1 more than 4 times another.
2 x 4 = 8
8 + 1 = 9

Their product is 18.
9 x 2 = 18

Usually, with this type of problem, it's easiest just to use trial and error. Go through the factors of 18, and eventually you'll find a pair that fits the given criteria.

Can someone please help me?

Answers

the answer is 62.8 cm^2.

cylinder surface area formula is 2*pi*a(a+h) where a is radius and h is height.
plug in your numbers in the right places and you have your answer!

Identify each expression that represents the slope of a tangent to the curve y= -x^3+17x^2-x+3 at any point (x,y).

Answers

This is seriously so long I'm not sure it will even fit on a single line. The formula for the derivative using the limiting process is \lim_(h \to 0) (f(x+h)-f(x))/(h). And of course this is a problem because if h approaches 0, we would have a 0 in the denominator of that fraction and that is definitely not allowed! Every x in the function will be replaced with (x+h) to give us this: \lim_(h \to 0) (-(x+h)^3+17(x+h)^2-(x+h)+3)/(h). When we expand that we will get this very long numerator (I'm purposely leaving out the limit as h approaches 0 part to save space): (-(x^3+2x^2h+xh^2+x^2h+2xh^2+h^3)+17x^2+34xh+17h^2-x-h+3-(-x^3+17x^2-x+3))/(h). Simplifying that leaves us with this: (-x^3-2x^2h-xh^2-x^2h-2xh^2-h^3+17x^2+34xh+17h^2-x-h+3+x^3-17x^2+x-3)/(h). We have a lot of terms that cancel each other out so when we do that we are left with \lim_(h \to 0) (-3x^2h-3xh^2-h^3+34xh+17h^2-h)/(h). That is one of your choices for answers, the third one down on the left to be specific. Now we can factor out an h: \lim_(h \to 0) (h(-3x^2-3xh-h^2+34x+17h-1))/(h). That h on the top outside the parenthesis cancels with the h on the bottom. Now, as h approaches 0 we have no problems! Yay! That means when we now replace h with 0, we have this: -3x^2-0-0+34x+0-1, or simplified we have -3x^2+34x-1 which is also a choice for your answers, top one on the right. Those are your 2 answers for that dertivative. It's much simpler when you learn the rules!

Pls help ASAP! Consider this linear function:
Y= 1/2x + 1
Plot all ordered pairs for the values in the domain.
D: { -8,-4,0,2,6}

Answers

A graph of the linear function y = 1/2(x) + 1 is shown in the image attached below.

What is the slope-intercept form?

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

  • m represent the slope or rate of change.
  • x and y are the points.
  • b represent the y-intercept.

Since the given linear function y = 1/2(x) + 1 is in slope-intercept form, we would start by plotting the y-intercept:

y = 1/2(x) + 1

y = 1/2(0) + 1

y = 1 ⇒ (0, 1)

y = 1/2(-8) + 1

y = 1 ⇒ (-8, -3)

y = 1/2(-4) + 1

y = 1 ⇒ (-4, -1)

y = 1/2(2) + 1

y = 1 ⇒ (2, 2)

y = 1/2(6) + 1

y = 1 ⇒ (6, 4)

Next, we would use an online graphing tool to plot the given linear function for the values in its domain { -8,-4,0,2,6} using table, as shown in the graph attached below.

Read more on a graph here: brainly.com/question/4546414

#SPJ3

Final answer:

To plot the ordered pairs for the given domain of a linear function, substitute each value of x into the equation and solve for y.

Explanation:

To plot the ordered pairs for the values in the given domain, we substitute each value of x into the equation and solve for y. Let's do that for each value in the domain:

  1. For x = -8, y = (1/2)(-8) + 1 = -4 + 1 = -3. The ordered pair is (-8, -3).
  2. For x = -4, y = (1/2)(-4) + 1 = -2 + 1 = -1. The ordered pair is (-4, -1).
  3. For x = 0, y = (1/2)(0) + 1 = 0 + 1 = 1. The ordered pair is (0, 1).
  4. For x = 2, y = (1/2)(2) + 1 = 1 + 1 = 2. The ordered pair is (2, 2).
  5. For x = 6, y = (1/2)(6) + 1 = 3 + 1 = 4. The ordered pair is (6, 4).

The ordered pairs for the given domain are (-8, -3), (-4, -1), (0, 1), (2, 2), and (6, 4).

Learn more about Plotting ordered pairs of a linear function here:

brainly.com/question/29046277

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Helppp meeYou walk into a restaurant. In the room there are 10 people who are 21 years old , 3 people are 26 years old 7 people are 29 years old and 9 people who are 31 years old. 17 are men. how many people are in the restaurant.


PLEASE HELP!! ( 8 minutes till i have to turn in) Will thumbs up every answer. (46 and 29 aren't the answer btw).

Answers

You walk into a restaurant. In the room there are 10 people who are 21 years old , 3 people are 26 years old 7 people are 29 years old and 9 people who are 31 years old. 17 are men. how many people are in the restaurant. 

10 + 3 + 7 + 9 = 29

The answer is 30 yes all the math adds up to 29 but you need to count yourself which the riddle hasnt

What is the median of this data set? 23,37,49,15,82

Answers

Answer:37

Step-by-step explanation:

Answer:37

Step-by-step explanation: rearrange so it becomes 15, 23,37, 49,82 middle is then 37
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