A line is said to be perpendicular to another line if the two lines intersect at a right angle. Explicitly, a first line is perpendicular to a second line if (1) the two lines meet; and (2) at the point of intersection the straight angle on one side of the first line is cut by the second line into two congruent angles.
We want to find a perpendicular line to a given line, such that it passes through a point (and we want to separate the case where the point is on the line and when the point is not in the line, we will see that the construction is exactly the same).
Well, let's define the first line:
f(x) = a×x + b
where a is the slope and b is the y-intercept.
and the point (x₁, y₁).
We know that any perpendicular line to the above one will have a slope equal to:
s = -(1/a)
So the perpendicular line will be something like:
y = -(1/a)×x + c
Now we need to find the value of c, and here we need to use the point (x₁, y₁).
If the line passes through this point, this means that when x = x₁, the value of y must be y₁.
So we can just replace these in the equation:
y₁ = -(1/a)×x₁ + c
now we can solve for c:
c = y₁ + x₁/a
Then the equation of the line is:
y = -(1/a)×x + (y₁ + x₁/a)
And as you can see, here we did not use the fact that (x₁, y₁) belongs or not to the original line, so the construction is exactly the same in both cases.
If you want to learn more, you can read:
https://brainly.com/question/23905413
BRAINIEST FOR CORRECT ANSWER
Please solve these all for me i really need them
Answer:
9: 5y 10: 40x-4 11: 992a+5b 12: 24 list A: 24, 16, 21 list B 16, 24, 21
Step-by-step explanation:
I don’t have the rest but all of the problems are really easy
Nicholas has a collection of books. He has 115 fantasy and science-fiction books. These books are 46% of his collection. How many books does he have in his collection?
Answer:
i think 250
Step-by-step explanation:
Drug Name Half-life
-----------------------------------
Acetaminophen 1-4 hours
Ibuprofen 1.8-2 hours
Loratadine 8.4 hours
Lithium 8 hours
Diphenhydramine 5.3-11.7 hours
The table above displays the half-lives of 5 common house hold drugs. The half-life (h) is the time is takes for a substance to reduce to half its initial value (A0). Half life can be used to solve for the amount (A) of a substance left after t time by using the following equation:
A=A^0⋅(12)^t/h
If Scott was administered 300 mg of Lithium, which of the following represents how much lithium, rounded to the nearest hundredth of a mg, could be left in Scott's blood stream after 12 hours?
Select one:
A. 157.23
B. 106.07
C. 212.17
D. 188.99
Answer:
B. 106.07
Step-by-step explanation:
To make use of the given formula for amount remaining, we need to know the original amount (300 mg), the elapsed time (12 h), and the half-life of the substance of interest (8 h).
SetupUsing the given formula with the relevant values, we have ...
A = (300 mg)·(1/2)^(12/8)
EvaluationUsing a calculator to evaluate this expression, we find the amount of Lithium remaining in Scott's system after 12 hours to be ...
A ≈ 106.07 mg
Ellie is making a batch of pancakes
and her recipe calls for 1 1/2 cups of
flour and 1 1/4 cups of milk. If she only
has 1 cup of milk, how much flour
should she use to make the same
pancake recipe?
As part of an experiment, Janelle spins a multicolored spinner 100 times and concludes that the probability of the arrow landing on orange is an unlikely event. If Janelle’s conclusion is true, which of these could be the probability of the event?
A. 0 B. 0.3 C. 0.5 D. 1
Answer:
B: 0.3
But before you submit your answer, ask, "Is it bussin Janelle?"
Write an explicit formula for a , the nth term of the sequence 7, 14, 28, ...
Answer:
The sequence 7, 14, 28, ... is a geometric sequence with first term 7 and common ratio 2. The explicit formula for a geometric sequence is a_n = a_1 r^(n-1), where a_n is the nth term, a_1 is the first term, and r is the common ratio. In this case, a_n = 7 (2)^(n-1).
Here are the first few terms of the sequence:
n = 1: a_1 = 7
n = 2: a_2 = 14
n = 3: a_3 = 28
n = 4: a_4 = 56
n = 5: a_5 = 112
As you can see, the formula works for all values of n.
Step-by-step explanation:
30 POINTS!!!
In this discussion, you have the opportunity to have some hands-on fun. With a
tape measure determine the diameter and circumference of at least three circular
objects. Calculate the ratio of the circumference to the diameter.
Take a look at Khianna's post:
I used a tape measure to determine the diameter and circumference of an orange
juice can, a trash can, and a lamp shade. Here is what I found:
Circumference
4.65 in
Ratio
3.1
OJ Can
Diameter
1.5 in
8 in
6 in
Trash Can
3.12
24.96 in
18.8 in
Lamp Shade
3.13
The ratio was close to Pi, but never actually equaled 3.14, maybe because of an
error when I measured the objects.
After you complete your measurements, use the diameter to calculate the exact
circumference of each object as shown on the next page.
Use the diameter to calculate the exact.value of the circumference of each object.
Look how Khianna added to her post:
If I used the diameter I measured, the exact value for each object's circumference would be: diameter or circumference OJ can 1.5 in 1.5 pi and 4.71 in trashcan eight in a pie in 25.12 in lampshade six and six pie and 18.84 in
Use a measuring tape to determine the diameter and approximate for conference of three household items
Find the ratio of the circumference to the diameter for each circle identify what the value of this ratio should be
Use pi and the diameter to calculate the exact value of the circumference
Use the approximation pi equals 3.14 to find the approximate circumference
Answer:
Diameter x Pi = Circumference
Find the perimeter of the trapezoid shown.
A. 23.5 m
B. 20 m
C. 12 m
D. 8 m
Answer:
B
Step-by-step explanation:
5+7+4+4=20
bag is filled with 12 green marbles, 4 white marbles, and 2 blue marbles. What is the probability of drawing a marble that is blue?
A) 2% B)11% C)13% D) 20%
Answer:
B 11%
Step-by-step explanation:
The total number of marbles is
12+4+2 = 18
P( blue) = number of blue marbles / total marbles
= 2 blue/ 18 total
= 1/9
=.11111
= 11.11%
Write an explicit formula for a_na
n, the nth term of the sequence 11,9,7,...
no need to explain
Please help me I am stuck on question C.
help me pleasw and thank you what is -2x + 8 - 5x
Pls help meeeee dew 5 minutes ago!!!
Answer:
D
Step-by-step explanation:hope this helps...lilshorty
in a certain chemical the ratio of zinc to Copper is for 211 a jar of the chemical contains 385 grams of copper how many grams of zinc does it contain.
Answer: well what are my choices?
Step-by-step explanation:
Use the Pythagorean theorem to find the unknown side of the right triangle.
Hypotenuse length = ____
thank u so much this is worth 15 points
Answer:
The answer is 41.
Hypotenuse length=41
Answer:
40×9÷2= 180
Hope this helps!!
Questions in a nutshell:
Let me repost this question 20 times and it will work
Teehee I will give brainiest to whoever answers correctly Teehee
What is 5 x 5 x 20 x 80 to the power of 10?
Answer:
1.048576e+46
Step-by-step explanation:
(5x5)x20x80 to the power of 10
(25x20)x80 to the power of 10
500x80 to the power of 10
40000 to the power of 10
the answer is 1.048576e+46
Answer:
1.048576E46
Step-by-step explanation:
brainliest please tryna rank up.
You are a waiter at a restaurant. A family had a bill of $116.17. They leave you a 20% tip. How much of a tip did you get?
Answer:
Hello there! :) The tip they would leave you would be of $23.23
Step-by-step explanation:
The first step is to devide 116.17 by 100, which would equal 1.1617, which is obviously not your answer or a valid amount of money. But, you now take this 1.1617 by 20. Why? Becuase 20% is the same as 20 out of 100. Now you multiply 1.1617 × 20 and you will get $23.23.
Dont use me for points please
Answer:
1. is 351.25 ft^2.
2. is 72.4 rounded up to 73 sections.
3. is 450 meters.
4. is $129.
IM STRUGGLING PLZ HELP
Answer:
Height= 3ft
Step-by-step explanation:
Height of the scale drawing = 2 inches
1 inch = 1.5ft of actual playhouse
if 1 in = 1.5ft, then 2 in = 3ft because 1.5 x 2 = 3
Help, I'm thinking it's a and c but I'm not sure
Answer:
Its B.
Step-by-step explanation:
(7-5)² = x²
2² = x²
x² = 2²
x = ±2
x = -2
x = 2
x1 = -2
x2 = 2
What is the area of this polygon?
A) 24 cm2
B) 16 cm2
C) 40 cm2
D) 18 cm2
Answer:
C) 40 cm²
Step-by-step explanation:
area of top triangle = 1/2 x 8 x 6 = 24 cm²
area of bottom triangle = 1/2 x 8 x 4 = 16 cm²
24 cm² + 16 cm² = 40 cm²
The time it takes a bricklayer to lay bricks varies directly with the number of bricks. The brick layer's data is shown in the table. If x = time, and y = the number of bricks, which equation models the bricklayer's direct variation?
Answer:
50
Step-by-step explanation:
2 = 100
100 ÷ 2 = 50
half of a hundred is 50
Answer:
50
Step-by-step explanation:
2 = 100
100 ÷ 2 = 50
answer=50
When he receives his first memory from the old man, what did Jonas experience for the first time?
A. the colors of the rainbow
B. the painful feeling of a sunburn
C. the feeling of snow and of riding a sled down a hill
D. the feeling of driving a car on an open road
Answer:
C. The feeling of snow and of riding a sled down a hill.
Step-by-step explanation
I read the book.
whats the slope and y-intercept sorry i keep getting it wrong
Answer:
-2 & 3/2
Step-by-step explanation:
=> -4x - 2y = -3
=> -4x + 3 = 2y
=> (-4/2)x + (3/2) = y
Compare this to y=mx+c
m=slope = -4/2 = - 2
y-intercept = c = 3/2
Answer:
2 & 3/2
hope this helps have a great rest of your day!
Step-by-step explanation:
0= - z/3 + 4
Can you help me?
Answer:
z=12
Step-by-step explanation:
subtract both sides by 4:
-z/3=-4
then multiply both sides by -3:
z=12
Answer:
Step-by-step explanation:
Jd
would you pls answer this question?
Answer:
24÷6= 4
so h= 3×4= 12feet
how much is a $450 snowboard with 7.25% sales tax
I need help!! ASAP!! (Classify each number as rational or irrational.)
Please answer this correct
Answer:
C), or y = 200(1.18)^x, because we have 200 bacteria to start with and 1.18 because if you multiply something by 1.18 that is essentially 118% more than the number, or 18% more than the number.
Hope this helps!
explain to me how to find the volume of a shape like im a 5 yr old because thats the best way ill understand it.
Answer:
length x width x height
Step-by-step explanation:
I'm 43
Answer:
Length x height x width.
Step-by-step explanation:
Examples:
1 x 2 x 3 = 1 x 2 = 2 + 0 = 2 x 3 = 3 + 3 = 6 so the answer is 6.
2 x 3 x 2 = 2 x 3 = 3 + 3 = 6 x 2 = 6 + 6 = 12 so the answer is 12.
Here's one more in a different way:
3 x 5 x 4 = 5 + 5 + 5 = 15 = 15 + 15 = 30 x 2 = 30 + 30 = 60.