Recall from Intermediate Algebra that two non-vertical lines are perpendicular if and only if they have negative reciprocal slopes. That is to say, if one line has slopem1and the other has slopem2thenm1 · m2 = −1.Please note that a horizontal line is perpendicular to a vertical line and vice versa, so we assumem1 ≠ 0andm2 ≠ 0.Below, you are given a line and a point which is not on that line. Find the line perpendicular to the given line which passes through the given point.
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
The line is [tex]y = -4 x[/tex]
Step-by-step explanation:
From the question we are told that
The line is [tex]y = \frac{1}{4} x + 8[/tex]
The point is P(0,0 )
Generally the equation for a line is [tex]yn = mx + c[/tex]
Now comparing this with the given equation we see that
[tex]m =\frac{1}{4} = slope[/tex]
[tex]C =8 = intercept [/tex]
Generally the slope of the perpendicular to the given line is mathematically evaluated as
[tex]m_1 = - \frac{1}{m}[/tex]
=> [tex]m_1 = - \frac{1}{ \frac{1}{4}}[/tex]
=> [tex]m_1 = -4 [/tex]
Generally from the univesal equation of a line and the given point we have that
y = mx + c at p(0,0) and [tex]m_1 = -4[/tex] is
0 = -4 (0 ) + c
=> c = 0
Hence the equation perpendicular to the line given at the point given is
[tex]y = -4 x[/tex]
Related Questions
Method of Least Squares, Evaluation of Cost Equation Lassiter Company used the method of least squares to develop a cost equation to predict the cost of moving materials. There were 80 data points ft the regression, and the following computer output was generated: Intercept $19,050 Slope Coefficient of correlation 0.91 Standard error $220 The activity driver used was the number of moves.
Required:
1. What is the cost formula?
2. Using the cost formula, predict the cost of moving materials if 340 moves are made.
3. What percentage of the variability in moving cost is explained by the number of moves? (Round percentage to two decimal places.)
Answers
Answer:
(1) The cost formula is: y = $19,050 + $12·x.
(2) The cost of moving materials if 340 moves are made is $23,130.
(3) 82.81% of the variability in moving cost is explained by the number of moves.
Step-by-step explanation:
The computer output for the regression analysis of 80 data points is as follows:
Intercept: $19,050
Slope: 12
Coefficient of correlation: 0.91
Standard error: $220
(1)
The general formula of regression equation is:
y = a + b·x
Here,
a = intercept
b = slope
The cost formula is:
y = $19,050 + $12·x
(2)
Predict the cost of moving materials if 340 moves are made as follows:
[tex]y = 19050 + 12\cdot x\\=19050+12\times 340\\=19050+4080\\=23130[/tex]
Thus, the cost of moving materials if 340 moves are made is $23,130.
(3)
The coefficient of determination R² specifies the percentage of the variance in the dependent variable (Y) that is forecasted or explained by linear regression and the forecaster variable (X, also recognized as the independent-variable).
The coefficient of determination R² can be computed by squaring the correlation coefficient value.
[tex]R^{2}=(r)^{2}=(0.91)^{2}=0.8281[/tex]
Thus, 82.81% of the variability in moving cost is explained by the number of moves.
How far has the car gone
Answers
Answer:
uhh how am i suposed to know that u ahve o image
which of the following must be true to prove abc = def by the aas the theorem
Answers
Simplify the expression: (4x2 - 3x + 1) - (3x2 - 5x + 4)
Answers
Answer:
x² + 2x - 3
Step-by-step explanation:
Step 1: Write expression
(4x² - 3x + 1) - (3x² - 5x + 4)
Step 2: Distribute negative
4x² - 3x + 1 - 3x² + 5x - 4
Step 3: Combine like terms (x²)
x² - 3x + 1 + 5x - 4
Step 4: Combine like terms (x)
x² + 2x + 1 - 4
Step 5: Combine like terms (constants)
x² + 2x - 3
(3x - 15)° 0 + 25)
105°
Find the value of a
Ox=35
O x 40
O x = 60
* = 65
Answers
A jury pool has 17 men and 24 women, from which 12 jurors will be selected. Assuming that each person is equally likely to be chosen and that the jury is selected at random, find the following probabilities:
Give all answers accurate to six decimal places.
a) all men
b)all women
c) 8 men 4 women
d) 6 men 6 women
Answers
Answer:
since [tex]17+24=41[/tex]
a) [tex]\frac{\binom{17}{12}}{\binom{42}{12}}[/tex]
b) [tex]\frac{\binom{24}{12}}{\binom{42}{12}}[/tex]
c) [tex]\frac{\binom{17}{8} \cdot \binom{24}{4}}{\binom{42}{8}\cdot\binom{36}{4}}[/tex]
d) [tex]\frac{\binom{17}{6}\cdot\binom{24}{6}}{\binom{17}{6}\cdot\binom{36}{6}}[/tex]
Just calculate these. If there is anything wrong just let me know.
what is the quotient in simplest form
12/7÷3
Answers
Answer:
5.150214592274678
Step-by-step explanation:
Answer:
12/21
Step-by-step explanation:
12/7 /3 = 12/7 * 1/3
12/7 * 1/3 = 12*1 / 7*3
12*1 / 7*3 = 12/21
what the heck
is b,e,g,h i dont have letters its literally just blank squares
Answers
Ask your teacher. I think that'll be the best decision for you since I can't do anything for you as a user in brainly.
3. The average rate of change of the function f(x) on the interval -2 is less than or equal to X which is less than or equal to 4 is -3.5. If f (4)=11 then which
of the following is the value of f(-2)?
(1) -11
(3) 21
(2) -21
(4) 32
Answers
I hope this help!!!!!!!
The value of the function f(x) at x = - 2 is equivalent to 32.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis and results of the given problemGiven is that the average rate of change of the function f(x) on the interval -2 is less than or equal to [x] which is less than or equal to 4 is -3.5.
In the range of {- 2 ≤ x ≤ 4}, the rate of change of f(x) is -3.5. This means we can write -
r = {f(4) - f(-2)}/(4 + 2)
f(4) = 11 and [r] = - 3.5. So, we can write -
- 3.5 = {11 - f(-2)}/6
11 - f(-2) = -3.5 x 6
11 - f(-2) = - 21
f(-2) = 11 + 21
f(-2) = 32
Therefore, the value of the function f(x) at x = - 2 is equivalent to 32.
To solve more questions on functions, expressions and polynomials, visit the link below -
brainly.com/question/17421223
#SPJ2
The local television station is hosting a telethon for a local children’s charity. They have asked students and adult sponsors from high school clubs and organizations to volunteer to answer the pledge phones. The television station has the following guidelines for volunteers:
Because of the number of available phone lines, the station can handle no more than 20 total volunteers, which includes students as well as their adult sponsors.
There must be at least one adult sponsor for every 4 students who volunteer.
The group of volunteers must be able to process at least 120 calls per hour. From previous telethons, the station estimates that each high school student can process 9 calls per hour, but adult sponsors usually only handle about 4 calls per hour.
Answers
A flywheel is attached to a crankshaft by 12 bolts, numbered 1 through 12. Each bolt is checked to determine whether it is torqued correctly. Let A be the event that all the bolts are torqued correctly, let B be the event that the #3 bolt is not torqued correctly, let C be the event that exactly one bolt is not torqued correctly, and let D be the event that bolts #5 and #8 are torqued correctly. State whether each of the following pairs of events is mutually exclusive.a. A and Bb. B and Dc. C and Dd. B and C
Answers
Answer:
a
Mutually exclusive
b
Not Mutually exclusive
c
Not Mutually exclusive
d
Not Mutually exclusive
Step-by-step explanation:
From the question we are told that
The number of bolt is n = 12
The event that all the bolt are torqued correctly is A
The event that the 3rd bolt is not torqued correctly is B
The event that exactly one bolt is not torqued correctly is C
The event that the [tex]4^{th}[/tex] and [tex]8^{th}[/tex] are torqued correctly is D
Generally for an event to be mutually exclusive it means that both event can not occur at the same time
Considering a
The A and B are mutually exclusive because they can not occur at the same time
Considering b
The event B and D are not mutually exclusive because they can occur at the same time
Considering c
Event C and D are not mutually exclusive because they can occur at the same time
Considering d
Event B and C are not mutually exclusive because they can occur at the same time
Find the common ratio of the geometric sequence 18,-72,288,...
Answers
Answer:
The common ratio of the geometric sequence is -4
Step-by-step explanation:
Geometric Sequence
A geometric sequence is defined as a series of numbers that follow a fixed pattern: Each term equals the previous term times a fixed number called the common ratio. The recursive formula is:
[tex]a_n=a_{n-1}*r[/tex]
Where r is the common ratio.
We are given three terms of a geometric sequence:
18,-72,288,...
To find the common ratio, just divide each term by the previous term:
[tex]\displaystyle r=\frac{-72}{18}=-4[/tex]
Make sure it's a fixed number and test with the third term:
[tex]\displaystyle r=\frac{288}{-72}=-4[/tex]
Since both numbers coincide, the common ratio of the geometric sequence is -4
How do we explain the Riemann sum process that leads to the definite integral that computes arc length?
Answers
Step-by-step explanation:
Consider two points on a curve, (xᵢ, yᵢ) and (xᵢ₊₁, yᵢ₊₁). The distance between them can be found with distance formula:
d = √((xᵢ₊₁ − xᵢ)² + (yᵢ₊₁ − yᵢ)²)
d = √((Δx)² + (Δy)²)
Factor out Δx:
d = √(1 + (Δy/Δx)²) Δx
Adding up the distances from i=1 to i=n, the total arc length can be approximated as:
s ≈ ∑ᵢ₌₁ⁿ √(1 + (Δy/Δx)²) Δx
Taking the limit as n approaches infinity, we get the exact value of s:
s = lim(n→∞) ∑ᵢ₌₁ⁿ √(1 + (Δy/Δx)²) Δx
Which can be written as a definite integral:
s = ∫ₐᵇ √(1 + (dy/dx)²) dx
John Paul gave the cashier $60 to pay for 8 bags of potatoes. The cashier gave him $24.32 in change. What is the cost in dollars and cents for each bag of potatoes?
Answers
Answer:
$4.46
Step-by-step explanation:
$60- 24.32= $35.68
So $35.68=8 bags of potatoes.
Then ÷8 to find 1 bag.
$35.68 ÷8 = $4.46
$4.46=1 BAG
Figures R, S, and T are all scaled copies of one another. Figure S is a scaled copy of R using a scale factor of 3. Figure T is a scaled copy of S using a scale factor of 2. Find the scale factors for each of the following:
1. From T to S
2. From S to R
3. From R to T
4. From T to R
Answers
Answer:
1/2
1/3
6
1/6
Step-by-step explanation:
When we are finding the opposite of a scale factor, the scale factor is always the reciprocal. E.g. From S to R, the scale factor is 3, so from R to S, the scale factor is 1/3 so:
1. From T to S, it's the reciprocal of the scale factor (2) so 1/2
2. From S to R, it's the reciprocal of the scale factor (3) so 1/3
3. From R to T, is the from a figure to a figure to a figure so we can multiply the two scale factors (2 and 3) to get 6
4. From T to R, that's the opposite of R to T, so it's the reciprocal of the scale factor from R to T (6) so 1/6
3t-5=0
Help solve pleo
Answers
Answer:T = 0.6
Step-by-step explanation:Simplifying
3t + -5 = 0
Reorder the terms:
-5 + 3t = 0
Solving
-5 + 3t = 0
Solving for variable 't'.
Move all terms containing t to the left, all other terms to the right.
Add '5' to each side of the equation.
-5 + 5 + 3t = 0 + 5
Combine like terms: -5 + 5 = 0
0 + 3t = 0 + 5
3t = 0 + 5
Combine like terms: 0 + 5 = 5
3t = 5
Divide each side by '3'.
t = 1.666666667
Simplifying
t = 1.666666667
Answer:
t = 5/3
t = 1 2/3
Step-by-step explanation:
Hi !
3t - 5 = 0
3t = 0 + 5
3t = 5
t = 5/3
t = 1 2/3
Good luck !
Simplify and show work
5x - (6 - x)
Answers
Answer:
6x-6
Step-by-step explanation:
5x-(6-x)
First you distribute the negative to (6-x) which makes -6+x, then you just subtract that from 5x which makes 5x-6+x then you just simplify into 6x-6.
the number of painted turtles in a pond is one less than half of the number of bullfrogs. Let f represent the number of bullfrogs. Write an expression fro the number of painted turtles
Answers
Answer:
X = 1/2f - 1
Step-by-step explanation:
X is how many painted turtles in the pond. This would be the expression that you would you use to find the actual number of turtles, but we are just leaving it at the expression.
Lizzie invested $2,000 into an account that earned 5% interest per year. When she
cashed out the investment, it was worth a total of $2,205.
Create an equation (using the word bank) that describes Lizzie's investment based on t,
the number of years she kept the account open.
Word Bank:
1.05
0.05
$2.205
$205
t
$2,000
Answers
Step-by-step explanation:
The way to approach the problem is this
After one year she has 2000*1.05
After two years she has the money from the last year plus interest, so she has 2000*1.05*1.05
After t years she has 2000*1.05
HURRY HURRY (function)
Answers
Answer:
h
Step-by-step explanation:
x-13=62 idk know it
Answers
pls mark me as a brainliest
+13 +13
——————-
x= 75
Convert and round to the nearest HUNDREDTH. 1 cup is about 236.59 mL
Answers
PLS HELP I HAVE AN HOUR TO TURN THIS IN!!!!!
15 POINTS!!!!!!
Answers
Answer:
the answer is A
Step-by-step explanation:
I=360 ........
Determine the range of the graph - Domain and Alternate notation is what I need like in the example attached
Answers
Answer: (2,6),(-6,7)
Step-by-step explanation:
Subtract using the number line.
57−(−17)
Answers
Answer:
74
Step-by-step explanation:
Using the Additive Inverse, it is the same as saying 57+17 = 74
please give brainliest, have a nice day
Answer:
Hi there!
Your answer is
74
Step-by-step explanation:
Two negatives equal a positive.
57 + 17=74
Hope this helps!
If Georgina travels 455 km in 7 hours how far will she travel in 9 hours at the same rate
Answers
Answer:
585 km
Step-by-step explanation:
rate of speed formula: distance/time
455/7=65
65*9=585
DRAW tHE MISSsiNG NOTE IN THE BLANK IN COmPLEtE EACH mEASURE
Answers
Answer:
This is me drawing notes in the blank
Doodle* doodle* drawing noise* drawing noise* There you go ;)
Answer: What is this supposed to mean
Step-by-step explanation:
P.S follow me on ticktok nuggie_dude lol
I need help can u help me please and thanks
Answers
Answer:
17.74
Step-by-step explanation:
The fraction is easily converted to one with a denominator of 100 (a power of 10):
[tex]\dfrac{37}{50}=\dfrac{37\cdot 2}{50\cdot 2}=\dfrac{74}{100}=0.74[/tex]
Then the number of interest is ...
17 37/50 = 17 74/100 = 17.74
find the derivate of : y = ln(x)/5x
y'=
Answers
y’=1/5 + 1/5 x In(x)
Write the equation of the line fully simplified slope-intercept form.
HELP ME PLEASE
Answers
Answer:
y=-x+3
Step-by-step explanation:
The y-intercept is at 3 and you can see it has a slope of -1
The equation of line will be y = -x + 3.
It is given that in the graph, line is passing through some points at x-axis and y-axis.
We have to find the fully simplified intercept of the line.
What is the general equation of a line ?
The equation of a line is y = mx + c , where m is the slope of the line and c is a constant.
We have the x-intercept (3,0) and y-intercept (0,3) on the graph.
Slope of these line through these points will be ;
m = (y2-y1) / (x2-x1)
m= (3-0) / (0-3)
m= 3/-3
m= -1
Also , we will get the value of c = 3 .
The equation of line after putting the value of m and c will be ,
y = -x + 3
Thus, the equation of line is y = -x + 3
To learn more , about general equation of line click here ,
brainly.com/question/4227212
#SPJ2