Which of the following equations contains the point (8, 5) and is perpendicular to the line y = 2x − 3?
Answer:
[tex]y = \ -\displaystyle\frac{1}{2}x \ + \ 9[/tex]
Step-by-step explanation:
Given that the reference line is y = 2x - 3, with a slope of [tex]m_{reference} \ = \ 2[/tex].
We know that two non-vertical lines are perpendicular if the slope of one line is the negative reciprocal of the slope of the other. In other words, both slopes can be multiplied together to yield -1. Let [tex]m_{1}[/tex] be the slope of one line and [tex]m_{2}[/tex] be the slope of its corresponding perpendicular line,
[tex]m_{1} \ \times \ m_{2} \ = \ -1 \ \ \ \ \ \ \ \ \ \ \ \mathrm{or} \ \ \ \ \ \ \ \ \ \ \ m_{1} \ = \ \displaystyle\frac{-1}{m_{2}}[/tex].
Thus,
[tex]m_{reference} \ \times \ m_{perpendicular} \ = \ -1 \\ \\ \-\hspace{2.26cm} m_{perpendicular} \ = \ \displaystyle\frac{-1}{m_{reference}} \\ \\ \-\hspace{2.26cm} m_{perpendicular} \ = \ \displaystyle\frac{-1}{2} \\ \\ \-\hspace{2.26cm} m_{perpendicular} \ = \ -\displaystyle\frac{1}{2}[/tex]
Therefore, using the point-slope form for the equation of a line passing through the point [tex](x_{1}, \ y_{1})[/tex] is [tex]y \ - \ y_{1} \ = \ m(x \ - \ x_{1})[/tex]. Given that the perpendicular line passes through the point [tex](8,\ 5)[/tex], the equation of the perpendicular line is
[tex]y \ - \ 5 \ = \ -\displaystyle\frac{1}{2}(x \ - \ 8) \\ \\ y \ - \ 5 \ = \ -\displaystyle\frac{1}{2}x \ + \ 4 \\ \\ \-\hspace{0.85cm} y \ = \ -\displaystyle\frac{1}{2}x \ + \ 9[/tex]
Question 9
The probability that a vehicle will change lanes while making a turn is 55%.
Suppose a random sample of 7 vehicles are observed making turns at a
busy intersection.
Calculate the expected value.
Answer:
3.85 (rounded to 4 cars)
Step-by-step explanation:
Let X be the discrete random variable the number of vehicles changing lanes
X~B(7, 0.55)
The expected value is found by:
E(X) = 7 × 0.55
E(X) = 3.85
Mr. Henry planted 15 mango trees in his garden this morning. That is 25% of
the trees he is going to plant. How many mango trees is he going to plant in
all
The data set below shows a relationship between the number of hours tara works and her paycheck:{ 1, 25), (2, 40), (3, 55), (4, 70), (5, 85), (6, 100) what is Tara's hourly pay rate?
Step-by-step explanation:
Need to find out total hours and total pay and simplify the answer.
Total Hours = 1+2+3+4+5+6 = 21
Total Pay = 25+40+55+70+85+100 = 375
Pay ÷ Hours = 375 ÷ 21 = 17.86
Not convinced with this answer tbh but it's what I got.
I WILL GIVE BRAINLY!!!
-x - 8 ≤ 16
Please answer! Is the answer 24 or -24?
My last inequality before I got my answer was : -x ≤ 24.
But as we know if there is a varible that has no number associated with it we assume that the number for it is just one, but in this case -x would be -1x. So if I divide -1x/-1 that would be x, but if I divide 24/-1, that would be -24. So in the end someone just tell me if it's 24 or -24?!
Answer: The answer is X ≥ -24.
Explanation in the image.
a) Complete the table of values for y = 6 - 2x
0
1
2
3
Х
4
5
OT
10
-4
y
8
6
co
b) Draw the graph of y = 6 - 2x
on the grid.
4
2.
c) Solve 6 - 2x = 3
Step-by-step explanation:
the answer as shown in the photo
Can somebody, anybody please helppp
Simplifiy the expression.
x^2 + 3x - 28/ x^2 - 7x + 12
show your work! (this part is REALLY important) thanks(:
Answer:
Step-by-step explanation:
3x3 then 4 x v ?
How many 1/4s are in 1 1/2
solve for x??????????
Answer:
x=4
Step-by-step explanation:
you take both equations, and make them equal to each other. so....
5x-6=3x+2 subtract 3x from both sides
2x-6=2 then add 6 to the other side.
2x=8 then divide 8 by 2.
X=8
Harry is riding a train that goes 70 miles an
hour. How far will he travel is 3.5 hours?
Answer: 245 miles
Step-by-step explanation:
(70)(3.5)= 245
The length of one ramp is 16 feet. The vertical rise is 5 feet. Use pythagorean theorem to estimate the ramp’s horizontal distance. (round to the nearest tenth of a foot) *
Answer:
The ramp's horizontal distance is the distance in the x-axis. So the ramp's vertical distance I.e y-axis is 14 inches. And its length which is actually the hypotenuse ofthe right angled triangle 16 feet. But let's convert feet to inches first. 1 feet makes 12 inches Hence 16 feet makes 192 inches. From pythagoras a^2 =b^2 + c^2 where a the hypotenuse is 192 and b is 14. C is the ramp's horizontal distance. So we have (192)^2 = (14)^2 + c^2 C^2 = 192^2 - 14^2 = 36668 C = 191.48 From SOHCAHTOA. We have to use Sin So sin theta = (14/192) Theta = sin^(-1) (14/192) = 4.1815. Yes, it meets the FAC standard since the ramp's angle is less than 4.78
Step-by-step explanation:
use order of operations 7-2(-7-4)
Answer:
29
hope this helps
Simplify (x+2) (x+10) - (x-5) (x+4).find the numerical value of this expression when x=-3.
Simplify (x+2) (x+10) - (x-5) (x+4).find the numerical value of this expression when x=-3.
(x+2) (x+10) - (x-5) (x+4).put value of x= -3(-3+2) (-3+10) - (-3-5) (-3+4).-1 x 7 -(-8) x 1(-7) -(-8)-7+81Answer:
the result is -9
Hope this helps
Please mark brainlest
Summer Earnings
Hours worked Earnings in dollars
3
4
48
6
72
10
120
20
240
Which statements are true about the data in this table? Select all that apply.
The rate of change for the data is $12 per hour. $12 is also the constant of proportionality
If you graph the data, it would pass through the origin (0,0)
The data represent a direct variation and can be modeled by the function rule y = 12.
The data indicate a rate that is not constant
The rate of change for the data is $24 per hour. The data representa direct variation and can be modeled by the function ruley-242
The table is an illustration of a proportional relationship. and can be modeled by the function rule y = 12x
The entries of the table is given as:
Hours Earnings
4 48
6 72
10 120
20 240
Start by calculating the rate (m) of the function
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{72 - 48}{6-4}[/tex]
[tex]m = \frac{24}{2}[/tex]
[tex]m = 12[/tex]
The equation of the table is then calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
So, we have:
[tex]y = 12(x - 4) + 48[/tex]
[tex]y = 12x - 48 + 48[/tex]
[tex]y = 12x[/tex]
[tex]y = 12x[/tex] means that, the following statements are true:
The rate of change for the data is $12 per hour. $12 is also the constant of proportionalityIf you graph the data, it would pass through the origin (0,0) The data represent a direct variation and can be modeled by the function rule y = 12xRead more about proportional equations at:
https://brainly.com/question/14108707
Cube A has an edge length of 3 inches. Cube B has an edge length double that of Cube A.
What is the volume, in cubic inches, of Cube B?
A. 27in^3
B. 36in^3
C. 216in^3
D. 729in^3
Answer:
216
Step-by-step explanation:
Cube A volume
3*3*3=27
Cube B volume
6*6*6=216
Edge length of cube B=2(3)=6in
Volume:-
[tex]\\ \sf\longmapsto V=(6)^3[/tex]
[tex]\\ \sf\longmapsto V=6(6)(6)[/tex]
[tex]\\ \sf\longmapsto V=216in^3[/tex]
Dan takes an airplane to visit his parents. He pays the airline a total of $450. The cost of the ticket is $315. The airline also charges $15for every pound that the luggage goes over the 50 pound is Dan's luggage over the 50 pound limit?
Answer:
9
Step-by-step explanation:
Start with the total amount Dan paid and subtract the part of the payment that is for the ticket.
450-315=135
Assuming that all of that $135 was for luggage fees and each pound over the limit costs $15, then the question is, how many times did Dan pay $15 until he'd paid the full $135 luggage fee.
So divide $135 by $15.
135/15=9
So his luggage weighted 59 pounds, which is 9 pounds over the limit.
why do we learn about history? we are kids we can make a war
Answer:
Because if you didn't you would not know anything about the past.
Step-by-step explanation:
Yes
Help help help help help
Answer:
8
Step-by-step explanation:
The answer is 8 because there are 2 possibilities for each coin you flip heads and tails so if you flip three coins all at once you get 2*2*2, which equals to 8.
I hope this help!
Solve 2x2 – 6x + 10 = 0 by completing the square.
A)
x = 3∕2 + i , x = 3∕2 – i
B)
x = 3 + i, x = 3 – i
C)
x = 3∕2 + 1∕2 i, x = 3∕2 – 1∕2i
D)
x = 3 + i, x = 3 – i
Answer:
The answer is C.)
Step-by-step explanation:
I hope its help Please let me know.
At what rate would $1,200 earn $96 in 8 years?
Help help help help math math
Answer:
<4 = 67 degrees
Step-by-step explanation:
Find <3
30+37+x=180
subtract 37 and 30
x = 180 - 30 - 37
x = 150 - 37
x= 113
Find <4
180 - 113
67
PLEASE HELP ILL GIVE BRAINLIESTTTT
Answer:
f(-3)= 1
f(1)= -1
If f(x)= -2 then x = 3
If f(x) = 2 then x = -5
Step-by-step explanation:
f(x) can be replaced with any number. It just means y. For example, let's replace the (x,y) with the (-5,2). For this point, this is f(-5) = 2. When they ask for f(x), they are just asking what y is with a given coordinate x. So when they ask what f(-3) is, they are asking what y is with -3 being the x coordinate.
So, f(-3) = 1
f(1) = -1
For these questions:
If f(x) = -2 then x = ?
If f(x) = 2 then x = ?
They are asking what x is when y is -2 or 2. So here:
If f(x) = -2 then x = 3
If f(x) = 2 then x = -5
A submarine descends 45 1/2 feet from the ocean surface , climbs 30 feet ,and then descends an additional 18 3/4 feet. What must the submarine do now to reach the ocean surface?
A. Descends 94 1/4 feet
B. Climb 94 1/4 feet
C Descends 34 1/4 feet
D.Climbs 34 1/4 feet
Answer:
D.Climbs 34 1/4 feet
Step-by-step explanation:
-45.5 + 30 - 18.75 + h = 0
h = 34.25
The average price of an item is $42 with a standard deviation of $3
Find a 98% confidence interval about the mean (one decimal place).
Is a value of X=48 unusually high or is it normal? Choose correct explanation!
Step-by-step explanation:
standard deviation of $3
Find a 98% confidence interval about the mean (one decimal place).
Is a value of X=48 unusually high or is it normal? Choose correct explanation
66=3x
simplify your anwser as much as possible
Answer:
x =22
Step-by-step explanation:
66/3 =22
pls give me brainlies
What is the probability that a random sample of n=45 oil changes results in a sample mean time less than 20 minutes?
Step-by-step explanation:
https://youtu.be/wghLO8hQZrA
watch this video to get the answer and knowledge about this video to get the answer and knowledge about this video to get the answer and knowledge about this video to get the answer and knowledge about this video to get the answer and knowledge about
Which graph or graphs show that a 5 minute phone call costs $4?
The graph should show an increase of $ 0.80 for every minute that the call lasts.
A 5 minute phone call costs $ 4, with which, to determine the information that the graph should show, the following calculation must be performed:
4/5 = X 0.80 = X
Therefore, the graph should show an increase of $ 0.80 for every minute that the call lasts.
Learn more about maths in https://brainly.com/question/25834039
Answer:
Step-by-step explanation:
3. Use proportional reasoning to answer the following question.
When buying an item, discount is always taken off
before applying tax. How much does a $1200
phone cost with a 35% discount and 10% tax?
Answer:
5000
Step-by-step explanation:
I took the test so that's how I know
Factor the expression completely: 4x - 48
-
A) 2x - 12
B) 2x - 48
C) 4(x + 12)
D) 4(x - 12)
Answer:
D
Step-by-step explanation:
cant seem to figure this out
Answer:
log14=1.146
log18=1.255
Step-by-step explanation:
Use log rules to break up the given logs, to be able to use the information give
Using the product rule, log14 = log(7 x 2) = log7 + log2
Substitute .845 + .301 = 1.146
Using the quotient rule, log18 = log(2 x 3 x 3) = log2 + log3 + log 3
Substite .301 + .477 + .477 = 1.255