Given:
JK is formed by J(-12, 3) and K(8,-5).
Line r is the perpendicular bisector of JK.
To find:
The equation of line r is slope intercept form.
Solution:
Line r is the perpendicular bisector of JK. So, it passes through the midpoint of J and K.
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
[tex]Midpoint=\left(\dfrac{-12+8}{2},\dfrac{3+(-5)}{2}\right)[/tex]
[tex]Midpoint=\left(\dfrac{-4}{2},\dfrac{-2}{2}\right)[/tex]
[tex]Midpoint=\left(-2,-1\right)[/tex]
Slope of JK is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{-5-3}{8-(-12)}[/tex]
[tex]m=\dfrac{-8}{20}[/tex]
[tex]m=\dfrac{-2}{5}[/tex]
Product of slopes of two perpendicular lines is -1.
[tex]m_1\times m_2=-1[/tex]
[tex]-\dfrac{2}{5}\times m_2=-1[/tex]
[tex]m_2=\dfrac{5}{2}[/tex]
The slope of perpendicular line r is [tex]\dfrac{5}{2}[/tex] and it passes through (-2,-1). So, the equation of perpendicular line is
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-(-1)=\dfrac{5}{2}(x-(-2))[/tex]
[tex]y+1=\dfrac{5}{2}(x+2)[/tex]
[tex]y+1=\dfrac{5}{2}x+5[/tex]
[tex]y=\dfrac{5}{2}x+5-1[/tex]
[tex]y=\dfrac{5}{2}x+4[/tex]
Therefore, the equation of line r is [tex]y=\dfrac{5}{2}x+4[/tex].
The required equation of line "r" in slope-intercept form is y = 5/2x + 15
First, we need to find the equation of a line in slope-intercept form as
y = mx + b
m is the slope of the line
b is the y-intercept
Given the coordinate points J(-12, 3) and K(8,-5)
Get the slope of the line
Slope = -5-3/8+12
Slope = -8/20
Slope - -2/5
Slope of the line "r" perpendicular is 5/2
Get the y-intercept of line r
Substitute (8, -5) and m = 5/2 into y = mx + b
-5 = -5/2(8) + b
-5 = -20 + b
b = 15
Hence the required equation of line "r" in slope-intercept form is y = 5/2x + 15
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during a musical an orchestra is playing. as the music plays, the volume changes in the beginning of the piece can be modeled by the equation s=10|x-4|+50 where s represents the sound level in decibels and x represents the number of measures of music played. explain in words each step to find the following question:
at what number(s) measures played would the sound level be at 80 decibels?
Answer:
X = 1 ; x = 7
Step-by-step explanation:
Given the equation:
s=10|x-4|+50
s = sound level in decibels ; x = number of measures of music played
Take away 50 from Both right hand and left hand side of the equation
Recall s = 80
80 - 50 = 10│x - 4│+ 50 - 50
30 = 10│x - 4│
To get rid of the absolute value sign, append ± to left hand side
± 30 = 10x - 40
Minimum value of x : - 30 + 40 = 10x ; 10 = 10x ; x = 1
Maximum value of x : 30 + 40 = 10x ; 70 = 10x ; x = 7
aaaa help pls i didnt know how to add a picture in the last one
Answer:
x=23
Step-by-step explanation:
FInd the length of the hypotenuse
4.8+19.2=24
Then make it a ration
24/19.2=x/18.4
Cross multiply
19.2x=(24)(18.4)
19.2x=441.6
x=441.6÷19.2
x=23
Help :^ ;^;^;^;^;^;^;
Answer:
d = 0
Step-by-step explanation:
cancel equal terms on both sides of the equation
= 8d = 6d
move variable to the left and change its sign
8d - 6d = 0
2d = 0
divide both sides of the equation by 2
d = 0
Answer:
d = 0
Step-by-step explanation:
-7 and -7 cancel out
8d = 6d
collect like terms 8d - 6d
8d-6d=0
2d = 0
divide both sides
d=0
Divide. Give the quotient and remainder.
7520 : 39
quotient:
Remainder:
What does the slope of the graph represent?
A daycare charges $45 a week to tutor a child. If a parent is late to pick up their child, it is an additional $7 per hour. If in one month a parent pays $271, how many hours was this parent late this month?
Answer:
13 times
Step-by-step explanation:
Paul has $145 in his savings account. He earns $36 a week mowing lawns. If Paul saves all of his earnings, after how many weeks will he have $433 saved?
1: 8 weeks
2: 288 weeks
3: 252 weeks
or 4: 7 weeks
On average, Asia makes 14 out of 20 free throws. Assuming the relationship is proportional, how many more free throws is she likely to make if she shoots 150 free throws?
Answer:
105 free throws made if Asia shoots 150
Step-by-step explanation:
Find the percentage form of 14 out of 20
14 / 20 = 0.7 (70%)
Then calculate 70% of 150:
0.7 multiplied by 150 = 105
(Can check by doing 105 / 150 = 0.7)
Asia will make 1058 free throws out of a total of 150 shoots.
What is the percentage?
The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.
The percentage is just like the amount of that value but between 1 to 100 and it is very useful to predict for example if you say 678 then we have to know about the full number also but if you say 80% then it becomes clear.
Given that,
Asia makes 14 out of 20 free throws
Percentage free throws = free throws/total × 100
Percentage free throws = 14/20 × 100
Percentage of free throws = 70%
Now,
If Asia throws 150 then with the same proportion she will again make 70% of her throw free.
So,
70% of 150 = 150 × 70/100 = 105
Hence "Asia will make 1058 free throws out of a total of 150 shoots".
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2) Suppose 120 people are surveyed and asked about their eating habits. 50 people
stated that they like Raising Cane's chicken fingers, 80 people said that they like
Layne's chicken fingers. If 10 people don't like either, then...
a) What is the probability that someone surveyed likes both Raising Cane's and
Layne's chicken fingers?
Answer:
1/6
Step-by-step explanation:
Given that :
Total surveyed (u) = 120
n(Cane's chicken fingers) = 50
n(Layne's chicken fingers) = 80
n(do not like either) = 10
a)
What is the probability that someone surveyed likes both Raising Cane's and Layne's chicken fingers?
n(Cane's n Layne's) = 20
u = 120
P = required outcome / total possible outcomes
P(Layne's and Cane's chicken) = [n(Cane's n Layne's)/ u]
= 20 / 120
= 1/6
Can anyone help? T^T
4/3n - 8 = -6
Thanks :3
Answer:
CHERRY I NEED U
Step-by-step explanation:
A triangle has sides with lengths of 38 feet, 56 feet, and 69 feet. Is it a right triangle?
Answer:
No
Step-by-step explanation:
Assume that it is a right triangle for now
According to the Pythagorean Theorem...
(38)^2 + (56)^2 = (69)^2
4580 ≠ 4761
Both sides are not equal, and hence the Pythagorean Theorem can't be applied to the triangle. It is not a right triangle.
HELP PLEASE I NEED IT ASAP
Answer:
849.9 cm squared
Step-by-step explanation:
What is the slope of the line that goes through (5,-11) and (-9, 17)?
Answer:
-2
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 17 - -11)/( -9 -5)
= ( 17 +11)/( -9 -5)
28/-14
= -2
Answer: -2
Step-by-step explanation:
X=-9-5=-14
Y=17 - - 11=28
28/-14=-2
the function g is a transformation of f if g has a y-intercept at -1 which of the following functions could represent g
9514 1404 393
Answer:
A.
Step-by-step explanation:
The function f has a y-intercept of -5. The function g's y-intercept of -1 is 4 units up from that, so one way to represent g is ...
g(x) = f(x) +4
The required function is g(x) = f(x) + 4. Hence, Correct option is A.
Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent variable while Y is dependent variable.
According to the graph,
The given curve has y intercept at y = -5.
Which implies that when we add 4 to the function intercept shifts to y = -1 although it is the required intercept of new function g(x).
Thus, the required g is g(x) = f(x) + 4
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A finance magazine did a survey and found that the average American family spends $1,600 on a summer vacation. If the distribution is normal with standard deviation $411, find the amount a family would have spent to be the 80th percentile. PreviousNext
Answer:
$1945Step-by-step explanation:
Let X be the normal distribution
Kindly find attached a detailed annotation of the solution to the problem.
in the attached document, we found the value that corresponds to 80th percentile, hence we found the value such that the probability that the variable x is lower than this value is 0.8.
Also, from the calculation, we found that the value which corresponds to the 80th percentile is $1945
2+6k-18=-3k+11
show work
thanks!!
plz help
Answer:
k=3
Step-by-step explanation:
6k -16 =-3k+11
9k=27
divide both sides by 9
Four less than the product of 6 and a number equals 3
Answer:
-1/6 (written as a fraction)
Step-by-step explanation:
our goal here is to get n by itself
6n-4=3
add 4 to both sides
6n=-1
divide both sides by 6
n= -1/6 (a fraction)
(6×10^2) ÷ (3×10^-3)
Answer:
2*10²
Reduce the expression, if possible, by cancelling the common factors.
Scientific Notation:
Hi!
Lets go through this together.
Using the operation, PEMDAS, we start from left, then go to right.
since there are two pairs of parenthesis, we start with the one on the left.
(6x10^2)
so now, we do the exponent, 10^2
10x10= 100
So our answer for this part is 100.
Now we have (6x100)
6x100=600
So now, the equation is 600÷(3x10^-3)
Now, we do the parenthesis on the right.
(3x10^-3)
First, we do the exponent, 10^-3
10x-10x-10= 1,000
so now, the equation is (3x1,000)
Now, we multiply.
3x1,000=3,000
So now, the equation is 600 ÷ 3,000
600 ÷ 3,000 = 0.2
So, your answer is 0.2.
__________________________________________________________
(6 x 10^2) ÷ (3 x 10^-3)
=(6 x 100) ÷ (3 x 10^-3)
= 600 ÷ (3 x 10^-3)
= 600 ÷ (3 x 1,000)
= 600 ÷ 3,000
= 0.2
(also, the scientific notation is 2x10^2)
__________________________________________________________
Hope this helps!
Let me know if you need anymore help!
Yours truly,
~~~PicklePoppers~~~i need the answer to this question
Answer: 6√3 i
............................
A parking lot is 20 feet long. One tortoise starts at the edge of the parking lot and moves at a rate of 6 feet per minute. Another tortoise starts 4 feet from the edge of the parking lot and moves 2 feet per minute. Write an equation to represent when they will be in the same spot.
Answer:
Kindly check explanation
Step-by-step explanation:
Length of parking lot = 20 feets
Speed of tortoise which starts at the edge = 6 feets per minute
Speed of tortoise which starts 4 feets from the edge = 2 feets per minute
Equation to represent when they will be in the same spot.
Distance = speed * time
Distance of Tortoise at edge = 6ft/min * t = 6t - - (1)
Distance of the other tortoise = (4 + 2t) - - - (2)
Equating both (1) and (2)
6t = 4 + 2t
6t - 2t = 4
4t = 4
t = 4/4
t = 1
Hence, they'll be at the same spot after 1 minute.
10x+8= 5x -4
Pleaseeee help
Step-by-step explanation:
Here's the answer I hope it will help u
What is the sum of this expression?
2 1/16 + 7 3/8
A. 9 1/4
B. 9 7/16
C. 9 3/4
D. 9 7/8
Answer: [tex]9\frac{13}{24}[/tex]
Step-by-step explanation:
Add 2 and 7.
9
Add 1/16 and 3/8 = 13/24
9 13/24 is the answer.
Answer:
b. 9 7/16
Step-by-step explanation:
2 1/16 + 7 3/8
= 33/16 + 59/8
= 33/16 + 118/16
= 151/16
= 9 7/16
An online streaming service deducts $7 from Serena’s account every month of a year. After 1 year, how much do the streaming service fees change Serena’s account?
Answer:
$84
Step-by-step explanation:
This is a super simple question. All you have to know is how much money will be charged a month, and how many months there are in a year. Just simply multiply 7 by 12 as the streaming service is charging 7 dollars a month and there are 12 months in a year. After you multiply the two numbers, you should end up with 84 dollars charged after 1 year.
Please help asap! Add using the number line.
1.4+(−0.8)
Select the location on the number line to plot the sum.
Answer:
0.6
Step-by-step explanation:
1) 1.4-0.8 (A negative and a positive equals a negative, then you just subtract. On the number line you would start at 1.4 and go back)
hope this helps!
write 2x X(5y-y)/2 in a simplified form
Classify the following number: - 1/6
Answer:
fraction and integer
Step-by-step explanation:
1. Use a calculator to approximate the given value to four decimal places.
sin 52 degrees=____
2. Use the calculator to approximate the given value to four decimal places.
cod 18 degrees=____
8 - 5 + 2 = evaluate
Answer:
Your correct answer is 5.
Step-by-step explanation:
8 - 5 = 3
3 + 2 = 5
Therefore, your correct answer is 5.
Can someone please explain how they got 12??
Answer:
They got 12 by multiplying 3 × 4
Step-by-step explanation:
They used distributive property to multiply the 3 by each number in the parentheses
3 × x/3 = 1x = x
3 × 4 = 12
x + 12 = 6 × 3
They mutliplied 6 × 3 to get 18
x + 12 = 18
They then subtracted both sides by 12 to isolate the variable
x + 12 - 12 = 18 - 12
x = 6
Answer:
hope this helps! lmk if you still dont understand it!
:)
Step-by-step explanation:
you do 3*4 which gives you 12 and 3*x/3, but you should keep it as x
6*3 is 18
x+12=18 (solve for x)
-12=-12
x=6
check the answer:
3*(6/3+4)=6*3
3(2+4)=6*3
6+12=6*3
18=18
Need help asap! Tysm
. 。 • ﾟ 。 .
. . 。 。 .
. 。 ඞ 。 . • •
ﾟ Black was not An Impostor. 。 .
' 1 Impostor remains 。
ﾟ . . , . .
Answer:
Ohhhhhhh 3 inches
Step-by-step explanation: