The table shows a linear relationship between x and y. What is the rate of change of y with respect to x.
A. -9/2
B. 2/9
C. -2/9
D. 9/2
Answers
Answer:
A. -⁹/2
Step-by-step explanation:
Using any two pairs of values form the table, say (-12, 60) and (-6, 33),
Rate of change = ∆y/∆x
= (33 - 60) / (-6 -(-12))
= -27/6
= -9/2
Rate of change = -⁹/2
The rate of change of y with respect to x is -9/2
Option A is correct
For a linear relationship, the rate of change of y with respect to x is given by the formula:
[tex]\frac{\triangle y}{\triangle x} =\frac{y_2-y_1}{x_2-x_1} \\[/tex]
From the table:
[tex]x_1=-20, x_2=-12, y_1=96, y_2=60[/tex]
Substitute [tex]x_1=-20, x_2=-12, y_1=96, y_2=60[/tex] into the equation [tex]\frac{\triangle y}{\triangle x} =\frac{y_2-y_1}{x_2-x_1} \\[/tex]
[tex]\frac{\triangle y}{\triangle x} =\frac{60-96}{-12-(-20)} \\\\\frac{\triangle y}{\triangle x} =\frac{-36}{8}[/tex]
Reduce the expression to the lowest term by dividing the numerator and denominator by 4
[tex]\frac{\triangle y}{\triangle x} =\frac{-9}{2}[/tex]
The rate of change of y with respect to x is -9/2
Learn more on rate of change here: https://brainly.com/question/8728504
Related Questions
Solve by using trial and error method. 3x = 16
Answers
Answer:
5.3...
..............
The population of Yuba City, California is 61,360 people. What is 61,360 rounded to the nearest thousand? * 5 points
Answers
Answer: 61,000
Step-by-step explanation:
61,360 is nearest to 61,000 then too 62,000
Answer:
61,000
Step-by-step explanation:
if its under 5 rather it being 5 50 500 etc you put it to the smallest number in this case you look at the hundreds which is a 3.
18
Debbie, Kimi and Michael have
Ferraris.
Michael also has a Reliant Robin.
Jensen has a Mercedes and a Model
T.
Rubens also has a Mercedes.
Debbie also has a Bugatti Veyron.
Rubens has just bought a Toyota
Prius.
Who has the fewest cars?
(1 Point)
Answers
32 is 200% of what number
Answers
Answer:
64
Step-by-step explanation:
Liliana and Marcus are playing a word game. Liliana spells a word incorrectly and loses 18 points. Then Marcus
spells a word correctly and has the opposite score. Which is the correct way to represent the opposite of
Liliana's score is equal to Marcus's score"?
0 -18-18
O-(-18) --18
-(18) --18
-(-18) - 18
Answers
Answer:
The answer is B or -(-18) = 18
Step-by-step explanation:
on Edg 2021
Answer:
D
Step-by-step explanation:
Cuz I did it on a test and I got it right.
Does the expression (4r+6)
________
2
Also represent the number of females on the team this year? EXPLAIN.
Answers
Answer:
yes
Step-by-step explanation:
The NCAA basketball tournament begins with 64 teams, and after each round, half the teams are eliminated. The number of remaining teams t n) is an exponential function of the number n of rounds already played . Write the exponential function that represent the number of players after n rounds . How many players will be there after 4 rounds?
Answers
Answer:
64 (1/2) n
ssssssssssssssssssssssssssssssssssssssssssssss
8 grade solution plobem, first explantion gets brainest
Answers
Answer:
x=8
y=1/6x+4/6
y= 2
Step-by-step explanation:
-2x + 18 =2
Move the constant to the right
-2x =2 - 18
Calculate the difference
-2x = -16
Divide both sides of the equation by -2
And that’s how I got x=8
The other one is x - 6y = -4
X= 6y - 4
Move the variable to the left hand side by adding it’s opposite to both sides
X - 6y = 6y - 4 - 6y
Since two opposites add up to zero,remove them from the expression
And that’s how x - 6y = -4
using suitable identity find 97 ×103
Answers
Answer:
9,991
Step-by-step explanation:
[tex]97 \times 103 \\ \\ = (100 - 3)(100 + 3) \\ \\ {(100)}^{2} - {(3)}^{2} \\ \\ = 10000 - 9 \\ \\ = 9,991[/tex]
Joanna makes and sells candles online. She charges $7 per candle, and shipping is $5 per order. Select an expression that Joanna can use to find the total cost for any candle, n, order. 7 + n + 5 7 + n + 5 7n + 5 7n + 5 7 ÷ n + 5 7 ÷ n + 5 7n - 5
Answers
Answer: Total cost= 7n + 5
Step-by-step explanation:
7 is the M (money per every candle) and 5 is the B (additional fee for every order)
Areesh is trying to build a box fort. He has 8 feet of duct tape.
The instructions are to use 22.5 inches of the tape to secure the roof of the box fort. Then, the remaining
tape should be cut into 5 1/4 - inch sections to be used on the walls of the box fort. Areesh will use all of the
duct tape as instructed.
Determine the number of 5 1/4 - inch sections of tape Areesh can cut.
Answers
Answer:
14
Step-by-step explanation:
[tex]8 \times 12 = 96 [/tex]
[tex]96 - 22.5 = 73.5[/tex]
[tex]73.5 \div 5.25 = 14[/tex]
Step-by-step explanation:
Answer is 14 I hope you get it
please help im so lost
Answers
C converse of alternate interior angles
solve t(3+4) if t= 7
Answers
7(3+4)
3 + 4= 7
7 x 7 = 49
Answer:
=49
Step-by-step explanation:
7(3+4) substitute 7 into t
7(7) add numbers in brackets bec of BODMAS
49
1. In order to save for her high school graduation, Kathrina decided to save ₱200 at the end of every other month, starting the end of the second month. If the bank pays 0.250% compounded monthly, how much will be her money at the end of 5 years? (use j = 0.000417, n = 30)
2. Emma availed of a cash loan that gave her an option to pay ₱10,000 monthly for 1 year. The first payment is due after 6 months. How much is the present value of the loan if the interest rate is 12% converted monthly?
Answers
Answer:
1) 202.52
2) P107089
Step-by-step explanation:
Compound interest is calculated as
A = P (1 + r/n)^(nt), where
A = compounded interest
P = present value
r = interest
n = number of times interest applied
t = time taken
A = 200 (1 + 0.25%/30)^(30 * 5)
A = 200 (1 + 8.3*10^-5)^150
A = 200 * 1.0126
A = 202.52
Present Value Annuity Due is usually given by the formula
P = c*((1-(1+ i)^(-n))/i)*(1 + i ), where
P is the present value
C is the Cash flow per period
i is the interest rate and
n is the number of payments
P = 10000*((1-(1+ 12/1200)^(-1*12))/(12/1200))*(1+12/1200)
P = 113676
Also, it's worthy of note that
Effective Annual Rate = [(1 +stated rate/no. of compounding periods) ^no of compounding periods - 1]* 100
EAR = ((1+12/(12*100))^12-1)*100
EAR = 12.68%
And lastly, the
Future value = present value*(1+ rate)^time
113676 = Present value*(1+0.1268)^0.5
Present Value = 113676 / 1.1268^0.5
Present Value = 113676 / 1.0615
Present value = 107089
make a problem about simple interest
Answers
Answer:
Simple Interest (SI) = Amount (A) – Principal (P) = 6000 - 5400. = 600
Answer:
1. Robert deposits $ 3000 in State Bank of India for 3 year which earn him an interest of 8%.What is the amount he gets after 1 year, 2 years and 3 years?
Step-by-step explanation:
Solution:
In every $ 100, Robert gets $ 8.
(Since rate is 8% → 8 for every 100)
Therefore, for $ 1 he gets = $ 8/100
And for $ 2000 he gets = 3000 x 8/100
= $ 240
Simple Interest for 1 year = $ 240.
Simple Interest for 2 year = $ 240 x 2
= $ 480
Simple Interest for 3 year = $ 240 x 3
= $ 720
Therefore, Amount after 1 year = Principal (P) + Simple Interest (SI)
= 3000 + 240
= $ 3240
Amount after 2 years = Principal (P) + Simple Interest (SI)
= 3000 + 480
= $ 3480
Amount after 3 years = Principal (P) + Simple Interest (SI)
= 3000 + 720 = $ 3720
We observe from the above example that, the Interest cannot be calculated without Principal, Rate and Time.
Therefore, we can conclude that Simple Interest (S.I.) depends upon:
(i) Principal (P)
(ii) Rate (R)
(iii) Time (T)
And therefore, the formula for calculating the simple interest is
Simple Interest (SI) = {Principal (P) × Rate (R) × Time (T)}/100
Amount (A) = Principal (P) + Interest (I)
Principal (P) = Amount (A) – Interest (I)
Interest (I) = Amount (A) – Principal
Solve for the indicated variable in the literal equation. REAL ANSWERS ONLY!
Answers
Answer:
[tex] \large \boxed{l = \frac{P + 9}{ - 4} }[/tex]
See below for two alternative solutions.
Step-by-step explanation:
Goal
Solve for the l-term.Given Equation
[tex]P = - 3 - 4l - 6[/tex]Step 1
Make the l-term as the subject of equation by moving - 3 and - 6 to another side so we can leave l-term as the subject.[tex]P + 3 + 6 = - 4l[/tex]
Simplify by adding 3 and 6.
[tex]P + 9 = - 4l[/tex]
Remember that we cannot combine a variable and a constant. We can only combine a like term.
Step 2
Move -4 to divide P+9 so we can finally solve for l-term.[tex] \frac{P + 9}{ - 4} = l[/tex]
Alternative Solutions
1) We change the position of the negative sign of 4.[tex] - \frac{P - 9}{4} = l[/tex]
2) Simplify in the simplest form.[tex] \frac{P + 9}{ - 4} = l \\ \frac{P}{ - 4} + \frac{9}{ - 4} = l \\ - \frac{P}{4} - \frac{9}{4} = l[/tex]
A large store has a warehouse it uses for storage. Trucks back up to the loading dock where merchandise is unloaded, sorted, and stacked in the correct area of the warehouse. The large shelves in the storage area are 17 feet 8 inches apart so the forklift machines can operate between the shelves. Is that distance greater than or less than 216 inches?
Answers
Answer:
The distance is less than 216 inches.
Step-by-step explanation:
Each feet has 12 inches.
The large shelves in the storage area are 17 feet 8 inches apart
So, in inches, this distance is of:
17*12 + 8 = 212
This distance is less than 216 inches.
Write a two-step inequality that could be represented by the number line.
Answers
Answer:
0
Step-by-step explanation:
y = x^5 sin (2x) cos (4x)
find the derivative
Answers
y' = d/dx (x⁵ sin (2x) × cos (4x) + x⁵ sin(2x) ). ×
d/dx (cos(4x) )
y' = 5x⁴ sin(2x) cos(4x)+2x⁵ cos(2x) cos(4x) -4x⁵ sin(2x) sin(4x)
The derivative of the equation will be y' = 5y/x + 2y cot (2x) - 4y tan (4x).
What is differential equation?An equation containing derivatives of a variable with respect to some other variable quantity is called differential equations.
The derivatives might be of any order, some terms might contain product of derivatives and the variable itself, or with derivatives themselves.
They can also be for multiple variables.
y = x⁵ sin(2x ) cos(4x)
The differentiation;
y' = d/dx (x⁵ sin (2x) × cos (4x) + x⁵ sin(2x) ). × d/dx (cos(4x) )
y' = 5x⁴ sin(2x) cos(4x)+2x⁵ cos(2x) cos(4x) -4x⁵ sin(2x) sin(4x)
From the given equation;
y' = 5y/x + 2x⁵ cos(2x) cos(4x) - 4x⁵ sin(2x) sin(4x)
y' = 5y/x + 2y cot (2x) - 4y tan (4x)
Learn more about derivatives ;
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#SPJ2
A shade of green paint is made by mixing 2 cups of
yellow with 3.5 cups of blue.
Will a mixture that is 3 cups of yellow and 4.5 cups of
blue be more blue, more yellow, or the same shade of
green?
More blue
More yellow
Same shade
Explain your reasoning.
Answers
Answer:
7
Step-by-step explanation:
2×3.7=7 is easy and less money
What is 593832+872382828=
Plz answer /
Answers
Answer:
8,729,766,60
Step-by-step explanation:
593832+872382828= I'm 100% sure my answer is correct I worked it out on paper and calculated it after
Answer:
Step-by-step explanation:
872976660
Find the x-intercept and y-intercept of the following
equation
2x + 5y = -6
Answers
Answer:
x = -3
y = -6/5
Step-by-step explanation:
To find the x-intercept(s), substitute in 0 for y and solve for x.
2x + 5(0) = -6
x = -3
Find the y-intercepts.
To find the y-intercept(s), substitute in 0 for x and solve for y.
2(0) + 5y = -6
y = -6/5
good luck, i hope this helps :)
Zahir is going to the movies. The cost of a movie ticket is $10.50 and candy costs $3 for each box. He has a maximum of $20 to spend. How many boxes of candy can he buy?
b = # of boxes of candy he can buy
Answers
Answer:
3 boxes of candy
Step-by-step explanation:
$20.00 = $10.50 + 3(b)
3*3 = $9.00
$10.50 + $9.00 = $19.50
$20.00 - $19.50 = $0.50
($0.50 is the reminder).
Have a great day, all!!
Given that € 1 = £0.72
a) How much is € 410 in £?
b) What is the £ to € exchange rate?
Answers
Answer:
a) 295.2
Step-by-step explanation:
a) cross multiplication method
€1=£0.72
€410=x
x=€410×£0.72
converd improper fraction into mixed fraction 3/20
Answers
Answer:
Cannot be written as a mixed number
Step-by-step explanation:
Since 3/20 is a proper fraction, it cannot be written as a mixed number.
What is the distance between two points located at
(5,-5) and (-3,-5)?
Answers
Answer:the distance is 8
( this isn’t college math if anything it’s the ending and or beginning of 6th)
Step-by-step explanation:
I'm needing help with 4,5,6
Answers
4. Right
5. Acute
Hope this helps!
Answer:
4. acute
5. obtuse
6. obtuse
Step-by-step explanation:
If the probability of an event happening is 82/97, what are the odds against it happening?
Answers
Answer:
15/97?
Step-by-step explanation:
Just Minus the 82 and 97 to be the probability against it happening.
Sorry if I'm wrong
WILL MARK BRAINLIEST ONLY HAVE 10 MINUTES AND DOUBLE POINTS:
Jack scored 7,9,2,6,15,15 points 6 basketball games. Find the mean,median and mode scores for all the games
Answers
Answer:
mean = 9
mode = 15
median = 8
Step-by-step explanation:
Extra p!
Someone help me, Thanks!!
Answers
Answer:
Step-by-step explanation:
so confused right now
Answer:
Step-by-step explanation: the answer is breme