when a load of 5 pounds is placed on a spring, its length is 6 inches, and when a load of 9 pounds is placed on the spring, its length is 8 inches. what is the average rate of change of the length of the spring as the load varies from 5 pounds to 9 pounds? give units on your answer
Four inches every four and a half pounds
The average rate of change of the length of the spring as the load varies from 5 pounds to 9 pounds is 0.5 inches per pound.
What is average?It is a measure of how much the function changes per unit, on average, over the given interval.
We have,
5 pounds loaded on a spring:
The length of the spring is 6 inches.
9 pounds loaded on a spring:
The length of the spring is 8 inches.
The average rate of change in the length of the spring as the load varies:
= (8 - 6) / (9 - 5)
= 2 / 4
= 1 / 2
= 0.5 inches per pound
Thus the average rate of change of the length of the spring as the load varies from 5 pounds to 9 pounds is 0.5 inches per pound.
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Translate to a system of equations but do not solve
A nontoxic floor wax can be made from lemon juice and food grade linseed oil. The amount of oil should be twice the amount of lemon juice. How much of each ingredient is needed to make 42 ounces of floor wax?
Let x represent the number of ounces of lemon juice and y the number of ounces of linseed oil.
Complete the system of equations
x+y=
Answer:
The system of equations is:
x+y = 42
y = 2x
Step-by-step explanation:
Let x represent the number of ounces of lemon juice.
Let y represent the number of ounces of linseed oil.
A total of 42 ounces of floor wax is to be made, so:
x+y = 42
The amount of oil should be twice the amount of lemon juice. So:
y = 2x
so the system of equations is obtained.
Write the equation for the graph below. Points (-5,1) (-4,2) (-1,3)
Answer:
Concept: Derivation of Equations
Let us find the parent graph We can tell that the equation of the parent graph is [tex] \sqrt{x} [/tex]Hence we perform a transformation moving five units to the left and one unit upSo out result equation is [tex] \sqrt{x + 5} + 1[/tex]General note, if you move to the left its positive, if you move to the right its negative.If you move upwards its positive and downwards its negative.Give brainlistPLEASE HELP!! It’s urgent!! I will mark brainliest
Answer:
a,c,d
Step-by-step explanation:
Answer:
the answer is F, C, A
9 = 40 + 13
Helpppppp I need it due today
Its is equal to 9x6=53 Goodluck
Solve for x in the diagram shown.
A) 2.67
B) 4.5
C)5.625
D) 34.375
Answer: C
Step-by-step explanation:
Find the x-intercept and y-intercept of the line given by the equation below. Then graph the line.
x + y = 2
X-intercept:
y-intercept:
Help me please I don’t know it
Please help me with both the questions ty.
Answer:
4) 26+4/842-/×375-^×
5)/^9+37+×+454+12
Step-by-step explanation:
a number that can be written as a fraction of two integers is called ___ number. it has decimal presentation that termite or repeats
Answer:
it is called an irrational number
Step-by-step explanation:
I think that this is a fact answer, so I don't know how to explain it
True or false: sometimes, a quadratic expression cannot be factored.
Answer:
true
Step-by-step explanation:
george ate 2/3 container
Answer:
Step-by-step explanation:
and threw up after yes
The equation y - 3x - 5 = 0 when written in slope-intercept form is:
y = 3x - 5.
y=-3x + 5.
O y = 3x + 5.
Answer:
y = 3x + 5
Step-by-step explanation:
The zero seems to be a place holder to mess you up. Just ignore that it doesn't do anything. Add -3x and -5 to the both sides to create y = 3x + 5
Solve for the variable in the proportion below. Type the number only. Your answer should be a whole number.
2/4 =5/x
x =
What is 60 + 9.000000000
Answer:
69
Step-by-step explanation:
Answer:
69.000000000
Step-by-step explanation:
add 60 plus 9.000000000 and you get 69.000000000
Please help fast, thanks.
Answer:
b > 100
Step-by-step explanation:
The HCF of two numbers is 20. The LCM of both numbers is a multiple of 14. One number is greater than the other, work out the smallest possible numbers
Answer:
20
Step-by-step explanation:
Given that the HCF of two numbers is 20 and the LCM of both numbers is a multiple of 14.
So, the LCM of both numbers = 14n where n can be any natural number.
As HCF of two numbers is always smaller than or equal to the smallest number among both the numbers.
Here, the HCF of two numbers is 20, so the smallest number is greater than of equal to 20.
Hence, the smallest possible number is 20.
slope of -3,-2 and -1,-5
Answer:
14
Step-by-step explanation:
-3-2 is a slope and you add numbers
PLZ HELP
Do the ones you know!
The perimeter of the square below is 36 yards. What is the length of each side?
yards
Answer:
9 yards
Step-by-step explanation:
36 divided by 4 = 9
The length of each side is 9 yards.
What is perimeter?A closed shape's perimeter is the sum of the lengths of its outside boundaries. The lengths of all the sides are added to determine the measurement.
Given:
The perimeter of the square below is 36 yards.
The length of each side,
= perimeter/ number of sides.
= 36/4
= 9 yards.
Therefore, each side is 9 yards.
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Solve for a
-3=a+4
I need some help today
What is -23/6 - 7/3
A-37/6
B-30/9
C-16/6
D37/6
Answer:
A
Step-by-step explanation:
i solved it
It is 5:15 pm now. What time will it be in 40 minutes?
5:45 am
A5:45 pm
c5:55 pm
6:00 pm
Answer:
C:5:55
Step-by-step explanation:
5:15 plus 40 minutes will be 5:55
Answer:
C. 5:55 itssssss easyyy
Step-by-step explanation:
5:15
+40
55
Mrs. Matthews wrote three math expressions on the board.
She asked her students which expression would result in a product greater than 7.
Enter the number of the expression that Mrs. Matthews's students should have chosen.
Expression
will result in a product greater than 7.
Answer:
expression 3
because expression 1 = 1
and expression 2 = 7
What is the domain and range of the following ordered pairs: {(-6, -7), (-1, 1), (0,
9), (3,-2)}? *
Wh
Domain: {-6, -1,0, 3} Range: (-6, -1, 0, 3}
Domain: {-7,1,9, -2} Range: {-7,1,9,-2}
Domain: {-7,1, 9, -2} Range: (-6,-1, 0,3}
Domain: {-6,-1, 0,3} Range: {-7, 1, 9, -2}
Answer:
The answer is the last option (d.)
Step-by-step explanation:
The domain is the X values and the range is the Y values.
Answer:
Answer: Domain {-6,-1,0,3} Range: {-7,1,9,-2}
Step-by-step explanation:
I took the test and it was correct.
Rewrite the logarithm log8(2) as an exponential expression then find the value of the logarithm
Answer:
exponential expression:
8ᵇ = 2
log8(2) = 0.333333333 or 1/3
Answer:
log8(2) = 1/3
Step-by-step explanation:
I don't know if they mean this by an exponential expression but:
set x = log8(2), then
8^x = 8^(log8(2))
By logarithmic properties:
8^x = 2.
notice that 8 = 2^3.
By exponential properties:
8^x = (2^3)^x = 2^(3x)
So 2^(3x) = 2 = 2^1.
Comparing exponents gives:
3x = 1 <=> x = 1/3.
So log8(2) = 1/3.
Well happy New Year everyone. I've been thinking about the upcoming year "2021" and found something interesting. Reduced to its prime factors it becomes 43*47. Yes, it resolves into 2 CONSECUTIVE 2 digit prime numbers, which does NOT happen that often. The last time this occurred was in 1927 (41 * 47). However these are NOT consecutive prime numbers. (There's another prime number between 41 and 47). If we go back to 1763 (41 * 43), it resolves into two 2-digit CONSECUTIVE primes AND they are TWIN primes (prime numbers with a difference of 2).
And now, here's the question: Can anyone find some interesting factorizations of upcoming years? For example, the year 2033 = 19*107 and the year 2041 = 13*157. In each case the factors are less than 10. Obviously, this is not THE most vital question, so don't spend too much time on it. (Although I've been told that a solution will finally bring about World Peace!!! ) LOL
Answer:
As 2021 and 1927 does not have any product of primes
HCF and LCM of 2020 and 1926 is shown below
Step-by-step explanation:
2020 = 2^2 × 5 × 101
1926 = 2 x 3^2 x 107
2 is the HCF
2 x 2 x 3 x 3 x 5 x 101 x 107 = 1945260
1945260 is the LCM
2022 and 1928 both have product of primes and their HCF and LCM is
1949208 is the LCF and 2 is the HCF
1949208 - 1945260 = 3948
3948/2 = 1974
2022-1928 = 94
2020 - 1926 = 94
1974/94 = 21
and brings us back to our year again.
Happy New Year to you.
Suppose that Gx=f(x+11). Which statement correctly describes the graph? please hurry!
Given:
[tex]g(x)=f(x+11)[/tex]
To find:
The correct statement for the given transformation.
Solution:
The translation is defined as
[tex]g(x)=f(x+a)+b[/tex] .... (1)
Where, a is horizontal shift and b is vertical shift.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
We have,
[tex]g(x)=f(x+11)[/tex] ... (2)
On comparing (1) and (2), we get
[tex]a=11>0[/tex]
So, the graph of f(x) translated 11 units to the left.
Therefore, the correct option is A.
The following are the last 10 run scores Colin got in cricket: 1, 16, 5, 25, 26, 32, 5, 7, 1, 7 a) Work out Colin's mean score. b) Colin plays cricket again on Sunday. He gets 29 runs. What is his new mean score? Give your answers as decimals.
Answer:
a. 12.5 b. 14
Step-by-step explanation:
If you add all of the scores together (125) and then divide by the the number of scores in the sequence (10), you get 12.5, and then you need to add the 29 on to 125 and divide that by 11, because thats the new amount of numbers in the sequence, to get 14.
Please Help! Will mark brainliest!
Directions; Write a system of equations for each of the descriptions below, and then solve the systems. Hint: you can graph the equations to find the solutions.
A golfer completed 18 holes with a total of 79 strokes. On each hole, he met par, which was either four or five each time. How many holes were played in four-strokes?
Answer:
11
Step-by-step explanation:
Let a= times he hit 4 par
Let b = times he hit 5 par
a+b=18 => 4a+4b = 72
4a+5b=79
b=79-72=7
So a = 11
answer:
18 = 4a + 5b = 79, b = 79 - 72 = 7 → 11 holes
i hope this helps ♡♡♡