Why does multiplying the input of a linear function change
only the slope while multiplying the output changes both the slope and the
y-intercept?
Answers
Answer:
Step-by-step explanation:
If we have a linear function and we multiply the input of the function, we aren't really changing the values of the function, we're changing the rate at which those values are reached.
E.g. if you look at the attached picture, we have [tex]f(x) = 2x[/tex] and [tex]f_2(x) = 4x[/tex], which is just [tex]f(2x)[/tex]. The value when the red line is x = 1 is half that of the value of the blue line when x = 1.
The values of the f(2x) line are reaching the values of f(x) twice as fast, meaning it has a slope of twice as much. However, it still grows through the same intercept.
If you're interested in the calculus behind this, look up the chain rule of derivatives.
However, when you start changing the output of the function, you're changing the entire equation. It's not the same line anymore.
Related Questions
Shannon's rain-catcher has 8 inches of water in it. Each day, 3 inches of water are added to the rain-catcher. Let y represent the total number of inches of water in the rain-catcher after x days. Express the equation in the form of y=mx+b .
Answers
Answer:
y= 3x + 8
Step-by-step explanation:
y = mx + b
m = 3 inches of water added each day
x = 8 inches of water at start
y= 3x + 8 is the required equation.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, Shannon's rain-catcher has 8 inches of water in it. Each day, 3 inches of water are added to the rain-catcher.
We have,
m = 3 inches of water added each day
x = 8 inches of water at start
Converting in y = mx + b, we get,
y = 3x+8
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solve for b and simplify -17=-3/2b
Answers
Answer:
b = 34/3
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASEquality PropertiesStep-by-step explanation:
Step 1: Define equation
-17 = -3/2b
Step 2: Solve for b
Rewrite: -3/2b = -17Divide both sides by -3/2: b = 34/3Step 3: Check
Plug in b to verify it's a solution.
Substitute: -17 = -3/2(34/3)Multiply: -17 = -17Ricky bought a jacket for $52.00. If the sales tax is 9.5%, how much did he pay in total?
A.$4.94
B.$61.50
C.$49.40
D.$56.94
Answers
Answer:
D. $56.94
Step-by-step explanation:
52 * 0.095 = 4.94
Add $52 + $4.94
WILL GIVE BRAINLIEST!!!!! Given the equation y = x – 2, you substitute 3 for y. Check all true statements below.
A. You replaced y with 3 temporarily.
B. This is wrong because you can only substitute for x.
C. The equation becomes 3 = x – 2
D. The value of x is 5.
E. The equation y = x – 2 is still true, just with specific values.
Answers
Answer:
y=x-2
a. 3=x-2
b. this isn't wrong??
c. 3=x-2
d. add 2 to both side so taht x is on its own so 5=x
e. yes
Answer:
C and E
Step-by-step explanation:
Im not entirely sure about A, because you are substituting so technically you changed it but the equation is still true (just as E says) but with more specific values.
B is not right because you can replace either y or x
D is not right because if you switch the equation to get the value of x you would make x= -3-2 which would be -5, not 5.
Hope this helped :)
In ΔBCD, the measure of ∠D=90°, BC = 81 feet, and DB = 52 feet. Find the measure of ∠C to the nearest tenth of a degree.
Answers
Answer:
39.9°
Step-by-step explanation:
m∠C = β
sin β = [tex]\frac{52}{81}[/tex] ⇒ β = arcsin [tex]\frac{52}{81}[/tex] ≈ 39.9°
Answer:
39.9
Step-by-step explanation:
sinC=
sin C = \{52}{81}
sinC=
81
52
C=\sin^{-1}{52}{81})
C=sin −1 ( 81 /52 )
C=39.9393\ 39.9^
C=39.9393≈39.9∘
In the rhombus, the measure of angle 1 = 18x, the measure of angle 2 = x + y, and the measure of angle 3 = 30z. Find the value of x + y + z. The diagram is not drawn to scale.
Answers
Answer:
A. 93
Step-by-step explanation:
Each angle is 90 degrees.
18x = 90
x=5
x + y = 90
5 + y = 90
y = 85
30z = 90
z = 3
5 + 85 + 3 = 93
What is the y-intercept. Describe how you know in both the table and the graph.
Answers
Answer:
(4,0)
Step-by-step explanation:
Find the sum of the complex numbers.
(3 + 5i) + (10 + 71)
O A. 13 + 121
O B. 7 + 121
O
C. 13 + 2i
O D. 7 + 21
Answers
Answer:
A
Step-by-step explanation:
(3 + 5i) + (10 + 7i) =
3 + 5i +10 + 7i =
3 + 10 + 5i + 7i =
13 + 12i
90 POINTS! PLEASE HELP!
Select the correct answer What is the solution for x in the equation 5/3 * x + 4 = 2/3* x Ο Α x = 12/7 OB B. x = -4 OC 12/7 OD x = 4
Answers
x=-4 hope it helps! good luck
what is proportional to 35/80
Answers
Answer:
nhi pta... pdhai dhang se kiya kro
Mrs. Wally cut a 21 foot long ribbon into four equal lengths. How many feet long was each length of ribbon
Answers
the answer is:
Each equal length of ribbon is 5.25 ft
Step-by-step explanation:
21 divided by 4 is 5.25
To find the number of distributed quantities division operator is used. Each length of ribbon was 5.25 foot long.
What is division ?Division is a mathematical operation used to divide a number into equal parts. When a number is divided by another number, a quotient and remainder is obtained.
Given length of ribbon = 21 foot
Number of parts it has to be divided = 4.
So, to get the length of each part divide the total length by 4.
Thus, the length of each part is 21/4 = 5.25 foot.
Hence, the length Mrs. Wally' s each ribbon is 5.25 foot.
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Please help will make brainiest !!
Answers
Answer:
CB = 13.75
Step-by-step explanation:
Since we know that A, B, and C are the midpoint of the sides, we know that line CB is proportional to QR (by 2)..
So, 27.5/2 = 13.75
find the circumcenter
Answers
Answer: (0, -2)
Step-by-step explanation:
Simplify 7 +(-3). (1 point)
Answers
Answer:
4
Step-by-step explanation:
7-3=4
Answer:
7-3=4
Step-by-step explanation:
Im not quite sure if this is what you were asking for but here
pls give the answer
Answers
Answer:
It should be 245 m
Step-by-step explanation:
Separate it like this:
chop of the rectangle part and find the area of that and then add it to the trapezoid part
10*20 = 200.
Area of a trapezoid = 5+10/2 *6.
5+10 = 15. 1
5/2 = 7.5.
7.5*6 = 45.
45 + 200 = 245
P=50 L=? B=15 find ?
Answers
Answer:
40
Step-by-step explanation:
A=5
mhdyudpsitsyooatost
Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $2,791 was collected on the sale of 1,275 tickets. How many of each type of ticket were sold?
Answers
9514 1404 393
Answer:
379 adult tickets896 student ticketsStep-by-step explanation:
Let 'a' represent the number of adult tickets sold. Then (1275-a) is the number of student tickets sold. The total revenue was ...
5a +1(1275 -a) = 2791
4a = 1516 . . . subtract 1275 and simplify
a = 379 . . . . . divide by 4
1275-a = 896
379 adult and 896 student tickets were sold.
Eight year-old Alex is learning to ride a
horse. The trainer says that a horse
ages 5 years for every 2 human years.
The horse is now 50 years old in human
years. How can you determine the age
of the horse, in human years, when Alex
was born?
Hint: Use a table or a graph to
help you find the solution.
Show your work.
Answers
Answer:
The age of the horse, in human years, when Alex was born can be determined by simply deducting the Current age of Alex from the Current age of the horse in human years.
Therefore, the age of the horse, in human years, when Alex was born was 42 years.
Step-by-step explanation:
Current age of Alex = 8
Current age of the horse in human years = 50
Since the age of the horse is already stated in human years, it implies there is no need to convert the age of the horse again.
Therefore, since Alex is a human who was born 8 years ago, the age of the horse, in human years, when Alex was born can be determined by simply deducting the Current age of Alex from the Current age of the horse in human years as follows:
The age of the horse, in human years, when Alex was born = 50 - 8 = 42
Therefore, the age of the horse, in human years, when Alex was born was 42 years.
This can be presented in a table as follows:
Age of Alex Age of the Horse (in human years)
Eight years ago 0 42
Current age 8 50
there is a certain number. If you add 30 7 to it, then subtract 22 7 from the previous result, and then subtract that difference from 59/7, after that you will get 19 7. What is a certain number?
Answers
Step-by-step explanation:
59 / 7 - ( x + 30 / 7 - 22 / 7 ) = 19 / 7
59 / 7 - ( x + 8 / 7 ) = 19 / 7
59 / 7 - x - 8 / 7 = 19 / 7
- x = 19 / 7 - 59 / 7 + 8 / 7
- x = - 32 / 7
x = 32 / 7
HELP ASAPPPPPPPPP
Which numbers can be classified as rational? Select all that apply.
A. 5/6
B. Squared 11
C. 6.565656...
D. 0.23
E. 0.32416...
F. -5 3/8
Answers
9514 1404 393
Answer:
A, B, C, D, F . . . as written
Step-by-step explanation:
Any mixed number, fraction, or finite or repeating decimal is rational. The only one in your list that is irrational is E, which appears to be a non-repeating, non-terminating decimal.
__
Your B selection appears to be 11² = 121, an integer and a rational number.
If your B selection is supposed to be √11, then that number is irrational, as it is not the root of a perfect square.
E is irrational; B is rational as written, but irrational if it should be √11. All the others are rational.
Which line below is parallel to the line that y = 1/2x - 2?
A) y = 1/2x + 2
B) y = -1/2x + 2
C) y = 1/2 - 2x
D) y= 1/2 + 2x
Answers
Answer:
The answer is b
Step-by-step explanation:
Bc it is just basicly the x and y axis
please help i don't understand this
Answers
Answer:
Sorry.........................
Which expression is equivalent to 9q2-(3q - 7) +5q??
) ?
3
Answers
[tex]9q^2-(3q - 7) +5q= \\\\=9q^2-3q + 7 +5q= \\\\=9q^2+2q + 7[/tex]
Please help me out!
Answers
what is 2.99 x 0.6 in dollars and cents plz help:(
Answers
Answer:
the answer is 1. 794
Step-by-step explanation:
Answer:1.794 is the answer to you question.
Step-by-step explanation:
CHOOSE THE CORRECT CORRESPONDENCE.
TS <>
A. Side RU
B. Side TU
C. Side RT
Answers
Answer:
i believe its B side Tu
Step-by-step explanation:
Subtract 5x^2+8x-11 from 3x^2+8x-7
Answers
Explanation: First you’d need to rewrite the equation as (3x^2+8x-7)-(5x^2+8x-11). Then since you are subtracting, distribute the negative to the right side which will then give you -5x^2-8x+11 since you flip the signs. Then simply combined like terms. -5x^2 + 3x^2 is -2x^2. Then 8x-8x is 0 and lastly, +11-7 is 4. So in order, all together, your answer is -2x^2+4.
Johanna can jog 3,000 feet in 5 minutes. If she jogs at the same rate, how many feet can she jog in 8 minutes?
Answers
Answer:
4800
Step-by-step explanation:
3000\5=600
600*8=4800
Question 2 (1 point)
A video game has three villains who appear on screen at different intervals. One villain appears every 2 seconds, a second villain appears every
19 seconds, and a third villain appears every 10 seconds. How much time passes between the occasions when all three villains appear at the
same time?
Answers
Answer:
3 minutes tens seconds or 190 seconds
Step-by-step explanation:
Find the LCM.
Can someone help me please
Answers
The point to the left will be -2,6
The point at the bottom will be 2,2
The point to the right will be 1,5