Answers
Step-by-step explanation:
the key is x = 0.
also I see in the first table no "run-away" effect of some values, so my first suspicion is : it is linear.
let's test it.
a linear function is a line :
y = ax + b
remember, x = 0 is a key element.
y = a×0 + b
-3 = a×0 + b
-3 = b
so, we know, the line function is
y = ax - 3
now, for the a. let's use the next xy pair (1, 1).
1 = a×1 - 3
4 = a
aha ! our line function is therefore
y = 4x - 3
verify with the next 2 points (2, 5) and (3, 9)
5 = 4×2 - 3 = 5 correct
9 = 4×3 - 3 = 9 correct
linear type and equation confirmed.
the second table :
yes, we see relatively big y values compared to the x values.
and the y values follow the powers of 2
so it seems to to be exponential.
64 = 2⁶
32 = 2⁵
16 = 2⁴
8 = 2³
so, while x increases, the powers of 2 decrease. so, we must build something like y = 2^x, but it must run contrary to the increase in x.
the old trick : c-x.
again, x= 0 is key. when x = 0 we get the biggest y (64). that means that gives us c.
64 = 2^(c-x) = 2^(c-0) = 2^c = 2⁶
=> c = 6
so, we suspect the exponential function
y = 2^(6-x)
let's verify with the other points
(1, 32)
32 = 2^(6-1) = 2^(5) = 32 correct
(2, 16)
16 = 2^(6-2) = 2^(4) = 16 correct
(3, 8)
8 = 2^(6-3) = 2^(3) = 8 correct
so, yes, it is the exponential function
y = 2^(6-x)
Related Questions
PLEASE HELP ASAP! NO JOKE OR SCAM ANSWERS!! FULL ANSWERS ONLY!!!
Joy recently hired a mechanic to do some necessary work. On the final bill, Joy was charged a total of $991. The amount listed for parts was $475 and the rest of the bill was for labor. If the hourly rate for labor was $43, how many hours of labor was needed to complete the job?
(A) First write an equation you can use to answer this question. Use x as your variable. The equation is ___________
(B) Solve your equation in part (A) to find the number of labor hours needed to do the job. Answer: The number of labor hours was _____________
Answers
Answer:
12 hoursStep-by-step explanation:
Given:
The total amount = $991Cost of parts = $475Hourly labor rate = $43Number of hours = x(A)
The equation:
y = 43x + 475(B)
Solve for x:
43x + 475 = 99143x = 991 - 47543x = 516x = 516/43x = 12Which is the graph of the function y = 3x?
Answers
The graph would look like the picture above.
Rise 3, Run 1
9. For f(x) = -x + 8, which statement
is true?
A f(x + k) = f(x) + k
ction
B f(x - k) = f(x) - k
C f(x + k) = f(x) + f(k)
D f(x - k) = f(x) + k
Answers
[tex]▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ { \huge \mathfrak{Answer}}▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ [/tex]
The Correct choice is D
For the function f(x) = -x+8, f(x-k) = f(x)+k. Option (D) is correct.
What is function?Function is a combination of different types of variable and constants.
A function is denoted by f(x).
The given function is,
f(x) = -x+8,
Substitute x= x+k in the given function,
f(x+k) = -(x+k)+8
f(x+k) = -x-k+8
f(x+k) = -x+8-k
Substitute -x+8= f(x) here,
f(x+k) = f(x)-k
Substitute x= x-k in the given function,
f(x-k) = -(x-k)+8
f(x-k) = -x+k+8
f(x-k) = -x+8+k
Substitute -x+8= f(x) here,
f(x-k) = f(x)+k
Hence, option (D) is correct.
To know more about Function on:
https://brainly.com/question/12976942
EVALUATE THE FUNCTION REQUESTED. WRITE YOUR ANSWER AS A FRACTION IN LOWEST TERMS
I WILL GIVE BRAINLIEST I NEED THIS ANSWER ASAPP!
Answers
Answer:
The choice b.
[tex] \sin \: A = \frac{4}{5} [/tex]
Step-by-step explanation:
sinA = opposite/hypotenuse
[tex]sinA = \frac{28}{35} = \frac{4}{5} [/tex]
Can someone please explain how to do this problem? I'm struggling a bit.
Answers
Answer:
x=135/13
Step-by-step explanation:
9/13 × 15 = x
9 × 15/13 = x
135/13 = x
x = 135/13
I hope this helps :)
K to the power of negative 2 multiplied by 2
Answers
Answer:
2k-²
Step-by-step explanation:
i hope this is the answer ur looking for !
A bottle of milk is 63% full and contains 1260ml of milk.
How much milk did the carton contain when it was full?
Answers
9514 1404 393
Answer:
2 liters
Step-by-step explanation:
The applicable proportion can be written ...
amount/percentage = 1260 mL/63% = x/100%
2000 mL = x = 2 liters
The full carton held 2 liters of milk.
The sum of two consecutive odd numbers Is 364. Find the larger number.
Answers
Answer:
183
Step-by-step explanation:
If they are two consecutive odd numbers, than these two numbers will be close to half of the sum (364).
364/2=182
Now Find the two odd numbers in between 182, which are 181 and 183.
I had this type of question a few times recently, and this method worked every time :).
Bonus information:
For two consecutive odd/even numbers, find the half of the sum.
For three consecutive odd/even numbers, start off by finding the third of the sum. And so on...
Hope this helped! :D
Find the selling price of a $16,000 SUV with a 20% markup
Answers
Answer:
how are we ment to know
A little confused here!
Hey guys. I just need someone's help to clarify things with me.
As I was doing the equations, I got to:
x^-1
-----
x^13
I moved the x^-1 down to x^13 so they'd subtract. But when I did, x^-1 became positive.
So it became x^13 times x^1
Radical Rule: a^n x a^m is pretty much a^n+m
So my answer was 14.
How did x^-1 become positive in this case?
Answers
Step-by-step explanation:
Given [tex]\frac{x*x^{-2} }{x^{13}}[/tex]
= [tex]\frac{x*x^{-2} }{x^{13}} = \frac{x^{-1} }{x^{13}}[/tex]
According to the Negative Exponent Rule, [tex]a^{-n} = \frac{1}{a^{n}}[/tex]
Therefore, [tex]\frac{x^{-1} }{x^{13}} = \frac{1}{x^{1}*x^{13}} = \frac{1}{x^{13+1}}= \frac{1}{x^{14}}[/tex]
In other words, [tex]x^{-1}[/tex] became positive because of the Negative Exponent Rule. Once you bring [tex]x^{-1}[/tex] down towards the denominator, you're essentially removing its negativity and turning its exponent into a positive value. Once that takes place, then you could apply the Product Rule of Exponents onto the exponents in the denominator, where it states, [tex]a^{m}a^{n} = a^{m+n}[/tex].
Please mark my answers as the Brainliest if you find my explanations helpful :)
A bookstore orders a shipment of books. The books weigh 3.2 lb each. How much will the shipment of 100 books weigh? Write your answer in scientific notation.
Answers
Answer:
3.2 × 10²
im not really good at this but hope it helps.
2+31×1/10+14×1/100 is greater smaller or equal to 2.324 and 14+72×1/10+4×1/1000 is greater than smaller than or equal to 21.24 and 0.3×10 to the second power +0.007×10 to the third power is bigger than small that are equal to 0.3×10+0.7×10 to the second power
Answers
Answer:
3457
Step-by-step explanation:670
Mark is baking cookies for a bake sale he needs 2 1/2 Cups of flour for each batch of cookies and he needs to make 4 1/3 Batches how much flour does Smart need to make his cookies
Answers
Answer:
I know I'm late to answer this but its 10 [tex]\frac{5}{6}[/tex] I hope this helps :D
Step-by-step explanation:
Bird flying 4 feet above sea level seal is 6.5 below surface
Answers
The bird would still be 4 feet above sea level.
OMG I NEED HELP BADLY RN
What are the coordinates of the point at H?
A.
(-3 , -3)
B.
(-3 , 3)
C.
(3 , 3)
D.
(3 , -3)
Answers
Answer:
it would be B, it goes x axis to y axis
Explanation:
Start where the x and y axis meet. This is the origin.
Move to the left 3 units. You'll be directly under point H.
Then move 3 units up to arrive at point H.
Moving to the left 3 means x = -3. Moving up 3 means y = 3.
Together we have the location (x,y) = (-3,3)
You can think of the x,y location as if it was an address on a map or longitude/latitude coordinates.
6x²+2x-8÷(2x-2)=
How do you divide polynomials by binomials
Answers
9514 1404 393
Answer:
3x +4
Step-by-step explanation:
Polynomial long division is done the same way numerical long division is done.
The next quotient term is found by dividing the highest-degree dividend term by the highest-degree divisor term. The result is the exact quotient term. There is no need to go back and make an adjustment as there sometimes is with numerical long division.
Once you have the quotient term, you multiply that by the divisor and subtract from the dividend. This is the same procedure as is used with numerical long division. The difference is the new dividend, and the process repeats.
When the dividend is lower-degree than the divisor, that dividend is the remainder. For this division, the remainder is zero, so the quotient has no fractional part.
__
Both the quotient and the divisor can have any degree and any number of terms. It is useful to write both so all powers of the variable are accounted for, using 0 as a coefficient where necessary. This helps keep things straight when you're multiplying and subtracting. As you know, only "like" terms (terms of the same degree) can be combined by addition or subtraction.
Question 19 of 25
Does this graph show a function? Explain how you know.
O A. No; the graph fails the vertical line test.
OB. Yes, the graph passes the vertical line test.
O C. Yes, there are no y-values that have more than one x-value.
OD. No; there are y-values that have more than one x-value.
Answers
A graph may or may not represent a function.
The true statement is: (b) Yes, the graph passes the vertical line test.
The vertical line test is used to determine if a graph represents a function or not.
When a vertical line is drawn through the graph, the line would only intersect with the curve at a point.
This means that:
The graph represents a function.
Hence, option (b) is true
Read more about functions and vertical line tests at:
https://brainly.com/question/17081515
a little mermaid can't swim 12 miles downstream in the same amount of time she can swim 8 miles upstream. What is the little mermaid speed's in still water if the speed of the current is 4mph
Answers
A little mermaid can't swim 12 miles downstream in the same amount of time she can swim 8 miles upstream. The little mermaid speed's in still water is: 4/5 mile per hour.
The distance of the miles can be estimated by using the formula:
distance = speed rate × time
∴
[tex]\mathbf{time = \dfrac{distance}{ rate}}[/tex]
Let the current speed be = x
In the upstream direction;
the rate = swim speed - the current speed = 4 - xin the downstream direction;
the rate = 4 + x∴
[tex]\mathbf{t = \dfrac{8}{4 -x}= \dfrac{12}{4+x}}[/tex]
By cross multiply;
8 (4 + x) = 12 (4 - x)
32 + 8x = 48 - 12x
8x + 12x = 48 - 32
20x = 16
x = 16/20
x = 4/5 mile per hour
Therefore, we can conclude that the little mermaid speed's in still water is 4/5 miles per hour.
Learn more about speed here:
https://brainly.com/question/22610586?referrer=searchResults
The triangles shown below must be congruent
Answers
Answer:
A. True
Step-by-step explanation:
Two triangles that have two of their sides equal, as well as the angle between them also equal, are congruent
Answer:
ITS FALSE
Step-by-step explanation:
I DID IT
What is the domain of the function in this table?
A. {3, 4, 5, 6)
B. {2,4,5)
C. (3,4)
D. (3, 4), (4,4), (5,2), (6,5)
Answers
Answer:
3, 4 , 5 , 6 is your answer.
I HOPE IT WILL HELP YOU.
Thank you.
TEDDYLOVER....
Joel has just moved to a new town and wants to share plates of baked goods with his
neighbors. He has 20 cookies and 5 brownies to share and wants to split them equally
among the plates with no food left over. What is the greatest number of plates he can make to share
Answers
Answer:
Marta can arrange a maximum of 3 plates.
Solution:
Given, Marta has just moved to a new town and wants to share plates of baked goods with her neighbors.
She has 18 cookies and 15 brownies to share, and wants to split them equally among the plates with no food left over.
We have to find what is the greatest number of plates she can make to share?
Now, let the number of brownies per each plate be n.
Then, number of plates used =
Here, n is number of brownies per plate and is number of cookies per plate.
So, both n and should be whole numbers. Then, for to be whole number 6n must be an multiple of 5.
And to be particular, n should be a multiple of 5 as 6 is not multiple of 5.
So, possible n values are, 5, 10, 15. We need not take above 15 as number of brownies available are 15
In order to arrange in more plates we have to take less count in single plate. Then, n = 5.
Now, number of plates
Hence, Marta can arrange a maximum of 3 plates.
Plz if anyone understands this i really need an answer cuz I’m going to fail math i only have a 56% in math rn so plz help me
89/ (5/9 + 6/7)
A preson is taking test averages__________minute to read a question and ___________ minutes to answer the question it takes the person __________ minute to answer all the questions how many questions are on the test
Answers
Answer:
How long should it take to finish a 25-question test? If you give students an average of 30 seconds to one minute to answer the questions, then the average time to finish a test of this size would be around 15-30 minutes. Of course, some questions would take more time and some less.
Step-by-step explanation:
help me with this asap please
Answers
Answer:
It is linear. The constant rate of change is 3 cents per hour.
Step-by-step explanation:
15/5 = 3
24/8 = 3
36/12 = 3
72/24 = 3
christian ran 112.8 ft in 6 minutes. how many feet did christian run in 1 minute
Answers
Answer:
He ran 18.8 ft in 1 minute.
Step-by-step explanation:
Simply divide 112.8 by 6, to get the answer of 18.8, which would be how far he ran in 1 minute.
To check the work you could multiply 18.8 by 6 and it would get you 112.8 . I hope this helps you!
3[(5x + 1) - 2) = 2(4x - 3)
Answers
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Step-by-step explanation:
Exact Form:
x=−3/7
Decimal Form:
x=−0.¯¯¯¯¯¯¯¯¯¯¯428571
Steven has $50 yend on drinks for his coworkers. The
cholces are fresh orange juice, which costs $2 75 per
cup, and coffee, which costs $2.50 per cup. I Steven
spends $31 and purchases twice as many cups of coffee
as cups of orange juice, how many ops of orange julce
does he buy?
A-1
B-2
C-6
D-8
E-16
Answers
Answer:
I'm pretty positive it's C but I may be wrong, sorry if I am.
Step-by-step explanation:
HELP! solve!
50= -k
__
10
Answers
Answer:
so here tje answer is
50 / 10 = -k
so the value of k = 5
what is the
answer would love to now
Answers
Answer:
D
Step-by-step explanation:
It's between C and D.
3x^2 - 7x^2 = - 4x^2
- 4x^2 + 5x - 28 is the answer so it is D.
In a random sample of 175 community college students, the mean number of hours spent studying per week is 13.7 hours and the standard deviation is 4 hours.
Assuming the distribution of the number of hours community college students study per week is normally distributed, approximately how many of the students in the sample study between 9.7 and 17.7 hours per week?
Answers
Answer:
Approximately there are 119.47 students per week
Step-by-step explanation:
The # of students in the sample study between 9.7 and 17.7 hrs per week;
P (9.7 < x < 17.7) = P ((9.7 - 13.7)/4 < 7 < (17.7-13.7)/4)
P (-4/4 < 7 < 4/4)
P (-1 < 7 < 1)
0.8413 - 0.1587
0.6827
Therefore the # of student = n P
175 * 0.6827
119.47
PLEASE HELP 100 POINTS AND BRAINLEST TO WHOEVER CAN HELP ME!!!!!
Precalculus: Use Function Notation and Describe Graphs Project
Description
In this project you will use words and function notation to describe the connection between the transformation of a function’s graph and the affect on the function’s equation. Then you will explain how the Point-Slope equation for a line can be explained as a transformation of the parent function
.
Requirements
You may submit a Word document, or Powerpoint file or pdf.
Name your file: Last name first name Use Function Notation and Describe Graphs Project. (My project done in Word would be name “Parker Carla Use Function Notation and Describe Graphs Project.docx”)
Projects that are not named properly will be reset for you to resubmit your project.
Blank projects or irrelevant files will result in the project being reset and the student losing access to auto-progression.
Answer the following questions using words and the appropriate equation from the Transformation Equations Bank.
What must be done to a function’s equation so that its graph is shifted vertically upward?
What must be done to a function’s equation so that its graph is shifted horizontally to the right
What must be done to a function’s equation so that its graph is stretched vertically?
Describe what the graph of looks like.
Explain how the Point-Slope equation, is a transformation of .
Answers
Answer:
esult in the project being reset and the student losing access to auto-progression.
Answer the fol
