x -10 -3 4 11
y 1 6 30 120
Is the relationship linear, exponential, or neither?
Answers
Answer: Option C, neither.
Step-by-step explanation:
Here we have the table:
x: -10 -3 4 11
y: 1 6 30 120
This means that if our function is f(x), then:
f(-10) = 1
f(-3) = 6
f(4) = 30
f(11) = 120
We want to know if this represents a linear equation or an exponential equation or neither.
First, let's try with a linear equation.
We know that a linear equation can be written as:
f(x) = a*x + b
Then let's input the known values and let's see if this equation works.
We can use two of the known points to get:
f(-10) = 1 = a*-10 + b
f(4) = 30 = a*4 + b
With these equations, we can find the value of a and b, once we find these values, we can see if the equation also works for the other two points.
1 = a*-10 + b
30 = a*4 + b
First, we need to isolate one of the variables in one of the equations.
I will isolate b in the first one:
b = 1 + a*10
Now we can replace this in the other one to get:
30 = a*4 + 1 + a*10
30 = 1 + a*14
30 - 1 = a*14
29 = a*14
29/14 = a = 2.07
and using the equation b = 1 + a*10 we can find the value of b:
b = 1 + 2.07*10 = 1 + 20.7 = 21.7
Then the equation we get is:
f(x) = 2.07*x + 21.7
Now we need to see if this works for the other two points:
for x = -3, we need to get: f(-3) = 6
f(-3) = 2.07*-3 + 21.7 = 15.49
We did not get the value we expected, then we already know that the relationship is not linear.
Now let's see if the relationship can be exponential.
An exponential function is written as:
f(x) = A*(r)^x
Let's do the same as above, let's use two of the known points to find the values of A and r
f(-3) = 6 = A*(r)^(-3)
f(4) = 30 = A*(r)^4
Now we have the system of equations:
30 = A*(r)^4
6 = A*(r)^(-3)
If we take the quotient of these two equations, we get:
(30/6) = (A*(r)^4)/( A*(r)^(-3))
5 = (r^4)*r^3 = r^(4 + 3) = r^7
(5)^(1/7) = r = 1.258
And the value of A is given by:
30 = A*(1.258)^4
30/( (1.258)^4 ) = 11.98
Then the exponential equation is something like:
f(x) = 11.98*(1.258)^x
Now let's see if this equation also works for the other two points:
for x = -10, we should get f(-10) = 1
Let's see that:
f(-10) = 11.98*(1.258)^(-10) = 1.2
And for x = 11 we should get f(11) = 120
f(11) = 11.98*(1.258)^(11) = 149.6
So we get values closer to the ones we should get, but not the exact ones, so this is not an exponential relation.
Then the correct option is C, neither.
Related Questions
3x-(2x-1)=7x-(3*5x)+(-x+24)
Answers
Answer:
[tex]\boxed{\boxed{\sf x=\frac{23}{10}}\: \sf or \:\boxed{x=2.3}}[/tex]
_________________
[tex]\boxed{\sf Step\: By\:Step:- }[/tex]
[tex]\sf 3x-\left(2x-1\right)=7x-\left(3\times \:5x\right)+\left(-x+24\right)[/tex]
Remove the parentheses:
[tex]\to\sf 3x-\left(2x-1\right)=7x-3\times \:5x-x+24[/tex]
Combine like terms:
[tex]\sf ^*7x-x=6x[/tex]
[tex]\to\sf 3x-\left(2x-1\right)=6x-3\times \:5x+24[/tex]
Multiply 3 and 5x = 15x:-
[tex]\to\sf 3x-\left(2x-1\right)=6x-15x+24[/tex]
Combine like terms:
[tex]\sf ^*6x-15x=-9x[/tex]
[tex]\to\sf 3x-\left(2x-1\right)=-9x+24[/tex]
Expand: 3x-(2x-1)= x+1
[tex]\to\sf x+1=-9x+24[/tex]
Subtract 1 from both sides:
[tex]\to\sf x+1-1=-9x+24-1[/tex]
[tex]\to\sf x=-9x+23[/tex]
Add 9x to both sides:
[tex]\to\sf x+9x=-9x+23+9x[/tex]
[tex]\to\sf 10x=23[/tex]
Divide both sides by 10:
[tex]\to\sf \cfrac{10x}{10}=\cfrac{23}{10}[/tex]
[tex]\to\sf x=\cfrac{23}{10}[/tex]
________________________________
18 is 80% of wthat?
Answers
Answer:
18 is 22.5% of 80 .
Step-by-step explanation:
Determine which lines, if any, are parallel. Choices may be repeated and some might not be used at all. Question 6 options: m∠20 + m∠21 = 180° ∠13 ≅ ∠17 ∠4 ≅ ∠9 m∠14 + m∠17 = 180° ∠10 ≅ ∠23 ∠8 ≅ ∠19 1. a || b 2. b || c 3. a || c 4. d || e 5. doesn't prove lines parallel
Answers
Answer:
Step-by-step explanation:
The answers are shown below:
1. m∠20 + m∠21 = 180-----> a || b
2. ∠13 ≅ ∠17 -----> a || c
3. ∠4 ≅ ∠9-----> d || e
4. m∠14 + m∠17 = 180°------> a||c
5. ∠10 ≅ ∠23 ------> b||c
6. ∠8 ≅ ∠19 --------> d || e
What are parallel line?The fundamental characteristics listed below make it simple to recognise parallel lines.
Straight lines that are always the same distance away from one another are called parallel lines.No matter how far apart they are from one another, parallel lines can never intersect.m∠20 + m∠21 = 180-----> (Co - interior angle)
a || b
∠13 ≅ ∠17 -----> Corresponding angle
a || c
∠4 ≅ ∠9-----> alternate exterior angle
d || e
m∠14 + m∠17 = 180°------> (Co - interior angle)
a||c
∠10 ≅ ∠23 ------>alternate interior angle
b||c
∠8 ≅ ∠19 (Vertically opposite angle)
d || e
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PLEASE HELP DUE IN 5 MINUTES
Answers
Answer:
x=7
y= 18
Step-by-step explanation:
brandy has a rectangular wooden deck that measures 7 feet by 12 feet. She build an addition to the deck that is 4 feet longer. What is the Perimeter of her deck now
Answers
Answer:
Step-by-step explanation:
46 feet
The New perimeter of Brandy deck is 46 feet .
Perimeter of a rectangleThe entire length of all the sides of a rectangle is called the perimeter. As a result, we can calculate the perimeter of a rectangle by adding all four sides.
How can we find new perimeter of a deck?Using the given information,
Width = 7 Feet
Length = 12 feet
Perimeter = 2 (Width + Length)
= 2(7+12)
=2(19)
=38
Perimeter when deck is 4 feet longer = 38 + 4+4=46 Feet
Hence, the new perimeter of a deck is 46 feet.
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According to the table, what was the hiker’s total displacement?
A.0
B.6 km north
C.10 km northeast
D.20 km
Answers
Answer:
A: 0
Step-by-step explanation:
Important to remember - total displacement is the direct distance between the start and finish points, and isn't always equal to the total distance travelled.
In the case of the table above, the hiker travels the same distance in opposite directions, which actually means they cancel each other out! Traveling 4 km to the west, then 4 km to east means you end up in the same spot, right? So your total displacement is 0! (or 4 - 4, which equals 0). Same happens with the north-south hikes - the hiker ends up in the same spot, as the displacement is equal to 6 - 6 = 0.
So, the total displacement of the hiker is 0. (Even though the hiker travelled 20 km!)
Which numbers are irrational numbers?
Select each correct answer.
1.33
V20
TT
V196
Answers
Answer:
20−−√ Is a irrational number
TT is a irrational number
Step-by-step explanation:
-k+4(k+1)=2k whats k
Answers
Step-by-step explanation:
-k + 4(k + 1) = 2k
-k + 4k + 4 = 2k
-k + 4k - 2k = -4
(-1 + 4 - 2)k = -4
k = -4
what is the light....................
Answers
The image that you sent is not clear because it's too small
i need help pls
Determine if the lines are parallel, perpendicular, or neither.
x – 3y = 15 and y = -3x + 4
A- Parallel
B- Perpendicular
C- Neither
Answers
Hello! Please help with this question I would really appreciate it
Answers
Answer:
.
Step-by-step explanation:
Answer
You got the standard form correctly
Step-by-step explanation:
Multiply [tex](4x+6)^{2}[/tex]
f ( x ) = [tex]4x^{2}[/tex] + 48 x + 144+ 5
f ( x ) = [tex]4x^{2}[/tex] + 48 x + 149
4 is a
48 is b
149 is c
Find the products 1/ 5a^2b - 1/3c and -25ab - 1/6 cd
Answers
Answer:
find it yourself
Step-by-step explanation:
hahahhaha
The required product of the given expression is given as -2/25a³b² + 2/15ab + 7/180abcd.
Given that,
To find the products [1/5a²/b - 1/3c] × [-2/5ab - 1/6cd].
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Given expression,
= [1/5a²/b - 1/3c] × [-2/5ab - 1/6cd]
= 1/5a²/b[-2/5ab - 1/6cd] - 1/3[-2/5ab - 1/6cd]
= -2/25a³b² - 1/60abcd +2/15ab + 1/18abcd
= -2/25a³b² + 2/15ab + 7/180abcd
Thus, the required product of the given expression is given as -2/25a³b² + 2/15ab + 7/180abcd.
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Fine the measure of the angle indicated in bold.
Answers
Answer:
43) i cant see which one is in bold but x=10
44) x=5 22x is bold so it's A) 110º
45) x=6 14x+6 is bold so it's D) 90º
46) x=6 6+14x is in bold so it's B) 90º
47) x=-9 x+74 is in bold so it's E) 65º
Step-by-step explanation:
3x+15+14x-5=180 10=x
21x+5=22x 5=x
14x+6+15x=180 6=x
6+14x=16x-6 6=x
x+74+x+124=180 -9=x
What’s the solution to |a+4|=6
Answers
Point DD is located at (-2,-6)(−2,−6) on the coordinate plane. Point DD is reflected over the x-axis to create point D'D. Point D'D
is then reflected over the y-axis to create point D''D
What ordered pair describes the location of D''?D
Answers
Answer:
(2,6)
Step-by-step explanation:
since DD is at (-2,6) and you're reflecting it just count 6 spaces from the point to the x-axis then go up 6 more the point will be at (-2,6) and if you go to the right 2 spaces to the y-axis then go two more you'll end up at (2,6)
Is A = {x:x+3 = 3 and x € N } an empty set? Explain.
Answers
Answer:
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Step-by-step explanation:
gdhdhsjsjsjndbdksksnsbjjsndbxjw gdhdhsjsjsjndbdksksnsbjjsndbxjwgdhdhsjsjsjndbdksksnsbjjsndbxjwgdhdhsjsjsjndbdksksnsbjjsndbxjwgdhdhsjsjsjndbdksksnsbjjsndbxjwgdhdhsjsjsjndbdksksnsbjjsndbxjwgdhdhsjsjsjndbdksksnsbjjsndbxjwgdhdhsjsjsjndbdksksnsbjjsndbxjwgdhdhsjsjsjndbdksksnsbjjsndbxjwgdhdhsjsjsjndbdksksnsbjjsndbxjwgdhdhsjsjsjndbdksksnsbjjsndbxjwgdhdhsjsjsjndbdksksnsbjjsndbxjw
Given set is A = {x:x+3 = 3 and x € N }
A is an empty set .
Reason :-
Put x = 1 then x+3 = 1+3 = 4
Put x = 2 then x+3 = 2+3 = 5
If we put x = 1,2,3...
We get { 4,5,6...}
So there is no natural number for x to get x+3 = 3
So ,There is no element to write for the set A
A is an empty set .
Note :-If x€W then x+3 = 0+3 = 3 then A is not an empty set .
1. Raffy wants to buy a watermelon that weighs about 2.8 kgs. The watermelon is priced at Php 25.50 per kilo. How much is the total cost of the watermelon?
answer pls i need it now :(
Answers
Answer:
82.875
Step-by-step explanation:
25.50 × 2 = 51
25.50 ÷ .8 = 31.875
51 + 31.875 = 82.875
Hope this was fast enough
Jane types at a rate of 12 words per minute.
How many words does she type in 3 minutes
Answers
Answer:
36 words in a minute
Step-by-step explanation:
12 x 3 = 36 m
a sea turtles was recorded to swim at a speed of 6 miles in 30 minutes. at this same rate, how far would the turtle travel in 90 minutes?
Answers
Answer:
The turtle will go 18 miles in 90 minutes.
Step-by-step explanation:
6 divided by 30 = 0.2
0.2 x 90 = 18
18 miles
yuta has $10.he gives $3 to his friends taiko.then,yuta wins $2 .But,yuta then lends $4 to karen.How much money does Yuta now have?
Answers
Answer:
5 dollars
Step-by-step explanation:
because 10 - 3 + 2 - 4 = 5
Teddy thinks of a number. He says, “ If I increase the number ny 20%, I get 60” What number was he thinking of?
Answers
50 x 120% = 60
In algebraic expression the cube of the product of 3 and a number
Answers
Answer:
(3x)³
Step-by-step explanation:
In the algebraic expression, "... the cube of the product of 3 and a number":
Let x represent a number.
The given algebraic expression states that both the integer, 3, and a number, x, raised to the third power.
Hence, the algebraic expression of "... the cube of the product of 3 and a number" is: (3x)³.
Determine a relationship between the x- and y-values. Write an equation.
Answers
Answer:
no hablo english perra
Step-by-step explanation:
Answer:
y = x - 5
Step-by-step explanation:
(1,-4) and (2,-3)
Slope= (-3- - 4)/2-1) = 1/1 = 1
Point (1,-4)
y-intercept = y - (slope)(x)
y-intercept: -4 - (1)(1) = -4 -1 = -5
value of 4 the power of -4
Answers
Answer:
[tex]\frac{1}{125}[/tex]
Step-by-step explanation:
Each time a number is raised to a negative power, you fraction it again. So, first its 1/4, then again, to 1/16, to 1/64, 1/256
will give brainliest
Answers
Answer: 25.12
Step-by-step explanation:
Answer: 25.12
Step-by-step explanation: I am pretty sure this is wright hope this helps :)
Len's recipe for blueberry muffins calls for 110.25 grams of brown sugar for the
muffin batter and an additional 55.45 grams of brown sugar for the topping.
Len wants to make 4.5 batches of muffins.
How much brown sugar will Len need?
Enter your answer in the box
g
Answers
Answer:
Firstly. 110.25 + 55.45 = 165.7
1 muffin = 165.7
4.5muffin= x
cross multiply
X = 4.5 x 165.7
745.65✅
PLEASE HELP what is x in : x + 11 = 18
Answers
The answer is 7
A tip you can do is get the sum subtract the number you do have so you would get your X value. So 18-11=7
Answer: x = 7
------------------------------
x + 11 = 18
x = 18 - 11
x = 7
[tex] \\ [/tex]
I hope to help :p
Simplify the expression.
5+2⋅[(2+2)⋅5+5]
Answers
Answer:
55
Step-by-step explanation:
Remember PEMDAS
solve parentheses first : (2+2) = 4
Then multiply inside the brackets 4 x 5 = 20
20+5 = 25
Then multiply 2 x 25 = 50
50+5 = 55
Your answer would be 55
:)
Jake receives $40 from his aunt birthday He spends $75% on the money and saves the rest What percent of the $40 does he save
Answers
Answer:
$10
Step-by-step explanation:
100% is $40
Every 25% is $10
So he has 25% or $10 left
Let X be a number of weeks, than you have
(60 + 7 * X) - ( 120 + 5 * X) = 0
Solve for X and you get X = 30 weeks
The key here is to recognize that when they both have equal amounts the difference between their amounts will be 0c
(-2, 7) and (5, -8)
As a slope
Show work please
Answers
Slope: -15/7
Step-by-Step Explanation:
To find the slope if two points, you use the formula (y2 - y1)/(x2 - x1) where the first set of points is (x1, y1) and the second set of points is (x2, y2). After taking in these points, we can plug them into the formula.
((-8) - 7)/(5 - (-2)
Simplify:
-15/7
