Answers
Step-by-step explanation:
it is a linear function, if the change in y is constant in relation to the changes of x.
in other words, if the slope y change/x change is the same for every point.
when we look at the table, we see x changes constantly by +2.
and y changes constantly by -6.
so, the change rate/slope is constantly -6/2 = -3.
and therefore it is a linear function.
the equation looks like (the slope is always the factor of x)
y = -3x + b
b we get by using one of the x,y pairs like 1,4
4 = -3×1 + b = -3 + b
b = 7
so, the full equation is
y = -3x + 7
Step-by-step explanation:
Given the table of values, {(-3, 16), (-1, 10), (1, 4), (3, -2), (5, -8)}:
We must determine whether the given relation or data can be modeled by a linear equation. It is necessary to analyze the pattern that exists between changes in y-values, along with the changes in x-values.
X-coordinates:Subtracting the x-coordinates provides a constant difference of 2:
Starting with the first two rows, given by the ordered pairs, (-3, 16) and (-1, 10): Subtract the two x-coordinates: -1 - (-3) = -1 + 3 = 2.For the second and third rows, given by the ordered pairs, (-1, 10) and (1, 4): Subtract the two x-coordinates: 1 - (-1) = 1 + 1 = 2.If you perform these same steps throught the remaining rows, then you'll get the same difference of 2.
Y-coordinates:We can perform the same steps for the y-coordinates. Subtracting the y-coordinates provides a constant difference of -6.
Starting with the first two rows, given by the ordered pairs, (-3, 16) and (-1, 10): Subtract the two y-coordinates: 10 - 16 = -6.For the second and third rows, given by the ordered pairs, (-1, 10) and (1, 4): Subtract the two y-coordinates: 4 - 10 = -6.If you perform these same steps throught the remaining rows, then you'll get the same difference of -6.
SlopeSince the constant change in y = -6, and the constant change in x = 2, then we can calculate for the slope as: Δy/Δx = -6/2 = - 3. Hence, the constant rate of change = -3.
As demonstrated throughout this post, we can infer that there is a linear pattern that exists between the x- and y-values.
Therefore, the data can be modeled by a linear equation because the rate of change is constant.
Linear Equation:In order to establish the linear equation that represents y as a function of x, we can use the slope, m = -3, and one of the given ordered pairs, (1, 4), to solve for the value of the y-intercept, b. Substitute these values into the slope-intercept form, y = mx + b:
y = mx + b
4 = (-3)1 + b
4 = -3 + b
Add 3 to both sides to isolate b:
4 + 3 = -3 + 3 + b
7 = b
Therefore, the linear equation that represents the given data is: y = -3x + 7.
Related Questions
Two trains leave a train station traveling on parallel and adjacent tracks. Train A is traveling due north at a constant speed of 76 miles per hour. Train B is traveling due south at a constant speed of 44 miles per hour. If both trains leave the station at the same time, in approximately how many minutes will the trains be 22 miles apart? O 11 O 18 O 60 o 98
Answers
Answer:
TWO TRAINS IM SORRY LOLLL
Answer:
18 minutes
Step-by-step explanation:
can someone help me with this problem?
Answers
Answer:
B) f^-1(x)=3-5x
Step-by-step explanation:
y=3-x/5
rearrange the equation so you have x variable on the left side
5y=3-x
+x +x
5y+x=3
-5y -5y
x=3-5y
so answer is b)
f^-1(x)=3-5x
(05.03)
An equation is shown below:
2/3 x + 8/3 = 2x
What is the solution to the equation? (4 points)
Answers
x=2
1:Subtract 2x from both sides.
2:Combine 2/3 x and -2x to get -4/3
3:Subtract 3/8 from both sides. Anything subtracted from zero gives its negation.
4:Multiply both sides by -3/4,the reciprocal of -4/3
5:Multiply − 3/8 times − 4/ 3 by multiplying numerator times numerator and denominator times denominator.
6:Do the multiplications in the fraction −8(−3) over 3x4.
x=24/12
Divide 24 by 12 to get 2.
x=2
Robert is making a photo album. 12 photos fit on a page. How many pages will he need for 432 photos?
Answers
Answer:
12 photos fit on page = 1
432 photos fit on page = 432/12
= 36 pages
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Answer:
36 pages
Step-by-step explanation:
There are 12 photos per page, and Robert has 432 photos. So, we can divide the number of photos he has by the number of photos that fits on each page. By doing so, you'll calculate the number of pages he needs. This calculation is shown below:
[tex]\frac{432 \ photos}{1} *\frac{1 \ page}{12 \ photos} = 36 \ pages[/tex]
You can see that the units for photos cancel out, resulting in units for pages.
So, Robert will need 36 pages in order to fit all 432 photos into his photo album.
What is an equation of the line that passes through the points (0,-2) and (-5,4)
Answers
Answer: y = -6/5x - 2
Step-by-step explanation:
Slope = Change in y/Change in x
Our y intercept is -2 because of our point (0,-2)
What is the answer to (6 1/2)/2
Answers
Answer:
3.25
Reasoning:
[tex]\frac{6.5}{2}[/tex]
[tex]3.25[/tex]
Use the distributive property and then combine like terms to simplify each expression. 4(x-2) + 4(x + 4)-(8x + 1)
Answers
Answer:
8(×2)+8(×+4)-(4×+9)
lucio es un poco bromista al llegar a la tortearía dijo: me da dos tercios de torta y media el dependiente que si sabia matemáticas lo despacho correctamente
*Que cantidad de torta le dio?
*como resolviste el problema?
Answers
Answer:
Step-by-step explanation:
In the given case, we can conclude The customer received one and one-sixth (1 1/6) of a cake.
The question is asking us to determine how much cake the customer received. The phrase 'dos tercios' translates to 'two-thirds' in English. So, the customer received two-thirds of a cake.
Since the customer also received half of a cake, we can add these two quantities together: two-thirds + one-half.
In order to add these fractions, we need a common denominator. The least common multiple of 2 and 3 is 6. So, we can rewrite two-thirds as four-sixths and one-half as three-sixths. Adding these fractions together gives us seven-sixths (or one and one-sixth).
Therefore, the customer received one and one-sixth (1 1/6) of a cake.
Learn more about the topic of Addition of fractions here:
https://brainly.com/question/14427715
#SPJ3
Your mom decides she will give you $8, instead of $5 for each chore. You complete 12 chores. Will you have enough money for the lego set?
Answers
Average price of one Lego set = $20
You get $8 per choresTotal chores=12Total price
[tex]\\ \sf\longmapsto 12(8)=\$96[/tex]
You have enough price
Question 2: Select the property shown
by the statement: If 7 = x and x = y, then
7 = Y
A. Commutative
B. Associative
C. Reflexive
D. Symmetric
E. Transitive
Answers
Answer:
1. option C, i.e., symmetric property.
2. option B, i.e., Integer
3. option D, i.e., zero product property
Step-by-step explanation:
Symmetric property: According to this property it a=b the b=a.
By symmetric property, we can say that, if y=7 then 7=y.
Therefore, the correct option is C, i.e., symmetric property.
Closure property: According to this property, if a∈S and b∈S, then a*b∈S.
Subtraction of natural numbers is not always natural.
Subtraction of integers is always integer.
Subtraction of irrational number is not always irrational number.
Subtraction of odd number is always even.
Therefore, the correct option is B, i.e., Integer.
Given statement is (a-b)*0=0.
According to zero product property if ab=0, then a=0 or b=0.
So, the given statement is true by zero product property.
Therefore, the correct option is D, i.e., zero product property.
Layla has a points card for a movie theater.
She receives 30 rewards points just for signing up.
She earns 13.5 points for each visit to the movie theater.
She needs at least 50 points for a free movie ticket.
Which inequality can be used to determine xx, the minimum number of visits Layla needs to earn her first free movie ticket?
Answers
Answer:
2
Step-by-step explanation:
Answer:
30+13.5=43.5 so she needs 6.5 more points
Step-by-step explanation:
What is the value of x?
Answers
Step-by-step explanation:
19x - 4 = 110 ( alternate Exterior angle )
→ 19x = 110 + 4 = 114
→ x = 114/19
→ x = 6
therefore, value of x is 6°.
HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE
5x+2y<8 graph the inequality
Answers
What is theValue of x ?
Answers
Answer:
10
Step-by-step explanation:
x is 10
convert 40 yards to feet
Answers
Answer:
120 feet
.................................
Step-by-step explanation:
1 yard = 3 feet
How does the graph of g(x) = [tex](x+12)^{2}[/tex] relate to the graph of f(x) = [tex]x^{2}[/tex]
Answers
Answer:
Horizontal translation of the parent graph
Step-by-step explanation:
Definitions:In the vertex form of a quadratic function, f(x) = a(x - h)² + k, where:
(h, k) = vertex of the grapha = determines the width and direction of the graph's opening.A horizonal translation to the parent graph is given by, y = f(x - h), where:
h > 0 ⇒ Horizontal translation of h units to the righth < 0 ⇒ Horizontal translation of |h | units to the leftIn the graph of g(x) = (x + 12)², the vertex occurs at point (-12, 0).
While the vertex of the parent graph, f(x) = x² occurs at point, (0, 0).
Answers:Since the vertex of g(x) occurs at point, (-12, 0), substituting the value of (h, k ) into the vertex form will result into:
g(x) = a(x - h)² + k
g(x) = [x - (-12)]² + 0
g(x) = (x + 12)² + 0
g(x) = (x + 12)²
Therefore, the graph of g(x) = (x + 12)² represents the horizontal translation of the parent graph, f(x) = x², where the graph of g(x) is horizontally translated 12 units to the left.
Students and adults purchased tickets for a recent Math Fun Night fundraiser. 350 tickets were sold and $2,950 was collected. Each student ticket sold for $5 and adult tickets were sold for $10 each. How many adult and student tickets were sold? Let x=_______ Let y=______. I have no idea how to solve this, maybe you can help? If so, start off with the let statements and can you send the steps along with it too?
Answers
Answer:
fun one
110 student tickets
240 adult tickets
Step-by-step explanation:
what i did is use two equations
x+y<= 350
and 5×+10y<3950
graph both on desmos or smash them together to find x and y and you get 110 student tickets and 240 adult tickets
product of the polynomial 5x3 + 9x2 + 6x + 1 and the monomial x ?
Answers
Answer:
5x^4+9x^3+6x^2+x
Step-by-step explanation:
What are the group of boxes or cells in a table that go side to side (horizontal) is called?.
Answers
Answer:
A group of boxes in a table that go side to side (horizontal) are called: Grids.
:)
A group of boxes in a table that go side to side (horizontal) are called Grids.
What is a grid answer?
A pattern of intersecting horizontal and vertical lines that creates a grid of squares is known as a rd. A grid is also a system of wires that connects several locations in a region with electricity: a power grid.When straight lines cross over one other to form squares, it is said to be in a grid pattern. The grid on maps is designed to guide you in finding a certain object or location. ...an ironwork grid.An illustration of a grid would be the lines on graph paper. noun. (football) (football) the field.Learn more about grid
brainly.com/question/28586483
#SPJ2
(+4)-(+4)-(-10)+(+4)-(+8)+(-16)-(-10) I only need the procedure Thanks
Answers
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
How to find displacement from velocity.
Answers
Answer:
The average velocity of the object is multiplied by the time traveled to find the displacement. The equation x = ½( v + u)t can be manipulated, as shown below, to find any one of the four values if the other three are known.
What is 2.29 rounded to the nearest whole ounce?
Answers
Answer: To round 2.29 to the nearest whole number consider the tenths' value of 2.29, which is 2 and less than 5.
Step-by-step explanation:
The picture attached is the problem
Answers
(9/2 , -9/4)
So C is the answer
IDENTIFY TWO SEGMENTS THAT ARE MARKED PARALLEL TO EACH OTHER.
PLEASE HELP, WILL GIVE BRAINLIEST.
Answers
Hey there!
I believe segment ED and AB are parrarel to each other.
Hope this helps! :)
Have a great day!
A car salesman has 5 used cars for sale. They have a mean price of $7000. What is the total price of all 5 cars?.
Answers
Answer:
Step-by-step explanation:
5 used cars for sale. They have a mean price of $7000
. What is the total price of all 5
cars?
We are given total number of cars = 5 cars.
The mean of all of five cars = $7000.
Note: Total sum/value could be calculated by multiplying mean with the total numbers we have.
Total price = Mean × Total number of cars.
According to problem, mean is 7000 and total number of cars is 5.
Therefore, Total price of all 5 cars = 7000 × 5 = $35000.
We are given total number of cars = 5 cars.
The mean of all of five cars = $7000.
Note: Total sum/value could be calculated by multiplying mean with the total numbers we have.
Total price = Mean × Total number of cars.
According to problem, mean is 7000 and total number of cars is 5.
Therefore, Total price of all 5 cars = 7000 × 5 = $35000.
SOMEONE PLEASE ANSWER‼️‼️‼️ILL MARK BRAINLYEST PLEASE ‼️‼️
In the triangle LMN, LM = 13, MN = 17, LN = 10. Which is the largest angle?
A. LNM
B. LMN
C. This cannot be determined
D.MLN
Answers
Answer:
b. LMN
Step-by-step explanation:
The angle opposite to the largest side is the largest angle, which means that angle MLN is the largest angle. Hence, option D is correct.
What is an angle?Two lines converge at a location, creating an angle. An "angle" is the term used to describe the length of the "opening" between these two rays. The letter is used to represent it. Angles are frequently expressed in degrees and radians, a unit of roundness or rotation.
The given lengths of the sides are,
LM = 13
MN = 17 and LN = 10
Then, the angle which is opposite to the side MN will have the greater angle then angle MLN has the greater angle.
To know more about Angles:
https://brainly.com/question/28451077
#SPJ2
Solve for x
8-2x=-12
PLEASE HELP WHAT IS X
Answers
Answer:
x=10
Step-by-step explanation:
Pls help ::::………..
——-////
Answers
Answer:
you will have $133920 intrest monthly and $151920 in the bank
Step-by-step explanation:
Suppose you give $100 to a bank which pays you 5% simple interest at the end of every year. After one year you will have $105, and after two years you will have $110. This means that you will not earn an interest on your interest. Your interest payments will be $5 per year no matter how many years the initial sum of money stays in a bank account.
Transposing the formula R=R0 (1+at) for t gives?
Answers
thats ur answer,hope it helps
Answer:
t
Step-by-step explanation:
7.4x10^7 in standard form
Answers
Answer: 740000000
Step-by-step explanation:
Answer:
0.000074
7.4×10−5
To write in standard notation, move the decimal point on
7.4
over as many times as the power of ten given.
Move to the left if the given power has a negative exponent
Move to the right if the given power has a positive exponent
Therefore:
7.4×10−5=0.000074