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
The purpose of a budget is to figure out how to use money in a way that best meets your wants and needs. TRUE OR FALSE. Brainly
Answers
Pls help if you only know the correct answer!!! Thanks!!
Answers
Answer:
Step-by-step explanation:
16. To get to school, Enzo can travel 1.2 km
east on Rutherford Street and then south
on Orchard Avenue to his school. Or, he
can take a shortcut through the park, as
shown. His shortcut takes him 20 min.
a
Rutherford Street
home
Orchard Avenue
shortcut
school
Enzo's walking speed is 6 km/h.
a) What angle does Enzo's shortcut make
with Rutherford Street? Describe any
assumptions you must make.
b) How much time does Enzo save by
taking his shortcut? Explain your answer.
Answers
Answer:
a)it is a 45 degree angle
b) Enzo saves 8 minutes if he takes the shortcut
Step-by-step explanation:
a) In the picture it looked like a square and if Rutherford street is 1.2 km so is Orchard avenue, and if its a true square it must be 90 degrees so you cut that is half and you get your answer of 45 degrees .
b) It takes Enzo 20 min to walk the shortcut and his walking speed is 6 km/h
you divide 20 by 1.3 or one third and you get 2 so the short cut is 2 km long, and we know Rutherford st. and Orchard ave. is 1.2 km each
2.4 km=length of Rutherford and Orchard together
shortcut is 2 km
divide 2.4 by 0.4 or .4 and you get 6
so if it takes him 20 min on the shortcut it should save him 8 minutes.
The volume of a rectangular prism is 550 cubic meters.
The length of the rectangular prism is 8 meters,
the width is x - 2, and the height is x + 5.
Find the value of x, and the dimensions of the rectangular prism.
Enter your answer as an integer or decimal.
V = lwh
X=
Width=
Meters
Height=
Answers
The value of x and the dimensions of the rectangular prism are as follows;
x = 7.5 m
length = 8 m
width = 5.5m
height = 12.5 m
volume of a rectangular prism = lwh
volume = 550 m³
l = 8
w = x - 2
h = x + 5
Therefore,
v = lwh
550 = (x + 5)(x - 2)8
550 = (x² - 2x + 5x - 10)8
550 = (x² + 3x - 10)8
550 = 8x² + 24x - 80
8x² + 24x - 80 - 550 = 0
8x² + 24x - 630 = 0
4x² + 12x - 315 = 0
using quadratic formula,
where
a = 4
b = 12
c = -315
-b ± √b² - 4ac / 2a
Therefore,
x = -10.5 or 7.5
x cannot be negative .
so, x = 7.5
x = 7.5 m
length = 8 m
width = 7.5 - 2 = 5.5 m
height = 7.5 + 5 = 12.5 m
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Please help, thanks. I don't understand how to do this.
Answers
Answer:
3m(a-2b)+(a-2b)^2
= 3m(a-2b)+(a-2b)(a-2b)
= (a-2b)(3m+a-2b)
The first term of an arithmetic sequence is 10. The 7th term is 28. What is the common difference of the arithmetic sequence?
Answers
Answer:
the answer is A1
Step-by-step explanation:
{a7} = 10 = a1 + 7*4
10 = a1 + 28
-28 - 28
-18 = a1
Which is equivalent to the expression below 6a-7+2a-4
Answers
have a nice day
Find and intercept the slope of this line.
Answers
Step-by-step explanation:
the 4th answer option is correct.
the slope of the line is expressed as the ratio
y coordinate change / x coordinate change
when going from one point to the other.
Graph this inequality:
y ≤ 1/4x
Answers
Someone help me on B and C!!!!
Answers
Answer:
(Answer of part B) First of all diameter of Mars in ordinary number = 6780 kmNow radius = Diameter/2 = 6780/2 = 3390 So radius of Mars in ordinary number = 3390 km(Answer of part C) Mass of earth = 5.97 × 10³⁴ Mass of mercury = 3.3 × 10²³Difference between the masses of Earth and Mercury = (5.97 × 10³⁴) - (3.3 × 10²³) = 2.67 × 10¹¹So, difference = 2.67 × 10¹¹Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Find the measures of angles x and y in the figure.
Answers
Answer:
x = y = 60°
Step-by-step explanation:
The angle adjacent to 120° inside the triangle is
180° - 120° = 60°
The triangle is isosceles ( 2 congruent legs ) with the 2 base angles being congruent , then
y = 60°
The vertex of the triangle = 180° - (60 + 60)° = 180° - 120° = 60°
x is vertically opposite the vertex and is congruent , so
x = 60°
Find the cost per roll if a bag of five lunch rolls is $2.50
Answers
[tex]\rule{300}{3}[/tex]
[tex]\text{Hi!}[/tex]
To find the cost per item (or in your case "rolls"), you will first have to divide the cost of the lunch rolls [tex](2.50)[/tex] by the amount of lunch rolls there are [tex](5)[/tex].
So in this case, it would look like
[tex] \textbf{$2.50/5} [/tex][tex]\text{$2.50 ÷ 5}[/tex][tex]\text{$2.50 / 5}[/tex][tex]\text{2.50}[/tex] ÷ [tex]\text{5}[/tex]
[tex]\text{=$0.50}[/tex]= [tex]\text{\ 0.50}[/tex]
[tex]\boxed{\$0.50{}}[/tex]
[tex]\rule{300}{3}[/tex]
What is (-2) power 35?
Answers
Answer: − 34359738368
A bee travels 50 meters in 2 seconds. At this speed, how long would it take for the bee to travel 375 meters?
Calculate the bee's unit rate of meters per second.
What is the equation of constant proportionality? (y=kx)
Answers
Answer:
15 seconds
Step-by-step explanation:
Help plz explain work
Answers
Answer:
i cant see anything
Step-by-step explanation:
.
A mountain climber started at zero elevation. The first day he hiked 10 miles up
the mountain, the second day it got steeper and only hiked 3 miles, the third day he
had to detour and went down 4 miles and the last day he went up 1 mile. How far
did he get up the mountain?
Answers
Answer:
14 miles if that's how far he went up
17miles if you're calculating his distance covered
The distance he hiked up the mountain is 10 miles.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that a mountain climber started at zero elevation. On the first day he hiked 10 miles up the mountain, on the second day it got steeper, and only hiked 3 miles, On the third day he had to detour and went down 4 miles, and on the last day, he went up 1 mile.
The total elevation will be calculated as below:-
Elevation = 10 + 3 + 1 - 4
Elevation = 14 - 4
Elevation = 10 Miles
Therefore, the distance he hiked up the mountain is 10 miles.
To know more about an expression follow
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I have no idea how to do these plz help and plz make sure it’s right because I only have 5 questions and will mark brainiest:)
Answers
Answer: the answer is d
Step-by-step explanation:
Solve the attached problem please
Answers
Answer:
41910.
Step-by-step explanation:
We can calculate this by first finding the sum for k = 1 to 50 then subtracting the sum for k = 1 to 14.
We use the formula (1/6)n(n+1)(2n+1)
So for 1 to 50 its 1/6 * 50* 51 * 101 = 42925
and for 1 to 14 it comes to 1/6*14*15*29 = 1015
So the answer is 41910.
( ꈍᴗꈍ)
introduction to algebra explain
Answers
Answer:
Algebra is the branch of Maths that uses alphabetical letters to find unknown numbers. These letters are also called variables. ... Algebra involves the simple operation of mathematics like addition, subtraction, multiplication, and division involving both constant as well as variables. For example, x+10 = 0.
Step-by-step explanation:
In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. It includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields.
Hiiii!
Here's what algebra is:
Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols. In elementary algebra, those symbols (today written as Latin and Greek letters) represent quantities without fixed values, known as variables. ... The letters x and y represent the areas of the fields.
In simple words: a generalization of arithmetic in which letters representing numbers are combined according to the rules of arithmetic.
Hope it helps! ( ꈍᴗꈍ)
-Nezuko
i need help again...
Answers
Answer:
2 again and the next one is 3
Step-by-step explanation:
3/8 rounded to the nearest thousand
Answers
Answer:
0.38
Step-by-step explanation:
First, we convert the fraction to a decimal number by dividing the numerator by the denominator:
3 / 8 = 0.375
There are two parts to the decimal number above:
Integer Part: 0
Fractional Part: 375
Now, we will make the Fractional Part just two digits (nearest hundredth) by using our rounding rules.*
In this case, Rule II applies, so 3/8 (or 0.375) rounded to the nearest hundredth in decimal format is:
0.38
Answer:
.375
Step-by-step explanation:
3/8=.375
Solve inequality 5x+ 3 divided by 2 > 3x+2
Answers
Step-by-step explanation:
divide 3÷2 (5x+1.5>3x+2)
move the terms (5x-3x>2-1.5)
2x>0.5
divide by 2
x=0.25
An image viewed on a computer screen has a height of 2 inches and a width of 3 inches. If the image is enlarged 150%, what are the height and width of the enlarged image?
The enlarged image will have a height of
in. and a width of
in
Answers
Answer:
I think its 3 and 4.5. I looked it up.
Step-by-step explanation:
Look up 2 in enlarged by 150% and I clicked on the first link and then do the same for 3.
The enlarged image will have a height of 3 in. and a width of 4.5 in.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
An image viewed on a computer screen has a height of 2 inches and a width of 3 inches.
If the image is enlarged 150%
so, the height and width of the enlarged image is,
height = 2*150%
=3
width= 3*150%
=4.5
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can someone explain how to do this for me? i don't get it like what am i supposed to do..
Answers
Answer:
You need to select ALL of the fractions listed that are GREATER than 1/2.
One of those is 3/4.
Step-by-step explanation:
Make all of the fractions equal to 1/2, and then compare to what they really are. For example, taking 3/4 and making it equal to 1/2, which would be 2/4. Since it is 3/4 though, we know that it is GREATER than 1/2.
1\4-2\7 plese show your work
Answers
Answer:
-1/28
Step-by-step explanation:
You need to convert 2/7 and 1/4 into the same denominator. The GCD is 28. 2/7=8/28 and 1/4=7/28. 7/28-8/28=-1/28
Answer:
-1/28
Step-by-step explanation:
You have to find the least common multiple for 7 and 4, the denominators, to add the fractions. The LCM of 7 and 4 would be 28. You would have to multiply 7 by 4 and 4 by 7, meaning you have to multiply the numerators by the same number. 1x7/4x7-2x4/7x4= -1/28.
How to factor using grouping.
Answers
Step-by-step explanation:
step 1:-group the first two terms together and then the last terms together.
step 2:-factor out a GCF from each separate binomial.
step3:-factor out the binomial
As a civil engineer, you are drafting the plans
for a new water treatment plant. The water
mains for this plant measure 48 inches in
diameter. At each joint between pipes in the
main, a strip of rubber will be bonded to the
outside of the pipe joint to improve the seal.
About how long will the rubber seal be when
it is trimmed to fit around the pipe?
Answers
The distance around a circle is the circumference.
Circumference = Pi x diameter.
Circumference = 3.14 x 48
Circumference = 150.72 inches
Round the answer as needed.
Simplify the expression 5 (x - 7) + 4x=
Answers
What is a dot product.
Answers
Answer:
In mathematics, the dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. ... Algebraically, the dot product is the sum of the products of the corresponding entries of the two sequences of numbers
Step-by-step explanation:
What is the equation of the parabola? If correct will award brainliest, scam answers will be reported!
Answers
Answer:
Equation of parabola: y = a(x-h)2 + k or x = a(y-k)2 +h, but the simple version is y2 = 4ax.
Step-by-step explanation: