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 FM radio station KAMB broadcast from an antennae atop a 150 meter tall radio tower at a frequency of 90 MHz with a total radiated power of 40 kilowatts. Neighbors have complained about problems they attribute to excessive radiation from the tower, but the city engineer who measured the radiation level near the base of the tower found it to be well below the accepted standard. You have been hired by the HOA to assess the engineer's report. You know a few things about electromagnetic radiation and therefore conclude that we must find the optimum place on the ground to measure the maximum radiation emitted from the antennae. From your extensive knowledge in physics, you know that the intensity of radiation, I, is given by the formula:
I=12/32π*Psin2(θ)/r^2
where P is the power output, r is the distance from the top of the tower to the point on the ground, and θ is the angle measured from the tower to r.
Find the distance R from the base of the tower to the optimum location for taking the radiation reading. (m)
What is the maximum radiation reading from the ground in kw/m^2
If the city code requires that electromagnetic radiation be under 200 microwatts per square meter, is this antenna operating within city code? Yes or No
Answers
Answer: 150 m, 5.305*10^-5 kW/m^2, No
Step-by-step explanation:
See attachment, hope this helps
Using the radiation intensity formula we will have to:
a) [tex]150 m[/tex]
b) [tex]5.305*10^{-5} kW/m^2[/tex]
c)No
From the data informed, we have:
[tex]h=150m\\P=40KW[/tex]
Using the given formula and performing some mathematical operations:
[tex]I=\frac{12Psin^2(\theta)}{32(\pi)r^2} \\I= \frac{12(40)(R/r)^2}{32(\pi)r^2} \\= \frac{15R^2}{r^2\pi } \\= \frac{15R^2}{(R^2+150^2)^2\pi} \\[/tex]
deriving the given equation, we will have:
[tex]=\frac{(R^2+150^2)^22R-R^2(2(R^2+150^2))2R}{(R^2+150^2)^2}[/tex]
So from this equation we have that the answer of the letter A corresponds:
[tex]R=150[/tex]
For letter B we will have to develop this equation:
[tex]I= 5.30X10^{-5}[/tex]
As for the letter C, when converting the value found, it should give 200 microwatts, which is false.
Learn more: brainly.com/question/10148635
Find the measure of each angle indicated.
Please show your work
Answers
Evaluate the expression below.
5^{0}5
0
Answers
The 5-0-5 Agility Test is one of the most commonly recognised agility tests, despite its inability to actually measure agility. Instead, this is a change of direction speed test, which contrary to common belief, may not be capable of distinguishing between dominant and non-dominant leg performances.
4-0,9+(-0,11)-(-1,3) PLEASE HELP
Answers
Answer:
-20
Step-by-step explanation:
PEMDAS
a certain store is selling packages of 10 pencils and 4 pens. the manager wants to make a larger package in the same ratio. if the large package has 10 pens, how many pencils are in the large package?
Answers
Answer: 25 pencils
Step-by-step explanation:
2 × 5 = 10
5 × 5 = 25
Consider the ratio of boys to girls of 4:5.
a) What is the total number of parts?
b) What fraction of the total are boys?
c) What fraction of the total are girls?
d)If there were 18 students in total,how many of them are boys?
e)If there were 18 students in total, how many of them are girls?
Answers
Step-by-step explanation:
[tex]a)[/tex]
[tex]4+5=9 (parts)[/tex]
[tex]b)[/tex] our total is [tex]9[/tex] our boys are [tex]4\\[/tex]
our fraction is [tex]^4/_9[/tex]
[tex]c)[/tex] [tex]^5/_9[/tex]
[tex]d)[/tex] our whole used to be [tex]9[/tex] but we doubled it so it is [tex]18[/tex]
so we double [tex]4[/tex] which equals [tex]8[/tex]
[tex]^8/_{18}[/tex]
[tex]e)[/tex] [tex]^{10}/_{18}[/tex]
Brainliest please
solve pls brainliest
Answers
Answer:
1/4
Step-by-step explanation:
The constant of proportionality is 1/4.
Answer:
b
Step-by-step explanation:
The form of an equation representing proportion is
y = kx ← k is the constant of proportionality
y = [tex]\frac{1}{4}[/tex] x ← is in standard form
with k = [tex]\frac{1}{4}[/tex]
Solve by substitution.
x-2y=2
2x-5y=3
I give Brainliest
Please explain step by step.
Answers
[1] x = 2y - 1
// Plug this in for variable x in equation [2]
[2] 2•(2y-1) - 5y = -3
[2] - y = -1
// Solve equation [2] for the variable y
[2] y = 1
// By now we know this much :
x = 2y-1
y = 1
// Use the y value to solve for x
x = 2(1)-1 = 1
The maximum land speed of a cheetah is about 120km/hour.
What is this speed limit, rounded to the nearest whole number, in m/s?
Answers
Answer:
33 m/s
Step-by-step explanation:
120 km/h × (1 h)/(3600 s) × (1000 m)/(1 km) ≈ 33 m/s
_____
Additional comment
In general, units conversion is done by multiplying by a factor whose numerator and denominator have equal values, but different units. The units in that fraction need to be arranged to cancel the units you don't want and leave the units you do want.
Pls help this is due today and i have no idea
Answers
Answer:
x=38°
Step-by-step explanation:
sinx/21 =sin(38°)/21
sinx=21Sin(38°)/21
x = arcsin(21Sin(38°)/21)
x=38°
You need to raise a total of $1,000 for your trip. There are 20 days before you leave. You estimate that you will be able to sell 25 candy bars per day. How much should you charge for each candy bar?
Answers
Answer:
1,000 ÷25 = 40 so 40÷20= $2.00
your answer is $2.00 hope this helps
here is a screenshot please help 15 points
Answers
you're so cool! I hope you have an awesome day!
Answers
Answer:
The functions each have a positive Slope
a.)True, False
Step-by-step explanation:
Function A Slope: (y2-y1)/(x2-x1) = (7-3)/(2-1) = 4
Function B Slope: Count Four Boxes up from the 2 intercepts and then 2 over --> 4/2 = 2
These are both positive but 4 does not equal 2
a.) We have just proved that they have different slopes now we must determine if they have the same b. Because we know the slope of Function A we can simply move backward to get to x=0
When X=0 y= 3-4 = -1 And because in Function B we can clearly see the b at y=4 this is false.
Hope this helps and makes you have an Awesome Day!
If h(x) = 15x - 171, find h(3)
Answers
H(3) means to replace x in the equation with 3 and then solve:
15(3) - 171
45-171
-126
Answer: -126
The standard diameter of a golf ball is 42. 67 mm. A golf ball factory does quality control on the balls it manufactures. Golf balls are randomly measured to ensure the correct size. One day, an inspector decides to stop production if the discrepancy in diameter is more than 0. 002 mm. Which function could represent this situation?.
Answers
The absolute value function that could represent this situation is:
[tex]|D - 42.67| = 0.002[/tex]
The absolute value function is defined by:
[tex]|x| = x, x \geq 0[/tex]
[tex]|x| = -x, x < 0[/tex]
It measures the distance of a point x to the origin.The diameter should be of 42.67 mm with an allowance of 0.002 mm. Thus, the absolute value of the difference between the diameter and of 42.67 should be of 0.002, that is:
[tex]|D - 42.67| = 0.002[/tex]
A similar problem is given at https://brainly.com/question/24514895
answer the three questions pls
Answers
3.60 divided by 12 is 0.3 or 30 cents. 5 divided by 20 is 0.25 or 25 cents. 6.40 divided by 32 is 0.20 or 20 cents
Which of the following is the difference of two squares

4g-16h
16a^2-4y^2
2x^2-4y^2
25m^3+100n^2
Answers
Answer:
2nd option
Step-by-step explanation:
A difference of squares has the general form
a² - b²
where the terms on either side of the subtraction ( the difference ) are both perfect squares.
The only one fitting this description is
16a² - 4y²
= (4a)² - (2y)² ← difference of squares
Clarke earns
2.5
%
interest a savings account each year. If Clarke deposits
$
2
,
000.00
into a savings account, how much interest will Clarke earn during the first year?
Answers
Answer:
$ 50.00
Step-by-step explanation:
Hope this helps!
Mr. Walker asked his students to use the associative property to find an expression that is equivalent to (13 + 15 + 20) + (20 + 47 + 18). The expressions that four students created are shown in the table below.
Expressions Generated by Students
Student
Expression
Jeremy
(20 + 13 + 15) + (20 + 47 + 18)
Layla
(20 + 47 + 18) + (13 + 15 + 20)
Keith
(13 + 20) + (20 + 47 + 18) + 15
Melinda
(13 + 15 + 20 + 20) + (47 + 18)
How many of the students correctly applied only the associative property to rewrite the expression?
one
two
three
four
Mark this and return
Answers
Answer:
Jeremy
Step-by-step explanation:
You need to add 20+13+15=48 Then you add 20+47+18=85.
Can someone help please no links
Answers
Answer:
-4 or 4 I would have to go with-4!!
Step-by-step explanation:
I hope this helps in any way!!
(a−2b)^3 when a=−4 and b=−1\2
Answers
Answer:
- 125
Step-by-step explanation:
What’s that answer please
Answers
A painter checks a canvas to be sure it is rectangular. One of the canvas’ diagonals measures 48 inches. If the canvas is a rectangle, what is the measure, in inches, of the other diagonal?
A.)24
B.)12
C.)96
D.)48
Answers
Answer:
D)48
Step-by-step explanation:
Step by step explanation
A fish is at 12.85m below sea level and a turtle is at 3.5m right above the fish. State the position of the turtle.
Answers
Answer:
9.35
Step-by-step explanation:
because you take 3.5 away from 12.85
Answer:
9.35
Step-by-step explanation:
SAME EXPLANATION PO
HELP ME PLEASE!!!!!!!!!!!!
Answers
i frist 1 1 2
Step-by-step explanation:
Y
Answer:
Step-by-step explanation:
i think for number 1 is growth and number 2 decay and for 3 growth...hope this helps!
what is -3 (x+2) = 16 -x
Answers
Answer:
x = -11
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityTerms/Coefficients
Step-by-step explanation:
Step 1: Define
Identify.
-3(x + 2) = 16 - x
Step 2: Solve for x
[Distributive Property] Distribute -3: -3x - 6 = 16 - x[Addition Property of Equality] Add x on both sides: -2x - 6 = 16[Addition Property of Equality] Add 6 on both sides: -2x = 22[Division Property of Equality] Divide -2 on both sides: x = -11( 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
-4 1/2 + 2 3/4
Guys help me Im having trouble on this EEEEEEEEEE
Answers
50 Points Per Answer
Create a function in factored form for a roller coaster.
• Your coaster ride must have at least 3 relative maxima and/or minima
• The ride length must be at least 2 minutes (blueprint must use seconds)
• The coaster ride starts at 250 feet
• The ride dives below the ground into a tunnel at least once
• The ride must have one “turn around/bounce” (Mutliplicity 2)
• The ride must have at least one “twist/swerve” (Multiplicity 3)
• The ride must hit ground level at least three times (Three real zeros)
Answers
Answer:
Since you have 3 local extremas, you will have a polynomial function of degree 4. The domain of the function is [0, 4].
Use these initial conditions as your guidelines:
f(0) = 250
f(x) has at least one x-intercept (crosses the x-axis) and must be in the interval (0, 4].
f(x) decreases in any of the following intervals: (0, 1) or (2, 3)
Remember, you will have an arbitrary function that satisfies these conditions.
Step-by-step explanation:
I did :Your coaster ride must have at least 3 relative maxima and/or minima
The sum of two numbers is 110.The larger number is 2 less than 7 times the smaller.Find the Large number
Answers
Answer:
The larger number is 96.
Step-by-step explanation:
[tex]let \: the \: two \: numbers \: be \: a \: and \: b \\ a + b = 110 \\ let \: a \: be \: the \: larger \: number \\ a = 7b - 2 \\ we \: can \: get \: the \: value \: of \: b \: by \: substituting \: the \: value \: above \: for \: a \: in \: eq \: 1 \\ 7b - 2 + b = 110 \\ 8b - 2 = 110 \\ 8b = 110 + 2 \\ 8b = 112 \\ b = \frac{112}{8} \\b = 14\\ calculate \:the \: value \: of \: a \: using \: the \: equation \: above \\ a + b = 110 \\ a = 110 - 14 \\ a = 96 \\ hence \: the \: large \: number \: is \: 96[/tex]
