Which equation represents the linear function that is shown on the graph below?
ANSWERS:
y= 1/2x +4
y= 1/2x -2
y= 4x -2
y= -2x +4
Answers
which is the same as y = (1/2)x - 2 or can be written as [tex]y = \frac{1}{2}x - 2[/tex]
If you wanted the decimal form version, then the equation would be y = 0.5x - 2
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Explanation:
The four points on this line are
(4,0)
(6,1)
(8,2)
(10,3)
Let's pick two of these points to find the slope.
The two points I'll pick are (4,0) and (6,1)
The first point is (4,0) so (x1,y1) = (4,0) meaning that
x1 = 4
y1 = 0
The second point is (6,1) so (x2,y2) = (6,1) meaning that
x2 = 6
y2 = 1
Using the slope formula, we find...
m = (y2 - y1)/(x2 - x1)
m = (1-0)/(6-4)
m = 1/2
m = 0.5
The slope in fraction form is 1/2. This means that each time we move up 1 unit, we move to the right 2 units.
slope = rise/run = 1/2
Rise = 1
Run = 2
The fraction 1/2 is equivalent to the decimal form 0.5
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Let's use the slope m = 0.5, along with the point (x,y) = (4,0) to find the y intercept b
y = m*x + b
y = 0.5*x + b
0 = 0.5*4 + b
0 = 2 + b
0 - 2 = 2 + b - 2
-2 = b
b = -2
The y intercept is -2 meaning that the line crosses the vertical y axis at -2.
Therefore the equation is y = 0.5x - 2 after we update y = mx+b
This is the same as y = (1/2)x - 2 or y = 1/2x - 2 which is why choice B is the answer. The parenthesis help make it clear that x is not in the denominator; though technically they aren't needed.
The equation y = (1/2)x - 2.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
We have points from the graph (6,1) and (8,2).
The slope of the equation is;
m = (2-1) / (8-6)
m = 1/2
And the y-intercept;
We have the slope-intercept form of the equation,
y = mx + b
y = x/2 + b
To find the y-intercept, we substitute the point (6,1)
b = -2
Therefore, we have the equation of the linear function y = (1/2)x - 2.
To learn more about the function;
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Related Questions
Only the Fahrenheit one plz
Answers
F = 1.8C + 32
The temperature C is given as -20
So, all you have to do is plug the given C temperature in the formula to get the corresponding F temperature as follows:
F = 1.8(-20) + 32 = -36 + 32 = -4 degrees Fahrenheit
on Monday 2/3 of the team practiced Tuesday 7/8 Wednesday 1/2 and Thursday 3/4 on which date were the most team members present at practice
Answers
Monday =2/3 (8/8)=16/24 16 out of 24 showed
Tuesday=7/8 (3/3)=21/24 21 out of 24 showed
Wednesday=1/2 (12/12)=12/24 12 out of 24 showed
Thursday =3/4 (6/6)=18/24 18 out 24 showed
On Tuesday, 21 out of 24 players showed up and that is the most team members showed up.
The Clemson Tiger Football team won the 2016 College Football National Championship. During the regular season, they won 11 games and lost 1. The data set below is the number of points by which they won (positive values) or lost (negative value) each game.
{6,6,59,19,6,46,7,3,54,−1,22,49} = {-1,3,6,6,6,7,19,22,46,49,54,59}
What is the median? ________
What is the mode? _________
What is the mean? _________
What is the 5% trimmed mean? (Round to the nearest whole number when determining the number of values to trim).
Are these averages parameters or statistics?
Answers
median is the middle value, since there is an even number, add the 2 middle numbers and divide by 2
median = 9 +17 = 26/2 = 13
mode is the number that is repeated most often
mode = 6
mean is the average of all the numbers, when added they equal 276
276/12 = 23
mean = 23
5% trimmed mean = 218 /10 = 21.8
the averages are statistics since the points of a football game can vary
6x+24/x^2+7x+12 simplify
Answers
6x+24/x^2+7x+12
becomes
6(x+4) 6(x+4)
------------------ = ---------------- Cancel the factors (x+4)
(x^2+7x+12) (x+4)(x+3)
6
= -------------
x+3
A suit is on sale for $154. If the original price of the suit was $440, what percent was discounted for the sale?
Answers
so, if we take 440 to be the 100%, what is 286 off of it in percentage anyway?
[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 440&100\\ 286&p \end{array}\implies \cfrac{440}{286}=\cfrac{100}{p}\implies p=\cfrac{286\cdot 100}{440}[/tex]
if f'(2) = 3.1 and g'(2)=7.3 then the graph of f(x)+g(x) has slope 10.4 at x=2.True or false
Answers
To determine the slope of the f(x) + g(x) in terms of x is equal to,
f'(x) + g'(x)
Then, substitute x with 2,
f'(2) + g'(2)
Substituting the known values,
3.1 + 7.3 = 10.4
Hence, the answer is TRUE.
Final answer:
The statement is true, as the slope of the graph of f(x)+g(x) at x=2 is the sum of the slopes of f and g at that point, which equals 10.4.
Explanation:
The statement is true.
In calculus, the derivative of a function at a particular point measures the rate at which the function is changing at that point. It is analogous to the slope of the tangent line to the graph of the function at that point.
When we are given that f'(2) = 3.1 and g'(2) = 7.3, these values represent the slopes of the functions f and g at x = 2, respectively.
To find the slope of f(x) + g(x) at x = 2, we simply add the slopes of f and g at that point. This is based on the rule that the derivative of the sum of two functions is the sum of their derivatives, or symbolically, (f+g)' = f' + g'.
Therefore, the slope of the graph of f(x)+g(x) at x=2 is indeed 10.4 (3.1 + 7.3).
What is the distance between 0.5 to -1.5
Answers
For the initial value problem y' −xy = x, y(0) = 1. write down the first four nonzero terms of the series
Answers
The exact solution is easy enough to find. We can separate the variables:
[tex]y'-xy=x\iff \dfrac{\mathrm dy}{\mathrm dx}=x(1+y)\implies \dfrac{\mathrm dy}{1+y}=x\,\mathrm dx[/tex]
[tex]\implies\ln(1+y)=\dfrac{x^2}2+C[/tex]
[tex]\implies y=Ce^{x^2/2}-1[/tex]
Given that [tex]y(0)=1[/tex], we have
[tex]1=C-1\implies C=2[/tex]
Then recall that
[tex]e^x=\displaystyle\sum_{n\ge0}\frac{x^n}{n!}[/tex]
to write the solution as
[tex]y=2\displaystyle\sum_{n\ge0}\frac{\left(\frac{x^2}2\right)^n}{n!}-1[/tex]
[tex]y=1+2\displaystyle\sum_{n\ge1}\frac{\left(\frac{x^2}2\right)^n}{n!}[/tex]
so the first four terms of the series are
[tex]1+x^2+\dfrac{x^4}4+\dfrac{x^6}{24}[/tex]
2+1.25f=10−2.75f solve for f
Answers
2 + 1.25f = 10 - 2.75f
Add 2.75f to both sides.
1.25f + 2.75f = 4f
4f + 2 = 10
Subtract 2 from both sides.
4f = 8
Divide both sides by 4 to solve for f.
f = 2
I hope this helps!
The value of f is 0.02.
What is an expression ?Expression is a formation of numbers and variables with mathematical operations.
According to the given question we have to solve for f or we can say we have to find the value of f for the given expression which is
2+1.25f=10−2.75f (lets multiply each term by 100 to remove
decimals )
∴ 200 + 125f = 1000 - 275f
125f + 275f = 1000 - 200
400f = 800
f = 800/400
f = 2.
As we have multiplied by 100 we have to divide by 100 we obtain the exact result.
So, 2/100 is = 0.02
f = 0.02.
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rewrite y^2(9y^2+4y-9) in standard form
Answers
Simplify.
(y² · 9y²) + (y² · 4y) + (y² · -9)
Simplify.
9y⁴ + 4y³ - 9y²
~Hope I helped!~
PLZ HELP IM FAILING!!!!!! The linear equation y−3=4(x+5)y−3=4(x+5) y minus 3 equals . 4 open x plus 5 close is in what form.
Answers
y-3 = 4(x+5) is "the equation of a straight line in point-slope form." That's it.
The weight of 1000 identical samples of a substance is 10 pounds. What is the weight of 10 samples?
Answers
The height of Niagara falls is 182.How many yards high is Niagara falls
Answers
To convert the height of Niagara Falls from meters to yards, we multiply the given height of 182 meters by the conversion factor of 1.09361 yards per meter, which gives us approximately 199.18 yards.
Explanation:The height of Niagara Falls is provided in this question as 182. However, no units are given so let's assume this is in meters as that's a common unit for height. The conversion factor from meters to yards is approximately 1 meter = 1.09361 yards. Therefore, we multiply the given height in meters by this conversion factor to get the height in yards.
First, identify the height given in the question- here it is 182.Next, apply the conversion factor: 182 meters * 1.09361 yards/meter.Doing this multiplication gives us approximately 199.18 yards.So, Niagara Falls is approximately 199.18 yards high when converted from meters.
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How do i solve this equation and how did you do it
Answers
then f(1) = (3(1) + 7)²
= 10²
⇒ f(1) = 100 [OPTION E]
Makayla's local movie theater has a moviegoer club that charges an annual registration fee of 25 dollars.However, movie tickets are discounted for members at 6 dollars per ticket, instead of 9 dollars per ticket.Let m equal the number of movie tickets Makayla purchases in a year. Write a function to model the amount of money Makayla spent going too the movies during the year she joined the club. C(m)=6x+25 The domain is best represented by: A)integers B)whole numbers C)rational numbers D)real numbers Algebra chestercat
Answers
A lawn is in the shape of a trapezoid with a height of 40 feet and bases of 60 feet and 140 feet. How many bags of fertilizer must be purchased to cover the lawn if each bag covers 1800 square feet?
Answers
By decreasing each dimension by 1 unit, the area of a rectangle decreased from 40 square feet (on the left) to 28 square feet (on the right). Find the percent decrease in area.
Answers
The percent decrease in the area of a rectangle from 40 square feet to 28 square feet is calculated by dividing the difference in areas (12 sq ft) by the original area (40 sq ft) and multiplying by 100%. The result is a 30% decrease in area.
Explanation:The percent decrease in the area of a rectangle can be found by first calculating the difference in the areas and then dividing that difference by the original area. In this case, the original area of the rectangle was 40 square feet and it decreased to 28 square feet, a difference of 12 square feet.
We use the formula for percentage change which is:
(change in value) / (original value) × 100%
Here, the change in value is the difference in areas (12 square feet) and the original value is the original area of the rectangle (40 square feet). Thus we calculate:
(12 sq ft/ 40 sq ft) * 100% = 30%
So, the percent decrease in the area of the rectangle is 30%.
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Check the answer that best describes the relationship between f(x) and x. (for example if f(x) is θ(x)θ(x) check that as your answer and not o(x)o(x) or ω(x)ω(x) even though these are true also in this case.)
Answers
f(x) is the value of a function f evaluated at the value x. The formal definition of a function is a particular set of rules that associates a particular value with another. For an analogy: you can think of f as a machine that takes in an input, transforms it according to a certain set of rules, and produces an output. In this analogy, x would be the input and f(x) would be the output.
Rose bought 7/20 kilogram of ginger candy and 0.4 kilogram of cinnamon candy. Which did she buy more of? Explain how you know.
Answers
Answer:
Rose bought cinnamon candy more of.
Step-by-step explanation:
Rose bought ginger candy = [tex]\frac{7}{20}[/tex] kilogram
= 0.35 Kilogram
She bought cinnamon candy = 0.4 kilogram
As we know 1 kilogram = 1000 grams
0.35 kilogram = 1000 × 0.35 = 350 grams ginger candy
0.4 kilograms = 1000 × 0.4 = 400 grams cinnamon candy
Therefore, She bought cinnamon candy more.
Find f`(x) for the following function. Then find f(5),f(0),f(-9).
f(x)=2x+1 (simplify)
Answers
f(5)=11, f(0)=1 and f(-9)=-17.
We can calculate the gradient using these values:
Gradient=(11-1)/(5-0)=(-17-1)/(-9-0)=(-17-11)/(-9-5)=2.
The length of a ribbon is 3/4 meter. Sun Yi needs pieces measuring 1/3 meter for an art project. What is the greatest number of pieces measuring 1/3 meter that can be cut from the ribbon? How much ribbon will be left after Sun Yi cuts the ribbon?
Answers
Jane saved $ 800. Her sister has 10 times as much money. How much money does Jane's sister have? Use number or words to explain your answer.
Answers
A data set a has a mean of 7,a median 5,and a mode of 8.wich of the the numbers 7,5,and 8 must be in the data set?
Answers
A store had 888 sodas, both diet and regular. The ratio of diet sodas to regular sodas was 8:4. How many diet sodas were there?
Answers
so, diet sodas,
74*8=592
there were 592 diet sodas.
Hope this helps.
Answer:no. I don’t understand. Where did the 12 come from
Step-by-step explanation:
I REALLY NEED HELP WITH MY CALC CORRECTIONS. THIS IS THE THIRD TIME IVE POSTED THIS. I NEED HELP ASAP PLS!! I HATE CALC 1
Answers
If a = 2 and b = 3, f(1) = 2(1)^2 + 3(1) = 5
So there is a 'jump' in values of x at x = 1. So its not continuous at x=1.
2. For continuity at x = 1, ax^2 + bx must = 2 that is when a + b = 2.
3. for continuity at x = 2 , ax^2 + bx must be = 0 that is when a*2^2 + 2b = 0
- that is 4a + 2b = 0.
4. we have system of equations:-
a + b = 2
4a + 2b = 0
this gives a = -2 and b = 4 So f(x) is continuous when a = -2 and b = 4.
Prove or disprove that the product of two irrational numbers is irrational
Answers
The product of two irrational numbers can be either rational or irrational.
The product of two irrational numbers is not always irrational. To understand this, let's consider an example and a counterexample.
Example of an Irrational Product
Take the square root of 2 (\/(2)) and the square root of 3 (\/(3)). Both of these numbers are irrational. Their product is:
\/2 × \/3 = \/6
Since \/6 cannot be expressed as a fraction of two integers (making it irrational), this is an example where the product of two irrational numbers is irrational.
Counterexample of a Rational Product
Now, consider another example with \/(2) and \/(2). Since both are irrational, their product is:
\/2 × \/2 = 2
Here, 2 is a rational number because it can be written as a fraction (2/1). Therefore, this is a counterexample where the product of two irrational numbers is rational.
In summary, the product of two irrational numbers can be either rational or irrational depending on the specific numbers involved.
How can you check to see if this equation is correct? 12+39=49
Answers
Answer:
By solving it.
Step-by-step explanation:
In order to see if the equation is correct, you just have to perform the operations in both sides of the inequality and then check if those are equal, that means that the equation is correct, for example if both sides of the equation give as a result 10 then the equation is correct, now let´s do it with the problem:
12+39=49
51=39
Since 51 is not equal to 39 that means that the equation is not correct.
a consumer purchased a computer after a 15% price reduction. if x represents the computer's original price, the reduced price can be represented by
Answers
Jana is doing an experiment. She is on a dock that is 10 feet above the surface of the water. Jana drops the weighed end of a fishing line 35 feet below the surface of the water. She reels out the line 29 feet, and then reels it back in 7 feet. What is the final distance between Jana and the end of the finishing line?
Answers
Assumption: Line of reference is the surface of the water.
Final distance between Jana & fishing line = (dock height) +(reels out) -(reels back)
Final distance between Jana & fishing line = 10 + 35+ 29 - 7 = 67 feet
ANSWER: 67 feet
A video editor takes 15 hours to add a
Answers
now, since the Level III one does it in 15 hours, in 1 hour alone, how much has it done? well, it only has done 1/15 of the whole work.
the Level II has 1 hour done only 1/25 of the whole work then, and the Level I has only done 1/34 of the whole work.
now, say they all do it in "t" hours, so how much have they edited in 1 hour altogether then? well, they have only done 1/t.
[tex]\bf \stackrel{\textit{Level III rate}}{\cfrac{1}{15}}+\stackrel{\textit{Level II rate}}{\cfrac{1}{25}}+\stackrel{\textit{Level I rate}}{\cfrac{1}{34}}~~=~~\stackrel{\textit{total work done}}{\cfrac{1}{t}} \\\\\\ \textit{doing a quick prime factoring, we end up with an LCD of }\underline{2550}~thus[/tex]
[tex]\bf \cfrac{1}{15}+\cfrac{1}{25}+\cfrac{1}{34}=\cfrac{1}{t}\implies \cfrac{170~+~102~+~75}{2550}=\cfrac{1}{t}\implies \cfrac{247}{2550}=\cfrac{1}{t} \\\\\\ 247t=2550\implies t=\cfrac{2550}{247}\implies t=10\frac{80}{247}\implies t\approx 10hrs,~19min[/tex]