Answers
You mean like graph? Yeah.
Write in Function form
[tex]\frac{y-3}{x-6}=2\\y-3=2(x-6)\\y=2(x-6)+3\\y=2x-12+3\\y=2x-9[/tex]
So (y-3/x-6)=2 does represent "line"
[tex]\frac{y-6}{x-4}=5[/tex]
multiply x-4 all side.
[tex]y-6=5(x-4)[/tex]
Notice how the equation is similar to "Tangent" so it's clearly a line.
About reasoning, No idea how to explain but this might help...
Whenever you get rid of the fraction part, it'll leave only y-f(a)=f'(a)(x-a) which is a Tangent Line (It explains it.)
And when you simplify in Function Form, you'll get an exact linear function "[tex]y=mx+b[/tex]"
Related Questions
Johanna can jog 3,000 feet in 5 minutes. If she jogs at the same rate, how many feet can she jog in 8 minutes?
Answers
Answer:
4800
Step-by-step explanation:
3000\5=600
600*8=4800
The function P(x) = –0.015x^2 + 1.2x – 11.5 gives the profit, in thousands of dollars, when a company sells a new product at x dollars per unit. Which of the following statements best interprets the average rate of change of this function from x = 50 to x = 55?
The profit increases by $375 for every $1 increase in the selling price.
The profit decreases by $375 for every $1 increase in the selling price.
The profit increases by $1875 for every $1 increase in the selling price.
The profit decreases by $1875 for every $1 increase in the selling price.
Answers
Answer:
The profit decreases by $ 375 for every $ 1 increase in the selling price.
Step-by-step explanation:
From the definition of the secant line we get that the average rate of change of [tex]P(x) = -0.015\cdot x^{2}+1.2\cdot x -11.5[/tex], where [tex]x[/tex] is the selling price of the product, measured in dollars per unit, is:
[tex]r = \frac{P(55)-P(50)}{55-50}[/tex] (1)
Now we evaluate the function at each bound:
x = 50
[tex]P(50) = -0.015\cdot (50)^{2}+1.2\cdot (50)-11.5[/tex]
[tex]P(50) = 11[/tex]
x = 55
[tex]P(55) = -0.015\cdot (55)^{2}+1.2\cdot (55)-11.5[/tex]
[tex]P(55) = 9.125[/tex]
Then, the average rate of change is:
[tex]r = \frac{9.125-11}{55-50}[/tex]
[tex]r = -0.375[/tex]
Hence, the profit decreases by $ 375 for every $ 1 increase in the selling price.
The statements that best interprets the average rate of change from x = 50 to x = 55 is (b) The profit decreases by $375 for every $1 increase in the selling price.
The profit function is given as:
[tex]P(x) = -0.015x^2 + 1.2x - 11.5[/tex]
Calculate P(x), when x = 50.
So, we have:
[tex]P(50) = -0.015(50)^2 + 1.2(50) - 11.5[/tex]
[tex]P(50) = 11[/tex]
Calculate P(x), when x = 55.
So, we have:
[tex]P(55) = -0.015(55)^2 + 1.2(55) - 11.5[/tex]
[tex]P(55) = 9.125[/tex]
The average rate of change from x = 50, to 55 is then calculated using:
[tex]m = \frac{P(55) - P(50)}{55-50}[/tex]
So, we have:
[tex]m = \frac{9.125 - 11}{55-50}[/tex]
[tex]m = \frac{-1.875}{5}[/tex]
Divide
[tex]m = -0.375[/tex]
The function is in 1000 units.
So, we have:
[tex]m = -0.375\times 1000[/tex]
[tex]m = -375[/tex]
-375 implies a decrease of $375 for every $1 increase in sales
Hence, the correct statement is (b)
Read more about average rates at:
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Find the value of a. The diagram is not to scale.
Answers
Answer: B. a = 144 degrees
Step-by-step explanation:
180=36+a
144=a
Step-by-step explanation:
hope it's obvious both the reason is being cointerior angle
plz follow me
Figure A is a scale image of Figure B.
A
11
1
Figure A
10
Figure B
What is the value of x?
Answers
9514 1404 393
Answer:
x = 4.4
Step-by-step explanation:
The longer side is 11/10 times the length of the shorter one:
x = (11/10)(4) = 4.4 . . . units
In ΔBCD, the measure of ∠D=90°, BC = 81 feet, and DB = 52 feet. Find the measure of ∠C to the nearest tenth of a degree.
Answers
Answer:
39.9°
Step-by-step explanation:
m∠C = β
sin β = [tex]\frac{52}{81}[/tex] ⇒ β = arcsin [tex]\frac{52}{81}[/tex] ≈ 39.9°
Answer:
39.9
Step-by-step explanation:
sinC=
sin C = \{52}{81}
sinC=
81
52
C=\sin^{-1}{52}{81})
C=sin −1 ( 81 /52 )
C=39.9393\ 39.9^
C=39.9393≈39.9∘
"Samuel spent $16 for 4 erasers and 2 pencils. Alva spent $10.50 for 3 erasers and 1 pencil. How much do 5 erasers and 3 pencils cost?"
Answers
Please someone help me
Answers
Answer:
D
Step-by-step explanation:
Answer:
uhh what kinda symbols r those
Step-by-step explanation:
Simplify:
3p+2p-p
Please help ASAP !!
Answers
Answer: 4 P
Step-by-step explanation: hope this helps!
The solution of the given expression 3p+2p-p will be 4P.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given expression is 3p+2p-p. The expression will be simplified as:-
E = 3p+2p-p
Add the values 3p and 2p first.
E = 5p - p
Subtract p form 5p.
E = 4p
Therefore, the solution of the given expression 3p+2p-p will be 4P.
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The perimeter of a rectangular parking lot is 312m .
If the length of the parking lot is 95 m, what is its width?
Answers
Answer:
61 meters
Step-by-step explanation:
The perimeter of a rectangle is 2l + 2w, l being the length and w being the width. Substitute the known value into the equation and solve:
312 = 2(95) + 2w
312 = 190 + 2w
122 = 2w
w = 61
can anyone help me please!! i dont get it (explain too)
MARKING BRAINLIEST
Answers
Answer:
i=
Step-by-step explanation:
Solve for the line, Thank you!
Answers
Explain
What inequality is represented by this graph?
Answers
Answer:
I believe it would be B
Step-by-step explanation:
im not good at explaining, but basically that would make the most sense, forgive me if im wrong, im not good at math TwT
In the 48 years between 1842, the average rate of erosion at horseshoe falls was 33 divided by 50 metre per year. In the 22 years between 1905 and 1927 the rate of erosion was 7 divided by 10 meter per year . Approximately how much total erosion occurred during these two time periods
Answers
Answer:
47. 08 meters
Step-by-step explanation:
Given that:
In 48 years between 1842 :
Rate of erosion = 33/50 meters per year
Between 1905 - 1927 (22 years)
Rate of erosion = 7/10 meters per year
Approximately how much total erosion occurred during these two time periods ;
Total erosion that occured within 1842:
Rate of erosion * number of years
(33/50)m * 48
0.66 meters * 48
= 31.68 meters
Total erosion that occured between 1905 - 1927:
Rate of erosion * number of years
(7/10)m * 22
0.7 meters * 22
= 15.40 meters
total erosion which occurred during these two time periods ;
31.68 meters + 15.40 meters
= 47.08 meters
Answer:
47. 08 meters
Step-by-step explanation:
Given that:
In 48 years between 1842 :
Rate of erosion = 33/50 meters per year
Between 1905 - 1927 (22 years)
Rate of erosion = 7/10 meters per year
Approximately how much total erosion occurred during these two time periods ;
Total erosion that occured within 1842:
Rate of erosion * number of years
(33/50)m * 48
0.66 meters * 48
= 31.68 meters
Total erosion that occured between 1905 - 1927:
Rate of erosion * number of years
(7/10)m * 22
0.7 meters * 22
= 15.40 meters
total erosion which occurred during these two time periods ;
31.68 meters + 15.40 meters
= 47.08 metersStep-by-step explanation:
Shannon's rain-catcher has 8 inches of water in it. Each day, 3 inches of water are added to the rain-catcher. Let y represent the total number of inches of water in the rain-catcher after x days. Express the equation in the form of y=mx+b .
Answers
Answer:
y= 3x + 8
Step-by-step explanation:
y = mx + b
m = 3 inches of water added each day
x = 8 inches of water at start
y= 3x + 8 is the required equation.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, Shannon's rain-catcher has 8 inches of water in it. Each day, 3 inches of water are added to the rain-catcher.
We have,
m = 3 inches of water added each day
x = 8 inches of water at start
Converting in y = mx + b, we get,
y = 3x+8
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Which of the following transformations is the only one that can change the lengths of its sides but remain similar??
A) Translation
B) Rotation
C) Reflection
D) Dilation
Answers
Answer:
D
Step-by-step explanation:
It is dilation because transformation is moving and sliding, rotation is spinning, reflection is a mirroring of the shape upon a certain line or axis, and dilation is the change in size leaving 1 point the same.
Guessing the initial of a students middle name
Answers
Answer:
1/26
Step-by-step explanation:
Please help meeee :)))))
Answers
What is accounting? What is the role of accounting in values?
Answers
Answer:
Found this on google, "Accounting creates values by maintaining transparency of accounts. Since man lives in the society, he has got a social life. For leading a social life he has to perform financial and material transactions daily. For carrying out these transactions successfully the existence of a sound environment is necessary."
Answer: Accounting is the process of recording financial transactions pertaining to a business.
Step-by-step explanation: The purpose of accounting is to accumulate and report on financial information about the performance, financial position, and cash flows of a business. This information is then used to reach decisions about how to manage the business, or invest in it, or lend money to it.
You are pouring 50 pounds of sand into a wagon. The linear function y= 10x represents the weight y (in pounds) of the sand in the wagon after you have poured x bags of sand into the wagon. Which graph represents the situation?
Answers
Answer:
You have 50 lb of sand, and you are pouring this into a wagon.
We have the relationship:
y = 10lb*x
Where x is the number of bags of sand that you poured into the wagon.
We know that in total, you have 50 lb of sand, then let's find the domain of this function (Domain is the set of the possible values of x)
The minimum will be when x = 0, you poured 0 bags at this point.
And the maximium will be when y = 50lb
y = 50lb = 10lb*x
50lb/10lb = x = 5
Then the domain is 0 ≤ x ≤ 5
Then we only will graph this in that range of values.
The graph will be something like:
Find the slope I’m sorry I need help with this one I’m finding the answer but don’t understand it sorry
Answers
The sum of the ages of Martin and his son Sherwin is 47 years. Martin's age is 2 years more than 4 times the
age of Sherwin. Find their present age.
Answers
Answer:
In the picture above it shows how to answer the questions step by step. If there's a mistake, pls inform me.
Algebra 1
Solve for n.
-1 sn + 12 < 19
Write your answer as a compound inequality with integers.
Answers
Answer:
i think the answer is -7/s
Step-by-step explanation:
Let's solve for n.
(−1s)(n)+12<19
Step 1: Add -12 to both sides.
−ns+12+−12<19+−12
−ns<7
Step 2: Divide both sides by -s.
−ns
−s
<
7
−s
n>
−7
s
Answer:
n>
−7
s
Which function is linear?
A. 9y+3=0
B. Y-4x=1
C. Y=2+6x⁴
D. X-2y=7
E. X/y+1=2
Answers
Answer:the answer is A
Step-by-step explanation:
Please help me out i don’t know what right and left is!!! please tell me :(((
Answers
Answer:
put your fingers out in the shape of L's. Which ever finger has the L facing the proper way, is left, and the other is right.
Step-by-step explanation:
Liana is studying the activity of nurse sharks. She starts at a position that is 25 feet below sea level. She rises 9 feet, then descends 12 feet to take a photo of a sleeping shark. Find her position relative to sea level when she took the photo.
Answers
Answer:
I believe the answer is -28
Step-by-step explanation
I gotchu bro
The answer is -28 because Liana starts at 25 below sea level (which is the same thing as -25) If she rises 9 feet, then you know to add because she is going up so your just gonna add. Next she descends 12 feet, so she went down, so subtract. So i know the answer is going to be -28 because -25+9 is -16, then imma subtract -16 and 12 so, -16 - 12= -28. There ye go
A store sells mugs. Each mug cost the same amount.
Answers
Answer:
nobody won't be able to answer this without some more details.
Answer:
that's nice
Step-by-step explanation:
if u actually need help ask this question again or put the whole question in the comments section
ur welcome
3. Nathan usually drinks 48 ounces of water per day. He read that he should
drink 72 ounces of water per day. If he starts drinking 72 ounces, what is the
percent increase?
Answers
Answer:
50%
Step-by-step explanation:
A line passes through (2, -1) with slope 3.
What is the equation of the line in point-slope form?
A. y - 1 = 3(x + 2)
B. 3(y + 2) = x - 1
C. y - 2 = ( 1/3 x + 1)
D y + 1 = 3(x - 2)
Answers
Add 1
y = 3x + 7
B. 3y + 6 = x - 1
Subtract 6, then divide by 3
3y = x - 7
y = 1/3x - 7/3
C. y - 2 = 1/3x + 1
Add 2
y = 1/3x + 3
D. y + 1 = 3x - 6
Subtract 1
y = 3x - 7
When put on a graph, D passes through (2, -1)
Answer is D.
Mike wants to put 150 square feet of artificial turf in his front yard. This is the maximum area
of artificial turf allowed by his homeowners association. He wants to have a rectangular area
of turf with length one foot less than 3 times the width. Find the length and width. Round to
the nearest tenth of a foot.
Answers
Answer:
Step-by-step explanation:
Area of the rectangular area = Length * width
A = LW ...... 1
If he wants to have a rectangular area of turf with length one foot less than 3 times the width, then
L = 3W - 1 ...... 2
Substitute 2 into 1
A = (2W-1)W
A = 2W^2 - W
Since area = 150sq.ft
150 = 2W^2 - W
2W^2 - W - 150 = 0
Factorize
2W^2 - W - 150 = 0
W = 1±√1+4(300)/2(2)
W = 1±√1201/2(2)
W = 1±34.655/4
W = 35.655/4
W = 8.91375
W = 8.9 (to nearest tenth)
Get the length
L = A/W
L = 150/8.9
L = 16.85
L = 16.6ft
Hence the length is 16.6ft and the width is 8.9ft
4x =64 find x in exponential equations
Answers
Answer:
X=16
Step-by-step explanation:
4/64
x=16