Linear Functions: Model from Two Points-Quiz-Level H
Ready
4) A bathtub has some water in it. Mia turns on the faucet to add more water. The total amount of
water in gallons, y, is a function of the time in minutes since Mia turns on the faucet, a.
4) The graph of the linear function passes through the points (4, 24) and (6, 30).
What is the equation of the function?
?
Answers
The equation of function for the given problem is y = 3x + 12.
What is point slope form of the line?
For linear equations, the general form is y - y1 = m(x - x1).
It draws attention to the line's slope and one of the line's points (that is not the y-intercept).
Given:
A bathtub has some water in it. Mia turns on the faucet to add more water.
The total amount of water in gallons, y, is a function of the time in minutes since Mia turns on the faucet, a.
The graph of the linear function passes through the points (4, 24) and
(6, 30).
We have to find the equation of function.
Let the linear function passes through the points (4, 24) and (6, 30).
First to find the slope of equation using given points.
\(m = \frac{y_2-y_1}{x_2-x_1} = \frac{30-24}{6-4} = \frac{6}{2} = 3\)
Now to find the equation of function.
Consider the point slope form of the line,
\(y-y_1=m(x-x_1)\)
Plug the values of m = 3 and \((x_1,, y_1) = (4, 24)\)
⇒
\(y-24=3(x-4)\\y-24=3x-12\\y=3x-12+24\\y=3x+12\)
Hence, the equation of function for the given problem is y = 3x + 12.
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Related Questions
The plane was going 150 knots when it landed in the Hudson River. What was the plane’s speed in miles per hour (mph). Note: 1 knot = 1. 15 mph. Round you answer to the nearest 10th
Answers
Answer:
172.5
Step-by-step explanation:
I multiplied the 150 by 1.15 and got the answer 172.5.
Have a great day!
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A truck can be rented from Company A for $120 a day plus $0.20 per mile. Company B charges $80 a day plus $0.40 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
Answers
Answer:
Let the truck is driven X miles per day
Charges of company A will be = 90+0.4X
Charges of company B will be =30+0.7X
Let us find out value of X when charges of both companies are same
which means that 90+0.4 X= 30+0.7X
90-30 = 0.7X-0.4X
60 = 0.3X
60/0.3 = X
X= 200
The charges of both companies will be same if truck is driven 200 miles per day
Company A will have better deal if truck is driven more than 200 miles per day ( because per mile rate of company A is less than company B)
Step-by-step explanation:
at one college, gpa's are normally distributed with a mean of 2.8 and a standard deviation of 0.4. about what percentage of students at the college have a gpa below 2.4?
Answers
The percentage of students at the college have a gpa below 2.4 is 15.87%.
Given,
The gpa's are normally distributed with given mean and SD.
mean \(\bar{x}\)= 2.8
SD σ=0.4
raw score=2.4
The z score can be calculated by using the formula
z=\(\frac{x-\bar{x}}{\sigma}\)
z=\(\frac{2.4-2.8}{0.4}\)
\(z=\frac{-0.4}{0.4}\)
z=-1
Using the z table we get the value P(z<-1), it is 0.8413, as it is less than we subtract it from 1 and we get 0.1587. As the value we got is negative, we used left tail z table to get the value of the z.
To get the percentage, we have to multiply by 100,
0.1587 x100
=15.87%
Therefore, the percentage of students at the college with gpa below 2.4 is 15.87%.
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CAN SOME ONE PLEASEEEE HELL
Answers
Answer:
missing exponent= 7
Step-by-step explanation:
i hope this helps :)
Identify the height of a triangle in which b=(x−2) m and A=(x2−4) m2. A) h = (2x + 4) m B) h = (2x + 2) m C) h = (x + 2) m D) h = (x + 4) m
Answers
The height of the given triangle is given by option c) h = (x+2)m.
Given the triangle with base b = (x - 2) m and area A = (x² - 4) m²,
we are to determine the height of the triangle using the formula for the area of a triangle.
Area of a triangle = (1/2) × base × height
We have the base and area of the triangle, but the height is unknown.
Therefore, let's find the height of the triangle, h.
A = (1/2) × b × h(x² - 4)
= (1/2) × (x - 2) × h
h = [(x²- 4) / (x - 2)] × 2h
= [(x - 2)(x + 2)] / (x - 2)h
= x + 2
Therefore, the height of the triangle is h = x + 2, which is option C). h = (x + 2) m.
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The question is in the image. The final answer is also in the other image.
Answers
We have that because the central angle is 90°, the sector represents 1/4 of a circle with a radius of 10 yd.
So, length of the safety rail is given by:
\(l=\frac{1}{4}\cdot2\pi r\)Where:
r = 10 yd
pi = 3.14
Substitute, we have:
\(l=\frac{1}{4}\cdot2(3.14)(10)=\frac{1}{4}\cdot62.8=15.7\text{ yd}\)The Answer is 15.7 yd
Next, area of the deck is given by:
\(A=\frac{1}{4}\pi r^2\)Substitute the values:
\(A=\frac{1}{4}(3.14)(10)^2=\frac{1}{4}(3.14)(100)=\frac{314}{4}=78.5\text{ yd}^2\)The answer is 78.5 yd^2
Michael draws a straight line on a graph that passes through the point (0,
3).
Choose the equation that best fits Michael's line.
B.
A
y = x - 3
C. y = 3x
D.
y = x + 3
y = 3x +1
Answers
its b so please mark me as a brainliest
Johnny rode his bike StartFraction 4 over 7 EndFraction of a mile from his house to the lake on a straight path. Then, he turned around and rode his bike 3 and StartFraction 1 over 8 EndFraction miles in the opposite direction. About how far is Johnny from his house? 1 and one-half miles 2 miles 2 and one-half miles 3 miles
Answers
Answer:
1 1/2 miles
Step-by-step explanation:
(aka option A on edge)
A pew research poll asked u.s. adults whether fathers today were doing as good a job of fathering as fathers of 20-30 years ago. the table shows their responses. if we select a respondent at random from this sample, what is the probability that the person responded "same" or "better"?
Answers
Using it's concept, it is found that there is a 0.4901 = 49.01% probability that the person responded "same" or "better".
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Researching the problem on the internet, it is found that 424 + 566 = 990 out of 2020 respondants said that they were doing the same or better, hence:
p = 990/2020 = 0.4901
0.4901 = 49.01% probability that the person responded "same" or "better".
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Special right triangles
Answers
In the right triangle figure in the image the value of the missing sides are
d = 4.04b = 2.83How to find side dThe sides of the right triangle is worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
For side d we use tan
tan 30 = d/7
d = 7 * tan 30
d = 4.04
For side b using cos
cos 45 = 2/b
b = 2 / (cos 45)
b = 2.828
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HELP!!!Where does the graph of y = sin x from x = 0 to x = 2π start? A. at its minimum B. at an x–intercept C. at its maximum D. between an x–intercept and its maximum
Answers
Answer:
B. at an x–intercept
Step-by-step explanation:
You can find a graph of the sine function in numerous places.
y = sin(0) = 0
y = 0 for x = 0
so, on the given interval, it starts at an x-intercept.
On Friday there were 8 snowboarders for every 3 skiers at Slovak ski resort. On Saturday the ratio of the number of snowboarders to the number of skiers was 4:7 there were 168 snowboarders at the ski resort on Friday there were the same number of people at the ski resort on Saturday as there were on Friday how many more skiers were there than snowboarders at the ski resort on Saturday
Answers
Answer:
There are 46 more skiers than snowboarder
Step-by-step explanation:
Given
Ratio of Snowboarders to Skiers
On Friday:
\(Ratio = 8 : 3\)
On Saturday:
\(Ratio = 4 : 7\)
Population = 168
Required
Determine the difference in the number of skiers and snowboarders on Saturday
On Saturday, we have
\(Ratio = 4 : 7\)
Calculate Total
\(Total = 4 + 7\)
\(Total = 11\)
Calculate the number of skiers
\(Skiers = \frac{7}{11} * 168\)
\(Skiers = \frac{1176}{11}\)
\(Skiers = 107\) (Approximated)
Calculate the number of snowboarders
\(Snowboarders = \frac{4}{11} * 168\)
\(Snowboarders = \frac{672}{11}\)
\(Snowboarders = 61\) (Approximated)
Calculate the difference
\(Difference = 107 - 61\)
\(Difference = 46\)
Hence, there are 46 more skiers than snowboarder
Answer:63
Step-by-step explanation:
Find sin F and sin G
pleaseeee help
Answers
The values of sinF and sinG are 0.96 and 0.28 respectively.
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
The functions are;
sinθ = opp/hyp
cosθ = adj/hyp
tanθ = opp/adj
Taking reference from angle F , 96 is the opposite and 28 is the adjascent, therefore;
sinF = 96/100 = 0.96
Taking reference from angle G, 96 is the adjascent and 28 is the opposite
sin G = 28/100
sin G = 0.28
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I need help, I don't just need to answer I need to know the steps on how to solve it asap
Answers
Jestion 8/10
To file your federal and state taxes you
can use tax preparation software for federal taxes,
but can't for state taxes
must prepare the same tax forms for both
can use tax preparation software for state taxes,
but can't for federal taxes
must prepare different forms for each type of
government (if your state requires it) on
Answers
Tax prep software can be used for federal taxes but not always for state taxes, which may require separate forms.
While documenting your government and state charges, you have a couple of choices for how to plan and submit them. One choice is to involve charge planning programming for government charges, which can simplify the cycle and more smoothed out.
In any case, you for the most part can't involve a similar programming for state charges, as each state has its own expense code and necessities.
All things being equal, you might have to set up your state burdens independently, either by finishing up paper structures or utilizing separate duty readiness programming planned explicitly for your state.
A few states bring concurrences with specific expense programming suppliers to the table free or limited programming to occupants, so it merits checking with your state's duty position to see what choices are accessible to you.
It's critical to take note of that while government and state burdens frequently require comparative data, they might require various structures and estimations, so giving close consideration to the particular prerequisites for each kind of tax is significant.
Furthermore, on the off chance that you live in an express that doesn't have a personal expense, you may just have to record a government expense form.
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A student number for a high school requires that
student identification number consist of 6 characters.
The first 4 characters can be any number without
restriction. The last 2 characters are letters and cannot
repeat. How many student ID's are possible?
(Hint: There are 10 digits and they are: 0 1 2 3 4 5
6 7 8 9.)
A: B: C: D: E: F:
————— student ID’s
Answers
Therefore , the solution of the given problem of combination comes out to be 6,500,000.
Define combination.Combinations are mathematical operations that count the variety of configurations that can be made from a set of objects, where the direction of the selection is irrelevant. You can choose any combination of the components in any order. Combinations and permutations can be confused.
Here,
Berry, we'd like to estimate the amount of potential student IDs.
among the available figures are;
Ten numbers: 0 1 2 3 4 5 6 7 8
26 alphabets, as well
There are 10 options for the first digit.
Ten alternatives for the second digits
Three digits, 10 options
10 options for the fourth digit
26 options for the first alphabet
Second Alphabet: There are 25 options available if we choose all the other alphabets outside the one we first chose.
the number of potential student IDs will therefore be;
=>10 * 10 * 10 * 10 * 25 * 26 = 6,500,000
Therefore , the solution of the given problem of combination comes out to be 6,500,000.
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PLEAS HELP ASAP 50 POINTS IF RIGHT: A landscaper is creating a bench for a pool deck. A model of the bench is shown in the image.
A rectangular prism with dimensions of 7 feet by 3 feet by 4.8 feet.
Part A: Find the total surface area of the bench. Show all work. (6 points)
Part B: The landscaper will cover the bench in ceramic tiles except for the bottom that is on the ground. If the tiles cost $0.89 per square foot, how much will it cost to cover the bench? Show all work. (6 points)
Answers
Part A: To find the total surface area of the rectangular prism, we need to calculate the areas of all six faces and then add them together.
Given dimensions:
Length = 7 feet
Width = 3 feet
Height = 4.8 feet
Surface Area of each face:
Front and back faces: Length * Height
= 7 feet * 4.8 feet
= 33.6 square feet
Top and bottom faces: Width * Length
= 3 feet * 7 feet
= 21 square feet
Side faces: Width * Height
= 3 feet * 4.8 feet
= 14.4 square feet
Total Surface Area:
2 * (Front and back faces) + 2 * (Top and bottom faces) + 2 * (Side faces)
= 2 * 33.6 square feet + 2 * 21 square feet + 2 * 14.4 square feet
= 67.2 square feet + 42 square feet + 28.8 square feet
= 137 square feet
Therefore, the total surface area of the bench is 137 square feet.
Part B: To calculate the cost of covering the bench with ceramic tiles, we need to multiply the total surface area by the cost per square foot.
Cost per square foot = $0.89
Total Surface Area = 137 square feet
Total cost to cover the bench:
= Cost per square foot * Total Surface Area
= $0.89 * 137 square feet
= $121.93
Therefore, it will cost $121.93 to cover the bench with ceramic tiles.
correct answers only pls. Unless you will be reported. Also please include explanation.
Answers
Answer:
The answer is B) -3 and 1/3
Explanation:
The answer must be between -3 and -4 because that is the location on the plot.
You count two ticks on the plot. The first one is 1/3. The second one is 2/3.
There is no third one because 3/3 would bring you to the next number.
The dot is on the first tick, meaning that it is 1/3. If the dot is between -3 and -4, you can conclude that the answer is -3 and 1/3.
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Answer:
B -3 1/3 because that is the place on the plot
Kyleigh saw 10 blue, 8 red, and 42 white cars drive by her house in 1 hour. What is the
experimental probability that the next car the drives by her house will not be a white car?
Answers
Answer:
18/60 or 3/10
Step-by-step explanation:
10+8+42=60
10+8=18
=18/60
or
18/6=3
60/6=10
=3/10
suppose that s is a nonempty set of real numbers that is bounded. prove that infs~sups.
Answers
It is given that a set of real numbers s is non-empty and bounded. The objective is to prove that inf s ≤ sup s. This statement can be justified as below.
Firstly, as per the definition of bounded set, it is known that the set s has both lower and upper bounds. Thus, the infimum and supremum of s exist and are denoted as inf s and sup s, respectively.
Since s is non-empty and bounded, it can be observed that every element of the set s is greater than or equal to inf s and less than or equal to sup s.
Therefore, inf s is the greatest lower bound of s and sup s is the least upper bound of s, implying that inf s ≤ sup s. Hence, it is proven that inf s ≤ sup s for a non-empty set s of real numbers that is bounded.
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Which of the following are measures of central tendency of the first psychology exam in a semester?
►The average score on the exam was an 85.
►The median score on the exam was an 80.►The correlation coefficient was +0.85.
►The most frequently occurring exam score was an 82.
►The scores varied from 95 to 65.
►The standard deviation was 5.
Answers
The measures of central tendency of the first psychology exam in a semester are the average score, which was an 85.
The correlation coefficient and the range of scores from 95 to 65 are not measures of central tendency either.
The standard deviation is a measure of variability, not central tendency, that the measures of central tendency of the first psychology exam are the average and median scores. This states that the mode, correlation coefficient, range of scores, and standard deviation are not measures of central tendency.
Hence, the measures of central tendency for the first psychology exam in a semester are the average score (85) and the median score (80).
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The measures of central tendency for the psychology exam scores include the average, median, and mode.
Explanation:The measures of central tendency of the first psychology exam in a semester include the average score, median score, and mode (most frequently occurring score).
The average score on the exam was 85, which represents the mean of all the scores.
The median score on the exam was 80, which represents the middle value when all the scores are arranged in order.
The most frequently occurring score was 82, which represents the mode of the scores.
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Which problem could be solved with the expression 3 (5 – 2) - 1?Choose 1 answer:Stephanie had 3 apples. She then found 5 more but immediately ate 2 of them. Several minuteslater, she ate 1 more. How many apples does she still have?Orlando had 5 action figures but decided to give 2 of them to his younger brother. His parents wereso impressed with his kindness that they tripled the action figures he had left. Since he got so manynew action figures, he then gave 1 more to his brother. How many action figures does he now have?Of Ralph's 5 toy cars, he gave 2 to his sister. After that, he found 1 more toy car. Then, he decidedto go to the store and triple his number of cars. How many toy cars does Ralph have now?Stuck? Review related articles/videos or use a hint.Report a problem
Answers
The given expression is 3 x (5-2)-1
From the options
If Orlando has 5 actions figures.
He decides to give 2 of them to his younger brother, then he will have (5-2) action figures left
His parents were happy with him and tripled what he had left
3 x ( 5 -2 ) action figures.
If he had so many actions figures after that and he gave his brother 1 more action figure then he will have
3 x ( 5-2) - 1 action figures left.
The right answer is therefore option B
2x^2 + 8x factor out the gcf
Answers
Answer:
2x(x + 4)
Step-by-step explanation:
The greatest common factor of 2x^2 and 8x is 2x. So, we can factor out 2x to get:
2x(x + 4)
The definition of a greatest common factor (GCF) is the largest number that is a factor of two or more numbers. In this case, 2x is the GCF of 2x^2 and 8x because it is the largest number that divides both numbers evenly.
Here are the steps on how to factor out the GCF:
Find the GCF of the two numbers. In this case, the GCF is 2x. Write the GCF as a factor of each number. Combine the factors to get the factored expression.In this case, the factored expression is 2x(x + 4).
The answer is:
⇨ 2x(x + 4)Work/explanation:
Let's find something that \(\sf{2x^2}\) and \(\sf{8x}\) have in common.
In other words, we find their GCF (greatest common factor).
The GCF of \(\sf{2x^2}\) and \(\sf{8x}\) is 2x.
So I factor it out :
\(\sf{2x(x+4)}\)
Hence, the answer is 2x(x + 4).Model With Mathematics A photographer is
placing photos in a mat for a gallery show.
Each mat she uses is x in, wide on each side.
The total area of each photo and mat is
shown
Answers
Answer:
a. The possible dimensions of the total area are;
The width of the total area is (2·x + 8) inches
The length of the total area is (2·x + 10) inches
b. The dimensions of the photos are as follows;
The length of the photos are 10 inches
The width of the photos are 8 inches
Step-by-step explanation:
a. Given that the area, A = 4·x² + 36·x + 80
We get;
A = 4 × (x² + 9·x + 20) = 4 × (x + 4) × (x + 5) = (2·x + 8)·(2·x + 10)
Therefore, the possible dimensions of the total area (photo + mat) are;
The width of the total area (photo + mat) = (2·x + 8) in.
The length of the total area (photo + mat) = (2·x + 10) in.
b. The dimensions of the photos alone are shorter than the dimensions of the photo and mat combined by 2·x each
Therefore, we have the dimensions of the photos are as follows;
The length of the photo = (2·x + 10) in. - 2·x in. = 10 in.
The width of the photos = (2·x + 8) in. - 2·x in. = 8 in.
can help me any one . If ₹640 is divided between Bishu and Arpana in the ratio of 5 : 3 , lets find how many each would get.
Answers
Answer:
a/q ratio 5:3 total money is divided in 8 parts so 1 part =rs 80 so b&a got 80×5=400 & 80×3 =240 resp
Answer:
first find the total = 5+3=8
now 5/8×640 =5×80 = 400 rupees
3/8×640 =3×80 = 240 rupees
so Bishu gets 400 rupees and Arpana gets 240 rupees.
hope you understood!!
Study and Learn
pasagutan plss..
Answers
35 x 35 is also 35^2 and that equals 1,225
9 x 9 x 9 is also 9^3 and that equals 729
4 x 4 x 4 x 4 is also 4^4 and that equals 256
2 x 2 x 2 x 2 x 2 is also 2^5 and that equals 32
Algebra 2
The first one please
Answers
The co-terminal angle to 5π/6 in the unit circle is C. 17π/6
What are co-terminal angles in a unit circle?Co-terminal angles in a unit circle are angles that share the same terminal point
Given the angle 5π/6, we desire to find the angle that shares the same terminal point in the unit circle. We proceed as follows.
We know that x = 5π/6 + 2π
Taking the L.C.M which is 6, we have that
x = (12π + 5π)/6
x = 17π/6
So, the angle is C. 17π/6
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What is this trying to ask me ???
Answers
In ∆ABC,
∠A = 60°∠B = 60°BC = 12 units∠BDC = 90°To Find :Area of ∆ABC = ?Solution :As, we have :
∠A = 60°∠B = 60°So, By angle sum property of triangle :
∠A + ∠B + ∠C = 180°
\( \tt : \implies 60\degree + 60\degree + \angle C = 180\degree\)
\( \tt : \implies 120\degree + \angle C = 180\degree\)
\( \tt : \implies \angle C = 180\degree - 120\degree\)
\( \tt : \implies \angle C = 60\degree\)
Now, we have :
∠A = 60°∠B = 60°∠C = 60°As, all angles are of same length, therefore it is a equilateral triangle.
We know that sides of equilateral triangle are equal.
\( \tt : \implies AB = BC = AC\)
Now, we have BC = 12 units.
Hence, all sides are of 12 units.
Now, we know that area of equilateral triangle is :
\( \large \underline{\boxed{\bf{Area_{(equilateral \: triangle)} = \dfrac{\sqrt{3}}{4} side^{2}}}}\)
\( \tt : \implies Area = \dfrac{\sqrt{3}}{4} \times (12 \: units)^{2}\)
\( \tt : \implies Area = \dfrac{\sqrt{3}}{\cancel{4}} \times \cancel{144} \: units^{2}\)
\( \tt : \implies Area = \sqrt{3} \times 36 \: units^{2}\)
\( \tt : \implies Area = 36\sqrt{3} units^{2}\)
So, Area of given triangle is 36√3 units².
marcus, a college senior, is considering repayment plans for his student loans. compared with income based repayment plans, the standard repayment plan will generally:
Answers
Compared with income-based repayment plans, the standard repayment plan will generally Minimize the amount of interest paid.
Income-driven repayment plans give installment options for numerous government student credit borrowers that bring down their monthly installment amount. if you enlist in an Income-Driven Repayment arrangement, your month-to-month payment is based on your salary and family size and not totally on how much you owe. The month-to-month installment on income-driven repayment plans will be lower than the standard repayment plan. The installment may indeed be zero for borrowers with low or no income. The lower loan installments may make income-driven repayment plans a great choice for borrowers who are battling to reimburse their student loans. However, indeed in spite of the fact that the remaining debt is excused after 20 or 25 a long time of repayment, the credit forgiveness may be taxable.
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Check the attachment
Answers
Answer:
\(a\:\dfrac{\sqrt{a^3}}{a^4} =\dfrac{\sqrt{a}}{a^2}\)
Step-by-step explanation:
I believe this question is wrongly or part of it has been truncated in the screenshot
I have simplified the original expression and checked my answer.
\(\mathrm Simplify \;\;a\dfrac{\sqrt{a^3}}{a^4}\\\\\sqrt{a^3} = a^{\dfrac{3}{2}} = a^{(1 + \frac{1}{2})} = a \cdot a^\frac{1}{2} = a \sqrt{a} \\\\a\dfrac{\sqrt{a^3}}{a^4}\\\\ = \dfrac{a\cdot a\cdot \sqrt{a}}{a^4}\\\\= \dfrac{a^2\sqrt{a}}{a^4}\\\\= \dfrac{\sqrt{a}}{a^{(4-2)}}\\\\\\=\dfrac{\sqrt{a}}{a^2}\)