Answers
Part A
The equation is g = -2.5m + 20
The +20 represents us starting with 20 gallons. The -2.5m portion indicates losing 2.5 gallons per minute. So after m minutes, we'll have -2.5m+20 gallons left.
The smallest m can be is m = 0
Let's plug in g = 0 and solve for m to find the largest possible m value
g = -2.5m + 20
-2.5m + 20 = g
-2.5m + 20 = 0
-2.5m = -20
m = (-20)/(-2.5)
m = 8
At the 8 minute mark is when g = 0. So this is when the tub is completely empty. We cannot go beyond this point because g would become negative. So m = 8 is the largest m can get.
This means m is between 0 and 8, including both endpoints.
The domain is [tex]0 \le m \le 8[/tex]
The domain is continuous because the number of minutes is continuous. We cannot have a jump in time from something like m = 1 to m = 2 without values in between. In other words, to go from m = 1 to m = 2, we need to pass by something like m = 1.5
No matter what two values you pick in the interval mentioned, there is always going to be some midpoint and infinitely many other values to deal with.
-------------------------
Answers:
Domain: [tex]0 \le m \le 8[/tex]The domain is continuous======================================================
Part C
See the graph below. The table is included as well.
To generate the table, we select values of m from the domain found earlier. I'm using whole numbers for m, but you can use any real number you want from that interval.
Let's say we picked m = 2
That would mean,
g = -2.5m + 20
g = -2.5*2 + 20
g = -5 + 20
g = 15
So at the 2 minute mark, the tub will have 15 gallons left. That means we'll have a row with m = 2 and g = 15 pair up together. The rest of the table is generated in a similar fashion.
Once the table is set up, you plot all of the points and draw a line through them to complete the graph.
Because we're dealing with a linear function, we only need 2 points at minimum to graph it. However, you can generate as many points as you want. It could be good practice.
Side note: Stuff to the left of m = 0 and stuff to the right of m = 8 is not graphed, as these portions are not in the domain.
Related Questions
need help with this algebra ii question
Answers
Answer:
-23
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Functions
Function NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = x² + c
f(4) = -7
Step 2: Solve for c
Substitute in variables [Function f(x)]: -7 = 4² + cEvaluate exponents: -7 = 16 + c[Subtraction Property of Equality] Subtract 16 on both sides: -23 = csimplify:
[tex]x ^{4} - {x}^{2} {y}^{2} + {y}^{4} [/tex]
x4-x2y2+y4
Answers
Answer:
[tex] {x}^{4} - {x}^{2} {y}^{2} + {y}^{4} \\ {x}^{4} + {y}^{4} - {(xy)}^{2} [/tex]
Please , I need help ASAP !!
Answers
Answer:
c
Step-by-step explanation:
cccccccc cccccccccdkdksksk
How do i solve this?????
Answers
Answer:
Step-by-step explanation:
A water tank is a cube of side 2m the depth of the water in it is 60cm. What is the volume of the water in the tank?
Answers
Answer:
8 METERS CUBES I THINK
Step-by-step explanation:
VOLUME IS LENGTH TIMES WIDTH TIMES HEIGHT
2 METERS TIMES 2 METERS TIMES 2 METERS IS 8 METERS
The pH scale measures how acidic or basic a substance is. Bleach is said to have a
55 POINTS!!! WILL MARK!!! ANSWER FAST!!!pH of less than 14 and greater than 11. Model the normal range of pH values of bleach, using a compound inequality.
11 > x > 14
11 < x < 14
11 ≤ x ≤ 14
11 ≥ x ≥ 14
Answers
Answer:
11 < x < 14
Step-by-step explanation:
Bleach ph value ranges from 11-13
Need done ASAP
Mr. Brauch tells Granny that there's no way that ABC =
ADEF. Granny tells
him That they are not only congruent, but she can prove it by SSS. Who is right?
Answers
Answer:
Granny is correct
Step-by-step explanation:
Hope it helps
solve pls brainliesttt
Answers
Answer:
-343
-125
Here you go
Answer:
1. -343
2. 25
3. v+21=47 v= 26
Step-by-step explanation: Hope this helps!
rectangular equation for the curve whose parametric equations are x = 2cosθ, y = cos2θ.
Answers
The rectangular equation for the curve is [tex]y = \frac{x^{2}}{2} -1[/tex].
In this question, we have a set of parametric equation which must be reduced into a single rectangular equation both by algebraic and trigonometric means, that is to say:
[tex]x = f(\theta), y = g(\theta) \to y = h(x)[/tex]
If we know that [tex]x = 2\cdot \cos \theta[/tex] and [tex]y = \cos 2\theta[/tex], then the rectangular equation is:
[tex]y = \cos 2\theta[/tex]
[tex]y = \cos^{2}\theta - \sin^{2}\theta[/tex]
[tex]y = 2\cdot \cos^{2}\theta -1[/tex]
[tex]\cos \theta = \frac{x}{2}[/tex]
[tex]y = 2\cdot \left(\frac{x}{2} \right)^{2}-1[/tex]
[tex]y = \frac{x^{2}}{2} -1[/tex]
The rectangular equation for the curve is [tex]y = \frac{x^{2}}{2} -1[/tex].
We kindly invite to check this question on parametric equations: https://brainly.com/question/23070611
Distance from earth to the moon is 238,900 . From earth to the sun is 92935,700 ,about how many times the distance from earth to the moon is distance from earth to the sun
Answers
Answer: the sun is 389.015069067 times further away from earth to the moon
Step-by-step explanation: 92935700/238990=389.015069067
Assume that y varies inversely as x. If
Y
y = 10 when
=
x = 4, what is the value for y when
x = 6?
Answers
Answer:
x=5
Explanation:
y∝1x∴y=k⋅1x∴x⋅y=k;
When x=4;y=10∴4⋅10=kork=40.
So variation equation is x⋅y=40
When y=8;x=408=5∴x=5 [Ans]
Step-by-step explanation:
not surre
Answer:
6.67
Step-by-step explanation:
10=4
y=6
10×4/6
Help! Pls...........
Answers
Answer:
I don't know sorry sorryy
VI. PRACTICE TASKS
OSOBE
Practice Task 1
Directions: Place the decimal point to make each product correct.
1. 6.75
X 0.18
1215
2. 11.28
X 0.36
40608
3.10.15
X 0.15
15225
4.
1.15
X 0.25
02875
5.
3.22
X 1.12
39284
Pleassse answer this pleassssee
Answers
Step-by-step explanation:
1 _ 1.215
2_ 4.0608
3_1.5225
4_0.2875
5_3.6064
8+2x-4=6+2(x+1) please help
Answers
Answer:
Step-by-step explanation:
7.C.J. says the quotient of -3/4 divided by 1/4 is - 1/3
a What is the correct quotient?
bWhat mistake did CJ likely make?
a. He multiplied the reciprocals of both fractions.
b. He added -3/4 and 1/4
c. He multiplied-3/4 by 1/4
d. He multiplied using the reciprocal of -3/4.
Answers
The correct quotient is -3
The mistake CJ likely made is multiplying using the reciprocal of -3/4. The correct option is d. He multiplied using the reciprocal of -3/4
From the question,
We are to determine the correct quotient.
The given division operation to be carried out is -3/4 divided by 1/4
The correct quotient can be determined as shown below
[tex]-\frac{3}{4} \div \frac{1}{4}[/tex]
Multiply [tex]-\frac{3}{4}[/tex] by the reciprocal of [tex]\frac{1}{4}[/tex]
The reciprocal of [tex]\frac{1}{4}[/tex] is [tex]\frac{4}{1}[/tex]
Then, we get
[tex]-\frac{3}{4} \times \frac{4}{1}[/tex]
This gives
[tex]-\frac{12}{4}[/tex]
= -3
The correct quotient is -3
The mistake CJ likely made is multiplying using the reciprocal of -3/4.
Hence, the correct quotient is -3
The mistake CJ likely made is He multiplied using the reciprocal of -3/4. The correct option is d. He multiplied using the reciprocal of -3/4
Learn more here: https://brainly.com/question/13124034
7. In a quiz bee, Marlon scored 132 points during the first round. This score was thrice as much as his score during the second round. What score did he get in two rounds?
Answers
Answer:
II + III = 176
II = 44
III = 132
Step-by-step explanation:
Third round: 132
Second round: 3x=132
x=44 (second round)
2rounds: 132+44=176
solve the inequality. graph your solution
6(y+1)>6
Answers
Step-by-step explanation:
[tex]6(y + 1) > 6 \\ 6y + 6 > 6 \\ 6y > 0 \\ y > 0[/tex]
PLEASE HELP!!!!! A satellite telescope has a parabolic dish. Satellite signals are collected at the focal point (focus) of the
parabola. The distance from the vertex of the parabolic dish to the focus is 40 feet. The vertex of the dish is
located at a point 50 feet above the ground and 100 feet to the east of a computer that reads and records
data from the telescope. The diameter of the dish is 160 feet.
Answers
The dish illustrates operations on a parabola.
The depth of the parabolish dish is 160 feet.
The bowl is said to be a parabola.
So, we have:
[tex]\mathbf{(x -h)^2 = 4p(y - k)}[/tex]
Where:
[tex]\mathbf{Focus: p = 40}[/tex]
[tex]\mathbf{Vertex:(h,k) = (0,0)}[/tex]
From the question, the diameter is 160 feet.
So, the radius (r) is:
[tex]\mathbf{r = \frac{160}{2} = 80}[/tex]
So, the coordinate of the depth of the parabola would be:
[tex]\mathbf{(x,y) = (60 + 100,y)}[/tex]
[tex]\mathbf{(x,y) = (160,y)}[/tex]
Substitute these values in [tex]\mathbf{(x -h)^2 = 4p(y - k)}[/tex]
So, we have:
[tex]\mathbf{(160 - 0)^2 = 4 \times 40 \times (y -0)}[/tex]
[tex]\mathbf{160^2 = 160y}[/tex]
Divide both sides by 160
[tex]\mathbf{160 = y}[/tex]
Rewrite as:
[tex]\mathbf{y = 160 }[/tex]
Hence, the depth of the parabolish dish is 160 feet.
Read more about parabolas at:
https://brainly.com/question/4074088
Find the measure of the angle with the red dot (NOT X.)
Picture Included. Thank you!
Answers
Step-by-step explanation:
I can't see picture very well but as I see first angle is
-4x+5 and second is -13x+39 ( if it isn't, correct me)
sum of this angles is 180° because they are inner angles
(-4x+5) + (-13x+39) = 180
-4x+5 -13x+39=180
-17x+44=180
-17x = 180-44
-17x= 136
x= -8
angle -4x+5 will be:
-4*-8 + 5= 32+5= 37°
If f(x) = –2x3, g(x) = 3x – 5, and h(x) = x – 1, what is f(g(h(3)))?
–129
–54
–53
–2
Answers
Answer:
[tex]f(x) = - 2 {x}^{3} \\ g(x) = 3x - 5 \\ h(x) = x - 1 \\ g(h(x)) = 3(x - 1) - 5 \\ = 3x - 3 - 5 = 3x - 8 \\ f(g(h(x)) )= - 2 {(3x - 8)}^{3} \\ f(g(h(3)) )=- 2 {(3(3) - 8)}^{3} \\ = - 2 {(9 - 8)}^{3} \\ f(g(h(3)) )=- 2[/tex]
. The temperature fell 13°c on each of the first 2 days of the week. It rose 7°c on each of
the next 3 days and fell 9°c on each of the last 2 days. If the temperature was originally
34% what was the final temperature?
Answers
Answer:
The final temperature was 9 degrees.
Step-by-step explanation:
You can first multiply 13x2, 7x2, and 9x2. Then you subtract 26 and 18 from 34. then add 14
A relation R exists such that for every input (x ), the output is −x . Which statement about the relation R is correct?
Answers
Answer:
R is a function.
Step-by-step explanation:
P(x) = 4x3 + 5x + 9, D(x) = 2x + 1
Two polynomials P and D are given. Use either synthetic or long division to divide
P(x)
by
D(x),
and express P in the form
P(x) = D(x) · Q(x) + R(x)
Answers
please help me for my practice problems
Answers
m = slope(rise/run), b = y-intercept
1/2
y = 1/2x - 3
-7/4
y = -7/4x +4
-1/2
y = -1/2x - 3
-1/4
y = -1/4x + 2
1
y = x
-1
y = -x
:) Answer fast if you can
Answers
Answer:
The answer is B
Step-by-step explanation:
Hope it helps
Solve for the unknown angles
Marking you the brainliest provided you got it
right and with step by step explanation
Answers
Step-by-step explanation:
The angles a and b are congruent, also c and x are congruent.
a = b = 180° - 85° = 95° (supplementary, linear pair)c = x = 85° (corresponding, alternate interior)Find an equation for the graph below
Answers
Answer:
y=4/5x-0.8
Step-by-step explanation:
-3x-5y=-7
Find slope of perpendicular line
Answers
Answer:
5/3
Step-by-step explanation:
We need to rewrite the equation in slope intercept form
y =mx +b where m is the slope
-3x-5y = 7
Add 3x to each side
-5y = 3x+7
Divide by -5
y = -3/5 x -7/5
The slope of this line is -3/5
Perpendicular lines have slopes that are negative reciprocals
-1 / (-3/5)
5/3
The slope of the perpendicular line is 5/3
What’s the answer to this H(-3)=3/4(8x+2)-4.5
Answers
Please mark brainelist
If Marie were to paint her living room alone, it would take 7 hours. Her sister Barbara could do the job in 8 hours. How many hours would it take them working together? Express your answer as a fraction reduced to lowest terms, if needed.
Answers
Answer:
[tex]\sf\longmapsto \: 3.73 hours [/tex]
Step-by-step explanation:
[tex]\sf\longmapsto \: \frac{1}{7 } + \frac{1}{8} [/tex]
[tex]\sf\longmapsto \: \frac{15}{56} [/tex]
Now, Reciprocal–
[tex]\sf\longmapsto \: \frac{56}{15} [/tex]
[tex]\sf\longmapsto \: 3.73 hours [/tex]
The time taken together Marie and his sister to paint the living room are 3.73 hours or 3 hours and 43.8 minutes.
What are work and time?Work is the completion of any task for example if you have done your homework in 5 hours then you have done 5 hours.
Another illustration of labor is when you finish your meal in an hour, which means that you finished your work in an hour.
Given that,
Marie take 7 hours to paint
1 work → 7 hour
1 hour → (1/7) work
Barbara takes 8 hour
1 work → 8 hour
1 hour → (1/8) work
Let's suppose together they take x hour
1 work → x hour
1 hour → (1/x) work
Now,
1-hour work together = 1-hour work of Marie + 1-hour work of Barbara
(1/x) = (1/7) + (1/8)
(1/x) = (7 + 8)/56
x = 56/15
x = 3.73
x = 3 hour and 0.73 × 60 = 43.8 minutes.
Hence "The time taken together Marie and his sister to paint the living room is 3.73 hours or 3 hours and 43.8 minutes".
For more information about the work and time relation,
brainly.com/question/6912604
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