In the table below, y is a linear function of x.
х
y
5
3
5
13
7
-11
What is the value of y when x = 0?
Answers
Answer:
y= -7
Step-by-step explanation:
y=ax+b
Find a where a=y2-y1 /x2-x1
y2=13,y1=5 x2=5,x1=3
substituting the values
a=13-5/5-2
a=8/2
a=4
substituting a into the formular
y=4x+b
taking x and y values let say 3 and 5 for x and y
the equation becomes
5=4(3)+b
5=12+b
5-12=b
-7=b
substituting the values of a and b into the equation
y=4x-7
when x=0
y=4(0)-7
y=0-7
y=-7
so when x=0,y=-7
Related Questions
1 8. 1 (minutes) 0 5 6 g(t) (cubic feet per minute) 12.8 15.1 20.5 18.3 22.7 Grain is being added to a silo. At time t = 0, the silo is empty. The rate at which grain is being added is modeled by the differentiable function g, where g(t) is measured in cubic feet per minute for 0 st 58 minutes. Selected values of g(t) are given in the table above. a. Using the data in the table, approximate g'(3). Using correct units, interpret the meaning of g'(3) in the context of this problem. b. Write an integral expression that represents the total amount of grain added to the silo from time t=0 to time t = 8. Use a right Riemann sum with the four subintervals indicated by the data in the table to approximate the integral. πί c. The grain in the silo is spoiling at a rate modeled by w(t)=32 sin where wſt) is measured in 74 cubic feet per minute for 0 st 58 minutes. Using the result from part (b), approximate the amount of unspoiled grain remaining in the silo at time t = 8. d. Based on the model in part (c), is the amount of unspoiled grain in the silo increasing or decreasing at time t = 6? Show the work that leads to your answer. =
Answers
Hi there!
a)
We can approximate g'(3) by finding the slope of g(t) over an interval containing t = 3.
We can use the endpoints t = 1 and t = 5 min for the best estimate.
[tex]slope = \frac{y_2 - y_1}{x_2 - x_1} = \frac{20.5-15.1}{5-1} = \boxed{1.35 \frac{ft^3}{min^2}}[/tex]
This means that the rate of grain being added to the silo is INCREASING at a rate of 1.35 ft³/min². (Or in other words, the grain is being poured at an increasingly greater rate)
b)
The total amount of grain added is the integral of g(t), so:
[tex]\text{total amount of grain} = \int\limits^8_0 {g(t)} \, dt[/tex]
We can do a right riemann sum by using the right endpoints (t = 1, t = 5, t = 6, t = 8) to calculate.
Riemann sums are essentially rectangles added up to calculate an approximate value for the area under a curve.
The bases are the spaces between each value in the chart, while the heights are the values of g(t).
Using the intervals and values in the chart:
[tex]1(15.1) + 4(20.5) + 1(18.3) + 2(22.7) = \boxed{160.8 ft^3}[/tex]
c)
We can subtract the two integrals to find the total amount of unspoiled grain.
With g(t) being fresh grain and w(t) being spoiled grain, let y(t) represent unspoiled grain.
[tex]y(t) = \int\limits^8_0 {g(t)} \, dt - \int\limits^8_0 {w(t)} \, dt[/tex]
Use a calculator to evaluate:
[tex]y(t) = 160.8 - \int\limits^8_0 {w(t)} \, dt = 160.8 - 99.05 = \boxed{61.749 ft^3}[/tex]
d)
We can do the first derivative test to determine whether the amount of grain is increasing or decreasing. (Whether the first derivative is positive or negative at this value).
For the above integral, we know that the derivative is:
[tex]y'(t) = g(t) - w(t)[/tex]
Plug in the values for t = 6:
[tex]w(6) = 32 \cdot \sqrt{sin(\frac{\pi (6)}{74})} = 16.06[/tex]
[tex]y'(6) = g(6) - w(6) = 18.3 - 16.06 = 2.23 \frac{ft^3}{min}[/tex]
This value is POSITIVE, so the amount of unspoiled grain is INCREASING.
Pythagoras lost 13 pounds from January to June. If Pythagoras gains 1.2 times Euclid’s weight, Pythagoras’s weight would still be pound less than he did in January. What is Euclid’s weight?
(a) Write an equation that represents the scenario. Begin by defining your variable.
(b) Solve the equation. Show your work.
(c) What is Euclid’s weight?
(d) Jake adopts a third dog, Riemann. Riemann weighs exactly twice what Euclid weighs. The combined weight of the three dogs is pounds. What is Riemann’s weight, and what is Pythagoras’s weight? Show your work.
Answers
Answer:The weight of Euclid is 10.625 pounds, and the weight of Riemann is 21.25 pounds.
Let the current weight of Euclid = x
Let the current weight of Pythagoras = T
Let the January weight of Pythagoras = y
The expression that represents the given scenario is written as;
when Pythagoras lost 13 pounds: T = y - 13
when Pythagoras gains 1.2 times Euclid's weight: = T + 1.2x
when Pythagoras weight is 1/4 pound less than weight in January:
T + 1.2x + 0.25 = y
y- 13 + 1.2x + 0.25 = y
1.2x - 12.75 = 0
Euclid's weight is calculated as follows;
1.2x = 12.75
The weight of Riemann is calculated as follows;
The average length of a female dolphin is about 181 inches (in).
What is this length in feet (ft) and inches (in)?
The length is ft in.
Answers
Answer:
15 ft 1 in
Step-by-step explanation:
To convert inches into feet, we divide by 12.
12 goes into 181 fifteen times, so the # of feet is 15 feet.12 x 15 = 180.181 - 180 = 1, so the # of remaining inches is 1 inchTherefore, the answer is 15 ft 1 in.
If 500’ roll of wire costs 18.44 what I’d the first of wire per foot
Answers
Answer:
27.1149675 feet (27 feet 1⅜ inch)
Step-by-step explanation:
i think
Select the correct answer.
Which pair of expressions are equivalent?
Answers
Answer:
D
Step-by-step explanation:
None of the others make sense. In answer D x+y is the same as x-y+2y because you add the y's and its the same thing as x+y.
Hope It Helped :)
To find the height of a pole, a surveyor moves 150 feet away from the base of the pole and then, with a transit 4 feet tall, measures the angle of elevation to the top of the pole to be 42°. To the nearest foot, what is the height of the pole?
Answers
Answer: The answer is 139 feet
H = height of the pole =?
BC = ED = height of the transit = 4 ft
CD = BE = distance moved away from the base of the pole = 140 ft
Consider the ΔABE
tan44 = AE/BE
tan44 = h/140
h = 140 tan44
h = 135.2 ft
H = height of pole = AE + ED = h + ED = 135.2 + 4
H = 139.2 ft
Step-by-step explanation:
HELPPP PLSSSSSSSSS
There are 15 players on the basketball team. The cost of traveling to a tournament
is $650 plus $75 per player. If the team has a $1500 budget for this tournament,
how many of the 15 players can go? Write an inequality and solve the problem.
Answers
1500-650=950
950/75=12
12 players can attend
A music-streaming service charges $9 per month for a single user. Additional users within the same household can be added for $3 per month. Write an equation that shows how the monthly cost, y, depends on the number of additional users in the household, X. Do not include dollar signs in the equation. y=
Answers
The equation that shows the monthly cost is y = 9 + 3x
What is the equation that represents the monthly cost?
The monthly cost is a function of the charge for a single user and the cost of additional users. The monthly cost increases with the number of additional users.
The charge for a single user can be considered a fixed cost since it remains constant while the cost of the additional user can be considered a variable cost since it increases with the number of users.
Y = 9 + 3x
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Answer: Y = 3x + 9
Step-by-step explanation:
NO LINKS!!! Please help me with this problem. Part 5
Answers
The width of the Mississippi River at the St. Louis riverfront is approximately 1649.984 feet.
How to determine the width of the Mississippi River
After apply Pythagorean theorem and angle properties for triangles, we have the following geometric diagram, attached below. By the law of the sine we can obtain the width of the Mississippi river ([tex]CD[/tex]), in feet:
[tex]\frac{2163.747\,ft}{\sin 123.690^{\circ}} = \frac{CD}{\sin 39.382^{\circ}}[/tex] (1)
[tex]CD \approx 1649.984\,ft[/tex]
The width of the Mississippi River at the St. Louis riverfront is approximately 1649.984 feet. [tex]\blacksquare[/tex]
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A slot machine has 3 dials. Each dial has 40 positions, two of which are "Jackpot." To win the jackpot, all three dials must be in the "Jackpot" position. Assuming each play spins the dials and stops each independently and randomly, what are the odds of one play winning the jackpot?
Answers
Answer: there is a 1.2% of winning
Step-by-step explanation: there is a 1.2% chance of winning.
Step-by-step explanation:
The odds of one player that wins the jackpot should be 0.00156%.
Given that,
There are 3 dials.
In each dial, there are 40 positions.
So, the probability of receiving the jackpot should be \frac{1}{40}
40
1
Now the odds of one player that wins the jackpot should be
\begin{gathered}= \frac{1}{40} \times \frac{1}{40} \times \frac{1}{40} \\\\\end{gathered}
=
40
1
×
40
1
×
40
1
= 0.00156%
Therefore we can conclude that the odds of one player that wins the jackpot should be 0.00156%.
Ruth drove 60 miles in one hour. At this rate, how many miles will she drive in 5 hours?
Answers
Answer:
Knowing that it's 60 miles per hour, that would mean we multiply 60 x 5
Meaning, it would be 300 miles in five hours
Step-by-step explanation:
Answer: 300 miles
Step-by-step explanation: 60 * 5 = 300
If tan (θ )=0.532 , and α is the complement of θ , then tan (α) =
Answers
Answer:
tan(α) = 89.468
Step-by-step explanation:
90 - 0.532
Help show work pls :) ill mark brainliest
Answers
Answer:
52.2
....
....
...
..
.....
....
Mr. Miller owns two hotels and is ordering towels for the rooms. He ordered 27 hand towels and 48 bath towels for a bill of $540 for the first hotel. He ordered 50 hand towels and 24 bath towels for a bill of $416 for the other hotel.
What is the cost of one hand towel and one bath towel?
A.
The cost of one hand towel is $9 and the cost of one bath towel is $4.
B.
The cost of one hand towel is $8 and the cost of one bath towel is $5.
C.
The cost of one hand towel is $5 and the cost of one bath towel is $8.
D.
The cost of one hand towel is $4 and the cost of one bath towel is $9.
Answers
This question is based on the concept of solving a two linear equation.
Thus, the cost of one bath towel is $9 and one hand towel is $4.
Given:
Number of ordered of hand towels is 27 and bath towels is 48 and for a bill of $540 for the first hotel.
Number of ordered of hand towels is 50 and bath towels is 24 and for a bill of $416 for the other hotel.
We need tom determined the cost of one hand towel and one bath towel.
According to the question:
Let the hand towels be h and bath towels be b.
Therefore, equation of first hotel is
27h + 48b = 540........(1)
Equation of second hotel is
50h + 24b = 416.........(2)
Now, solving both equation for h and b.
Equation (2) multiplying by -2.
-100 h -48 b = - 832..................(3)
Now, solve equation (1) and (3)
27h + 48b = 540 and -100h - 48b = - 832
⇒ -73 h = - 292
⇒ h = -292 / -73
⇒ h = 4
Therefore, the cost of 1 hand towel is $4.
Now, putting the value of h = 4 in equation (1).
⇒ 27(4) + 48b = 540
⇒ 108 + 48b = 540
⇒ 48b = 540 - 108
⇒ 48b = 432
⇒ b = 432/48
⇒ b = 9
Therefore, the cost of 1 bath towel is $9.
Thus, the cost of one bath towel is $9 and one hand towel is $4.
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Amy spent 3/10 of her 365. 25 paycheck on new winter clothing how much money does Amy have left
Answers
.3 * 365.25 = 109.575
365 - 109.575 = 255.425 = $255.43
Directions Type your answer in the space provided.
Hunter wants to make money over the summer by selling lemonade. He has $50 in savings. He spends 520 on a pitcher and reusable cups. Doing the math, he realizes that sugar, lemons, and water will cost $. 75 per serving. What is the greatest number of cups that can be made before Hunter runs out of his budget?
Answers
Hunter can make a maximum of 59 cups before he runs out of money.
What is an inequality?An inequality is an expression that shows the non equal comparison of two or more variables and numbers.
Let x represent the number of cups that hunter can buy, He already spent 520 cents ($5.2) hence:
0.75x ≤ 50 - 5.2
x ≤ 59.7
Hunter can make a maximum of 59 cups before he runs out of money.
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Which values are solutions of the inequality 7 > 2 - 4?
Choose ALL that apply.
6
7
10
11
20
Answers
Answer: This question does not make sense since 2 minus 4 is -2 and 7 > -2, which means this inequality is true by itself. There are no "solutions" to this inequality since there are no variables. Maybe you made a typo?
Edit: I found the actual question on the internet (it's 7 > z - 4) and the answers are 6, 7, and 10.
This is because simplifying this inequality gives us 11 > z, and 6, 7, and 10 are the only values that are below 11.
Answer:
7 > z - 4
7 6 10
Step-by-step explanation:
you have a typo,
what is 2 6/7 as an improper fraction
Answers
Answer:
20/7
Step-by-step explanation:
Check the picture
Calculus problem: A drug manufacturer has developed a time-release capsule with the number of milligrams of the drug in the bloodstream given by
S = 40[tex]x^{\frac{19}{7} }[/tex] − 560[tex]x^{\frac{12}{7} }[/tex] + 1960[tex]x^{\frac{5}{7} }[/tex]
where x is in hours and 0 ≤ x ≤ 7. Find the average number of milligrams of the drug in the bloodstream for the first 7 hours after a capsule is taken. (Round your answer to the nearest whole number.)
Solution: _____ mg
Answers
Step-by-step explanation:
You can find your answer by taking integral from 0 to 7 and then dividing it by 7.
PLS HELP I WILL MARK BRAINLIEST!!!
In a game, for every 3 enemies defeated, you earn 5 points. If you defeated 27 enemies, how many points would you have earned?
Answers
27 x 5 = 135
9. Which of these decimals is the LEAST in value?
0.511 0.453 0.552 0.044
O 0.453
0.511
0.552
0.044
Answers
Answer:
0.044 os the answer. brainiest pls?
Answer:
The last one 0.044
Step-by-step explanation:
3what is the value of 1/4 of 6times
Answers
Answer:
[tex]1 \frac{1}2}[/tex]
Step-by-step explanation:
The question is asking [tex]\frac{1}{2}[/tex] times 2. You multiply 6 with the numerator to get [tex]\frac{6(1)}{4}[/tex] Simplify it and get 6/4, or one and one-half
For the function f(x)=x^2−12x+32, find x when f(x)=−4.
Answers
Answer:
X=6
Step-by-step explanation:
Explanation in the picture
1. Substitute f(x) = -4 into f(x)= x^2 - 12x + 32
Step-by-step explanation:
f(x)=x^2-12x+32
divide both sides by 4
answer -1/4x^2+3x-8
sorry if im wrong lol
Find 6 3/5 divided by 3 1/5 Write in simplest form
Answers
Answer:
[tex]\frac{33}{16}[/tex]
Step-by-step explanation:
33/16 is the answer
Use the long division method to find the result when 6x3 + 19x2 + 10x + 1 is
divided by 2x + 1.
Answers
Answer:
Hope this answer helps you !
What is the measure of angle x?
Answers
Answer:
83
Step-by-step explanation:
all triangles =180° total
180-53-44=83°
What is the value of x?
A. 15
B. 21.2
C. 10.6
D. 7.5
Answers
Answer:
c.10.6
Step-by-step explanation:
we take sin the angle on the length of the side that opposite to it ...
The value of x from the triangle is x = 10.6
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as ABC
Now , the measure of hypotenuse of the triangle = 15
Let the angle be θ = 45°
From the trigonometric relations ,
sin θ = opposite / hypotenuse
On simplifying the equation , we get
sin 45° = x / 15
where sin 45° = 0.7071
So , the value of x = 0.7071 x 15
The value of x = 10.6
Hence , the value of x from the triangle is x = 10.6
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why does 0.5g equal 500 mg
Answers
Answer:
in kg 1.1 equals to 1gram and 100mg
so in 0.5 equals to 500 mg
hope it helps (θ‿θ)
Help me!
What is 25% of 948?
Answers
Answer:
237
Step-by-step explanation:
25 percent *948
= (25/100)*948
= (25*948)/100
= 23700/100 = 237
It takes 56 pounds of seed to completely plant an 8-acre field. How many acres can be planted per pound of seed?
Answers
Answer:
7
Step-by-step explanation:
8 divided by 56 equals 7
Answer:
1/7 acre
Step-by-step explanation:
The number of acres planted is presumed to be proportional to the number of pounds of seeds:
acres/pounds = 8/56 = x/1
x = 1×8/56 = 1/7
1/7 acre can be planted per pound of seed.
_____
Additional comment
When you recognize that 56 = 8×7, there is a tendency to want to divide 56 by 8. That would result in the unit rate ...
(56 lb)/(8 ac) = 7 lb/ac
That is, it takes 7 pounds of seed to plant 1 acre. The question asks how many acres can be planted with 1 pound. Clearly, that is 1/7 of the amount of seed required for 1 acre, so 1 pound will plant 1/7 acre.