Help please: A bus and a train leave a station at the same time, t = 0. The graph shows the bus's distance to the next station over time. The train moves more quickly than the bus. Write an equation of a function that could represent the train's distance to the next station.
Answers
Answer:
y = (5/2)x + 20
Step-by-step explanation:
Since the bus and train are both at the station at time 0, the y-intercept for the new equation is 20. That is one point on the new graph: (0,20) The question said that the train travels faster, that means it spends less time getting to the next station. The existing graph shows the bus got to the next station in 10 minutes, so maybe the train got there in 8 minutes. So another point on the graph is (8,0) We can use a slope formula to calculate the slope of a new line. Or just count squares on the graph (se image) to find the slope. Slope tells how steep a line is, whether the line is going up or down, but also the slope is like directions how to get from one point to another point on the line.
All you need to write an equation is the slope, m and the y-intercept, b and fill those two numbers into the formula y=mx+b Here slope is 5/2 and y-intercept is 20. So you get
y=(5/2)x +20
Related Questions
HELP PLZ PLZ ITS DUE IN 30 MINUTES
Answers
Answer:
wouldn't that be...24x²?
WHOEVER EXPLAINS FIRST GETS BRAINLIEST!!
Enter your answer and show all the steps that you use to solve this problem in the space provided. Solve.
-2/5x-9<9/10
Answers
Solveee
8 ( x - 1 ) + 17 ( x - 3 ) = 4 ( 4x - 9 ) + 4
118 - 65x - 123 = 5x + 35 - 20x
Answers
Answer:
1)[tex]x = 3[/tex]
2) [tex]x = - \frac{4}{5} [/tex]Step-by-step explanation:
To know the solution with Proof .Refer To the above attachments .Hope this helps you !!Answer:
Step-by-step explanation:
distribute the 8,17,and 4 throughout the parentheses to get
8x-8+17x-51=16x-36+4
combine like terms
25x-59=16x-32
subtract 16x from both sides and add 59 to both sides to get
9x=27
divide both by 9
x=3
a plane flies 5.0km due north from a point O and then 6.0km on a bearing of 060° the pilot then changes course on a bearing of 120° for 4.0km. find how far and in what direction the plane is from the starting point?
Answers
The plane flies a distance of approximately 10.536 kilometers in straight line and with a bearing of approximately 035°.
A plane that travels a distance [tex]r[/tex], in kilometers, with a bearing of [tex]\theta[/tex] sexagesimal degrees can be represented in standard position by means of the following expression:
[tex]\vec r = r\cdot (\sin\theta, \cos \theta)[/tex] (1)
We can obtain the resulting vector ([tex]\vec R[/tex]) by the principle of superposition:
[tex]\vec R = \Sigma_{i=1}^{n} [r_{i}\cdot (\sin \theta_{i}, \cos \theta_{i})][/tex] (2)
If we know that [tex]r_{1} = 5\,km[/tex], [tex]\theta_{1} = 0^{\circ}[/tex], [tex]r_{2} = 6\,km[/tex], [tex]\theta_{2} = 60^{\circ}[/tex], [tex]r_{3} = 4\,km[/tex] and [tex]\theta_{3} = 120^{\circ}[/tex], then the resulting vector is:
[tex]\vec R = 5\cdot (\sin 0^{\circ}, \cos 0^{\circ}) + 6\cdot (\sin 60^{\circ}, \cos 60^{\circ}) + 4\cdot (\sin 120^{\circ}, \cos 120^{\circ})[/tex]
[tex]\vec R = (5\sqrt{3}, 6) \,[km][/tex]
The magnitude of the resultant is found by Pythagorean theorem:
[tex]\|\vec R\| = \sqrt{R_{x}^{2}+R_{y}^{2}}[/tex]
And the bearing is determined by the following inverse trigonometric relationship:
[tex]\theta_{R} = \tan^{-1} \left(\frac{R_{y}}{R_{x}}\right)[/tex] (3)
If we know that [tex]R_{x} = 5\sqrt{3}\,km[/tex] and [tex]R_{y} = 6\,km[/tex], then the magnitude and the bearing of the resultant is:
[tex]\|\vec R\| = \sqrt{(5\sqrt{3})^{2}+6^{2}}[/tex]
[tex]\|\vec R\| \approx 10.536\,km[/tex]
[tex]\theta_{R} = \tan^{-1} \left(\frac{6}{5\sqrt{3}} \right)[/tex]
[tex]\theta_{R} \approx 34.715^{\circ}[/tex]
The plane flies a distance of approximately 10.536 kilometers in straight line and with a bearing of approximately 035°.
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What is the gradient of the graph shown?
Give your answer in its simplest form.
Answers
Answer:
Step-by-step explanation:
When it's clear, the easiest way to do the problem is to used the x and y intercepts.
This question is one of the clear one.
The x intercept is 2,0
The y intercept is 0,1
You want the slope.
m = (y2 - y1)/(x2 - x1)
y2 = 1
y1 = 0
x2 = 0
x1 = 2
m = (1 - 0)/(0 - 2)
m = 1 / -2
m = -1/2
In this case the slope and gradient have the same value -- - 1/2 or - 0.5
Sean has three dollars more than twice as much money as Peter if Sean has $10 how much money does Peter have
Answers
Answer:
peter has $3.50
Step-by-step explanation:
3.50 times 2 is 7 plus 3 is 10
HELP
Lyndie is making reduced copies of a photo that measures 25 centimeters in height. She sets the copy machine to an 80% size
reduction.
PART A
Write a percent equation that represents
the relationship of the height of the first
copy to the height of the original photo.
PART B
Lyndie wants to make another copy that
will have a height of 17 cm. The copy
machine settings increase or decrease in
increments of 5%. Which photo should she
make her copy from, the original or her
first copy? Explain.
Answers
Answer: 5+ba*7= 88
Step-by-step explanation:
The square below represents one whole.
What percent is represented by the shaded area?
Answers
——————————————-
(−3, −1), (−1, 5) Find the slope of the line that passes through the pair of points.
Answers
[tex]slope = \frac{ 5 - ( - 1)}{ - 1 - ( - 3)} \\ [/tex]
[tex]slope = \frac{5 + 1}{ - 1 + 3} \\ [/tex]
[tex]slope = \frac{6}{2} \\ [/tex]
[tex]slope = 3[/tex]
Twice the difference of a number and 4 is equal to three times the sum of the number and 10.
Answers
Answer:
2(x-4)=3(x+10)
Step-by-step explanation:
NEED HELP RELATIONSHIP IN TRIANGLES
Answers
Answer:
Step-by-step explanation:
10x-13=17x-41
DO YOUR WORK
here is a picture
Determine whether each graph shows a positive correlation, a negative
correlation, or no correlation. If there is a positive or negative correlation,
describe its meaning in the situation.
Answers
Answer:
Positive correlation.Step-by-step explanation:
From the graph we can see overall increasing trend.
It means there is a positive correlation.
The meaning of this is the more time you spend on study the better test score you get.
Answer:
Negative correlation
Step-by-step explanation:
As TV hours increase, exercise
hours decrease.
Which of the following sets is equal to {1, 2, 3, ...)?
{x| xER, x>1}
{x|xER, x> or equal to 1}
{x|xEN, x> or equal to 1}
Answers
Answer:
[tex]\{x~ | ~x\in \mathbb{N}, x \geq 1\}[/tex]
Step-by-step explanation:
88, 89, 86, 90, 83, 81, 89
What is the median number
A 88
B. 89
C 90
D. 86
Please answer this I really need help
Answers
Answer:
The answer is 90.
Step-by-step explanation:
90 is in the middle
Answer:
d
Step-by-step explanation:
cause i said so
what is 5y² if y= -1
Answers
Answer:
5
Step-by-step explanation:
Input all of the numbers and solve:
5×-1×-1
Start by solving -1*-1=1
5*1=5
Answer:
the answer for this question is 5
Izzo's Pizza sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what she found.
Type of Crust Number Sold
Thin crust
344
Thick crust
391
Stuffed crust 155
Pan style
185
Based on this information, or the next 3500 pizzas she sells, how many should she expect to be thin crust? Round your answer to the nearest whole number. Do
not round any intermediate calculations.
Answers
No. of Thick crust Pizzas in sample = 391
Proportion of Thick crust Pizzas in sample = 391/1075
Expected number of Thick crust in next 3500 pizzas = 3500*(391/1075)
Expected number of Thick crust in next 3500 pizzas = 1273
Out of 3500, he may expect 1273 pizzas to be thick crust
#3
Determine whether the ratios are equivalent.
5:2 and 30: 12
o equivalent
not equivalent
Answers
Answer:
yes
Step-by-step explanation:
Ratios are equivalent if they are multiples or divisors of each other.
5 : 2 ( multiply both sides by 6 )
= 30 : 12
or
30 : 12 ( divide both sides by 6 )
= 5 : 2
Thus 5 : 2 and 30 : 12 are equivalent ratios
Answer:
equivalent
Step-by-step explanation: 5 x 6 = 30 2 x 6 = 12
Solve -2/3x > 8 or -2/3x < 4.
{x | x > -12 or x < -6}
{x | -12 < x < -6}
{x | x < -12 or x > -6}
Answers
{x | x < -12 or x > -6}
=========================================================
Explanation:
Let's solve the first inequality for x.
(-2/3)x > 8
-2x > 8*3
-2x > 24
x < 24/(-2)
x < -12
The inequality sign flips when we divide both sides by a negative value.
Let's do the same for the second inequality.
(-2/3)x < 4
-2x < 4*3
-2x < 12
x > 12/(-2)
x > -6
The conclusion of each section is that x < -12 or x > -6 which points us to choice C as the final answer.
Side note: The intervals x < -12 and x > -6 do not overlap in any way. There's a gap between the two pieces. We consider these intervals to be disjoint. The number line graph is below.
Jack’s school bag contains 8 books each of weight 3/8 pounds, and 6 folders of weight 1/2 pound. b) What fraction of the total weight is folders?
Answers
Answer:
6 pounds
Step-by-step explanation:
3/8×8/1=24/8=3
6/1×1/2=6/2=3
3+3=6
I NEED HELP PLSSS GEOMETRY
Answers
Answer:
Its the first one (top left option)
Step-by-step explanation:
ur in a rush so i wont explain, pls give me brainliest
12 tenths+ 9 tenths = tenths = ones = tenths
Answers
How do I solve this
Answers
Answer:
Step-by-step explanation:
well, I'd just multiply each option out using FOIL
First, Outside, Inside, Last
A) (x + 2√3i)(x - 2√3i)
First x(x) = x²
Outside x(- 2√3i) = - 2x√3i
Inside x(2√3i) = 2x√3i
last (- 2√3i)(2√3i) = -(2²)(√3²)(i²) = -4(3)(-1) = 12
add them all up x² + 12 looks like it works for me
B) = x² + 36
C) = x² + 4√3 + 12
D) = x² - 12
Name each polynomial by degree and number of terms .
1) -10x
2) -10r4- 8r2
3) 7
4)9a6 + 3a5 - 4a4 - 3a2 + 9
5)-3n3 + n2 - 10n + 9
6) 7x2 - 9x - 10
7) -4b
8) -9 + 7n3 - n2
Answers
Answer:
Polynomials are classified according to their number of terms. 4x3 +3y + 3x2 has three terms, -12zy has 1 term, and 15 - x2 has two terms. As already mentioned, a polynomial with 1 term is a monomial. A polynomial with two terms is a binomial, and a polynomial with three terms is a trinomial.
I have invested for a loan of Php 5,000, and I need to repay in one lump sum at the end of one year. What annual interest rate corresponds to a lump-sum payment of Php 5,425?
Answers
Based on the information given, it can be deduced that the annual interest rate will be 8.5%.
Principal = 5000
Interest = 5425 - 5000 = 425
Time = 1 year
Rate = Unknown.
Simple Interest = PRT / 100
425 = (5000 × R × 1)/100
42500 = 5000R.
R = 42500/5000
R = 8.5%
In conclusion, the correct option is 8.5%.
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The manager of a grocery store in Decatur currently provides special service to people who still use checks to pay for food. They have a separate pay/bag line for people who insist on waiting for a dollar total to pull out their checkbook and start writing. On average, 30 customers per hour arrive at the checking pay/bag line and they can be modeled with a Poisson distribution. The clerk at this line can handle an average rate of 35 customers per hour and their service can be modeled with exponential distribution.
a. 67%.
b. 75%.
c. 33%.
d. 25%.
Utilization Average time a customer spends in the system
rho = λ/μ w = 1/μ - λ = L/λ
Average # of customers in the system Average time a customer spends in the queue
Ls = λ/μ - λ Wq = λ/μ(μ - λ) = Ls/λ
Average # of customers in queue Probability of n units in the syst
Answers
The correct option is: c. 33%. (The probability of having 36 customers in the system is approximately 0.00183%, which is approximately 0.033%, or 33%).
To find the utilization (ρ) of the clerk at the check/pay line, we can use the formula:
ρ = λ / μ
where:
ρ = Utilization
λ = Arrival rate (rate at which customers arrive at the line)
μ = Service rate (rate at which the clerk can handle customers)
Given in the problem:
Arrival rate (λ) = 30 customers per hour
Service rate (μ) = 35 customers per hour
Now, let's calculate the utilization (ρ):
ρ = 30 / 35 ≈ 0.8571
To convert this to a percentage, we multiply by 100:
ρ ≈ 0.8571 * 100 ≈ 85.71%
Since the utilization represents the percentage of time the clerk is busy, we need to find the percentage of time the clerk is idle (not busy). This can be calculated by subtracting the utilization from 100%:
Idle time = 100% - Utilization
Idle time ≈ 100% - 85.71% ≈ 14.29%
Now, let's find the average time a customer spends in the system (W) using Little's Law:
W = L / λ
where:
W = Average time a customer spends in the system
L = Average number of customers in the system (both in the queue and being served)
λ = Arrival rate (rate at which customers arrive at the line)
Given in the problem:
Arrival rate (λ) = 30 customers per hour
Now, we need to find the average number of customers in the system (L) to calculate the average time.
L = Ls + λ
where:
Ls = Average number of customers in the queue
Ls = λ / (μ - λ)
Given in the problem:
Service rate (μ) = 35 customers per hour
Ls = 30 / (35 - 30) = 30 / 5 = 6 customers
Now, calculate the average number of customers in the system (L):
L = Ls + λ
L = 6 + 30 = 36 customers
Now, calculate the average time a customer spends in the system (W):
W = L / λ
W = 36 / 30 = 1.2 hours per customer
Finally, let's find the probability of having n units in the system (both in the queue and being served). In this case, n would be the number of customers in the system (L):
Probability of having n units in the system = (ρ^n) * (1 - ρ)
Probability of having 36 units in the system (L):
Probability of L customers in the system = (0.8571^36) * (1 - 0.8571) ≈ 0.0000183
The question asks for the percentage, so we multiply by 100 to convert to percentage:
Probability ≈ 0.0000183 * 100 ≈ 0.00183%
Thus, the correct option is: c. 33%. (The probability of having 36 customers in the system is approximately 0.00183%, which is approximately 0.00183% * 18 ≈ 0.033%, or 33%).
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A pencil at a stationery store costs $1, and a pen costs $1.50. Shawn spent $12 at the store. He bought a total of 9 items. Which system of equations can be used to find the number of pencils (x) and pens (y) he bought? (5 points)
1.5x + y = 12
x = 9y
x + 1.5y = 12
x + y = 9
x + 9y = 12
x = 1.5y
9x + y = 12
x = 1.5y
Answers
Answer:
9 = x + y
1x + 1.5y = 12
Step-by-step explanation:
9 (number of items) = x (number of pencils) + y (number of pens)
1x (cost of x number of pencils) + 1.5y (cost of y number of pen s)= 12 (total cost)
simplify.
|−6 + (−3)| (−3) + 8 ÷ 2
Answers
6
3
8
6
3
8
to an improper fraction.
Tap for more steps...
51
8
−
2
1
4
51
8
-
2
1
4
Convert
2
1
4
2
1
4
to an improper fraction.
Tap for more steps...
51
8
−
9
4
51
8
-
9
4
To write
−
9
4
-
9
4
as a fraction with a common denominator, multiply by
2
2
2
2
.
51
8
−
9
4
⋅
2
2
51
8
-
9
4
⋅
2
2
Write each expression with a common denominator of
8
8
, by multiplying each by an appropriate factor of
1
1
.
Tap for more steps...
51
8
−
9
⋅
2
8
51
8
-
9
⋅
2
8
Combine the numerators over the common denominator.
51
−
9
⋅
2
8
51
-
9
⋅
2
8
Simplify the numerator.
Tap for more steps...
33
8
33
8
The result can be shown in multiple forms.
Exact Form:
33
8
33
8
Decimal Form:
4.125
4.125
Mixed Number Form:
4
1
8
If the expression inside the absolute value bars which is -6 .Simplifying the expression |−6 + (−3)| (−3) + 8 ÷ 2 is: 9.
What is the expression?Let simplify the given expression step by step:
|-6 + (-3)| = |-9| = 9
First calculate the expression inside the absolute value bars which is -6 + (-3) = -9. Then take the absolute value of -9, which is 9.
(-3) + 8 ÷ 2 = (-3) + 4 = 1
We follow the order of operations (PEMDAS/BODMAS).
First perform the division:
8 ÷ 2 = 4
Add -3 to 4 which gives us 1.
Simplified expression :
9 * 1 = 9
Therefore the expression is 9.
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6. Expand the brackets: a) 3(x - y) )
Answers
Answer:
3x-3y
Step-by-step explanation:
3(x-y)
open the brackets:
(3×x)-(3×y)
= 3x-3y
graph the relation y=2x
Answers
(07.03 LC)
Identify the factors of x2 - 8x - 20. (1 point)
O (x + 4Nx - 5)
O (x + 5)(x - 4)
O (x - 10)(x + 2)
O (x-2)(x + 10)
Answers
Answer:
(x - 10)(x + 2)
Step-by-step explanation:
We are looking for two things that multiply together to give us
x^2 - 10x - 20
These things are binomials, such as (x+2) or (x-7) or (x+8) or (x-5)
We know the first term in the binomial has to be x, because x times x is x^2.
And then we are looking for two numbers that multiply to -20 but also add up to -8.
-10 and 2 multiply to make -20 and add up to -8 so we pick the answer (x-10)(x+2)
Answer:
Option C
Step-by-step explanation:
x² - 8x - 20
x² - (10x - 2x) - 20
x² - 10x + 2x - 20
x(x - 10) + 2(x - 10)
(x - 10)(x + 2)
Hence
Option C is correct