The deceleration of the train is -3 ms^-2.
Given:
A train is moving along a Straight track with a speed of 30 ms^-1 when it reaches point A. the driver applies the brakes and the train decelerates at a constant speed until it comes to a stop 150 m from point A
we know that:
v^2 - u^2 = 2as
where
v = 0
u = 30 ms^-1
s = 150 m
0^2 - 30^2 = 2a*150
0 - 900 = 300*a
-900 = 300*a
a = -900/300
a = -3 ms^-2
Negative acceleration is nothing but the deceleration so a = -3 ms^-2.
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Q8.
Solve the simultaneous equations
2x + 3y = 5p
y = 2x + p
where p is a constant.
Give your answers in terms of p in their simplest form.
Answer:
x = 1/4p
y = 3/2p
Step-by-step explanation:
2x + 3y =5p__________________equ 1
y = 2x + p____________________equ 2
sub equ 2 for y in equ 1
2x + 3(2x + p) = 5p_______________open brackets
8x = 2p______________________divide both sides by 8
x = 1/4p
sub 1/4p for x in equ 2
y = 2(1/4p) + p___________________open brackets
y = 3/2p
The model shows that 3 1/5 divided by 4/5 = 4.
What happens if you divide by 8/5 instead of 4/5
The solution after divide by 8/5 instead of 4/5 will be 2.
What is mean by Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts.
Or, A number which is expressed as a quotient is called fraction.
It can be written as the form of p : q, which is equivalent to p / q.
Given that;
The model shows that 3 1/5 divided by 4/5 = 4.
Now,
Substitute 8/5 instead of 4/5, we get;
⇒ 3 1/5 ÷ 8/5
⇒ 16/5 ÷ 8/5
⇒ 16/5 × 5/8
⇒ 2
Thus, The solution after divide by 8/5 instead of 4/5 will be 2.
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Answer:
Step-by-step explanation:
What are the roots of the equation x 2 + 16 x + 80 = 0 x 2 +16x+80=0 in simplest a + b i a+bi form?
The quadratic equation x² + 16 · x + 80 has two roots: x₁ = - 1 / 10 + i (4 / 5), x₂ = - 1 / 10 - i (4 / 5).
How to determine the roots of a quadratic equation
In this question we find a quadratic equation of the form a · x² + b · x + c = 0, whose roots can be found by using the quadratic formula:
x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c)
Where b² - 4 · a · c is the discriminant of the quadratic formula, which offers three cases of solutions:
b² - 4 · a · c > 0: Two different real roots. b² - 4 · a · c = 0: Two equal real roots. b² - 4 · a · c < 0: Two conjugate complex roots.If we know that a = 1, b = 16 and c = 80, then the roots of the quadratic equation are, respectively:
x = - 16 / 160 ± (1 / 160) · √(16² - 4 · 1 · 80)
x = - 1 / 10 ± (1 / 10) · √(- 64)
x = - 1 / 10 ± i (4 / 5)
The roots are - 1 / 10 + i (4 / 5) and - 1 / 10 - i (4 / 5).
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a determined gardener has 100 ft of deer-resistant fence. she wants to enclose a rectangular vegetable garden in her backyard, and she wants the area that is enclosed to be at least 600 ft2. what range of values (in ft) is possible for the length of her garden? (enter your answer using interval notation.)
The range of values for the rectangle length is 20 ≤ y ≤ 30 .
What is a rectangle made of?
With four sides, four corners, and four right angles (90°), a rectangle is a closed 2-D object. A rectangle's opposing sides are equal and parallel. Rectangles are two-dimensional shapes, and as such, they have length and width as their defining characteristics.The garden is to be rectangular shape.
Let x = width
Let y = length
Set the equations for perimeter and area.
2(x + y) = 100 -----> perimeter
x + y = 50 ------> perimeter
xy = 600 ----> area
We have two equations to work with.
x + y = 50 eq1
xy = 600 eq2
Substitute eq1 into eq2. We can get eq2 in terms of x.
x(50 - x) = 600
-x2 + 50x = 600
-x2 + 50x - 600 = 0
Divide both sides of the equation by -1, so that we have a positive x2. The goal is to try to use FOIL to factor.
x2 - 50x + 600 = 0
(x - 30)(x - 20) = 0
x = 30 and x = 20
Next, we plug in these values of x into eq1 to solve for y.
y = 50 - x and y = 50 - x
y = 50 - 30 y = 50 - 20
y = 20 y = 30
Based on this, the range of values for the length is
20 ≤ y ≤ 30
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i need help like immediately
1/4 (8x+4)=2x-4
Answer: the statement is false
Step-by-step explanation:
How do I find the measure of the triangles? Help.
Answer:
Step-by-step explanation: I am guessing that it is 180
PLEASE HELP ME QUICK!!!
Guys, what is the answer to 5-x=12?
Answer:
x= -7
Step-by-step explanation:
here you go.....
please mark brainliest
Help needed with this equation thx
The geometric system has a length of f = 4 cm and a length of g = 6 cm.
How to find the missing lengths of a geometric systemHerein we find a geometric system formed by two rectangles, the rectangle ABCD has an area of 60 square centimeters and the rectangle APQD has an area of 24 square centimeters. The area of a rectangle is equal to the product of the lengths of its base (b) and its height (h), both in centimeters.
First, describe the area formulas for the rectangles ABCD and APQD, both in square centimeters:
Rectangle ABCD
(g + 9) · f = 60 (1)
Rectangle APQD
g · f = 24 (2)
Where:
g - Length of the side QD, in centimeters. f - Length of the side BC, in centimeters.Second, use distributive property in (1):
By (1):
g · f + 9 · f = 60
Third, use substitution by (2) on (1) and determine the value of f:
(2) in (1):
24 + 9 · f = 60
9 · f = 36
f = 4
Fourth, determine the value of g:
By (2):
g = 24 / f
g = 24 / 4
g = 6
The lengths of f and g are 4 and 6 centimeters, respectively.
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a box contains tiles. each tile has certain properties: each tile is made of wood or plastic. each tile is red, yellow, or blue. each tile is a triangle, square, pentagon, or circle. there is exactly one tile for each combination of properties. for example, there is one red circle that is made of wood. steve chooses one tile, and ellen chooses a different tile. what is the probability that the two chosen tiles differ with respect to all three properties?
1/24 is the probability that the two chosen tiles differ with respect to all three properties
1/2 chance that the tiles materials will be different (wood or plastic). 1/3 chance exists that the tiles will have different colors (r, y or b) 1/4 chance where the tile shapes will change (t, s, p or c)the probability that all three attributes of the two tiles will be different.1/2 * 1/3 * 1/4 = 1/24 The probability of an event occurring is a measure of its likelihood. It assesses the likelihood of an event. P(E) = Number of Favourable Outcomes/Total Outcomes is the probability formula.
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Given the function below, find value (a) of x if f(x)=7
The function f(x) = 2x + 1 has its value of x to be 3 when f(x) = 7
How to determine the value of the function?From the possible question, the definition of the function is given as
f(x) = 2x + 1
Also, from the question, we have:
f(x) = 7
Substitute 7 for x in the equation f(x) = 2x + 1
So, we have the following representation
2x + 1 = 7
Subtract 1 from both sides of the equation
This gives
2x = 6
Divide both sides by 2
x = 3
So, we can conclude that the value of x is 3
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Possible question
Given the function below, find the value of x if f(x)=7
f(x) = 2x + 1
the motel in the preceding example uses approximately600 bars of soap each day, and this tends to be fairly constant. lead time for soap delivery is normally distributed with a mean of six days and a standard deviation of two days. a service level of 90 percent is desired. the re-order point (rop) is:
The re-order point (ROP) for the new batch of the bars of soaps be placed when there is 4800 bars left in the inventory.
Define the term reorder point (ROP)?An exact level where the your stock has to be restocked is characterized as a reorder point (ROP). To put it another way, it advises you when to order so that you won't run out of supply.You'll need to be aware of the following factors in order to figure out the ROP for every item:Lead period: Days needed (in days) for the vendor to complete your orderSafeguard stock: The quantity of excess stock, if any, you maintain on hand to assist prevent stockoutsDaily usage: Average number of sales that particular item typically sees per day.ROP = (Daily usage x Lead period) + Safeguard stock
For the given question;
Lead time = 6 days
Safety stock = 2 days x 600 bars = 1200 bars
ROP = (600 x 6) + 1200 = 4800 bars.
Thus, the re-order point (ROP) for the new batch of the bars of soaps be placed when there is 4800 bars left in the inventory.
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Lola received $522.50 when she cashed her paycheck. Why is this important to us?
Because you can also cash a check at a bank if you have an account there.
If you have a checking account, you can write and mail a check to pay your bills. The bank will withdraw the money from your account.
As long as you have enough money in your account (as much or more than what you're trying to cash), you can cash a check and get money back immediately.
You can deposit money into a savings account. A savings account is a good way to save your money and earn money called interest.
Banks also offer electronic services. You can use these services even when the bank is closed.
Some banks have more than one branch or office. Use the branch closest to you if you are in a different town or state. All branches will have access to your account information.
Monica cashed her paycheck at Ready Cash. The fee at Ready Cash to cash a check is 10% of the amount of the check. Her paycheck was $538. how much was the fee for Monica to cash her paycheck
Answer:
$53.8.
Step-by-step explanation:
10% of $538 is like saying 538 times .10. After you multiply, you get $53.8 as the fee that Monica had to pay.
given that the probability of a family owning a dog is 0.91, and the probability of a family owning a cat and a dog is 0.15, what is the probability of a family owning a cat given that the family owns a dog?
The probability of a family owning a cat given that the family owns a dog is 0.164
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.
Here
probability of a family owning a dog is 0.91,
P(dog) = 0.91
probability of a family owning a cat and a dog is 0.15,
P(dog ∩ cat) = 0.15
according to conditional probability
the probability of occurring of B after event A takes place is
P(A|B)=P(A∩B)/P(A)
so, the probability of a family owning a cat given that the family owns a dog is
P(dog | cat) =P(dog∩cat)/P(dog)
= 0.15/0.91
=0.164
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it was 5 degrees above zero in the morning. By afternoon the temperature rose 27 degrees. How warm was it?
It was 33 degrees warm in the afternoon
How to determine how warm it was?From the question, we have the following parameters that can be used in our computation:
In the morning = 5 degrees above zero
Afternoon = Rise of 27 degrees
The degree of warmth in the afternoon is then calculated as
Degree of warmth = Temperature In the morning + Rise of the temperature
Substitute the known values in the above equation, so, we have the following representation
Degree of warmth = 5 + 27
Evaluate the sum
Degree of warmth = 33
Hence, the temperature is 33 degrees
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Which equations are true? Select all that apply.
Answer:
The equation that is true is equation two
Please help I will give the brainiest for the fastest answer.
Answer: Campbell to Hillsboro to Richmond to Winchester
(Note: Not taking the Washington route)
Step-by-step explanation:
Form Campbell all the way to Richmond have no other choices, From Richmond to Winchester has two choices, 12.2 mi +5.2 mi or 15.7 mi
12.2+5.2=17.4 mi while the other choice is only 15.7 mi
So taking the 15.7 mi option is faster
What is the equation of the line that passes through the point (−2,−7) and has a slope of 6?
The equation of the line in slope intercept form is y = 6x + 5
How to determine the equation of the line?The given parameters are
Slope, m = 6
Points, (x₁, y₁) = (-2, -7)
A linear equation can be represented as
y = slope * x + y-intercept
i.e.
y = m(x - x₁) + y₁
Substitute the known values in the above equation
So, we have the following equation
y = 6(x + 2) - 7
Expand
y = 6x + 12 - 7
Evaluate the like terms
y = 6x + 5
Hence. the linear equation is y = 6x + 5
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Find the solution for −0.5x − 3.69 = x − 1.9 − 2.39. x = 0.4 x = −0.4 x = 2.5 x = −2.5
The solution for the given expression -0.5x-3.69=x-1.9-2.3 is x= 0.34
The given problem is related to an algebraic expression which is the thought of expressing numbers utilizing letters or letter sets without indicating their real values, which is made up of factors and constants, at the side of logarithmic operations (expansion, subtraction, etc.). Expressions are made up of terms.
since the given expression is :
-0.5x-3.69=x-1.9-2.3
=>-0.5x-x=-1.9-2.3+3.69
=>-1.5x=-0.51
=>x=0.34
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1. Of the three lines in the graph, one has slope 1, one has slope 2, and one has slope
Label each line with its slope. HELP IM REALLY STUCK ON THIS
The length of a rectangle is 5 more than twice the width . If the length is 60 inches ,what is the width?
Answer:27.5 inches
Step-by-step explanation:
Bryan paid $144.00 for an item at the store that was 20% off the original price. What was the original price?
Answer:
$180
Step-by-step explanation:
[tex]P\times{(1-0.20)}=144[/tex]
[tex]P\times{0.80}=144[/tex]
[tex]P=\frac{144}{0.80}[/tex]
[tex]P=180[/tex]
four people (john, paul, george, and ringo) are seated in a row on a bench. the number of ways to order the four people so that john is next to paul is 12. how many ways are there to order the four people on the bench so that john is not next to paul?
The Number of ways that four people can be seated on the bench so that john is not next to paul is 12
Permutations :
In mathematics, An arrangement of things or items in a specific sequence is known as a permutation. One should think about both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important.
The arrangement of n items in r ways is given by
ⁿPr = n! /(n-r)!Here we have
4 people (John, Paul, George, and Ringo) are seated in a row on a bench
Here total No of ways that 4 can be seated = 4 × 3 × 2 × 1 = 24
The number of ways of seating the four people so that john is next to paul is 12
Then the number of ways the four people on the bench so that john is not next to paul can find as given below
= Total No of ways, 4 can be seated - No of ways that john next to paul
= 24 - 12 = 12
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factorise 2x^[2]-9x-5
Answer:
(2x + 1) and (x - 5)
Step-by-step explanation:
(2x + 1)(x - 5) = 2x^2 - 9x - 5
In the diagram below, \overline{TU} TU is parallel to \overline{QR} QR . If TUTU is 55 less than TSTS, QS=45QS=45, and QR=36QR=36, find the length of \overline{TS} TS . Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.
The length of TS, using similar triangles, is given as follows:
TS = x = 25.
What are similar triangles?Similar triangles are two triangles that share these two features:
Same angle measures.Proportional side lengths.In the context of this problem, the similar triangles are given as follows:
STU and SQR.
The proportional side lengths from these two similar triangles are given as follows:
TS = x and QS = 45.TU = x - 5 and QR = 36.Hence the proportional relationship that relates these lengths on the similar triangles is given as follows:
x/45 = x - 5/36
Applying cross multiplication, the length of TS, equals to x, is obtained as follows:
45(x - 5) = 36x
45x - 225 = 36x
9x = 225
x = 225/9
x = 25.
Missing InformationThe diagram is given by the image shown at the end of the answer.
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A midwife delivers 10 babies considering a % chance of delivering a boy and 50% chance of delivering a girl, answer the following questions what is the probability that 6 of the babies will be boys?
A midwife delivers 10 babies, with 50% chance of delivering a boy and 50% of delivering a girl. The probability that 6 out of 10 babies will be boys is 20.5%
The problem can be solved using binomial distribution, that is the probability of 2 possible outcomes in a number of trials.
The formula is given by:
P(x) = ⁿCx . P^x . (1 - P)^(n-x)
x = total number of event A
n = number of trials
P = probability of A in a single trial
Parameters given in the problem:
n = 10
x = 6
P = 50% = 0.5
Plug these parameters into the formula:
P(6 boys) = ¹⁰C₆ . (0.5)⁶ . (0.5)⁴
= 0.205 = 20.5%
Hence, the probability that 6 out of 10 babies will be boys is 20.5%
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Identify all of the roots of f(x) = x² + 2x + 2.
Answer: -1-1i and -1+1i
Step-by-step explanation:
how many 3-letter passwords can be made using the letters a through z if... a) repetition of letters is allowed? b) repetition of letters is not allowed?
If repetition is allowed then the required passwords generated are 17576.
If repetition is not allowed then the required passwords generated are 15600.
Given that;
We need to get 3 letter passwords using a through z by two case;
(a) If repetition is allowed
(b) If repetition is not allowed
Case (a): If repetition is allowed.
The total number of letters from a through z are 26
⇒ The total number of 3 letter passwords made are;
= 26³
= 26 * 26 * 26
= 17576
If repetition is allowed then the required passwords generated are 17576.
Case (b): If repetition is not allowed.
⇒ The total number of 3 letter passwords made are;
= 26 * 25 * 24
= 15600
If repetition is not allowed then the required passwords generated are 15600.
Therefore,
If repetition is allowed then the required passwords generated are 17576.
If repetition is not allowed then the required passwords generated are 15600.
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Solve the inequality for x. Show each step of the solution for full credit. (3 points - 2 points showing work, 1 point correct answer)
7x+1/2 >4
The value of x in the Inequality (7x + 1)/2> 4 is x > 1.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤.
In this case, the inequality is given as:
(7x + 1)/2> 4
Cross multiply
7x + 1 > 2 × 4
7x + 1 > 8
Collect like terms
7x > 8 - 1
7x > 7
Divide
x > 7/7
x > 1
Therefore, x > 1.
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Lena made $60 babysitting for 3 hours on Sunday. He made $140 for 7 hours
on Tuesday. What is the rate of change?
Answer:20 dollars per hour
Step-by-step explanation:60/3 = 20
20 dollars per hour
7 x 20 = 140