Find the gradient of the following line

Answer:

767

Step-by-step explanation:

The rate of the passenger train must be 45 miles per hour, and the rate of the freight train must be 30 miles per hour.

Let's denote the rate of the passenger train as "P" and the rate of the freight train as "F". We are given that the passenger train's rate exceeds the freight train's rate by 15 miles per hour. Therefore, we can write the following equation:

P = F + 15

We are also given that the two trains start from points that are 300 miles apart and meet after 4 hours. We can use the formula distance = rate × time to set up two equations:

Distance covered by the passenger train: P × 4

Distance covered by the freight train: F × 4

Since they meet each other, the sum of their distances should add up to 300 miles:

P × 4 + F × 4 = 300

Substituting P = F + 15 into the equation, we can solve for F:

(F + 15) × 4 + F × 4 = 300

4F + 60 + 4F = 300

8F = 240

F = 30

Now that we have the rate of the freight train, we can substitute it back into the equation P = F + 15 to find the rate of the passenger train:

P = 30 + 15

P = 45

Therefore, the rate of the passenger train must be 45 miles per hour, and the rate of the freight train must be 30 miles per hour.

For such more questions Train Rates

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The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown". In x + 2 = 7, x is a variable, but we can work out its value if we try! A variable doesn't have to be "x", it could be "y", "w" or any letter, name or symbol.

Answer:     Seven hundred thirteen point forty-nine.

Step-by-step explanation:    Hope this helps ;)

Answer:

free

Step-by-step explanation:

points .-.

Answer:

10

Step-by-step explanation:

every day he doubles the number of sold cars compared to the previous day.

so the sequence goes along the powers of 2 :

1

2

4

8

16

32

64

128

256

512

1024 - so, latest here, of course, at least 1000 cars were sold. that would be day 11.

but - maybe we reached the total of 1000 cars already before that.

as you can see, the number of cars sold on a day is 1 bigger than the sum of cars sold on all previous days.

e.g. 8 = 4 + 2 + 1 + 1

64 ÷ 32 + 16 + 8 + 4 + 2 + 1. + 1

therefore, 1024 is bigger by 1 than the sum of the cars Sikhs before that day. so, that sum is 1023 and bigger than 1000.

so, with the 512 cars sold on day 10 he reached and surpassed the total 1000 sold cars mark.

It takes 11 days for the salesman to sell at least 1000 cars.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

We can set up an inequality to represent the total number of cars sold after n days using a geometric series, where "a" is the initial number of cars sold, "r" is the common ratio of the series, and "n" is the number of days.

The inequality is : a(1-rⁿ)/(1-r) ≥ 1000

In this case, the initial number of cars sold is 1, the common ratio is 2, and we're trying to find the number of days it takes to sell at least 1000 cars. So we can plug these values into the inequality:

1(1-2ⁿ) ≥ 1000

1-2ⁿ ≥ 1000

2ⁿ ≤ 999

Now we can take the log base 2 of both sides

n ≤ log₂(999) +1

n ≤  9.97+1

n ≤ 11

As the number of days is an integer, it takes 11 days for the salesman to sell at least 1000 cars.

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Answer:

3=6

4=8

5=10

6=12

graph 1

Step-by-step explanation:

Answer:

80%

Step-by-step explanation:

1/5 is about 20%, so the remaining 4/5 is the remaining 80% of the air

Answer:

8/125cm3

Step-by-step explanation:

A=lxwxh

A=2/5 x 2/5 x 2/5

A=8/125cm

I hope this helps <3

Answer:

y =   35°

z =  90°

Step-by-step explanation:

the angle labeled as 35° and the angle labeled as 'y' are alternate-interior angles and are congruent

therefore, y = 35°

the third angle of the triangle on the left is 180-(90+35) = 55

therefore, this angle is vertical with the angle opposite it which is also 55°

to find 'z', you can add the two known angles of 55 and 35 and subtract the sum from 180 to get 90°

Answer:

If x, y increase at a constant rate, it is linear.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use trig ratios to solve for x. Side x is adjacent to the reference angle of 61 degrees, and the side that measures 59 is opposite the reference angle. This is the tangent ratio:

[tex]tan61=\frac{59}{x}[/tex] and

[tex]x=\frac{59}{tan61}[/tex] so

x = 32.7

Answer:

58 degrees

Step-by-step explanation:

well we know that every angle in a tringle adds up to 180 degrees.

so we know that 64 + angle 1 + angle 2 = 180

180-64=116

and since they are congruent (same value as one another) you just divide 116 by 2 and boom!

116/2=58

both are 58 degrees

Answer: 51 sq units

Step-by-step explanation:

after plotting the vertices, the height of the triangle is 6 and the base is 17

A = 1/2(6)(17)

A = 51 sq units

Answer:

[tex](a)\ f(8) = 200(1 + 3.1\%)^8[/tex]

(b) After 8 years, the savings account has $255.32

Step-by-step explanation:

Given

[tex]a = 200[/tex] ---- initial (i.e. when t = 0)

[tex]r =3.1\%[/tex]

[tex]t = 8[/tex]

Solving (a): Model the situation

For growth, an exponential function is represented as:

[tex]f(t) = a(1 + r)^t[/tex]

This gives:

[tex]f(8) = 200(1 + 3.1\%)^8[/tex]

Solving (b): The solution to (a)

We have:

[tex]f(8) = 200(1 + 3.1\%)^8[/tex]

Express percentage as decimal

[tex]f(8) = 200(1 + 0.031)^8[/tex]

[tex]f(8) = 200(1.031)^8[/tex]

[tex]f(8) = 200*1.2766[/tex]

[tex]f(8) = 255.32[/tex]

Answer:

Step-by-step explanation:

M^5

(2/3)^5

2^5/3^5

32/243

Answer:

0.13

Step-by-step explanation:

M ^5

Divide 2/3

Equals 0.6667

0.6667 ^ 5

Equals 0.13 Rounded

Answer:

5x

Step-by-step explanation:

Answer:

2x+3 is it simplified

Step-by-step explanation:

Answer: F. (25 − c) ÷ 4

Step-by-step explanation:

Emma had 25 cookies and gave c cookies to her mom and then divided the rest evenly amongst her 4 friends.

The cookies she shared to her friends are the 25 cookies minus the number of cookies she gave her mom which is:

= 25 - c

This (25 - c) was divided by 4 with each portion given to a friend so the total each friend got was:

= (25 - c) / 4

Answer:

D. (–2, –2); minimum

Step-by-step explanation:

It’s D you got to see the lowest part of the graph and you will call it mini except if the graph was going down you will call that point maximum.

Answer:

D. (-2, -2); minimum

Step-by-step explanation:

The vertex is the where the curve turns up/down which divides the figure into two halves.

From the given graph, the graph turns up at (-2, -2) , the graph moves down, therefore, the vertex (-2, -2); minimum.

Hope this will helpful.

Thank you.

Answer:

4:00 p.m is corrcet

Step-by-step explanation:

f ( 4 ) = - 10

___________

g ( x ) = 2 , x = 0

Answer:

y = 6

Step-by-step explanation:

5y + 1 = 31

Subtract 1 from each side

5y + 1-1 = 31-1

5y = 30

Divide by 5

5y/5 = 30/5

y = 6

Answer:

y = 6

Step-by-step explanation:

5y means 5 multiplied by something. 5y + 1 equals 31. So 5 multiplied by 6 equals 30 + 1 = 31, which is the given answer.

Answer:9 times 10 equal 90 $

Step-by-step explanation:

Answer:

5 < x

Step-by-step explanation:

24<5x-1

Add 1 to each side

24+1<5x-1+1

25 < 5x

Divide by 5

25/5 < 5x/5

5 < x

Answer:

X>5.

Step-by-step explanation:

First you swap sides, so 5x-1>24. Then simplify to 5x>25, divide 25 by 5 to get 5.

A. low unemployment

I hope this answer helps you...