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lina2011 [118]
3 years ago
7

Bus A and Bus B leave the bus depot at 5 pm. Bus A takes 30 minutes to do its route and bus B takes 35 minutes to complete its r

oute. At what time are they both back at the bus depot together? Give your answer as a 12-hour clock time.
Mathematics
1 answer:
DaniilM [7]3 years ago
7 0

Answer:

8:30 pm

Step-by-step explanation:

step 1

Decompose the numbers in prime factors

30=(2)(3)(5)\\35=(5)(7)

step 2

Find the LCM

The LCM of 30 min and 35 minutes will be given as

LCM=(2)(3)(5)(7)=210\ min

step 3

Adds 210 minutes to the starting time

First, converting 210 minutes to hours

Remember that

1\ h=60\ min

will need dividing 210 by 60

210/60=3.5\ h

therefore

5:00 pm+3.5 h=8:30 pm

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(Will award Brainlies & many many points, please help!)
iren [92.7K]

Answer:

B] f(n) = 6(3)n − 1; f(5) = 486

Step-by-step explanation:

First, you have to identify which type of relation the points have. From the graph you can tell that it's an exponential growth. The x values change in the same amount every time, in this case by 1.

So if the relation is exponential, if we divide the y coordinates you should get the same result every time.

18 / 6 = 3

54 / 18 = 3

162 / 54 = 3

So the y value increases 3 times. That means that the next value should be 162*3 = 486.

3 0
3 years ago
Read 2 more answers
Teddy has two piggy banks. The difference in the amount of money between the two banks is no more than $10. One piggy bank has $
just olya [345]

Answer:

2.69≤x≤17.31

Step-by-step explanation:

Lety the amount in the other Piggy bank be x.

The difference in the amount of money between the two banks is no more than $10 is expressed as;

|x-7.31| ≤ 10

The value in the modulus sign can be positive or negative

If positive;

x-7.31 ≤ 10

x ≤ 10+7.31

x≤17.31

If negative

-(x-7.31) ≤ 10

-x+7.31 ≤ 10

-x ≤ 10-7.31

-x ≤ 2.69

Multiply both sides by -1

x ≥ -2.69

The compound inequality representing the amount of money in the other bank is -2.69≤x≤17.31

4 0
2 years ago
Q..3/4 of a piece of metal has a mass on 15 kg. What is the mass of 2/5 of a piece of metal ?
Margarita [4]

Answer

8kg

Explanation

3/4--------15

2/5-------x

cross multiplying

3/4×X = 2/5×15

3X/4 = 30/5

3X/4 = 6

cross multiplying

3X = 4×6

3X = 24

dividing bothsides by 3

3X /3 = 24/3

X = 8

therefore, the answer is 8 kg

8 0
2 years ago
Help please it’s my last questions
mihalych1998 [28]

Answer:

The one u highlighted is correct. C.

Step-by-step explanation:

If u substitute -2 to 2x, it is -4. then substitute the second one -2 to-5y, it is +10. -4+10=6. Then for the second thing. Substitute 1 to 2x which is 2*1=2. Then substitute-4/5 to -5y which is +4. 2+4=6.

3 0
3 years ago
Based on the graph given for f (x) construct the graph of f¹ (x). for f (x) find E, F and the formula of f (x) when it is known
Lostsunrise [7]

Answer:

To find an inverse function, reflect a graph of a function across the line y=x (and find the resulting equation)

To reflect a linear function in the line y=x, find points on f(x) and then swap their x and y coordinates.

Points on f(x):  (0, -4)  (2, 0)  (5, 6)

Points reflected in line y=x:  (-4, 0)  (0, 2)  (6, 5)

Plot points (-4, 0)  (0, 2)  (6, 5) and connect to form a straight line - this is the inverse of the function:  f^{-1}(x)

To determine the equation of f(x):

Choose 2 points on f(x):  (5, 6) and (0, -4)

Calculate the slope (gradient) by using:

m=\dfrac{\triangle y}{\triangle x}=\dfrac{y_2-y_1}{x_2-x_1}=\frac{6--4}{5-0}=2

Using the slope-intercept form:  y = mx + b

(where m is the slope and b is in the y-intercept)

From inspection of the graph, we can see the line crosses the y-axis at -4,

⇒ f(x) = 2x - 4

As the line is actually a line segment (with endpoints (0, -4) and (5, 6), then

f(x) = 2x - 4,   0 ≤ x ≤ 5

To determine the equation of f^{-1}(x):

Rewrite f(x)  as  y = 2x - 4

Swap the x and y:  x = 2y - 4

Rearrange to make y the subject: y= \dfrac{1}{2}(x + 4)

Replace y with f^{-1}(x)

So the equation of the inverse is:   f^{-1}(x)= \dfrac{1}{2}(x + 4)

As the original function is a segment, then

f^{-1}(x)= \dfrac{1}{2}(x + 4), \ \ \ -4\leq x\leq 6

(shown in blue on the attached diagram)

** I can't see any points labelled E and F on the original function. If they are the endpoints of the line segment of f(x), then they are (0, -4) and (5, 6) **

4 0
2 years ago
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