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lina2011 [118]
4 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]4 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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larisa86 [58]

Answer:

See picture attached

Step-by-step explanation:

I hope this helps you.

Please give me brainliest if it's correct

7 0
3 years ago
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Pls work out and give detail. Use the slope formula to determine the slope of each line.
kolbaska11 [484]

Answer:

m=0

Step-by-step explanation:

Given

See attachment

Required

Determine the slope of the line

From the attachment, we have the following points

(x_1,y_1) = (-4,1)

and

(x_2,y_2) = (3,1)

The slope m is then calculated using:

m = \frac{y_2- y_1}{x_2 - x_1}

Substitute values for the x's and y's

m = \frac{1-1}{3 - (-4)}

m = \frac{1-1}{3 +4}

m = \frac{0}{7}

m=0

<em>Hence, the slope is 0</em>

7 0
3 years ago
Which is an equation of the parabola that intersects the x-axis at points (-1, 0) and (3, 0)? Show your work or explain how you
hichkok12 [17]

Answer:

\displaystyle \large{y=x^2-2x-3}

Step-by-step explanation:

The given points are (-1,0) and (3,0) to find an equation of parabola. Notice that they say or the given points are x-intercepts, which means they make it easier for us to find an equation of parabola using these x-intercepts.

Quick Note:

  • x-intercepts are simply the roots or solutions of quadratic equation, so if our root is x = -2 then we can write as (-2,0) and write back to x+2=0.

So what we are going to do is to write the roots’ equation back as \displaystyle \large{x+\alpha =0}

Our points or roots are given, therefore:

If x = -1 then x+1=0

If x = 3 then x-3=0

Then multiply x+1 with x-3 because if (x-1)(x+3)=0 then x-1=0 or x+3=0:

\displaystyle \large{(x+1)(x-3)=0}

Convert 0 to y since we want to find a function:

\displaystyle \large{(x+1)(x-3)=y}\\\displaystyle \large{y=(x+1)(x-3)}

Expand the expressions in and simplify to standard form:

\displaystyle \large{y=x^2-3x+x-3}\\\displaystyle \large{y=x^2-2x-3}

Therefore, the equation is \displaystyle \large{y=x^2-2x-3}

__________________________________________________________

Summary

If we are given the points \displaystyle \large{(\alpha ,0)} and \displaystyle \large{(\beta ,0)} with wideness of the graph or a-value = 1 then the parabola equation is:

\displaystyle \large{y=(x-\alpha )(x-\beta )}\\\displaystyle \large{y=x^2-\beta x-\alpha x+\alpha \beta }\\\displaystyle \large{y=x^2-(\beta +\alpha )x+\alpha \beta }

__________________________________________________________

Others

If you have any doubts about my answer, explanation or this question, do not hesitate to let me know in the comment!

3 0
3 years ago
Olivia helps paint a square mural in her classroom. Then she helps paint a mural in the hallway whose length is 5 feet longer an
attashe74 [19]
The square mural in Olivia's classroom has dimensions x by x.

Then she paints a mural of dimensions: x+5  (the length) by x-2  (the width).

Thus the second mural (the hallway mural) has the shape of a rectangle with dimensions (x+5) by (x-2), so the area of the second mural is
(x+5)(x-2).

<span>
each side of the classroom mural is 7 feet means that x = 7 ft, 
</span>
thus the area of the hallway mural is :
 (x+5)(x-2)=(7+5)(7-2)=12*5=60    (square feet)


Answer:
<span>C. (x + 5)(x – 2); 60 square feet</span>
5 0
3 years ago
What is the GCF of 16;14 ?
puteri [66]

Answer:

2

Step-by-step explanation:

Factors for 14: 1, 2, 7, and 14. Factors for 16: 1, 2, 4, 8, and 16.

The greatest common factor being 2, as they both have it.

8 0
3 years ago
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