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Viefleur [7K]
3 years ago
9

The distance on a bike path between Westfield and Southborough is 46 mi. Tracey leaves Westfield heading to Southborough cycling

at a constant rate of 15 mph. Emma leaves her house at the same time and cycles along the same path from Southborough to meet Tracey. Her cycling rate is 8 mph. How many hours will it take until the two friends meet along the bike path?
Mathematics
2 answers:
ipn [44]3 years ago
8 0

Answer: 2 hr.

Explanation: Think back to rate of change. <em>d</em> = <em>rt</em>, <em>r</em> = <em>d/t</em>, <em>t</em> = <em>d/r</em>. In this case, we will be using <em>d</em> = <em>rt</em>. Mph would be <em>r</em>, rate, so you would categorize 15 mph and 8 mph under rate. <em>t</em> should represent the time each cyclist traveled. Tracey's and Emma's distance, <em>d</em>, would be the same as their mph, hence Tracey's being 15<em>t</em> and Emma's would be 8<em>t</em>. When you add Tracey's distance plus Emma's distance, you end up with 46 mi. Now, you need to combine like terms, which should look like 15<em>t</em> + 8<em>t </em> = 46. Add 15 and 8 to get 23, so it should be 23<em>t</em> = 46 now. Then, divide both sides of the equation by 23 and now you should have your answer, <em>t</em> = 2 hr.

Elza [17]3 years ago
3 0

Answer:

2 hours

Step-by-step explanation:

I got it right on on my practice

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8 0
2 years ago
Evaluate the expression 2ab 3+ 6a 3 - 4ab2 when a=2 and b=4.<br> a.176<br> b.180<br> c.215<br> d.216
Tom [10]
The first step for solving this expression is to insert what a and b stand for into the expression. This will change the expression to the following:
2(2)(4)³ + 6(2)³ - 4(2)(4)²
Now we can start solving this by factoring the expression
2(2 × 4³ + 3 × 2³ - 4 × 4²)
Write 4³ in exponential form with a base of 2.
2(2 × 2^{6} + 3 × 2³ - 4 × 4²)
Calculate the product of -4 × 4².
2(2 × 2^{6} + 3 × 2³ -4³)
Now write 4³ in exponential form with a base of 2.
2(2 × 2^{6} + 3 × 2³ -2^{6})
Collect the like terms with a base of 2.
2(2^{6} + 3 × 2³)
Evaluate the power of 2³.
2(2^{6} + 3 × 8)
Evaluate the power of 2^{6}.
2(64 + 3 × 8)
Multiply the numbers.
2(64 + 24)
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Multiply the numbers together to find your final answer.
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This means that the correct answer to your question is option A.
Let me know if you have any further questions.
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5 0
3 years ago
To conserve water, many communities have developed water restrictions. The water utility charges a fee of $38, plus an additiona
earnstyle [38]

Using a linear function, the correct option regarding the situation is given by:

C) 57 ≤ 1.28x + 38 ≤ 87; To stay within the range, the usage should be between 14.8 and 38.3 HCF.

<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The bill is modeled by a linear function, with an <u>intercept of $38 and a slope of $1.28</u>, hence it is given by:

C(x) = 1.28x + 38

The bill should be between $57 and $87 dollars per month, hence:

57 <= C(x) <= 87.

The values of x are:

C(x) >= 57

1.28x + 38 >= 57

x >= 19/1.28

x >= 14.8.

C(x) >= 87

1.28x + 38 >= 87

x >= 49/1.28

x >= 38.3.

Hence option C is correct.

More can be learned about linear functions at brainly.com/question/24808124

#SPJ1

8 0
1 year ago
2y=2(3)+4. Help me plzzzzz
lesya692 [45]

Answer:

y=5

Step-by-step explanation:

Get rid of the parenthesis by multiplying

2y=6+4

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3 0
3 years ago
Read 2 more answers
Z+17=23 what is the anwser​
aliina [53]
The answer is 6 ,17+6=23
8 0
3 years ago
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