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Alinara [238K]
3 years ago
12

Samir begins riding his bike at a rate of 6 mph. Twelve minutes later, Chris leaves from the same point and bikes along the same

route at 9 mph. At any given time, t, the distance traveled can be calculated using the formula d = rt, where d represents distance and r represents rate. How long after Chris begins riding does he catch up to Samir? 4 min 12 min 24 min 40 min
Mathematics
1 answer:
kakasveta [241]3 years ago
3 0

<u>Answer:</u>

The correct answer option is 24 min.

<u>Step-by-step explanation:</u>

Let  us assume t to be Chris's time (in hours)  so we can write the following equation:

Samir's time (in hours)  =t + \frac{12}{60} = t + 0.2

Chris's rate  (r_1)=9 mph

Samir's rate  (r_2)=6 mph

Then putting the values in the formula to get:

r_1t = r_2(t + 0.2)

9t = 6(t + 0.2)

9t=6(t+0.2)\\\\9t=6t+1.2\\\\9t-6t=1.2\\\\3t=1.2\\\\t=0.4

<em>t = 0.4 </em>which will be 0.4*60=24

Therefore, Chris catches up Samir after riding for 24 minutes.

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What is the solution to 45+0.25m
Viefleur [7K]

Answer:

 m + 180

 ———————

    4  

Step-by-step explanation:

  1

Simplify   —

           4

Equation at the end of step  1  :

        1

 45 +  (— • m)

        4

Step  2  :

Rewriting the whole as an Equivalent Fraction :

2.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  4  as the denominator :

          45     45 • 4

    45 =  ——  =  ——————

          1        4    

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

45 • 4 + m     m + 180

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Final result :

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6 0
4 years ago
Find a compound proposition involving the propositional variables p, q, and r that is true when exactly two of p, q, and r are t
VLD [36.1K]

Answer:

Consider the proposition C=(p∧q∧¬r)∨(p∧¬q∧r)∨(¬p∧q∧r)

Step-by-step explanation:

This compound proposition C uses the outer disjunction (∨) then the proposition is true if and only if one of the three propositions (p∧q∧¬r),(p∧¬q∧r),(¬p∧q∧r) is true.

First, it is impossible that two or three of these propositions are simultaneously true. For example, if (p∧q∧¬r) and (p∧¬q∧r) are both true, then ¬r is true (from the first conjuntion) and r is true (from the second one), a contradiction. All the other possibilities can be discarded reasoning in the same way.

Since these propositions are mutually excluyent, C is true if and only if exactly one of the three propositions is true (and false otherwise). This can only happen if exactly two of p,q, and r are true and the other one is false. For example, (p∧q∧¬r) is true when p and q are true, and r is false.

8 0
4 years ago
In triangle abc, a is a right angle, and ab = 16√3, and the measure of b=30 degrees. What is the length of ac.
salantis [7]

Answer:

the length of ac is 16.

Step-by-step explanation:

Given;

A is right angle, = 90⁰

B is 30⁰

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              C

              ↓

               ↑

               A   →      ←  B

If this right angle triangle is considered, length bc is the hypotenuse and length ac is the opposite side of angle B.

The length of ac is calculated as follows;

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Therefore, the length of ac is 16.

             

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