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3 years ago

Gavin went on 25 runs last month that totaled 103 miles. Each run was a distance of either 3 miles or 5 miles. Which system of

Mathematics

1 answer:

Aleksandr [31]3 years ago

3 0

Answer:

3x+5y=105

x+y=25

Step-by-step explanation:

x is the number of 3 mile runs so the total distance travelled is 3x miles. y is the number of 5 mile runs so the total distance travelled is 5y miles. Together Gavin travelled 103 miles so 3x+5y=105.

The number of 3 mile and 5 mile runs he did in total were 25 so x+y=25.

So the answer is:

3x+5y=105

x+y=25

Done.

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2 years ago

Complete the table for the following function<br> y=(1/3)^x

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x=-3 then y= 27

x= -2 then y= 9

x=2 then y: $y=\frac{1}{9}$

x=3 then y: $y=\frac{1}{27}$

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Option C is correct.

Step-by-step explanation:

We are given the function: $y=(\frac{1}{3})^x$

and we need to fill the table

if x = -3 then y=?

Putting value of x in the given function:

$y=(\frac{1}{3})^x$

$y=(\frac{1}{3})^-3$

Applying exponent rule a^-b= 1/a^b

$y=\frac{1}{(\frac{1}{3})^3 }\\y=\frac{1}{\frac{1}{27}}\\y=27$

if x = -2 then y=?

Putting value of x in the given function:

$y=(\frac{1}{3})^x$

$y=(\frac{1}{3})^-2$

Applying exponent rule a^-b= 1/a^b

$y=\frac{1}{(\frac{1}{3})^2 }\\y=\frac{1}{\frac{1}{9}}\\y=9$

if x = 2 then y=?

Putting value of x in the given function:

$y=(\frac{1}{3})^x$

$y=(\frac{1}{3})^2$

Applying exponent rule a^-b= 1/a^b

$y=\frac{1}{(\frac{1}{3})^2 }\\y=\frac{1}{9}$

if x = 3 then y=?

Putting value of x in the given function:

$y=(\frac{1}{3})^x$

$y=(\frac{1}{3})^3$

Applying exponent rule a^-b= 1/a^b

$y=\frac{1}{(\frac{1}{3})^3 }\\y=\frac{1}{27}$

So, x=-3 then y= 27

x= -2 then y= 9

x=2 then y: $y=\frac{1}{9}$

x=3 then y: $y=\frac{1}{27}$

Graph of the function is shown in figure attached.

The graph of the function decreases from left to right.

Option C is correct.

Keywords: Solving Equations

Learn more about Solving Equations at:

#learnwithBrainly

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3 years ago

The number of 5-digit numbers that can be formed if the last digit is odd and no

Softa [21]

Answer:

13,440

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10 possible digits 0 - 9

5 possible numbers for position 5 (odd digits only)

8 possible numbers for position 1 (cannot be zero or the odd number selected for position 5)

8 possible numbers remain for position 2 (10 minus 2 already selected)

7 possible numbers remain for position 3 (10 minus 3 already selected)

6 possible numbers remain for position 4 (10 minus 4 already selected)

5•8•8•7•6 = 13,440

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