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kari74 [83]
2 years ago
8

Jamie and Owen joined a monthly walking challenge at their youth center. Jamie has already walked 120 minutes and plans to walk

20 minutes per day. Owen plans to walk 30 minutes per day. Let x represent the number of days and y represent the total number of minutes walked during the challenge. Which system of equations can be used to find the number of days it will take for Owen and Jamie to have walked the same number of minutes?
A) y= 20x + 120
y=30

B) y=20x
y=30x + 120

C) 120x + 20
y=30

D) y=120x
y=30x +20
Mathematics
1 answer:
Soloha48 [4]2 years ago
7 0
I think the best answer would be letter B. Y= 20x and Y= 30x+120. So by calculating it through substitution you will come up to 20x = 30x+120. By simplifying the equation it will give you an answer of 12 days. 
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The speed of a sparrow is x km/h in still air. When the
Semmy [17]

Answer:

x = 5m/s

Step-by-step explanation:

Distance flying out = 12 km  (headwind)

Distance flying back = 12 km (tailwind)

total distance = 12 + 12 =24 km

wind speed = 1km/h

speed going out (with headwind) = (x - 1) km/h

speed coming back (with tailwind) = (x + 1) km/h

Time taken to go out = distance going out / speed going out

= 12 / (x-1)

Time taken to come back = distance coming back / speed coming back

= 12 / (x+1)

total time = time taken to go out + time taken to come back

5 =[ 12/(x-1) ] + [ 12/(x-1)]

expanding this, we will get

5x² - 24x - 5 = 0

solving quadratic equation, we will get

x = -1/5 (impossible because speed cannot be negative)

or

x = 5 (answer)

4 0
1 year ago
A band director uses a coordinate plane to plan as how for a football game. During a show, the drummers will march along the lin
LenaWriter [7]

Answer:

The equation in slope-intercept form for the path of the trumpet players is y=\frac{x}{5}+\frac{12}{5}.

Step-by-step explanation:

Consider the provided information.

The drummers will march along the line y=-5x-8.

The trumpets players will march along a perpendicular line that passes through (-2,2).

The slope of line y=-5x-8 is: m₁ = -5.

The slope of perpendicular lines are: m_1\times m_2=-1

-5\times m_2=-1

m_2=\frac{1}{5}

Hence, the slope of the line should be 1/5.

The line passes through (-2,2).

Now use point slope form to find the equation of line.

y-y_1=m(x-x_1)

Substitute m=1/5, x₁=-2 and y₁ = 2 in above formula.

y-2=\frac{1}{5}(x+2)

y-2=\frac{x}{5}+\frac{2}{5}

y=\frac{x}{5}+\frac{2}{5}+2

y=\frac{x}{5}+\frac{12}{5}

Hence, the equation in slope-intercept form for the path of the trumpet players is y=\frac{x}{5}+\frac{12}{5}.

4 0
1 year ago
15 kilograms of rice are separated equally into 4 containers. How many kilograms of rice are in each container? Express your ans
Nadusha1986 [10]

Answer: Fraction= 3 3/4kg

Decimal= 3.75kg

Step-by-step explanation:

15 kilograms of rice are separated equally into 4 containers. To get the number of kilograms of rice are in each container, we divide the total kilograms of rice by the number of containers. This will be:

Kilograms of rice in each container=

15/4 =3 3/4kg as a fraction.

To convert the fraction to decimal, we divide 3 by 4 and add to 3. 3/4 equals 0.75. We then add 3 to 0.75. This will be:

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7 0
1 year ago
Solve 4/x-4=x/x-4-4/3 for x and determine if the solution is extraneous or not
4vir4ik [10]

<u>Answer:</u>

x = 4 (extraneous solution)

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

\frac { 4 } { x - 4 } = \frac { x } { x - 4 } - \frac { 4 } { 3 } \\ \frac { 4 } { x - 4 } - \frac { x } { x - 4 } = - \frac { 4 } { 3 } \\ \frac { 4 - x } { x - 4 } = - \frac { 4 } { 3 } \\ 3 ( 4 - x ) = - 4 ( x - 4 ) \\ 1 2 - 3 x = - 4 x + 1 6 \\ 4 x - 3 x = 1 6 - 1 2 \\ x = 4 \\

This solution is extraneous. Reason being that even if it can be solved algebraically, it is still not a valid solution because if we substitute back x=4, we will get two fractions with zero denominator which would be undefined.

7 0
1 year ago
Abbey wants to use her savings of $1,325 to learn yoga. The total charges to learn yoga include a fixed registration fee of $35
Brums [2.3K]
So for this, this can be written into the equation y=50x+35 (x = number of months, y = total cost).

To solve this problem, we need to plug in 1325 into the y-variable and solve from there.

1325=50x+35

Subtract 35 on each side to get 1290=50x

Then just divide by 50 on each side, and your answer should be 25.8=x


And because we cannot go past budget, we will have to round down to 25. In context, the maximum amount of months Abbey can do is 25 months.
8 0
1 year ago
Read 2 more answers
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